Math in Context (1998)

Page Contents

A      B      C      D      E      F      G      H      J      K      L      M      N      O      P      R      S      T      U      V      W      Y      Z

A

Acuna, J. E. (1983). Some Socio-Cultural Realities: Implications for Teaching and Learning. Journal of Science and Mathematics Education in Southeast Asia v6 n2 p17-20 Dec 1983. Discusses three aspects of Philippine culture that affect teaching and learning: (1) social structure; (2) language; and (3) values. Findings from cognitive growth research with Filipino children and adolescents are examined to identify ways of overcoming some sources of difficulties in these areas. (Author/JN) EJ301940

Allal, L. (1986). Competition and Cooperation in the Context of Games Used for Mathematics Instruction. Switzerland Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. A number decomposition game (DECO) was investigated in two versions of the game using the same arithmetic operations but differing in their structure of interdependence. The structure of interdependence is defined as the relationship of competition or cooperation between players and the criteria for successful attainment of game goals as defined by pre-established rules. Subjects for the study were 64 second and third grade students at two public elementary schools in Geneva, Switzerland. A two-way analysis of variance was used on grade crossed with game version as measured by percent of interactions, percent of mutual monitoring and control, adequacy of decomposition strategy, and percent of errors. For percent of interaction, all three effectsgrade, game version and their interactionwere significant. For monitoring and control, all were non-significant. For decomposition strategy, game was significant and for errors, game version was significant. Quantitative indicators of congruence of playing behavior with game rules, monitoring and control, and decomposition were examined by regression analysis. Quantitative and qualitative measures were used to identify player profiles for both versions of the game. These player profiles did not appear to have a systematic impact on game outcome. (JM) ED270319

Anderson, A. (1994). Mathematics in Context: Measurement, Packaging and Caring for Our Environment. School Science and Mathematics v94 n3 p146-50 Mar 1994. Presents examples using the context of packaging materials and their impact on the environment to help teachers and teacher educators combine mathematics and science through activities that involve higher order thinking and worthwhile tasks. (Author/MKR) UMI Report/ISSN: ISSN-0036-6803 EJ502092

Anderson, L., & Stein, W. (1992). Making Math Relevant: Students and Teachers Help Each Other through a Montana State University Program. Tribal College: Journal of American Indian Higher Education v3 n3 p13,18-19 Win 1992. Describes the American Indians in Mathematics (AIM) project developed by Montana State University's Center for Native American Studies and Mathematics Department. The AIM summer program uses new technologies and teaching methods and focused mentoring to create learning communities in classrooms, schools, and reservations. Discusses AIM's curriculum and cultural pedagogy. (DMM) Report/ISSN: ISSN-1052-5505 EJ446276

Apple, M. W. (1992). Thinking More Politically about the Challenges before Us: A Response to Romberg. Journal for Research in Mathematics Education v23 n5 p438-40 Nov 1992. Responds to Romberg's reaction and argues that the present conservative social context will determine the use to which the "Standards" are put. Expresses concern that unequal school finance policies in providing technologically rich classroom environments will result in educational stratification. (MDH) UMI Report/ISSN: ISSN-0021-8251 EJ456389

Aronson, M., & Others, A. (1996). Time Traveling with Children's Literature. Pull-Out Feature 1. Social Studies and the Young Learner v9 n1 suppl p1-4 Sep-Oct 1996. Presents a series of lesson plans that include investigations in science, mathematics, geography, current events, and social studies. The cross-curricular activities help students broaden their understanding of time as well as of the "neighbors" who live in their own and other time zones. (MJP) Report/ISSN: ISSN-1056-0300 EJ538447

Atweh, B., & Cooper, T. (1995). The Construction of Gender, Social Class and Mathematics in the Classroom. Educational Studies in Mathematics v28 n3 p293-310 Apr 1995. This study was conducted using observations in mathematics classes at two all-girls' schools. The class in the high socioeconomic school constructed content that was perceived as required for entry into higher education while the low socioeconomic school constructed mathematics needed for everyday-life transactions. (30 references) (Author/MKR) UMI Report/ISSN: ISSN-0013-1954 EJ512617

Atweh, B., & Others, A. (1995). Social Context in Mathematics Classrooms: Social Critical and Sociolinguistic Perspectives. Australia; Queensland Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. The study was conceptualized within the social critical perspective to investigate the effect of gender and socioeconomic background on the students' classroom communication and the hidden curriculum. Year 9 mathematics classrooms in two single-sex private schools were observed during the course of learning one chapter from the same textbook. One class was in a low socioeconomic girls' school and the other in a high socioeconomic boys' school. Being an exploratory study, these two types of schools were chosen to maximize differences between them. Constructs from sociolinguistics were employed to investigate the variation in discourse between the two classes. Comparison of the context of discourse in mathematics in the two classrooms showed that, even though the teachers and students were engaged in working from the same textbook, the actualized curriculum was quite different in both classes. The class in the boys' school was developing mathematics as a highly formal field of study, stressing mathematical structures, concepts, and language, whereas the class in the girls' school was developing mathematics as a set of skills or rules. Contains 40 references. (MKR) ED385438

Atweh, Bill, E., & Others, A. (1993). Contexts in Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (MERGA) (16th, Brisbane, Queensland, Australia, July 9-13, 1993). Australia; Queensland Available in microfiche only. EDRS Price - MF03 Plus Postage. PC Not Available from EDRS. Report/ISSN: ISBN-0-86856-902-X. These proceedings contain 4 keynote addresses and 88 papers concerning the theme of the conference: Contexts in Mathematics Education. The four keynote addresses are: (1) "Contemplating Cultural Context" (Bill Barton); (2) "Conceptualising Cultural and Social Contexts in Mathematics Education" (Alan Bishop); (3) "Mathematical Learning in the Social Context" (George Booker); and (4) "Childrens' Construction of Mathematical Ideas" (Carolyn Maher). The 88 contributed papers deal with mathematical content ranging from prenumber to calculus, learners ranging from preschool to adult, teachers, technology, affect, assessment, metacognition, psycholinguistics, and a wide variety of social issues. (MDH) ED367543

B

Baker, D. P., & Others, A. (1995). The Effects of Sex-Grouped Schooling on Achievement: The Role of National Context. Comparative Education Review v39 n4 p468-82 Nov 1995. Grade-12 results of the Second International Mathematics Study for Belgium, New Zealand, Thailand, and Japan suggest that when single-sex schooling is relatively scarce in a country, it influences student achievement by attracting students with unique characteristics. Achievement effects may be positive or negative depending on the function of single-sex schools in the national context. (SV) UMI Report/ISSN: ISSN-0010-4086 EJ516773

Ball, D. L., & Wilcox, S. S. K. (1989). Inservice Teacher Education in Mathematics: Examining the Interaction of Context and Content. Research Report 89-3. Michigan Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. National Center for Research on Teacher Education, 116 Erickson Hall, College of Education, Michigan State University, East Lansing, MI 48824-1034 ($4.75). This paper illustrates an approach to analyzing the content and contexts of inservice teacher education programs. Two inservice programs in mathematics for elementary teachers are compared. One program is part of a large urban school district's initiative to revise its mathematics curriculum. The other program is conducted by a local college; participants come from a number of demographically varied school districts. Despite these differences, the two programs appear to share the goal of teaching mathematics for conceptual understanding. They also face some predictably similar obstacles in attaining that goal: traditional views of mathematics and mathematics teaching and learning, the organization of schools and the conditions of elementary school teaching, elementary teachers' knowledge and skill. The analysis focuses on the interaction of each program's context and content. The analysis of context deals with factors of organization, surroundings, time, and timing, that contributed to shaping the conditions for teachers' learning. Both the settings of the inservice sessions themselves and the settings of the participating teachers' practice are analyzed. In examining program content, the analysis focuses on the programs' goal of teaching mathematics for understandingwhat each program meant by this goal, and what they thought teachers needed to know in order to teach for understanding, as well as their assumptions about how teachers would learn this. The paper concludes with a discussion of the interaction of context and content in inservice teacher education and raises questions critical for researchers interested in the effects of different approaches to working with practicing teachers as well as for policymakers and researchers intent on changing practice. (Author) ED320850

Barrett, E. (1991). Teaching Mathematics through Context: Unleashing the Power of the Contextual Learner. New York Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. Examining how students reconstruct stories they've heard can give insights into why students often have difficulty understanding and retaining mathematics. Behavioral psychologists refer to the phenomenon of piecing together a series of events as "chaining." This paper argues that the cognitive capacity to reconstruct a whole contextual structure from a few entities within it belongs to even the slowest learners, and that this capacity to retain contextually related information can be activated to facilitate learning and retention of mathematics. The document presents an example of converting a fraction into a decimal in which traditional algorithms are learned through a contextual approach, leading to gains in efficiency and meaning in the acquisition of the skill. Teachers are asked to consistently present an internal contextual view of mathematics to learners. (MDH) ED345932

Barrett, E., & Armour-Thomas, E. (1995). Finding and Activating the Real Gift for Learning Mathematics: Implications for Teachers' Scope and Sequence. New York Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. The paper compares "standard" mathematics training with the normal human experience of "contextual learning." Contextual understanding permits children to learn various patterns of events and circumstances in their surroundings. The conclusion is that every child is a competent contextual learner, and functions very effectively learning language and stories even before they attend school. The vast majority of lessons in mathematics are not presented as a developmental, contextual flow of related information. Instead, the information is fragmented, disconnected, and presented in steps to be memorized. The benefits of contextual mathematics teaching methodology are explored such as: (1) the learning of mathematics is accelerated due to its inherent contextuality which enables children to experience acceleration in their learning of stories; and (2) rote learning and remediation time is virtually eliminated from mathematics education. Specific examples and comparisons to everyday situations are presented to support the concept of contextual learning in mathematics. Teachers are encouraged to engage learners in mathematical experiences in ways that enable students to use their existing cognitive structures to construct new understandings. (AIM) ED399183

Bell, A. (1993). Principles for the Design of Teaching. Educational Studies in Mathematics v24 n1 p5-34 Jan 1993. Sketches a theory for designing teaching based on mathematical activity, situations, tasks, and interventions, exposing and resolving cognitive conflicts, changes of structure and context, feedback, reflection and review. Reviews the main psychological principles underlying this theory, then considers some examples of teaching designs in light of the theory. (Contains 44 references.) (Author/MDH) UMI Report/ISSN: ISSN-0013-1954 EJ471673

Bell, A., & Others, A. (1984). Choice of Operation in Verbal Arithmetic Problems: The Effects of Number Size, Problem Structure and Context. Educational Studies in Mathematics v15 n2 p129-47 May 1984. Determined effects of two task types on 12- and 13-year-olds' understanding of applications of multiplying and dividing positive numbers. Results indicate the persuasive nature of certain misconceptions and specific effects of context attributable to such aspects as relative familiarity. Implications of these and other results are discussed. (Author/JN) EJ301966

Belyk, D. (1992). Context for Learning: Science, Mathematics, Geography - IAEP: Alberta Report. Canada; Alberta Available in paper copy and microfiche. EDRS Price - MF01/PC03 Plus Postage. Report/ISSN: ISBN-0-7732-0799-6. Information collected as part of the International Assessment of Educational Progress II (IAEP II) about learning in Alberta (Canada) is provided, including information on the educational and cultural factors associated with student achievement and information on student attitudes, backgrounds, and experiences. Results for all participating countries (20 in science and mathematics and 9 in geography) have been distributed. This report indicates what 13-year-olds in Alberta have been able to achieve in science, mathematics, and geography. In Alberta, 119 randomly selected schools participated. Alberta students (n=1,459) did very well in science, scoring in the top one-third in all comparisons. The mathematics achievement of the 1,422 students was not as high, ranking in the middle third both nationally and internationally. Those who took the geography test, a brief assessment, scored in the top third in all comparisons. Results for participating countries are summarized for comparisons with Alberta and other Canadian provinces. Results and score distributions are presented in 27 tables. Appendix 1 gives an overall summary of test administration, and Appendix 2 describes quality control procedures. (SLD) ED360363

Bernardo, A. B. I., & Okagaki, L. (1994). Roles of Symbolic Knowledge and Problem-Information Context in Solving Word Problems. Journal of Educational Psychology v86 n2 p212-20 Jun 1994. Four experiments involving 440 college students in the Philippines and United States examined the effects of symbolic knowledge and problem-information context on translating relational statements into mathematical equations. Results indicate that symbolic knowledge is not always easily accessible in contexts that differ from ordinary problem-solving contexts. (SLD) UMI Report/ISSN: ISSN-0022-0663 EJ490262

Bishop, A. J. (1988). Mathematics Education in Its Cultural Context. Educational Studies in Mathematics v19 n2 p179-91 May 1988. Presents results of a series of analyses of educational situations involving cultural issues. Of particular significance are the ideas that all cultural groups generate mathematical ideas, and that "Western" mathematics may be only one mathematics among many. The values associated with Western mathematics and other issues are also discussed. (Author/PK) EJ376827

Bishop, A. J. (1992). Removing Cultural Barriers to Numeracy. Australia; Victoria Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. A plenary address to an Australian conference on adult literacy focuses on cultural barriers to numeracy. Mathematics, and therefore numeracy, is considered as part of cultural knowledge. It is noted that over the last decade there has been a growing awareness of the cultural basis of mathematical knowledge and teachers can no longer assume that mathematics is culture-free and therefore value-free. Numeracy is defined as "the particular mathematical knowledge needed by every citizen to empower them for life in that society." It is shown that particular groups have experienced alienation from and conflict with mathematics as it is commonly taught. These groups include ethnic minority children in westernized societies, second language students, indigenous "minorities" in westernized societies, girls in many societies, western "colonial" students, fundamentalist religious groups, children from lower-class and lower-caste families, physically disadvantaged students, and rural students. It is suggested that the key is to first recognize the existence and legitimacy of different mathematical practices, and then search for similarities between them. All mathematical knowledge is analyzable into six main categories: counting, locating, measuring, designing, playing, and explaining. Each of these is described and discussed in terms of teaching and learning activities. Some general principles for numeracy teaching are presented (e.g., even if content is specified by a curriculum, the context for activities and tasks is open to choice by students and teachers). Contains 27 references. (Adjunct ERIC Clearinghouse on Literacy Education) (LB) ED359840

Bishop, A. J., & Nickson, M. (1983). A Review of Research in Mathematical Education. Part B: Research on the Social Context of Mathematics Education. United Kingdom; England Available in microfiche only. EDRS Price - MF01 Plus Postage. PC Not Available from EDRS. Humanities Press, Inc., 171 First Ave., Atlantic Highlands, NJ 07716 ($9.25). Humanities Press holds rights for distribution in U.S. and Canada. All other rights held by NFER-Nelson, Darville House, 2 Oxford Rd. East, Windsor, Berkshire, SL4 1DF, England. Report/ISSN: ISBN-0-7005-0613-6. This second volume of a review prepared for the Cockcroft Committee of Inquiry into the Teaching of Mathematics in Schools in Great Britain reflects a sociological research basis in which neither mathematics nor mathematics teaching is the essential focus. Rather, as the introduction indicates, the concern is with the constraints (institutional and social) which surround the teaching of mathematics and with their effects upon teachers and pupils. Thus, the focus is on the social context in which the teaching and learning of mathematics takes place. Both research and non-research sources were included, integrated, and used as the basis of recommendations. Eight chapters are included, on: (1) the institutional aspect and within-school relationships, (2) pupils as a constraint, (3) societal constraints, (4) the structure of the teaching profession, (5) the effects of initial training of teachers of mathematics, (6) teacher characteristics, (7) in-servce training and professional development, and (8) some general conclusions. Finally, a list of references and the set of recommendations made to the Cockcroft Committee are included. (MNS) ED241281

Blume, G. W. (1981). Kindergarten and First-Grade Children's Strategies for Solving Addition and Subtraction Problems in Abstract and Verbal Problem Contexts. Report from the Program on Studies in Mathematics. Technical Report No. 583. Wisconsin Available in paper copy and microfiche. EDRS Price - MF01/PC12 Plus Postage. Grant No.: NIE-G-81-0009. The purpose of this study was to describe and compare kindergarten and first-grade children's performance on addition and subtraction problems presented in two contexts: verbal (in which problem data were linked to physical referents such as objects or people and their actions), and abstract (in which no such links to physical situations occurred). Fifty kindergarteners and 54 first-graders were individually interviewed in mid-year to observe their solution strategies and errors on 12 abstract and 12 verbal addition and subtraction problems. The kindegarten problems contained sums and minuends less than 10. For first-graders, the sums and minuends ranged from 6 through 15. All problems were based on the open sentences a+b=?, a-b=?, and a+?=c. Upon completion of the problems, subjects in each grade were clustered according to the solution strategies they employed and according to the types of problems they could solve. Results indicated that verbal and abstract problems were of equal difficulty for subjects in both grades. Although kindergarteners used essentially the same strategies to solve verbal and abstract problems, first-graders exhibited less frequent use of concrete representation strategies on abstract than on verbal problems. Subjects in the two grades committed essentially the same types of errors, although the frequency of occurrence of most errors was lower at the first-grade level. At both grade levels a variety of individual differences were evident in the types of strategies subjects used and the types of problems they could solve. (Author/MP) ED214652

Boaler, J. (1993). Encouraging the Transfer of "School" Mathematics to the "Real World" through the Integration of Process and Content, Context and Culture. Educational Studies in Mathematics v25 n4 p341-73 Dec 1993. Considered transfer of students' (n=100) mathematical understanding across different task contexts in an integrated process-content approach using open-ended activities and a typical English content-based approach. The integrated approach facilitated transfer. (Contains 26 references.) (MKR/Author) UMI Report/ISSN: ISSN-0013-1954 EJ487123

Boaler, J. (1993). The Role of Contexts in the Mathematics Classroom: Do They Make Mathematics More "Real"? For the Learning of Mathematics v13 n2 p12-17 Jun 1993. Suggests that contexts may be useful in mathematics instruction in relation to learning transfer and that the factors that determine whether a context is useful are complex. Discusses the context effect, learning in context, how well students identify with tasks taken out of an adult world, and the effects of ethnomathematics. (MDH) EJ473508

Boaler, J. (1994). When Do Girls Prefer Football to Fashion? An Analysis of Female Underachievement in Relation to "Realistic" Mathematics Context. British Educational Research Journal v20 n5 p551-64 1994. Reports on a study of the move away from abstract calculations toward "mathematics in context" among 50 British female secondary school students. Discusses implications of findings in relation to reported female underachievement and disinterest in school mathematics. (CFR) Report/ISSN: ISSN-0141-1926 EJ507518

Bockarie, A. (1993). Mathematics in the Mende Culture: Its General Implication for Mathematics Teaching. School Science and Mathematics v93 n4 p208-11 Apr 1993. Mathematics that exists in the Mende culture, an African tribe in Sierra Leone, includes counting, computation, ratios, fractions, forecasting games, and mathematical applications. Presents The Mende representations of these concepts and discusses implications of their integration into mathematics teaching. (MDH) UMI Report/ISSN: ISSN-0036-6803 EJ471684

Bodenhausen, J. (1992). Using Cognitive Research to Turn a High School 'Remedial' Mathematics Program Inside-Out: A Teacher's Perspective. California Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. The "Thinking Mathematics" approach to teaching is guided by two ideas: (1) that learning requires knowledge upon which new problems and situations are interpreted and (2) that mathematics skills are applied in context. This paper reports research that examined whether teaching mathematics students in high school remedial classes can be improved by applying the Thinking Mathematics approach. The teacher as researcher technique was employed in which the researcher examined how the research applied to teaching her own ninth-grade remedial classes in an urban high school with a multi-ethnic, multi-cultural student body over a 3-year period of time. In addition, observations of and discussions with colleagues teaching similar classes applying cognitive research were employed. Students scores on pre- and post-tests based on the district's proficiency exam were compared to those of students in similar classes and the students of the pre-study year. Two aspects of the teaching approach were described. First, warm-ups designed to help students develop number sense and skills in counting, estimation, proportional reasoning, mental mathematics, and properties were employed to begin each day. Secondly, situational problems on which primary instruction was based are presented and discussed. Results indicated that the percentage of students in the research classes passing the proficiency exam was 3 times that of students in comparison classes (16% to 48%). Student self-esteem concerning their mathematical ability rose significantly, student attendance was significantly better, and discipline referrals were significantly fewer. While recognizing flaws in the research design, the findings support the applicability of cognitive research to high school remedial mathematics classes. (Contains 52 references.) (MDH) ED355096

Bottge, B. A., & Hasselbring, T. T. S. (1993). Taking Work Problems off the Page. Educational Leadership v50 n7 p36-38 Apr 1993. Students do not associate traditional word problems with their own experiences because they describe situations textually, rather than contextually, and seem artificially geared to specific number operations and single correct answers. Aided by a state grant, elementary teachers in one Minnesota district are using video anchors to simulate real-life problems, motivate students, and imbue mathematics with real-world value. (MLH) UMI Report/ISSN: ISSN-0013-1784 EJ461129

Brennan, R. L. (1992). The Context of Context Effects. Applied Measurement in Education v5 n3 p225-64 1992. A conceptual framework and heuristic model for considering the existence, magnitude, and consequences of context effects are presented through an extension of some generalizability theory concepts. Context effects are often misunderstood, and current measurement models have serious limitations for examining them. Their importance needs to be evaluated in context. (SLD) Report/ISSN: ISSN-0895-7347 EJ461971

Brenner, M. E., & Others, A. (1995). The Role of Multiple Representations in Learning Algebra. California Available in paper copy and microfiche. EDRS Price - MF01/PC03 Plus Postage. Middle school prealgebra students (n=157) learned about functions in a 20-day unit that emphasized: (1) representing problems in multiple formats, (2) anchoring learning in a meaningful thematic context, and (3) discussing problem-solving processes in cooperative groups. They produced smaller pretest-to-posttest gains on symbol manipulation tasks, such as solving equations, and larger gains in problem representation tasks, such as translating word problems into equations, tables, and graphs, than did a comparison group taught in the standard way. Although the groups did not differ in their pretest-to-posttest gains in calculating correct answers for word problems, the treatment group produced a larger gain in using mathematical representations while solving word problems than did the comparison group. The same pattern of results was obtained for lower-achieving students and language-minority students. Implications for cognitive theory and educational practice are discussed. Contains 72 references. (Author) ED391659

Brown, R., & Porter, T. (1990). Mathematics in Context: A New Course. For the Learning of MathematicsAn International Journal of Mathematics Education v10 n1 p10-15 Feb 1990. Described are the background, structure, themes, methodology, projects, and assessment for the course. A list of themes is provided. Results of the piloting of the course are discussed. (CW) Report/ISSN: ISSN-0228-0671 EJ413953

Bryant, J. (1995). Language and Concepts in Geometry: Implications for Sign Language Research. Focus on Learning Problems in Mathematics v17 n3 p41-56 Sum 1995. Discusses the notions and language of spatial relations of various cultures, particularly those of deaf students. (MKR) Report/ISSN: ISSN-0272-8893 EJ520585

Bunch, S. M. (1995). The Context of Community: The Initiation of Graduate Students into the Discourse of Mathematics Education Researchers. Mississippi Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. This study focused on four students and a professor from a mathematics education doctoral program at a research university. Participant observation, informal interviews, and document collection were used to collect data on students' discourse competency development. Two overarching categories emerged during data analysis: (1) what students had to learn in order to be competent in their discipline's discourse (identified initially as the conversations and conventions to the discipline); and (2) how the students developed these competencies, beginning with the specific learning opportunities each student had and generalizing from those to more abstract categories such as exposure, practice, feedback, and the effects of mentoring. One of the most important things these students came to recognize was the conversational nature of the discourse they were attempting to learn. The students learned to produce the discourse of the mathematics education research community through several important experiences: (1) the exposure to the products of the professional conversation; (2) the exposure to the process of conversation; (3) the opportunities to try the discourse and get feedback on their attempts to use it; and (4) the occasional explicit instruction in producing acceptable written discourseall under the guiding hand of a mentor who was an active, influential member of the community. (MKR) ED394787

C

Capps, L. R., & Pickreign, J. (1993). Language Connections in Mathematics: A Critical Part of Mathematics Instruction. Arithmetic Teacher v41 n1 p8-12 Sep 1993. Examines aspects of language connections in the learning of mathematics in three sections that discuss the interaction between language, symbolism, and manipulatives; emphasis on context in language development; and language connections in problem solving. Presents implications for nonnative English speakers. (MDH) UMI Report/ISSN: ISSN-0004-136X EJ474891

Carey, D. A. (1992). The Patchwork Quilt: A Context for Problem Solving. Arithmetic Teacher v40 n4 p199-203 Dec 1992. Discusses how children's literature can be used as a context to develop problem-solving tasks. Illustrates this idea by developing tasks to teach concepts related to multiplication through the context of "The Patchwork Quilt," a children's book by Valerie Flournoy. Suggests activity extensions to determine unit sizes, draw scale models, and make a quilt. (MDH) UMI Report/ISSN: ISSN-0004-136X EJ458319

Carey, D. A., Campbell, P., & F., E. (1992). Research into Practice. Arithmetic Teacher v40 n3 p184-86 Nov 1992. Relates research findings on the way primary-grade students communicate mathematical ideas through the use of symbols to a framework for students to investigate the part-whole relationship of quantity. Discusses children's problem-solving abilities, linking word problems and symbols, the importance of context for understanding symbols, and the development of meaning for symbols. (12 references) (MDH) UMI Report/ISSN: ISSN-0004-136X EJ456427

Chapin, S. H., & Eastman, K. K. E. (1996). Implementing the Professional Standards for Teaching Mathematics; External and Internal Characteristics of Learning Environments. Mathematics Teacher v89 n2 p112-15 Feb 1996. Describes and presents examples of external and internal characteristics of learning environments that may help students' achievement and interest in mathematics. External characteristics include time, space, and support while internal characteristics include teachers' habits of mind. (MKR) UMI Report/ISSN: ISSN-0025-5769 EJ518933

Cheng, C. C., & Seng, C. C. P. (1985). The Matriculation Science Curriculum of the USM in the Context of the PPI and CAI Modes of Instruction. Journal of Science and Mathematics Education in Southeast Asia v8 n2 p7-17 Dec 1985. Discusses philosophy, aims and objectives, and structure of the Matriculation Science Curriculum of the University Sains Malaysia. Includes comments on instructional strategies, individualized learning, programmed instruction, systems approach to computer-assisted instruction (CAI) implementation, CAI authoring system, and various program implementation strategies. (JN) EJ338113

Chevallard, Y. (1990). On Mathematics Education and Culture: Critical Afterthoughts. Educational Studies in Mathematics v21 n1 p3-27 Feb 1990. Reviewed is a book, "Mathematics Education and Culture," which was a special issue of this journal in 1988. Questioned are some of the current tenets about the meaning and significance of the concept "culture" for a theory of mathematics education. Calls for an open scientific debate, unfettered by moral and ideological prejudices and fashionable notions. (Author/YP) UMI EJ410929

Chipman, S. F., & Others, A. (1991). Content Effects on Word Problem Performance: A Possible Source of Test Bias? American Educational Research Journal v28 n4 p897-915 Win 1991. The effects of problem content on mathematics word problem performance were explored for 128 male and 128 female college students solving problems with masculine, feminine, and neutral (familiar and unfamiliar) cover stories. No effect of sex typing was found, and a small, but highly significant, effect was found for familiarity. (SLD) UMI Report/ISSN: ISSN-0002-8312 EJ438616

Clarkson, P. C. (1992). Unknown/Careless Errors in a Mathematical Language Context: Further Investigation. Focus on Learning Problems in Mathematics v14 n4 p3-16 Fall 1992. Reports a study to examine careless errors fifth-grade students (n=58) make while solving mathematical word problems and explores the type of student who frequently makes such errors. Results indicated that frequency of these errors was significantly related to the noncognitive variables of the study. Discusses implications for remediation. (20 references) (MDH) Report/ISSN: ISSN-0272-8893 EJ460271

Cleves, I. (1991). Who Wants Education-Industry Links Anyway. Mathematics in School v20 n3 p36-37 May 1991. A survey of mathematics teachers was conducted to determine the value, advisability, and feasibility of using the workplace as a context for teaching mathematics. Results indicated that of the respondents, few were aware of published materials in this area, most felt that workplace-related materials were relevant and aimed at lower level students, and few had personal workplace experience. (MDH) UMI Report/ISSN: ISSN-0305-7259 EJ445017

Cobb, P., & Yackel, E. (1995). Constructivist, Emergent, and Sociocultural Perspectives in the Context of Developmental Research. Tennessee Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. Contract no.: RED-9353587. The overall intent is to clarify relationships between psychological constructivist, sociocultural, and emergent perspectives by grounding them in attempts to understand what might be happening in a variety of teaching and learning situations. The first part of the paper outlines an interpretive framework developed in the course of a classroom-based research project. At the level of classroom processes, the framework involves an emergent approach in which psychological constructivist analyses of individual activity are coordinated with interactionist analyses of classroom interactions and discourse. At the level of school and societal processes, the perspective taken is broadly sociocultural and focuses on the influence of individuals' participation in culturally-organized practices. In the second part of the paper, the framework is taken as background against which to compare and contrast the three theoretical perspectives. The emergent approach augments the psychological constructivist perspective by making it possible to locate analyses of individual students' constructive activities in social context. In addition, the purposes for which emergent and sociocultural perspectives might be appropriate are considered and observed to span the individual students' activities, the classroom community, and broader communities of practice. Contains 75 references. (Author/MKR) ED389535

Confrey, J., & Others, A. (1991). The Use of Contextual Problems and Multi-Representational Software To Teach the Concept of Functions. Final Project Report. New York Available in paper copy and microfiche. EDRS Price - MF01/PC05 Plus Postage. The "Curriculum and Evaluation Standards for School Mathematics (1989)" calls for the revision of existing secondary mathematics curricula which include an emphasis on contextual problems, multiple representations, and the use of computers. The focus of this revision significantly involves the acknowledgment of the key role of the concept of function as an organizing concept around which other important mathematical ideas revolve. This report describes a 2-year project centered around the issue of teaching function concepts utilizing a context-based curriculum in a technology-rich secondary mathematics classroom. The goal of the project was the production, through applied research, of an intermediate-range vision of what mathematics instruction in schools might be like if classrooms were provided with adequate technological resources and appropriate teacher development. The report addresses the following topics: (1) the rationale and purpose of the project; (2) an overall theoretical approach to functions, teaching, learning, and small-group interactions; (3) the design principles, interaction processes, and pedagogical impact of the multi-representational software tool called Function Probe; (4) the use of prototypes within contextual problem settings; (5) the particulars within the implementation process of this project; (6) data collection techniques and research methodology; and (7) research results for the teachers, the students, and small groups of problem solvers. A final chapter offers conclusions about, and implications of, the role of technology in teaching mathematics. An appendix describes the software features, requirements, and availability of the Function Probe tool. (58 references) (Author/JJK) ED348229

Cooney, T. J., Friel, S., & N., E. (1992). Implementing the Professional Standards for Teaching Mathematics. Arithmetic Teacher v39 n6 p62-64 Feb 1992. The direction provided by the National Council of Teachers of Mathematics' "Professional Teaching Standards," in the section on evaluating-teaching standards, is considered with respect to the issues of context, the definition of good teaching, and the link between mathematics and pedagogy. (MDH) UMI Report/ISSN: ISSN-0004-136X EJ440157

Cramer, K., & Post, T. (1993). Connecting Research to Teaching. Mathematics Teacher v86 n5 p404-07 May 1993. Reports research findings regarding the learning and teaching of proportional reasoning. Presents four tasks devised to assess students' proportional reasoning and describes four solution strategies for solving these tasks based on the analysis of seventh and eighth graders' correct responses. (MDH) UMI Report/ISSN: ISSN-0025-5769 EJ474871

Crooks, T. J. (1980). Grade Prediction: The Usefulness of Context-Specific Predictors. New Zealand Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. Six widely used college admissions variables and four course-specific measures (tests of entering mathematical skills and physics knowledge, and indexes of previous study of mathematics and physics) were correlated with final marks for 495 students in an introductory college physics course. The college admissions variables included scores on American College Test (ACT) mathematics, ACT natural science, ACT composite, School and College Ability Test (SCAT) quantitative, SCAT verbal, and high school percentile rank. Separate stepwise multiple regressions revealed that the complete set of predictor variables accounted for 43.5% of the variance in course mark, whereas the six admissions variables accounted for only 28.6%. Similarly, the specially constructed tests of mathematical skills and physics knowledge were substantially better predictors than the corresponding admissions variables. These results suggest that prediction of success in particular instructional settings can be substantially improved if skills and knowledge specific to each setting can be identified and measured. (Author/RL) ED194547

Csapo, B. (1991). Math Achievement in Cultural Context: The Case of Hungary. Hungary Available in microfiche only. EDRS Price - MF01 Plus Postage. PC Not Available from EDRS. Several recent experiences suggest that Hungarian students are among the best prepared mathematically in international comparisons of achievement. This paper outlines the cultural background of mathematics learning in Hungary that influences that international standing. Achievement factors in the whole cultural context include: the role of traditions in the development of the Hungarian system, the mathematics curriculum, school work standards, the role of extracurricular activities in selecting gifted students, social and socio-political factors, and the system of dealing with gifted students. (MDH) ED367539

D

Damarin, S. K. (1978). A Combinational Model for the Interpretation and Use of Propositions in the Context of Elementary Mathematics. Ohio Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. The author presents an organizational model which exhibits relationships among preservcie teachers' skills in the use of interpretation of logical connectives in mathematical contexts. The model also provides direction to teahcers of courses on mathematics and mathematics methods who seek to acquaint their students with those notions of logic recommended by CUPM. The model treats the translation from mathematical statements to logical statements, and conversely. An empirical test has yielded considerable support for the model. After a brief description of the model and this test, the author discusses implications for instruction, especially as they are related to statements and context of mathematical problems. (MN) ED159019

Davis-Dorsey, J., & Others, A. (1991). The Role of Rewording and Context Personalization in the Solving of Mathematical Word Problems. Journal of Educational Psychology v83 n1 p61-68 Mar 1991. The impact of personalizing mathematical word problems and rewording them for explicitness was tested with 68 second and 59 fifth graders. Second graders benefited from personalization and rewording in combination; fifth graders benefited from personalization, not rewording. Personalization makes problems more motivating and easier to represent mentally in relation to existing knowledge. (SLD) UMI Report/ISSN: ISSN-0022-0663 EJ436867

De Villiers, M. (1994). The Role and Function of a Hierarchical Classification of Quadrilaterals. For the Learning of Mathematics v14 n1 p11-18 Feb 1994. Discusses partitioning and hierarchical types of classification, a theoretical analysis of the role and function of hierarchical classification in mathematics, and the teaching of a hierarchical classification of quadrilaterals. (Contains 21 references.) (MKR) Report/ISSN: ISSN-0228-0671 EJ487126

E

"Early Childhood Education.". Contemporary Education v66 n3 p172-73 Spr 1995. Children's literature can provide a context in which young children can explore mathematical concepts in a meaningful way. This article highlights how young students in first-grade classrooms used stories about their families and pets to create and solve mathematical problems in a motivating, meaningful way. (SM) UMI Report/ISSN: ISSN-0010-7476 EJ512830

Easley, J. (1980). Alternative Research Metaphors and the Social Context of Mathematics Teaching and Learning. For the Learning of Mathematics v1 n1 p32-40 Jul 1980. Mathematics education is viewed as a process imbedded in social interaction. Alternatives to seven widely recognized modeling perspectives that provide conceptual foundations for mathematics learning are discussed. (MP) EJ255409

El Tom, M. E. A. (1980). Remarks on the Structure of University Mathematics Institutions in Third-World Countries. International Journal of Mathematical Education in Science and Technology v11 n3 p433-46 Jul-Sep 1980. The role and activities of university mathematics departments in Third-World countries are examined. These institutions are largely responsible for their nations' efforts at developing mathematics within their own borders, and it is concluded by the author that these structures are seriously deficient. (MP) EJ232864

Ernest, & Paul, E. (1988). The Social Context of Mathematics Teaching. Perspectives 37. United Kingdom; England Available in microfiche only. EDRS Price - MF01 Plus Postage. PC Not Available from EDRS. Curriculum and Resources Centre, School of Education, University of Exeter, St. Luke's, Exeter, United Kingdom EX1 2LU. Report/ISSN: ISBN-85068-099-9. This publication contains seven papers by the staff of the University of Exeter School of Education and by invited outside contributors. The focus is on issues that consider the social context of mathematics. The papers are: (1) "Images of Mathematics" (Leone Burton); (2) "Of Course You Could be an Engineer, Dear, but Wouldn't You Rather be a Nurse or Teacher or Secretary?" (Zelda Isaacson); (3) "Mathephobia" (Jenny Maxwell); (4) "The Politics of Numeracy" (Jeff Evans); (5) "What is Multicultural Mathematics?" (Marilyn Nickson); (6) "Multicultural and Anti-Racist Mathematics Teaching" (Derek Woodrow); (7) "Becoming a Mathematics TeacherGrounds for Confidence?" (John Hayter). (MNS) ED302434

F

Fielker, D. S. (1981). Removing the Shackles of Euclid: 3 Context. Mathematics Teaching n97 p31-37 Dec 1981. The process of investigating some of the properties of diagonals and other geometric concepts with a group of 11-year-old girls is presented. Possible changes that could have been made in the lesson are discussed, and examples of individual student work are provided. (MP) EJ257085

Fisher, E. L., & Others, A. (1985). Using Context and Relationships to Teach Math. Academic Therapy v21 n1 p23-27 Sep 1985. The use of context and relationships can help learning disabled adolescents solve math problems made more difficult by confusing language. Examples are offered. (CL) UMI EJ323789

Fordham, A. M. (1983). The Context of Teaching and Learning. Report on the First Phase of the IEA Classroom Environment Study. ACER Research Monograph No. 21. Australia; Victoria Available in microfiche only. EDRS Price - MF01 Plus Postage. PC Not Available from EDRS. Australian Council for Educational Research, 9 Frederick St., Hawthorn, Victoria, Australia 3122. Report/ISSN: ISBN-0-85563-246-1. This publication describes the first phase of the Classroom Environment: Teaching for Learning Study in Australia, a six-year international research effort to identify correlations between teaching practices and student achievement. The report's first chapter presents a resume of the study and reviews research findings on managerial and instructional teaching practices which were the major focus of the study. Research studies on the context in which learning and teaching occur are reviewed in chapter 2. Context variables in these studies were teacher characteristics, school policy and organization, instructional setting, and student characteristics. Chapter 3 deals with the selection of relevant teaching practices and contextual factors and the development of the survey questionnaire. The survey sought information on teaching methods, teacher characteristics, and mediating influences on teaching practices. Chapter 4 describes the target population of teachers, the selection of a representative sample of teachers, and the survey procedures used in the collection of data. Chapters 5, 6, and 7 are concerned with the analysis of data collected from teachers during the survey. The final chapter offers a perspective on the study and summarizes features occurring in classrooms in Victoria. The features discussed are grouped under the headings which framed the survey questionnaire. A copy of the survey questionnaire and tabulated findings are appended. (JD) ED235136

Forman, E., A., E., & Others, A. (1993). Contexts for Learning: Sociocultural Dynamics in Children's Development. North Carolina Not available from EDRS. Document Not Available from EDRS. Oxford University Press, Inc., Business Office, 2001 Evans Road, Cary, NC 27513 ($45). Report/ISSN: ISBN-0-19-506715-0. Sociocultural theory has challenged existing notions of cognitive development by suggesting that psychological functioning is specific to its social context and is dependent on the mastery of culturally defined modes of speaking, thinking, and acting. This book provides a representative sample of work on the social and cultural foundations of developmental processes. Following an introduction on the integration of individual processes in accounts of children's learning and development, the book is organized into three parts. Chapters in the first part focus on the traditional educational setting, the classroom, and the ways that activity, discourse, and modes of thinking are organized there. In the second part, the chapters deal more specifically with the role that interpersonal relationships play in the teaching/learning process. Finally, the chapters in the last part address the broader issue of the relationship between the institutions of the educational systemsuch as schools or after-school programsand the processes and outcomes of learning. Each part is followed by an integrative commentary chapter, which serves to highlight common issues across the individual chapters and, as each is written by scholars working within various theoretical frameworks, to provide a broad-based, multidisciplinary commentary. In a final general commentary, Jacqueline Goodnow places the issues raised in the volume as a whole in historical context and sketches an agenda for future work. (AA) ED383404

Forrester, M. A., & Others, A. (1990). Exploring Estimation in Young Primary School Children. Educational Psychology: An International Journal of Experimental Educational Psychology v10 n4 p283-300 1990. Presents results of a study of the role of context upon English children's estimation skills. Includes estimation tasks involving distance, area, and volume measurements and children's answers about how they carried out the tasks. Concludes that estimates in contexts perceived as mathematical differed from those involving perceptual-motor skills. Emphasizes importance of imagery and classroom experience. (DK) Report/ISSN: ISSN-0144-3410 EJ438473

G

Galbraith, P. (1996). Championship Tennis as a Probabilistic Modelling Context. Teaching Mathematics and Its Applications v15 n4 p161-66 Dec 1996. Suggests ways for using data from championship tennis as a means for exploring probabilistic models, especially binomial probability. Examples include the probability of winning a service point and the probability of winning a service game using data from tables and graphs. (AIM) Report/ISSN: ISSN-0268-3679 EJ545182

Garden, R. A. (1987). The Second IEA Mathematics Study. Comparative Education Review v31 n1 p47-68 Feb 1987. The Second International Mathematics Study tested mathematics knowledge and skills among 13-year-olds and final-year secondary students in 17 countries. Discusses population definitions; research administration; research design in relation to mathematics curricula; context variables (ethnic composition, language of instruction, tracking, rurality, school size, instructional time); and changes in national achievement levels since the first international study. (SV) UMI Report/ISSN: ISSN-0010-4086 EJ485413

Garofalo, J. (1992). Number-Consideration Strategies Students Use to Solve Word Problems. Focus on Learning Problems in Mathematics v14 n2 p37-50 Spr 1992. Illustrates and discusses one class of strategies to solve word problems referred to as "number-consideration strategies." Contrasts actions and goals of students who focus mainly on number considerations with those of students who focus mainly on problem understanding. (MDH) Report/ISSN: ISSN-0272-8893 EJ447737

Geeslin, W. E. (1973). An Exploratory Analysis of Content Structure and Cognitive Structure in the Context of a Mathematics Instructional Unit. Digraphs, graphs and task analysis were used to map out the content structure of a programed text (SMSG) in elementary probability; mathematical structure was operationally defined as the relationship between concepts within a set of abstract systems. The word association technique (WA) and paragraph construction technique (PC) were used to measure the existing relations (cognitive structure) in S's memory with respect to the probability theory present in the text. The purpose of this study was to measure the influence of content structure (mathematical structure) of the text on the subjects' cognitive structure. Control and experimental Ss (W=181) were sixth-grade, eighth-grade and high-school (grades 9-12) students. Experimental Ss read the probability text while the others read a programed text unrelated to probability. Ss were pre- and posttested and given retention tests. Results indicated that the experimental Ss' measured cognitive structure highly resembled the text's content structure following instruction. The WA and PC test also appeared to be useful for formative evaluation of the programed text and gave different information than did achievement tests. (JP) Available in paper copy and microfiche. EDRS Price - MF01/PC09 Plus Postage. ED084154

Geeslin, W. E. (1974). An Analysis of Content Structure and Cognitive Structure in the Context of a Probability Unit. This study examines the correspondence between a representation of subject-matter structure and a representation of the cognitive structure in students as a result of instruction. Eighty-seven eighth-grade students were assigned randomly to experimental and control treatments. The experimental students (N = 43) studied from a programmed text on probability developed by the School Mathematics Study Group (SMSG). The control group (N - 44) studied from a programmed text on factors and prime numbers. Digraphs, graphs and task analysis were used to map out the content structure. A word association test (WA) was used to measure the existing cognitive structure. The WA test, an achievement test and an attitude measure were given before, after and at a delayed post-experiment time. The results indicate that: (1) eighth-grade students were unfamiliar with the concepts of probability; (2) instruction in probability changed subjects' cognitive structure concerning concepts in probability; (3) the experimental group learned a significant portion of the structure of probability as a matter of instruction while the control group learned almost nothing; and (4) this learning of structure was retained until the retention-test time. (JP) Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. ED090026

Geeslin, William, E., Graham, & Karen, E. (1992). Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (PME) (16th, Durham, NH, August 6-11, 1992). Volumes I-III. New Hampshire Available in paper copy and microfiche. EDRS Price - MF06/PC39 Plus Postage. The Proceedings of PME-XVI has been published in three volumes because of the large number of papers presented at the conference. Volume 1 contains: (1) brief reports from each of the 11 standing Working Groups on their respective roles in organizing PME-XVI; (2) brief reports from 6 Discussion Groups; and (3) 35 research reports covering authors with last names beginning A-K. Volume II contains 42 research reports covering authors with last names beginning K-S. Volume III contains (1) 15 research reports (authors S-W); (2) 31 short oral presentations; (3) 40 poster presentations; (4) 9 Featured Discussion Groups reports; (5) 1 brief Plenary Panel report and 4 Plenary Address reports. In summary, the three volumes contain 95 full-scale research reports, 4 full-scale plenary reports, and 96 briefer reports. Conference subject content can be conveyed through a listing of Work Group topics, Discussion Group topics, and Plenary Panels/Addresses, as follows. Working Groups: Advanced Mathematical Thinking; Algebraic Processes and Structure; Classroom Research; Cultural Aspects in Mathematics Learning; Geometry; Psychology of Inservice Education of Mathematics Teachers; Ratio and Proportion; Representations; Research on the Psychology of Mathematics Teacher Development; Social Psychology of Mathematics Education; Teachers as Researchers in Mathematics Education. Discussion Groups: Dilemmas of Constructivist Mathematics Teaching; Meaningful Contexts for School Mathematics; Paradigms Lost - What Can Mathematics Education Learn From Research in Other Disciplines?; Philosophy of Mathematics Education; Research in the Teaching and Learning of Undergraduate Mathematics; Visualization in Problem Solving and Learning. Plenary Panels/Addresses: Visualization and Imagistic Thinking; "The Importance and Limits of Epistemological Work in Didactics" (M. Artigue); "Mathematics as a Foreign Language" (G. Ervynck); "On Developing a Unified Model for the Psychology of Mathematical Learning and Problem Solving" (G. Goldin); "Illuminations and ReflectionsTeachers, Methodologies, and Mathematics" (C. Hoyles). (MKR) ED383538

Gilpin, A. R. (1993). Table for Conversion of Kendall's Tau to Spearman's Rho within the Context of Measures of Magnitude of Effect for Meta-Analysis. Educational and Psychological Measurement v53 n1 p87-92 Spr 1993. Kendall's Tau is often considered equivalent to Spearman's Rho as an ordinal measure of correlation in spite of its different metric. Formulas for converting Tau to Rho are reviewed; and a table of corresponding values is presented for Tau, Rho, and several related indices. (SLD) Report/ISSN: ISSN-0013-1644 EJ463395

Gimenez, J., E., & Others, A. (1996). Becoming a Primary Teacher: Issues from Mathematics Education. Spain Not available from EDRS. Document Not Available from EDRS. Gracia Alvarez, S.L., Parcela 11, Nave 27, Poligono Calonge, 41007 Sevilla, Spain. Report/ISSN: ISBN-84-921796-0-0. This book is a collection of works by mathematics educators from Spain with an emphasis on preservice primary teacher education. This book aims to promote reflection upon and discussion of research issues as well as put out a call to action. Articles include: (1) "Contexts and Learning to Teach Mathematics. The Case of Prospective Elementary Teachers" (S. Llinares); (2) "History and Background of Spanish Primary Teacher Training on Mathematics and Its Didactics" (Modesto Sierra and Luis Rico); (3) "Epistemological Changes in Primary Education in Spain from 1970" (Maria Luz Callejo and Camino Canon); (4) "The Understanding of Mathematical Topics and Instructional Representations: The Case of Fractions and Rational Number by Prospective Elementary Teachers" (Salvador Llinares and Victoria Sanchez); (5) "Prospective Teachers' Pedagogical Content Knowledge about Multiplicative Structures" (Enrique Castro and Encarnacion Castro); (6) "Thinking about Mathematics and Its Teaching: An Experience with Preservice Teachers" (Marta Civil); (7) "Learning to Teach Mathematics: Types of Knowledge" (Lorenzo J. Blanco); "Habitual School Practices and Problem Solving Situations: The Case of Carlota" (Victoria Sanchez and Salvador Llinares); and (9) "Exploring an Integrated Model of Assessment with Prospective Teachers" (J. Gimenez and J. M. Fortuny). Contains 278 references. (DDR) ED401110

Goldman, E., & Others, A. (1991). Hypermedia Cases in Teacher Education: A Context for Understanding Research on the Teaching and Learning of Mathematics. Action in Teacher Education v13 n1 p28-36 Spr 1991. Describes how selected case examples are used in a mathematics course for prospective elementary teachers to provide a framework for discussing how children construct meaning in mathematics. The article examines the advantages of presenting cases in videodisc format with access to additional information through associated computer databases. (SM) UMI Report/ISSN: ISSN-0162-6620 EJ431993

Goodlad, S. (1985). Putting Science into Context. Educational Research v27 n1 p61-67 Feb 1985. Pupils, student tutors, and teachers at local London schools were asked for their opinions of the program in which London University undergraduates help teach science, mathematics, and engineering at their schools. Pupils found lessons easier to follow, tutors got useful practice in communicating scientific ideas, and teachers found lessons more enjoyable. (Author/CT) EJ314808

Goos, M. (1995). How Do You Know When You Understand? Using Explanation To Monitor and Construct Mathematical Understanding. Australia; Queensland Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. This paper addresses the evidence that secondary school students use to imply that they understand something in mathematics. As part of a larger study, an open-ended questionnaire probing several aspects of metacognitive self-knowledge, was administered to students (N=72) in four schools. Two previously identified types of understanding were identified in the students' responses: (1) instrumental (knowing how to do a piece of mathematics) and (2) relational (knowing why it works). Analysis of the data revealed that students who associated understanding with explaining also reported engaging in frequent mathematical discussions with other students. This result suggests a connection between metacognitive functioning and social interaction consistent with Vygotsky's views on learning. Observations of students in one of the classrooms participating in the study are used to add depth to the questionnaire data and suggest implications for teaching. Contains 17 references. (DDR) ED404177

Goos, M. (1996). Making Sense of Mathematics: The Teacher's Role in Establishing a Classroom Community of Practice. Australia; Queensland Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. This paper describes the actions of one secondary school mathematics teacher in establishing a community of mathematical practice within which students acquire not only knowledge and skills, but also the epistemological values of mathematics. Classroom observations over a period of 18 months, together with interview and questionnaire data, are used to sketch a model of the teacher's interactions with his students as he works toward creating a culture of mathematical sense-making. The results indicate four aspects of the teacher's role that are particularly important in establishing a classroom community of practice: (1) modeling mathematical thinking; (2) cognitive and social scaffolding; (3) encouraging individual reflection, self-monitoring and checking; and (4) introducing tools for mathematical communication. Contains 33 references. (DDR) ED404178

Gordon, S. (1993). Mature Students Learning Statistics: The Activity Theory Perspective. Mathematics Education Research Journal v5 n1 p34-49 Sep 1993. Through interviews and questionnaires explores five mature students' approaches to learning statistics from the theoretical perspective of activity theory. Analyses socio-historical factors relating to students' self-regulation of their cognitive activities and interpretation of the contexts affecting their approaches. Appendices include interview, attitudes, and statistics course surveys. (Contains 28 references.) (Author/MKR) Report/ISSN: ISSN-1033-2170 EJ485573

Greer, B. (1993). The Mathematical Modeling Perspective on Wor(l)d Problems. Journal of Mathematical Behavior v12 n3 p239-50 Sep 1993. An exploratory study assessed the degree to which 13- and 14-year olds (n=100) adjusted assumptions of direct proportionality suggested by surface structure of word problems. Virtually no errors were made on "straightforward" items, but many students showed no adjustment for realistic constraints on complex items. (Contains 21 references.) (MKR) Report/ISSN: ISSN-0732-3123 EJ484114

Griffiths, R., & Clyne, M. (1991). Once upon a Time.... Australian Mathematics Teacher v47 n1 p10-13 Apr 1991. Described is the use of story telling as a context to introduce mathematical concepts by providing a model, offering problem-posing situations, stimulating investigation, and illustrating concepts. Examples of appropriate stories are given for the primary and low secondary levels. (MDH) Report/ISSN: ISSN-0045-0685 EJ442073

Gross, F. E., & Others, A. (1993). The Power of Numbers. A Teacher's Guide to Mathematics in a Social Studies Context. An Interdisciplinary Curriculum. Massachusetts Available in microfiche only. EDRS Price - MF01 Plus Postage. PC Not Available from EDRS. Educators for Social Responsibility, 23 Garden St., Cambridge, MA 02138. Report/ISSN: ISBN-0-942349-05-9. This document is the teacher's guide for a curriculum designed to teach mathematics in a social studies context. It provides mathematical experiences in real world contexts that help students interpret, experiment, communicate, and look for multiple solutions to complex problems. The curriculum uses mathematics in context to help students develop higher order thinking and communication skills. This approach encourages students to interact with each other and the material. Students begin to see that skills and concepts are part of a connected body of knowledge. The context gives students a reason to learn and remember mathematical skills and shows them how these skills and concepts are applied in actual practice. It shows them that they can use mathematics for learning about the world. This book provides a variety of thematic contexts for mathematical skills and mathematical understanding, including polling, studying trends in census data, and designing a public rail transportation system for Los Angeles. Through these activities students participate in discussions, interpret and analyze data, make decisions, and present their ideas. In the context of thematic applications, students see how otherwise apparently unrelated skills are related. They learn about the interdisciplinary nature of real problems. Each of the two parts of the guide is divided into topical chapters. Each chapter starts with an overview and a list of mathematical concepts, skills, vocabulary, and materials involved in the activities in that chapter. Each activity includes a list of handouts that are located at the end of each chapter. Contains 20 references. (DK) ED370872

H

________. (1995). Homeside Activities: Grade 5. California Not available from EDRS. Document Not Available from EDRS. Developmental Studies Center, 2000 Embarcadero, Suite 305, Oakland, CA 94606-5300 ($13.95). Report/ISSN: ISBN-1-885603-64-9. Providing a low-key, nonthreatening way for teachers and parents to build partnerships for kids, this book presents short, concrete activities in English and Spanish to foster communication between teachers and parents and between parents and children. While the activities in the book are designed for grade 5, none of the activities have grade-specific references; they can also be used in mixed-grade and ungraded classrooms. The activities in the book make it easy for parents to contribute a "homeside" to their children's schoolside learning. The activities in the book are introduced once or twice a month in class, completed at home, and then incorporated into a follow-up classroom activity or discussion. Typically these 15- to 20-minute activities in the book are reciprocal parent-child interviews or opportunities to share experiences and opinions. The book begins with a description of "homeside activities" and their benefits, guidelines for teachers, and a letter to parents. The 18 teacher pages and activities in the book are on topics such as everyday math, poetry performance, opinions, family folklore, group work, and school year collage. (RS) ED396283

Hachigan, J. (1978). Applied Mathematics in a Liberal Arts Context. American Mathematical Monthly v85 n7 p585-88 Aug-Sep 1978. This description of a graduate applied mathematics program developed at Hunter College is for students with a liberal-arts background and is suitable to the economic and geographical location of New York City. The components of the program and its success are reported. (Author/MP) EJ191343

Hancock, C. (1988). Context and Creation in the Learning of Computer Programming. For the Learning of Mathematics v8 n1 p18-24 Feb 1988. Described and critiqued are two ideas which have proven valuable in teaching programming at the introductory level, the mental model and the programming plan. (PK) EJ371056

Hassett, M., & Others, A. (1992). Case for In-Context Placement Testing. AMATYC Review v14 n1 p68-74 Fall 1992. Discusses a new placement program that allows incoming university students to select courses on the basis of prior mathematics coursework and tests students after the first few days of review. Compares and contrasts this method with the previous program that tested students prior to placement. (MDH) Report/ISSN: ISSN-0740-8404 EJ455077

Heckman, P. E., & Weissglass, J. (1994). Contextualized Mathematics Instruction: Moving beyond Recent Proposals. For the Learning of Mathematics v14 n1 p29-33 Feb 1994. Discusses situated cognition and anchored instruction and makes recommendations for effecting change in mathematics curricula in the early school years based on the experience of the Educational and Community Change (ECC) Project, which is involved with reinventing education in a low-income, multilanguage area. (Contains 26 references.) (MKR) Report/ISSN: ISSN-0228-0671 EJ487128

Heller, P. M., & Others, A. (1989). Proportional Reasoning: The Effect of Two Context Variables, Rate Type, and Problem Setting. Journal of Research in Science Teaching v26 n3 p205-20 Mar 1989. Investigates the effects of two context variables on the performance of seventh-grade students on a qualitative and numerical proportional reasoning test. Explores the nature of the relationships between rational number skills, qualitative reasoning about ratios, and numerical proportional reasoning. (Author/YP) UMI EJ391133

Henderson, R. W., & Landesman, E. E. M. (1992). Mathematics and Middle School Students of Mexican Descent: The Effects of Thematically Integrated Instruction. Research Report No. 5. California Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. Dissemination Coordinator, National Center for Research on Cultural Diversity and Second Language Learning, Center for Applied Linguistics, 1118 22nd Street, N.W., Washington, DC 20037. Contract no.: R117G10022. This paper reports the effects of thematically integrated mathematics instruction on achievement, attitudes, and motivation in mathematics among middle school students of Mexican descent. A school-university collaborative effort led to the development and testing of a thematic approach undertaken as a means of contextualizing instruction for students considered to be at risk for school failure. Instruction relied heavily on small collaborative learning groups and on hands-on activities designed to help students make real-world sense of mathematical concepts. As hypothesized, experimental and control students made equivalent gains in computational skills, but experimental students (who received thematic instruction) surpassed controls in achievement on mathematical concepts and applications. The two programs did not have a differential effect on students' attitudes toward mathematics or self-perceptions of motivation in mathematics, but motivational variables did predict achievement outcomes for both groups. Issues related to the opportunity to learn the full range of mathematics content of the curriculum within a thematic approach are examined. (Contains over 50 references.) (Author) ED355117

Higginson, W. (1981). Mathematizing "Frogs": Heuristics, Proof, and Generalization in the Context of a Recreational Problem. Mathematics Teacher v74 n7 p505-15 Oct 1981. The mathematics of an educational game commonly known as "Frogs" is analyzed to see different mathematical concepts imbedded in it. (MP) Reprint: UMI EJ254210

Hirschhorn, D. B. (1990). Culture, Literacy, and Secondary Mathematics Education. Illinois Available in paper copy and microfiche. EDRS Price - MF01/PC05 Plus Postage. This paper discusses the role of the culture in secondary mathematics education. A historical and philosophical look at the relationship between the real world and mathematics and mathematics education is developed. The U.S. secondary mathematics curriculum is explored both historically and philosophically to try to ascertain its changing attitudes toward applications and the culture over time. Two University of Chicago School Mathematics Project (UCSMP) texts, "Transition Mathematics" and "UCSMP Algebra" were compared with other commercial textbooks to determine the number and type of cultural contexts. The four commercial textbooks studied were: "Heath Pre-Algebra"; Merrill's "Mathematics 7"; Dolciani's "Algebra 1"; and Saxon's "Algebra 1." Among the findings, the study concluded that UCSMP materials have about three times as many cultural contexts than the four commercial texts. UCSMP materials also had many more contexts in the non-traditional applications of mathematics such as demographics, business, politics, law, technology, etc. The appendices, which constitute over half of the document, provide lists of the cultural contexts found in each of the six textbooks analyzed. The bibliography contains 50 sources. (KR) ED326448

Howell, M. R., & Bell, P. (1981). A Language-Thinking Approach to Mathematical Problem Solving: A Staff Development Package. Mississippi Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. Designed for fifth grade mathematics teachers, the three inservice sessions described in this booklet balance the theoretical with the practical and show teachers how to help students through the activity of writing word problems based on their own experiences. Using a total language-thinking approach to helping students read and solve word problems, the first section, entitled "Language," involves teachers in demonstration lessons with students and discussions with other teachers on the relationship between reading and mathematics, the special language of mathematics, and the growth of language through the use of language. The second session, "Thinking," contains information on Jean Piaget's three stages of thought. It emphasizes the need for teachers to focus not only on language that promotes mathematical reading ability, but also on promoting and encouraging competent problem solving skills through a conscious attempt to teach for thinking. The third session, "Computation," involves the teachers in reviewing the content of the previous two sessions, going through the steps of solving problems, and spending time with other teachers discussing their successes, failures, and questions related to reading word problems in classrooms. An evaluation form, additional ideas and activities for student-developed word problems, and a list of references are included. (RL) ED198505

Hubbard, R. (1994). Addressing the Language and Cultural Problems of Overseas Students in the Context of Mathematics Classes. Higher Education Research and Development v13 n2 p133-42 1994. A Queensland University (Australia) action research project to help foreign students develop skills in the language of mathematics and adjust to the university environment is described. Student, teacher, and observer diary entries indicate students became aware of their language and cultural adjustment needs and made some progress in this direction. (Author/MSE) Report/ISSN: ISSN-0729-4360 EJ497745

J

K

Kawagley, O. (1990). Yup'ik Ways of Knowing. Canadian Journal of Native Education v17 n2 p5-17 1990. Explores traditional Yupik means of gaining knowledge through a blending of pragmatic, inductive, and spiritual methods. Proposes teaching mathematics and science to Native youth in a synergistic manner by capitalizing on Native knowledge, skills, and spiritual relationship to nature, then relating these to the Western perspective. Contains 14 references. (SV) Report/ISSN: ISSN-0710-1481 EJ420521

Kennedy, E. (1988). Estimation of the Squared Cross-Validity Coefficient in the Context of Best Subset Regression. Applied Psychological Measurement v12 n3 p231-37 Sep 1988. A Monte Carlo study was conducted to examine the performance of several strategies for estimating the squared cross-validity coefficient of a sample regression equation in the context of best subset regression. Results concerning sample size effects and the validity of estimates are discussed. (TJH) UMI EJ389943

Kilgore, S. B., & Pendleton, W. W. W. (1993). The Organizational Context of Learning: Framework for Understanding the Acquisition of Knowledge. Sociology of Education v66 n1 p63-87 Jan 1993. Reports on a review of research into the effects of organizational structure on the acquisition of knowledge. Asserts that the opportunity to learn has two dimensions: (1) the amount of exposure; and (2) the quality of exposure. Concludes that teachers and students make decisions about these dimensions, which are affected by inducements and information flows within the organization. (CFR) UMI Report/ISSN: ISSN-0038-0407 EJ473711

Knijnik, G. (1993). An Ethnomathematical Approach in Mathematical Education: A Matter of Political Power. For the Learning of Mathematics v13 n2 p23-25 Jun 1993. Presents two practices used by rural Brazilians to estimate area of land and volumes of tree trunks. Using an ethnomathematical approach, develops educational ideas involving the interrelations between academic and popular mathematical knowledge in the context of the struggle for land. Discusses contributions of this work to the process of social change. (MDH) EJ473510

Kouba, V. L., & McDonald, J. J. L. (1991). A Model for Inferring Components of Belief Systems by Interpreting the Content and Context Cues Used by Students to Situate Mathematical Tasks. New York Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. Confrontation with a mathematical task causes a student to focus initial attention upon particular content and context cues based upon that student's belief system; the student assigns subsequent meaning to that task based upon previous mathematical experience and knowledge. In order to make effective use of students' belief systems, educators need delineations both of the components of those systems and of the interactions of those systems with students' cognition. A model is presented for the inference of the positive and negative components of students' belief systems by interpretation of the content and the context cues that students use within their mathematical identification and construction techniques. Three assumptions that parallel those concerning teachers' belief systems are noted: (1) notions and beliefs are implicit within responses to questions or issues related to mathematical tasks and hence can be identified and described; (2) some beliefs can impede effective and efficient mathematical understanding and performance; and (3) eventually, educators may be able to modify instruction based upon knowledge of the components of students' belief systems. (33 references) (JJK) ED335215

Kupari, & Pekka, E. (1991). Mathematics Education Research in Finland: Yearbook 1989-90. Institute for Educational Research. Publication Series B. Theory into Practice 66. Finland Available in paper copy and microfiche. EDRS Price - MF01/PC04 Plus Postage. Institute for Educational Research, University of Jyvaskyla, Seminaarinkatu 15, SF-40100 Jyvaskyla, Finland. Report/ISSN: ISBN-051-680-606-6; ISSN-0782-9817. This Yearbook 1989-90 is made up of six articles. The articles depict the ongoing discussion taking place in Finland as it re-assesses the state of its mathematics education and planning measures for its development. The opening article presents an analysis of the president of the International Commission on Mathematical Instruction of some current trends in mathematics education. The following three articles represent then recent Finnish research on the area of mathematics education. The last two articles offer views about mathematics teaching and teacher education in Estonia and Czechoslovakia. The articles are: (1) Some Contemporary Tendencies in Mathematical Education (Miguel de Guzman); (2) Mathematics, Science and Technology Teachers' Conceptions about Their Professional Knowledge and Skills (Yrjo Yrjnsuuri); (3) Study Orientations of Mathematics by Upper Secondary School Students (Raija Yrjnsuuri); (4) "A Contextual Approach to the Teaching of Mathematics: Outlining a Teaching Strategy That Makes Use of Pupils' Real World Experiences and Strategies, and the Results of the First Teaching Experiment of the Project (Tapio Keranto); (5) Developments in the Teaching of Mathematics in Estonia (Olaf Prinits); and (6) The System of Teacher Education in Czechoslovakia with Special Reference to Mathematics Teachers' Education (Jaroslav Bartak). (MDH) ED345940

L

Lamon, S. J. (1996). The Development of Unitizing: Its Role in Children's Partitioning Strategies. Journal for Research in Mathematics Education v27 n2 p170-93 Mar 1996. Analyzes (n=346) grades 4-8 children's partitioning strategies in terms of a framework that translates economy in number or size of pieces and use of perceptual cues into sophistication in unitizing. Proportionately more students used economical partitioning strategies than used less economical cut-and-distribute strategies. (Author/MKR) UMI Report/ISSN: ISSN-0021-8251 EJ522095

Lancy, D. F. (1981). The Indigenous Mathematics Project: An Overview. Educational Studies in Mathematics v12 n4 p445-53 Nov 1981. A multidisciplinary team research project to document the relationship between environmental and cultural features of Papua New Guinea, cognitive development, and mathematics learning is described. (MP) EJ254349

Lawton, C. A. (1993). Contextual Factors Affecting Errors in Proportional Reasoning. Journal for Research in Mathematics Education v24 n5 p460-66 Nov 1993. Two studies (n=228 and n=175) showed that college students more readily solve proportion problems if the items in the problem are relatively distinct from one another. Translation of units of one item into units of another is easier if the items are substantially different. (MDH) UMI Report/ISSN: ISSN-0021-8251 EJ480148

Leder, G. C. (1974). Sex Differences in Mathematics Problem Appeal as a Function of Problem Context. Journal of Educational Research 67 8 351-3. It was shown that activities of sex-differentiated interest and appeal in everyday situations could be translated to a mathematics problem setting and retain this differential appeal for boys and girls. (Author/JA) EJ097036

Lees, L. H. (1994). Educational Inequality and Academic Achievement in England and France. Comparative Education Review v38 n1 p65-87 Feb 1994. In both France and England, students scored in the middle-to-high ranks on the International Assessment of Educational Progress, with large gaps between low and high achievers. Despite attempts to democratize education, educational achievement in both countries continues to be strongly linked to parents' social background, with limited access to elite schools. (KS) UMI Report/ISSN: ISSN-0010-4086 EJ486983

Lester, F., & K., J. (1989). Research Into Practice. Arithmetic Teacher v37 n3 p33-35 Nov 1989. Discusses the differences between mathematical problem solving typically used in the classroom and problem solving that is a part of everyday situations out of school. Suggests some teaching methods to align classroom instruction with the real world. Seventeen references are listed. (YP) UMI EJ406055

Levin, P., & Others, A. (1980). Field Guide for Studying Classroom Events and Their Cultural Context. Indigenous Mathematics Project. Working Paper 4. Papua New Guinea Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. This field guide was used as a basis for documenting classroom events at five community school sites in Papua New Guinea, as part of the Indigenous Mathematics Project in its ongoing research into primary mathematics learning. Methodology for evaluating the appropriateness of curriculum form and content is described and specific sections focus on ordering materials, the lesson packet, and the school in the community. The section on the lesson packet contains explicit instructions on interviewing the teacher, recording classroom activities, taking field notes, and interviewing students, and includes codes for noting classroom organization, language shifts, classroom interaction, and classroom talk. In the section on the school in the community are instructions for describing such factors as the physical setting, materials and resources, classroom activities, and language use in the community. One appendix contains sample field notes, sample language use and classroom interaction forms, and student questionnaire. A second appendix presents comments on the field guide. (MNS) ED229261

Lewis, J. C. (1994). The Effect of Context and Gender on Assessment of Estimation. Iowa Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. Whether boys and girls perform differently on mathematics estimation items with a picture format (applied context AC items) compared with items with a numbers-only (NC) format was studied when effects of computational skill, conceptual knowledge, and quantitative ability were controlled. Subjects were approximately 80,000 students from grades 4 through 8 who participated in the 1992 joint national standardization of the Iowa Tests of Basic Skills, Form K, and the Cognitive Abilities Test, Form 5. Because of the way items were selected for the estimation subtest, it was not meaningful to compare performance on AC items versus NC items alone. However, the interaction of gender with item type as mediated by computational skill, conceptual knowledge, and quantitative ability was examined. In general, males performed slightly better than females on these items, but there did not seem to be a consistent pattern of differences favoring one item type over the other for either gender group. In addition, differences were so small that there seemed to be little need for concern about gender bias attributable to applied context versus the numbers-only context. Eight tables and seven figures present the analyses. (Contains 13 references.) (SLD) ED372115

Linchevski, L., & Herscovics, N. (1996). Crossing the Cognitive Gap between Arithmetic and Algebra: Operating on the Unknown in the Context of Equations. Educational Studies in Mathematics v30 n1 p39-65 Jan 1996. Reports the results of a teaching experiment involving like terms and equations in algebra. Seventh-grade students (n=6) experienced difficulties in decomposing an additive term into a difference. (Author/MKR) UMI Report/ISSN: ISSN-0013-1954 EJ520677

M

________. (1995). Montessori(TM) Math by Colors CD Rom. Florida Not available from EDRS. Document Not Available from EDRS. Software Holdings, Inc., 1750 NW 65th Ave., Plantation, FL 33313 (CD-ROM disk (DOS version) 3-1/2", 5-1/4" disks available). Montessori(TM) Learning Software programs are purportedly built upon the core concept of the Montessori philosophy, that a major path to intellectual development is through a child's hands and senses. Math by Colors, recommended for ages 4 to 8, encourages hands-on discovery by allowing the child to choose the right color from the assembled paint tins grouped at the bottom of each picture. Color is chosen by correctly identifying the answer to a mathematics problem (MKR) ED386380

Maltby, F. (1993). Teaching Mathematics through "Thinking Actively in a Social Context.". Gifted Education International v9 n1 p45-47 1993. This article describes "Thinking Actively in a Social Context," a multiphase model to assist in the development of problem-solving courses based on student needs and experiences. An example of such an interdisciplinary course (simulating a new settlement on another planet) for high ability children in grades five, six, and seven is detailed. (DB) Report/ISSN: ISSN-0261-4294 EJ472670

Masingila, J. O. (1995). Examining Students' Perceptions of Their Everyday Mathematics Practice. New York Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. Students need, through their school mathematical experiences, to build on and formalize mathematical knowledge gained in out-of-school situations. This study examined middle school students' perceptions of how they use mathematics outside the classroom in an attempt to learn more about students' everyday mathematics practice and to close the gap between doing mathematics in school and out of school. Middle school students (n=20) were interviewed before and after keeping a log for a week in which they recorded their everyday mathematics usage. Through the interviews and log sheets, it was found that the mathematics the middle school students perceived using outside the classroom could be classified as one of the six activities that Bishop (1988) has called the six fundamental mathematical activities (counting, locating, measuring, designing, playing, and explaining) but was also strongly influenced by their view of mathematics as school mathematics. Contains 23 references. (Author/MKR) ED387347

Masingila, J. O. (1996). The Mathematics Practice of Carpet Layers: A Closer Look at Problem Solving in Context. New York Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. The majority of research on mathematics practice in everyday situations within cultures has investigated the use of arithmetic and geometry concepts and processes. To extend this research to a situation using measurement ideas, this paper investigates the mathematics practice of a group of carpet layers in an effort to detail how ordinary people "actively give meaning to, and fashion, processes of problem solving in the midst of ongoing activities in relevant Settings" (Lave, 1988). Data were collected by observing and informally questioning the employees of a carpet laying business. Four areas of mathematics concepts used by the estimators and/or installers were observed: measurement, computational algorithms, geometry, and ratio and proportion. Two general observations were made: (1) the estimators and installers were not concerned with square footage of a room but with the square feet of carpet needed in the room, and (2) all problems in carpet laying are optimization problems. (MKR) ED398068

Mason, M. M. (1995). Geometric Knowledge in a Deaf Classroom: An Exploratory Study. Focus on Learning Problems in Mathematics v17 n3 p57-69 Sum 1995. Examined geometric understanding and misconceptions among a deaf teacher and (n=5) deaf students. Students seemed to treat the sign for triangle as a picture of a triangle and not as a symbol representing the broad class of triangles. (MKR) Report/ISSN: ISSN-0272-8893 EJ520586

Matheson, N., & Others, A. (1996). Education Indicators: An International Perspective. District of Columbia Available in paper copy and microfiche. EDRS Price - MF01/PC13 Plus Postage. Report/ISSN: NCES-96-003. This publication compiles a comprehensive set of educational indicators using data from a variety of sources and presents results of interest to a U.S. audience about education in the United States and other countries. International indicators provide the United States with an opportunity to compare its performance with that of other countries, to identify areas for improvement, and to suggest new approaches to producing a world-class class educational system. The report presents data on many countries, but the primary comparisons are among the Group of Seven (G-7) countries, seven industrialized nations with large economies: Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States. The achievement indicators show that the performance of U.S. students is mixed. They perform well in reading in comparison with their peers in other countries, and less well in geography and science. Their weakest area relative to students in other countries is mathematics. The finance indicators presented in this publication show that public financial investment in education in the United States is among the highest of the G-7 countries on multiple measures. Indicators are divided into: (1) Participation and Student Flows; (2) Achievement and Attainment; (3) Education and Labor Market Destinations; (4) Contextual Factors; and (5) Societal Support for Education. (Contains 45 tables, 45 figures, and 15 references.) (SLD) ED403331

McConeghy, J. I. (1987). Mathematics Attitudes and Achievement: Gender Differences in a Multivariate Context. Illinois Available in paper copy and microfiche. EDRS Price - MF01/PC04 Plus Postage. As the technological revolution continues, there is an increased emphasis on mathematics and science. Many people feel that there are significant gender differences in both attitudes toward, and achievement in, these subjects. This study examined some of the attitudes toward mathematics and achievement in mathematics as measured by the 1977-78 and 1981-82 National Assessment of Educational Progress (NAEP) Mathematical Assessments. It explored the relationships between them, and between other types of influences, including those of community, school, and home, as well as gender, age and year. Attitudes toward mathematics were measured using a group of 14 statements which were used to construct three specific attitude scales and an overall Math Attitude Index. Achievement was measured using the NAEP percentile scores. Various analyses indicated that parents' education and race of student had the strongest influence and gender the least influence on achievement of the six significant independent variables identified. It is suggested that schools need to develop methods to encourage and help students who have been identified as being members of some of the subpopulations that have negative attitudes and lower achievement scores. (TW) ED284742

McGinn, M. K. (1995). Teacher's Mathematics Inside and Outside Classrooms: A Case Study of Mathematical Activity across Contexts. Canada; British Columbia Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. This study was based on recent research findings that mathematical activity is fundamentally situated and distributed across physical and social contexts. Interviews, observations, and examination of artifacts were used to explore ways in which a 2nd-grade teacher with seven years of experience understood and used mathematics inside and outside her classroom. The connections she made between school and nonschool mathematics, the ways she taught and learned mathematics in the classroom, and the ways she used mathematics outside the classroom were investigated. Data analysis revealed the following list of categories of mathematical activities within and across contexts: flexibly modifying plans, making sense, using physical objects, stating solutions, measuring and calculating new measures, recognizing multiple solutions, checking one's work, and drawing connections. Contains 35 references. (MKR) ED385440

Menon, R. (1995). The Role of Context in Student-Constructed Questions. Focus on Learning Problems in Mathematics v17 n1 p25-33 Win 1995. Analysis of student constructed questions about common and decimal fractions of (n=27) students in grades five and six revealed that students seemed to construct experience- and interest-based questions rather than textbook-type word problems which tended to be multistep problems. (12 references) (MKR) Report/ISSN: ISSN-0272-8893 EJ503917

Meyer, M. R. (1997). Mathematics in Context: Opening the Gates to Mathematics for All at the Middle Level. NASSP Bulletin v81 n586 p53-59 Feb 1997. Describes Mathematics in Context, a middle-level mathematics curriculum developed by researchers at the University of Wisconsin-Madison and the University of Utrecht, in the Netherlands. Instead of proceeding from a generalization to specific examples, the math originates in real problems; conversely, the mathematics learned is used to solve problems in practical situations. Five program principles are discussed. (MLH) Report/ISSN: ISSN-0192-6365 EJ539069

Millroy, W. L. (1992). An Ethnographic Study of the Mathematical Ideas of a Group of Carpenters. Monograph Number 5. Journal for Research in Mathematics Monograph n5 1992 Virginia Available in microfiche only. EDRS Price - MF01 Plus Postage. PC Not Available from EDRS. National Council of Teachers of Mathematics, 1906 Association Drive, Reston, VA 22091-1593 ($5). Report/ISSN: ISBN-0-87353-341-0; ISSN-0883-9530. The researcher conducted a six-month ethnographic study as an apprentice carpenter in Cape Town, South Africa, to document the valid mathematical ideas that are embedded in the everyday woodworking activities of a group of carpenters. A secondary objective was to examine and to give a firsthand account of the teaching and learning of mathematical ideas in the context of the researcher's apprenticeship. Finally, the study offers methodological techniques for identifying mathematics in thought and action and for differentiating the mathematics from routine applications of procedures. The results showed that many conventional mathematical concepts are embedded in the practices of the carpenters. They made extensive use of such concepts as congruence, symmetry, proportion, and straight and parallel lines in their everyday work. Furthermore, the carpenters' problem solving was enhanced by their strength in spatial visualization. Their explanations, in the form of convincing arguments, showed the sequential, logical reasoning that is related to the need in mathematics for proof and substantiation. The results also showed that the carpenters' mathematics has several unique characteristics: there was tacit mathematical knowledge in their actions, and reflection on actions led them to articulate their tacit knowledge; decontextualized questions posed were revised into concrete, contextualized problematics; and their ideas were framed by the context of the workshop and carpentry tools. Comparison, using the senses of touch and sight, was preferred to measuring and usually resulted in optimal solutions. To solve a problem such as "How many table legs can be cut from this plank?" spatial visualization practices were used to construct functional units, producing an optimal result that could not be obtained with formal procedures. The results are presented as a series of 20 narrative episodes, followed by an analysis. The epistemological, educational, and methodological implications of these results are discussed. (Contains over 100 references.) (Author) ED355089

Mitchell, M. (1992). Situational Interest: Its Multifaceted Structure in the Secondary Mathematics Classroom. California Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. Classroom boredom in the secondary mathematics classroom is a problem that can be addressed from knowledge of the intrinsic motivational variable of "interestingness." The lack of a theoretical model of interest is an obstacle in research that investigates this variable. This paper describes the three stages in the development of a model of interest. The first stage involved the development of a preliminary model according to the current research literature on interest. Working from the social ecological research orientation of (R. H.) Moos (1976, 1979) that emphasizes the importance of social perceptions as the key to manipulating an environment, the second stage included an elaboration on the initial model using naturalistic techniques to better understand student perceptions of interest in the mathematics classroom. In the third stage, a survey instrument was developed. Data was collected and quantitatively analyzed to assess the tenability of the model developed through stages one and two. Participants in the study consisted of 350 high school students from 3 different high schools in the Santa Barbara (California) area. The sample was composed of 147 boys and 188 girls, 30% of whom were not Anglo-American. Students responded to a Likert-type survey consisting of 45 items representing 7 different scales identified as the following: personal interest; situational interest; meaningfulness; involvement; group work; puzzles; and computers. Factor analysis, LISREL analysis, and correlational analysis were applied to the data. Results of the various analyses identified two general scales for personal interest and situational interest (SI) and five subscales for SI. In addition, the correlational analyses lent support to the conceptual distinction made between catching and holding interest. (Contains over 60 references.) (MDH) ED353157

Morgan, C. (1989). A Context for Estimation. Mathematics in School v18 n3 p16-17 May 1989. Reports students were more successful in estimation for a problem in context than for the pure computation. Describes students' strategies to make estimates in context. Discusses how to teach estimation. (YP) UMI EJ397095

Morony, W., & Olssen, K. (1994). Support for Informal Assessment in Mathematics in the Context of Standards Referenced Reporting. Educational Studies in Mathematics v27 n4 p387-99 Dec 1994. Argues that standards-referenced reporting frameworks, the Australian nationally developed Mathematics Profile in particular, require the use of teacher observation as an essential assessment practice if teachers are to report the full range of demonstrated student achievement. Supports student self-assessment. (14 references) (Author/MKR) UMI Report/ISSN: ISSN-0013-1954 EJ498212

Morrison, G. R., & Others, A. (1992). Learner Control of Context and Instructional Support in Learning Elementary School Mathematics. Educational Technology, Research and Development v40 n1 p5-13 1992. This study examined learner-control strategies for selecting problem context and level of instructional support on a computer-based mathematics unit on the metric system. Subjects were 240 sixth grade students assigned to 15 treatments. Performance was lowest under learner-control instructional support conditions even though subjects indicated positive attitudes toward learner-control strategies. (MES) UMI Report/ISSN: ISSN-1042-1629 EJ446167

Murphy, N. (1996). Multicultural Mathematics and Science: Effective K-12 Practices for Equity. ERIC Digest. Ohio Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. ERIC Clearinghouse for Science, Mathematics, and Environmental Education, 1929 Kenny Road, Columbus, OH 43210-1080. Report/ISSN: EDO-SE-96-1 Contract no.: RI93002013. Educational reform initiatives such as the National Council of Teachers of Mathematics (NCTM) Standards, National Science Education Standards, and Project 2061 provide guidelines to reduce the diversity gap in science and mathematics literacy. Schools are applying these guidelines to classroom practices by posing questions about what changes are feasible given the multiple pressures of today's schools. This digest provides references to successful practices which have increased mathematics and science achievement among diverse student populations. Topics discussed include: (1) Eliminating Tracking, Increasing Expectations and Course Requirements, and Changing Course Content Sequences; (2) Using Technology; (3) Enhancing Life Skills Through Mathematics and Science Literacy; (4) Capitalizing on Cultural Learning Styles and Culturally Relevant Curricula; (5) Engaging Parents as Active Partners; and (6) Increasing Affective and Academic Support for Students. Contains 23 references. (JRH) ED402146

N

Nasser, R., & Carifio, J. (1993). Developing and Validating Sets of Algebra Word Problems. Massachusetts Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. The validation of key contextual features of algebra word problems was studied in two phases. In the first phase, five experts were asked to assess the appropriateness of the concepts in the problems and the adequacy of the assignment of the contextual features to the problems. In the second phase, construct validity was established by having 6 judges rate each of the 16 word problems in random order on the contextual features of familiarity, imageability, and variable type (discrete or continuous). A repeated measures analysis of variance for the construct validity of the key contextual features showed that when one rater or judge and one of the problems were removed, agreement between problems and the criterion were extremely high. When a step-down analysis on each key context feature and variable type was done without one judge, the results indicate a convergence on the constructs devised. In effect, judges agreed with each other, and were correct on 93.5 percent of the ratings, which is strong evidence for both construct validity and reliability of the 16 problems. Seven tables present study findings. (Author/SLD) ED361349

Nasser, R., & Carifio, J. (1993). Key Contextual Features of Algebra Word Problems: A Theoretical Model and Review of the Literature. Massachusetts Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. One of the four algebra word problem structures found in K-12 textbooks is the propositional relation structure (Mayer, 1982). This type of problem asks students to establish equivalences between the variables or noun referents in the problem. The literature available indicates that students have inordinate difficulties, when trying to solve a propositional relation type of problem. The literature says little about how key context features are assigned to the text of the algebra word problem and how these features affect student performance or preference of algebra problems in general. Three key context features of algebra word problems were identified: familiarity, imageability, and variable type (discrete or continuous). These three key contextual features have been shown to have performance effects on arithmetic and algebra problems. The analysis in this paper examines these key context features of algebra problems in relationship to pictorial, symbolic, and verbal representational formats. In addition, an information processing model of the algebra word problem solving process is presented. The ways in which key contextual features may influence problem processing and the construction of solutions is discussed. This paper supplies a rationale, definitions, and a procedure for assigning key context features to an algebra word problem of the propositional relation type. These procedures were used to construct a set of 16 algebra word problems that systematically varied the key contextual features identified. These problem are proposed to be used to study several variables that may be important to understanding the nature of difficulties students face when solving a problem with a propositional relation structure. The model developed and presented could be generalized to other algebra problems of different structures or other domains. (Contains 45 references.) (MDH) ED355120

Nasser, R., & Carifio, J. (1993). The Effects of Cognitive Style and Piagetian Logical Reasoning on Solving a Propositional Relation Algebra Word Problem. Massachusetts Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. The purpose of this study was to find out whether students perform differently on algebra word problems that have certain key context features and entail proportional reasoning, relative to their level of logical reasoning and their degree of field dependence/independence. Field-independent students tend to restructure and break stimuli into parts and to perceive details more readily than field-dependent students. The underlying theoretical view is that context may be an important factor in how students approach, analyze, and restructure word problems. The sample included university students (n=37) and secondary school students (n=193) from two large high schools in two cities. The Gottschaldt Hidden Figures Test was used to assess field dependence/independence. Selected items from the Equilibrium Balance Test were used to assess Piagetian stages of logical reasoning. A 2 x 3 MANOVA was used to analyze the effects of cognitive style (dependence, independence) and operativity (concrete, transitional, formal). Overall, field-independent subjects who were formal operational reasoners performed highest across all the problem features. The results supported the influence of cognitive style, together with cognitive development, in mediating a student's ability to solve algebra word problems. Contains 34 references and 2 test references. (Author/LDR) ED364430

Nelson-Barber, S., & Estrin, E. E. T. (1995). Culturally Responsive Mathematics and Science Education for Native Students. (1) ways of knowing with regard to mathematics and science, rooted in varying world views; (2) approaches to learning and problem solving; (3) communication styles, strategies, and uses; and (4) cultural values about use and sharing of particular kinds of knowledge. Ethnoscience and ethnomathematics (forms embedded in cultural activities, the workplace, or everyday life) can serve to contextualize instructionto provide real-life connections that make classroom theories and practices meaningful. Several examples demonstrate how such connections can be made. A set of guidelines is presented for instruction that bridges cultures and situates mathematics and science learning in meaningful contexts for Native students, as well as for all underserved students. Contains 130 references. (SV) California Available in paper copy and microfiche. EDRS Price - MF01/PC03 Plus Postage. Far West Lab. for Educational Research and Development, 730 Harrison St., San Francisco, CA 94107. This monograph addresses concerns about mathematics and science instruction and educational outcomes for Native students. The sociocultural contexts of schooling and community come together in particular ways to influence how Native children learn and, consequently, their life outcomes. It is important to look beyond the performance of individual students to the systems in which they are educated and to the historical and social influences on how mathematics and science are conceptualized and taught. Methods for implementing current mathematics and science reforms are shaped by assumptions about what children should know and be able to do. This monograph seeks to make such assumptions and the Western cultural values underlying them more explicit, and suggests that a generic approach to reform is ineffective and inequitable. Student differences with implications for teachers' choices about instructional strategies include differences ED388483

Noss, R. (1988). The Computer as a Cultural Influence in Mathematical Learning. Educational Studies in Mathematics v19 n2 p251-68 May 1988. Examined is the cultural impactboth actual and potentialof the computer on children's mathematical education. The ways in which the introduction of the computer does and will change the ambient space in which children learn mathematics is considered. (Author/PK) EJ376831

Noss, R. (1994). Structure and Ideology in the Mathematics Curriculum. For the Learning of Mathematics v14 n1 p2-10 Feb 1994. Discusses the concept of ideology; analyzes the construction of meaning in music; discusses similarities and differences relative to mathematics, focusing on mathematical proof; and provides a framework to make sense of the mathematics curriculum and the way in which knowledge is constructed within it. (Contains 39 references.) (MKR) Report/ISSN: ISSN-0228-0671 EJ487125

O

O'Brien, T. C. (1981). Learning and Context: An Interview with A. I. Weinzweig, University of Illinois at Chicago Circle, Chicago, Illinois. Illinois Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. This document is a verbatim transcription of an interview conducted by Thomas C. O'Brien under the auspices of the Teacher's Center Project of Southern Illinois University at Edwardsville. The transcript presents the views of Professor A. I. Weinzweig for the University of Illinois at Chicago Circle. Distinctions between training and education, and a feeling that much of what American education offers is training for a world that no longer exists, are noted. Ideas about the ways young children learn and solve problems within specific contexts and ideas for teaching that recognize the cognitive nature of children are also presented. (MP) ED214758

P

Peak, L., & Others, A. (1996). Pursuing Excellence: A Study of U.S. Eighth-Grade Mathematics and Science Teaching, Learning, Curriculum, and Achievement in International Context. Initial Findings from the Third International Mathematics and Science Study. District of Columbia Available in paper copy and microfiche. EDRS Price - MF01/PC04 Plus Postage. World-Wide Web: http://www.ed.gov/NCES/timss Report/ISSN: NCES-97-198. The Third International Mathematics and Science Study (TIMSS) is the largest, most comprehensive, and most rigorous international comparison of education ever undertaken. During the 1995 school year, the study tested the mathematics and science knowledge of a half-million students from 41 nations at five different grade levels. In addition to tests and questionnaires, the TIMSS included a curriculum analysis, videotaped observations of mathematics classrooms, and case studies of policy issues. This report on eighth-grade students is one of a series of reports that will also present findings on student achievement at fourth-grade level, at the end of high school, as well as on various other topics. The report combines the major findings from each of the five parts of the study into a single story about U.S. eighth-grade mathematics and science achievement in a comparative perspective. Chapter 1 draws from the results of the student assessments to describe how U.S. students perform in mathematics and science. Succeeding chapters focus on factors which may have an important influence on achievement, and describe how our nation's schools, teachers, and students compare to those in other countries. Chapter 2 examines educational standards and the curriculum, based on data from the curriculum analysis, case studies, videotape study, and questionnaires. Chapter 3 focuses on how teachers actually teach the curriculum, drawing from results of the videotape study and questionnaires. Chapter 4 examines the working life of teachers, based on findings from the case studies and questionnaires. Chapter 5 describes the lives of students, both in and out of school, based upon case study and questionnaire data. The conclusions at the end of the report look across all of the findings for insights about factors associated with student performance and indicate questions for further study. (JRH) ED400209

Pedrotti, L. S., & Chamberlain, J. J. D. (1995). CORD Applied Mathematics: Hands-On Learning in Context. Mathematics Teacher v88 n8 p702-07 Nov 1995. The Center for Occupational Research and Development (CORD) developed an applied mathematics course that integrates algebra, geometry, trigonometry, and other strands; centers around hands-on laboratory experiences; and uses real-world problems found in the world of work. (MKR) UMI Report/ISSN: ISSN-0025-5769 EJ515327

Phelps, E., & Damon, W. (1989). Problem Solving with Equals: Peer Collaboration as a Context for Learning Mathematics and Spatial Concepts. Journal of Educational Psychology v81 n4 p639-46 Dec 1989. The effects of peer collaboration on mathematical and spatial reasoning were assessed for 152 fourth graders. Effects on learning with logical-physical materials were assessed 1 year later. Findings suggest that peer collaboration is effective for tasks that require reasoning but not for tasks that require rote learning or copying. (SLD) UMI EJ404608

Pinxten, R. (1991). Geometry Education and Culture. Learning and Instruction v1 n3 p217-27 1991. It is worthwhile to develop the concepts and conventions that emerge from the child's culture in the teaching of elementary school mathematics, specifically geometry. The discussion is based on experiences with 7- to 12-year-old Navajo children in studies toward the development of a culturally relevant mathematics curriculum. (SLD) Report/ISSN: ISSN-0959-4752 EJ438633

Prawat, R. S., & Jennings, N. (1997). Students as Context in Mathematics Reform: The Story of Two Upper-Elementary Teachers. Elementary School Journal v97 n3 p251-70 Jan 1997. This case study describes two experienced teachers' attitudes and actions during implementation of a new mathematics curriculum in California. It focuses on their attentiveness to learners' needs. One teacher viewed learners' needs largely through the prism of a fixed set of curricular demands, while the other focused on an equally rigid set of demandsmathematical ability. (EV) Report/ISSN: ISSN-0013-5984 EJ539897

R

________. (1993). Research, Issues, and Practices. Annual Curriculum and Instruction Research Symposium Conference Proceedings (1st, Vermillion, South Dakota, April 22, 1993). South Dakota Available in paper copy and microfiche. EDRS Price - MF01/PC04 Plus Postage. The purpose of the conference reported in this document was to promote the professional sharing of current educational issues, to provide a forum for dialogue concerning relevant educational topics, and to share University of South Dakota faculty research interests. The proceedings are comprised of 10 presentations: (1) "Japan Related Education in North and South Dakota Schools" (Robert Reinke and Robert W. Wood); (2) "Science for Native Americans: An Elementary School Teacher Inservice Project" (Paul B. Otto); (3) "How I Was Taught, How I Learned, and How I Plan to Teach Mathematics" (Constance L. Hoag); (4) "Computer Programming Contest Problems: Hypercard as a Tool for Student Preparation" (Deborah A. McAllister); (5) "A National Survey of University Reading Clinics" (Garreth B. Zalud); (6) "Stress] Who Me? Never]" (Maurine V. Richardson, James A. Richardson, and Donald L. Mattson); (7) "Doing Business in Taiwan: Going Beyond the Readily Observable Cultural Differences" (Lynne Roach and Hui-Ching Chang); (8) "The South Dakota Head Start/Public School Transition Project: An Overview" (Linda Good, Ray Thompson, Marilyn Urquhart, and Michael Madden); (9) "A Case for Implementing Law and Civic Education" (Roger Wolff); and (10) "What Methods are South Dakota Teachers Using To Teach Science in K-4 Public Schools" (Kathleen L. Matthew). (LL) ED363607

Radford, L. (1997). On Psychology, Historical Epistemology, and the Teaching of Mathematics: Towards a Socio-Cultural History of Mathematics. For the Learning of Mathematics v17 n1 p26-33 Feb 1997. Contributes to a reflection on the possibilities and the limits of a non-naive use of the history of mathematics for educational purposes. Discusses a problem related to the hypotheses that make it possible to confront past and modern conceptual developments. Contains 45 references. (DDR) Report/ISSN: ISSN-0228-0671 EJ545208

Randhawa, B. S., & Others, A. (1989). Sex Differences in Mathematics Performance and Perceptions of University Students. Canada; Saskatchewan Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. This study was intended to determine whether sex-linked mathematics achievement and contextual differences persist into the university years. A random sample of 150 first-year mathematics students enrolled at a midwestern university was identified. A common 30-item calculus readiness test and a 37-item questionnaire, dealing with students' perceptions of the context of mathematics learning, were administered to all students present on the testing day. One hundred examinees returned the questionnaire, and 131 completed the calculus readiness test. Of the 100 questionnaire respondents, 91 had taken the test. Data on these 91 subjects were used in subsequent analyses where data for both instruments were involved. When high school algebra grade was controlled, males scored significantly higher than did females on the calculus test. However, a multivariate analysis of variance of the seven components of the test produced a significant sex effect and univariate differences in favor of males were found for geometry, inequalities, and conceptual problems. The sex variable, coded as a dummy effect, did not enter the regression equation. Algebra study and hours of mathematics homework accounted for 53.5% of the variance in the test grades. Five data tables are included. (TJH) ED309181

Raudenbush, S. W., & Willms, J. J. D. (1995). The Estimation of School Effects. Journal of Educational and Behavioral Statistics v20 n4 p307-35 Win 1995. The specification and estimation of school effects, the variability of effects across schools, and the proportion of variation in student outcomes attributable to differences in school context and practice are considered. A statistical model is presented that defines school effects for parents choosing a school and for agencies evaluating school practices. (SLD) UMI Report/ISSN: ISSN-1076-9986 EJ520943

Raymond, A. M. (1995). Engaging Young Children in Mathematical Problem Solving: Providing a Context with Children's Literature.

Reusser, K. (1986). Problem Solving beyond the Logic of Things. Textual and Contextual Effects on Understanding and Solving Word Problems. Switzerland Available in paper copy and microfiche. EDRS Price - MF01/PC03 Plus Postage. This paper reports research into the linguistic and extra-linguistic or social-cognitive structure of problem presentation contexts. The effects of textual and social syntax were investigated, including the specific structure of the problem text by which situations, processes, actions, and number relations are implicitly or explicitly expressed, questioned, and commented upon. Also investigated was the nature of the pragmatic and social psychological context (case studies). The paper outlines and discusses an interrelated set of studies showing that: (1) subject matter related to, or factual attitudes toward a problem frequently don't play an important part in problem solving; (2) students often solve problems correctly without understanding them; (3) directionality and goals of problem solving processes strongly interact with textual and contextual cues; and (4) false contextual expectations can lead to abstruse errors of understanding and strange solution paths. The results are discussed as an analysis of social-cognitive behavior, in which the classroom is described as a format, a social-cognitive matrix, and a metacognitive matrix. Issues raised include questions about students' epistemic control behavior, and the personality of the problem solver. References, figures, and tables are appended. (Author/JM) ED270327

Rodriguez, A. J. (1997). Invited Paper. Science Teacher v64 n1 p8 Jan 1997. Criticizes the National Science Education Standards for using an example lesson that contradicts support for students engaging in scientific inquiry. Suggests a multiculturally inclusive approach engaging students in a role-playing activity as members of the University of Alexandria. Students are involved in scientific inquiry with Eratosthenes, who first measured Earth's circumference. Students learn both content and social context. (PVD) Report/ISSN: ISSN-0036-8555 EJ541742

Romberg, T. A. (1983). Allocated Time and Context Covered in Mathematics Classrooms. Wisconsin Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. Grant No.: NIE-G-81-0009. Data on how many minutes of instruction were allocated to various aspects of teaching initial addition and subtraction concepts and skills in the Developing Mathematical Processes (DMP) curriculum were summarized for 20 classrooms in grades 1-3. The same curriculum materials were used in each class at each grade level. The number of minutes spent on the 148 specific parts of the curriculum were observed. Each part was then classified in terms of 29 variables (40 codes). From this, data summaries of time spent on each code were prepared for each class. The summary data revealed that each class varied from others in important ways. However, four important features were apparent: (1) classes differed more on total allocated time than in terms of any other characteristic; (2) modification of the curriculum was generally made in all classes to stress practice and skill acquisition and to reduce the time spent on exploration and discussion of mathematical ideas; (3) if students were judged to be "poor," then even more practice and less exploration were given; (4) if students were judged to be "good," then in addition they were given opportunity to explore and discuss ideas. (Author/MNS) ED231616

Ross, S. M. (1983). Increasing the Meaningfulness of Quantitative Material by Adapting Context to Student Background. Journal of Educational Psychology v75 n4 p519-29 Aug 1983. The focus of the present experiments was to examine the effect of adapting the context of a presentation to a student's background. The results showed familiarity of context to be an influential factor in learning quantitative material. (Author/PN) Reprint: UMI EJ284897

Ross, S. M., & Others, A. (1985). Personalizing Context in Teaching Mathematical Concepts: Teacher-Managed and Computer-Assisted Models. Educational Communication and Technology v33 n3 p169-78 Fall 1985. Discusses design and validation of a teacher-managed model employing programed-type learning materials for teaching college-level statistics which matches context of lessons to student background and interests. Current work in developing and field-testing a computer-assisted model of this type for teaching arithmetic concepts to elementary school children is described. (MBR) UMI EJ328413

Ross, S. M., & Others, A. (1986). Adapting the Thematic Context of Mathematical Problems to Student Interests: Individualized versus Group-Based Strategies. Journal of Educational Research v79 n4 p245-52 Mar-Apr 1986. Strategies were examined for adapting the context of mathematical materials to student interests. Two groups were studied using four context variations. Implications for increasing students' confidence and proficiency in solving word problems is discussed. (Author/MT) EJ332376

Rossa, D. (1991). The Importance of Context in Learning Number Systems and Determining Meaning. Computer Science Education v5 n3 p22-24 Spr 1991. Presents eight points to emphasize when teaching the concept of place value. Contends that converting numbers from one base to another helps students understand the concept of place value and the importance of context in establishing meaning. Provides a BASIC computer program to make conversions. (MDH) Report/ISSN: ISSN-1040-7553 EJ450643

Roth, W.-M. (1992). Bridging the Gap between School and Real Life: Toward an Integration of Science, Mathematics and Technology in the Context of Authentic Practice. School Science and Mathematics v92 n6 p307-17 Oct 1992. Provides a rationale for a learning environment in science classrooms that integrates science, mathematics, and technology while solving authentic problems. Describes activities that can be used in such an environment and presents data regarding students' attitudes toward the described activities. (MDH) UMI Report/ISSN: ISSN-0036-6803 EJ455070

Roth, W.-M. (1996). Where is the Context in Contextual Word Problems?: Mathematical Practices and Products in Grade 8 Students' Answers to Story Problems. Cognition and Instruction v14 n4 p487-527 1996. Examined eighth graders' approaches to contextual word problems. Subjects were observed in two situations: open-inquiry field studies that included production of convincing representations (inscriptions) to support students' findings and; word problems with stories and student-produced data based on field studies. Analysis of mathematical practices showed word problems didn't become more contextual even though story situations were familiar, and inscriptions were produced by students. (KDFB) Report/ISSN: ISSN-0737-0008 EJ536362

Rowland, T. (1995). Hedges in Mathematics Talk: Linguistic Pointers to Uncertainty. Educational Studies in Mathematics v29 n4 p327-53 Dec 1995. Analysis of interviews with children ages 10-12, focused on prediction and generalization, reveals a category of words associated with uncertainty. These hedgesabout, around, maybe, thinkare used as shields against accusation of error. Linguistic frameworks are used to categorize different types of hedges. (Author/MKR) UMI Report/ISSN: ISSN-0013-1954 EJ518787

S

Saljo, R., & Wyndhamn, J. (1988). Cognitive Operations and Educational Framing of Tasks. Schools as a Context for Arithmetic Thought. Scandinavian Journal of Educational Research v32 n2 p61-71 1988. The contextual determination of cognitive activities was investigated in a primary school naturalistic experiment. Performance at a group level on an elementary arithmetic task is influenced by the immediate context. Use of analogies as heuristic aids and the functional meaning of the task as a pedagogical praxis are assessed. (TJH) UMI EJ378269

Sawada, D. (1992). Mathematics in a Literary Mode: The Narrative Structure of Communicative Classrooms. Canada; Alberta Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. The narrative structure of a classroom event describes the order in which the story of the event unfolds. This paper compares the narrative structure of a traditional classroom to that of a communicative classroom. The comparison is made in the form of a drama in which a communicative mathematics spokesperson relates the comparative mathematics method to an elementary school teacher. The drama is presented in three scenes. Scene I provides the setting. Scene II retells the story of the traditional mathematics classroom. The narrative structure of a traditional classroom is: What, When, How, Why, Who, and Where. In the course of the scene these parts are described. The traditional classroom scenario begins with the curriculum to be covered, the What; followed by the sequence in which topics would be introduced, the When; and the instructional methods to communicate the What When, the How. The Why asked by students is usually related to the What to be learned later. Then the student levels are determined to see Who would learn the What, When, and How. Where this takes place is relatively unimportant in the traditional classroom. Scene III retells the story of the communicative classroom. The narrative structure of this classroom is: Where, Who, Why, How, When, and What. The communicative classroom starts out with the context of the problem, the Where. The setting will then build upon the experiences of the students, the Who, presented with the question to be investigated, the Why. The next steps determine the method of investigation, the How, unfolding When, to discover the mathematics to be learned, the What. A chart contrasting the two approaches is provided. (MDH) ED355092

Saxe, G. B. (1988). The Mathematics of Child Street Vendors. Child Development v59 n5 p1415-25 Oct 1988. The influence of cultural practices on the cognitive development of largely unschooled children was investigated among 23 candy sellers and matched non-vendors between 10- and 12-years-old who resided in northeast Brazil. Findings are interpreted as supporting a model of cognitive development in which children construct novel understandings while addressing emerging problems of everyday cultural practices. (RH) UMI EJ380611

Scanlon, D., C., E., Bruening, T., & H., E. (1993). Defining the Social Context through Agricultural Research. Proceedings of the Annual National Agricultural Education Research Meeting (20th, Nashville, Tennessee, December 3, 1993). Pennsylvania Available in paper copy and microfiche. EDRS Price - MF01/PC19 Plus Postage. Selected papers are as follows: "Agriculture, Environmental Science and the Relationship of Agriculture to Academic Courses as Perceived by 10th Grade Students" (Newsom-Stewart; Sutphin); "Factors Related to Recruitment and Retention of Ethnic Minority Youth in the Ohio 4-H Program" (Bankston, Cano); "Hispanics in Agriculture" (Nichols, Nelson); "Factors Influencing Minority and Non-Minority Students to Enroll in an Introductory Agriscience Course in Texas" (Talbert, Larke); "Influence of Agriscience and Natural Resources Curriculum on Students' Science Achievement Scores" (Connors, Elliot); "Mathematical Problem-Solving Ability of Secondary Agriculture Teachers" (Miller, Gliem); "Factors Influencing Resource Sharing between Agriculture and Science Teachers Participating in the Agriscience Program" (Whent); "Evaluation of the Pilot Testing of the Biotechnology in Agriculture Curriculum in Oklahoma" (Horne, Key); "Agricultural Distance Education" (Miller, Honeyman); "Relationship between Levels of Cognition of Instruction and Learning Style of Horticulture Teachers" (Cano, Metzger); "Cognitive Learning Style Preferences of the Minnesota Farm Business Management Educators" (Joerger, Persons); "Relationship between Students' Ability to Demonstrate the Problem Solving Approach to Teaching in a Methods Class and Their Learning Styles" (Raven, Shelhamer); "Distance Education in Agriculture" (Miller, Honeyman); "Conceptual Model for Effectively Planning and Delivering Distance Education Courses and Programs in Agriculture" (Jackson, Bowen); "Extent Student Teachers Utilized the Problem-Solving Approach to Teaching during the Student Teaching Practicum" (Garton, Cano); "Training Needs of Area Specialized Extension Agents in the North Carolina Cooperative Extension Service" (Gibson, Hillison); "Relationships between Occupations of Home-Based Workers and Selected Demographic and Work Characteristics" (Furry, Radhakrishna); "Inservice Education Needs of Teachers of Pilot Agriscience Courses in Mississippi" (Newman, Johnson); "National Study of Student Teaching Requirements in Agricultural Education" (Deeds); "Cognitive Abilities of College of Agriculture Students across Traditional Content Areas" (Torres, Cano); "Quantitative Guide to Assess Institutional Excellence in Vocational Education" (Wardlow, Joerger); "Perceptions of Young Farmers Regarding the Role of International Agriculture in Agricultural Education" (Elbasher, Martin); "Interactive Video Network" (Swan); "Agricultural Literacy Assessment among Educators in Missouri Secondary Schools that Offer Agricultural Education Programs" (Harris, Birkenholz); "Safety Practices in Agricultural Science Laboratories" (Swan). (KC) ED366794

Schroeder, T. L. (1993). Using the Pythagorean Theorem in a Contextualized Problem. Canada; British Columbia Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. This qualitative assessment of tenth-grade students' (n=17) problem solving focused on the nature of students' thinking, their problem-solving strategies and heuristics, the mathematical approaches they selected, and the ways they monitored their own progress. The problem, presented orally and with photographs in a task-based interview, involved a sloping ramp connecting a fixed dock with a floating dock. The most direct method of solving the problem was to apply the Pythagorean theorem. There were two respects in which the context of this activity seemed to influence performance: (1) Students had difficulty translating from the given problem situation to a mathematical representation, and (2) because the problem involved right triangles, which the students had recently been studying, many students initially attempted to attack the problem using trigonometric tools, which was either inefficient or confusing. The discussion of results includes consideration of persistence in seeking a solution and cognitive monitoring of solution processes. Contains 11 references. (MKR) ED370764

Schwartz, W. (1988). Teaching Science and Mathematics to At-Risk Students. Equity and Choice v4 n2 p39-45 Win 1988. Cognitive, social, and organizational problems put some groups at a disadvantage in learning mathematics, science, and technology. Recent programs and policies have begun to improve these inequalities. Minorities and women can benefit from long-term programs that help them to recontextualize information, reduce their anxiety, and spend more time on tasks. (VM) EJ371506

Secada, W. G. (1996). Urban Students Acquiring English and Learning Mathematics in the Context of Reform. Urban Education v30 n4 p422-48 Jan 1996. Discusses whether urban schools' efforts at reforming mathematics should specifically address students acquiring English or assume students' needs will be addressed under the broader aegis of reform. The article addresses thoughts about the bilingual mathematics learner, curriculum, teaching, assessment, and evaluation in which collaborative efforts between mathematics reformers and bilingual educators could be productive. (GR) UMI Report/ISSN: ISSN-0042-0859 EJ519258

Seddon, T. E. (1990). Soundoff. Let's Abolish General Math]. Mathematics Teacher v83 n6 p418-19 Sep 1990. Strategies for teaching general mathematics effectively are discussed. Stressed are the use of calculators for arithmetic, individualized instruction, and teaching mathematics in context. Applications to vocational education are described. (CW) UMI Report/ISSN: ISSN-0025-5769 EJ415531

Senger, E. S., & Others, A. (1997). Mathematical Meaning in Context. Teaching Children Mathematics v3 n7 p362-66 Mar 1997. Describes a classroom project integrating children's literature, Japanese culture, and geometry that grew out of the local killing of a Japanese exchange student. Fourth-graders read "Sadako and the Thousand Paper Cranes" around which the interdisciplinary unit was developed. Topics covered included Japanese culture, American social issues, research skills, and learning mathematical concepts through folding 100 paper Origami cranes. (PVD) Report/ISSN: ISSN-1073-5836 EJ541743

Shadish, W., R., E., & Others, A. (1995). Special Feature. The Quantitative-Qualitative Debates: "DeKuhnifying" the Conceptual Context. Evaluation and Program Planning v18 n1 p47-96 Jan-Mar 1995. The five articles of this special section focus on the quantitative-qualitative debate in program evaluation. This section focuses on philosophical aspects of program evaluation, making it clear that the issues are far more complex than the simple quantitative-qualitative dichotomy described by T. S. Kuhn (1970) implies. (SLD) UMI Report/ISSN: ISSN-0149-7189 EJ504329

Shoenfeld, A. H. (1996). In Fostering Communities of Inquiry, Must It Matter That the Teacher Knows "The Answer"? For the Learning of Mathematics v16 n3 p11-16 Nov 1996. Discusses the similarities in learning outcomes from two very different environments: a research group and a problem-solving course. Provides examples that characterize the two environments and that point to similarities in outcomes. Speculates about why such similarities exist. (DDR) Report/ISSN: ISSN-0228-0671 EJ536689

Sierpinska, A. (1994). Understanding in Mathematics. Studies in Mathematics Education Series: 2. Pennsylvania Available in paper copy and microfiche. EDRS Price - MF01/PC09 Plus Postage. Falmer Press, Taylor & Francis Inc., 1900 Frost Road, Suite 101, Bristol, PA 19007. Report/ISSN: ISBN-0-7507-0334-2. This book discusses the act of understanding in mathematics. The first chapter, "Understanding and Meaning," inquires into the various senses and uses of the word "understanding" in ordinary language and discusses the notion of meaning and relations between understanding and meaning. The second chapter, "Components and Conditions of an Act of Understanding," is central to the book and discusses the act of understanding. Chapter 3, "Processes of Understanding," looks at whole processes of understanding, and the roles therein of explanations and validations, examples, previous knowledge, figurative speech, and activity, both practical and intellectual. The question of evaluation of understanding is dealt with in chapter 4, "Good Understanding." One of the problems raised is concerned with the relativity of any evaluation of understanding. Two important determinants of this relativity, namely the developmental stage of the understanding subject and the culture, are the objects of chapter 5, "Developmental and Cultural Constraints of Understanding." Contains 227 references. (MKR) ED378041

Sierpinska, A. (1995). Mathematics: "In Context," "Pure," or "with Applications"? For the Learning of Mathematics v15 n1 p2-15 Feb 1995. Argues that a curriculum based on mathematics such as it arises in solving everyday problems is unrealistic; the problem of transfer cannot be resolved by claiming that it should not exist in the first place. (49 references) (MKR) Report/ISSN: ISSN-0228-0671 EJ505586

Silver, E. A. (1990). Treating Estimation and Mental Computation as Situated Mathematical Processes. Pennsylvania Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. This paper discusses the central thesis that new research on estimation and mental computation will benefit from more focused attention on the situations in which they are used. In the first section of the paper, a brief discussion of cognitive theory, with special attention to the emerging notion of situated cognition is presented. Three sources of expertise as contextual are proposed: social theories about language and the development of thought; anthropology and the study of situated cognition; and the history and philosophy of scientific domains. In the second section, "Mathematics and Sense Making", a review of work on problem solving that dealt with the importance of context, especially with respect to the interpretation of problem solutions is presented. Situational factors that influence children's problem-solving performance are described though research findings on division with remainders in problem-solving situations. Finally, a situated perspective on further research regarding serious consideraiton of mental computation and estimation as situated mathematical processes is discussed. ED342645

Silver, E. A., & Lane, S. (1991). Assessment in the Context of Mathematics Instruction Reform: The Design of Assessment in the QUASAR Project. Pennsylvania Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. Recent reports on mathematics education reform have focused the attention of educational practitioners and policymakers on new goals for mathematics education and new descriptions of mathematical proficiency. QUASAR is a national project (Quantitative Understanding: Amplifying Student Achievement and Reasoning) designed to improve the mathematics instructional program for students attending middle schools, grades 6 through 8, in economically disadvantaged communities. QUASAR is a complex research study of educational change and improvement, in which a major effort will be made to study carefully different approaches to unblocking the path to mathematical power for poor students. Parallel goals for the study are: to ascertain conditions that appear conducive to mathematical success; to derive pedagogical principles for effective mathematics instruction for middle school students; to describe effective instructional programs that are adaptable to other schools; and to devise new assessment tools to measure growth in higher order thinking, reasoning, and communication as they relate to school mathematics. Included in this report are: (1) an introduction that describes the purpose, the rationale, and the goals of this project; (2) a discussion of the educational considerations and mathematical conceptualizations underlying the proposed methods of assessment for mathematical proficiency; (3) a discussion of construct-irrelevant test variance as a data-gathering consideration for the assessment of mathematical proficiency; (4) a discussion of the development of specifications for the assessment tasks in terms of focus and components; (5) a discussion of the specifications encompassing the scoring rubrics within the assessment procedures; and (6) a list of sample tasks and administrative information. (15 references) (Author/JJK) ED343776

Silver, E. A., & Lane, S. (1993). Balancing Considerations of Equity, Content Quality, and Technical Excellence in Designing, Validating and Implementing Performance Assessments in the Context of Mathematics Instructional Reform: The Experience of the QUASAR Project. Pennsylvania Available in paper copy and microfiche. EDRS Price - MF01/PC03 Plus Postage. Contract no.: 890-0572. Issues of educational equity and quality are explored in the context of the Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) project, a national educational reform project aimed at fostering and studying the development and implementation of enhanced mathematics instructional programs for students attending middle schools in economically disadvantaged communities. Currently operating at six school sites across the country, QUASAR is based on the premise that current poor mathematical achievement by disadvantaged students is not the result of lack of ability, but rather the result of educational practices that have blocked students from meaningful experiences. Assessment in QUASAR is embedded in the larger project. A major component is the QUASAR Cognitive Assessment Instrument (QCAI), which assesses student performance on open-ended tasks involving mathematical problem solving, reasoning, and communication, with a focus on efforts to obtain content appropriateness, technical measurement quality, and equity. Evidence of the validity of the QCAI for diverse linguistic and cultural groups is reviewed. The experience of QUASAR should be valuable to others interested in program and assessment improvement. One table and two figures illustrate the discussion. An appendix presents general rubric components. (Contains 58 references.) (SLD) ED361370

Silverman, I. W. (1979). Context and Number Conservation. Child Study Journal v9 n3 p205-12 1979. A replication study was conducted to determine whether conservation-of-number performance would be improved by questioning the subject only after the transformation is performed, rather than before and after the transformation, as is done in the standard conservation test. Subjects were preschoolers, aged 0-4 to 5-7. (Author/MP) Reprint: UMI EJ214840

Sleeman, D., & Others, A. (1988). Diagnosis and Remediation in the Context of Intelligent Tutoring Systems. United Kingdom; Scotland Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. Report/ISSN: AUCS/TR8712 Contract no.: MDA-903-84-K-0279. This paper provides an overview of the four major aspects of the PIXIE Intelligent Tutoring System: the field work undertaken to determine how teachers diagnose and remediate in introductory algebra; the set of experiments run to determine the relative effectiveness of Model-Based-Remediation (MBR) and Reteaching; systems work carried out to remedy shortcomings noted earlier in the Intelligent Tutoring System, PIXIE; and an experiment conducted to determine whether it is possible to enhance teachers' diagnostic capabilities. The major conclusions from the four phases of the work are: (1) the teachers involved in the study, essentially tutored algebra procedurally; (2) for algebra, when taught procedurally with this age group, reteaching seems as effective as MBR; (3) the initial basic PIXIE system has now been enhanced so that it can diagnose and remediate in several domains; and (4) this experiment concluded that exposure to the TPIXIE program did enhance the teacher trainees' ability to diagnose student errors. (Author/TW) ED294736

Smith, P. L. (1982). A Confidence Interval Approach for Variance Component Estimates in the Context of Generalizability Theory. Educational and Psychological Measurement v42 n2 p459-66 Sum 1982. Monte Carlo methods are used to explore the accuracy of a method for establishing confidence intervals for variance component estimates in generalizability studies. Previous research has shown that variance component estimation errors due to sampling are often larger than suspected. (Author/CM) Reprint: UMI EJ266476

Speiser, B., & Walter, C. (1996). Second Catwalk: Narrative, Context, and Embodiment. Journal of Mathematical Behavior v15 n4 p351-71 Dec 1996. Uses Muybridge's sequence of photos of a moving cat to examine how one might picture changes in the cat's velocity. Classroom implications include building on personally enacted physical experience and recognizing uncertainty as fundamental. Concludes that carefully examined case examples are essential in teaching students to learn and reason critically. (AIM) Report/ISSN: ISSN-0732-3123 EJ545174

Stanic, G. M. A. (1989). Social Inequality, Cultural Discontinuity, and Equity in School Mathematics. Peabody Journal of Education v66 n2 p57-71 Win 1989. To achieve equity in school mathematics, educators must question assumptions about its nature and worth. The article recommends a fresh look at school mathematics and its relationship to societal structure as a whole. A research and reform agenda guided by the constructs of cultural discontinuity and social inequality is suggested. (SM) UMI Report/ISSN: ISSN-0161-956X EJ432000

T

Taube, S. R. (1995). Reconstructing the Whole: A Gauge of Fraction Understanding. Texas Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. . This study analyzed graphical solutions of 344 students in grades 4 through college who were administered a 40-item assessment of basic fraction concepts. Of particular interest were six problems that required students to complete the whole given a fractional part presented in area contexts and set contexts. Results indicated that fourth graders frequently used the "doubling" strategy even if the fractional part showed two-thirds. In the set context, students sometimes connected the outer dots to form a rectangular unit that was totally unrelated to the given fractional part. Videotaped interviews of six fourth-grade students clearly revealed these dominant strategies. Nevertheless, there was improvement in student solution strategies as well as success in completing the unit as the grade level increased. Implied misconceptions held by both preservice teachers and elementary students include the assumption that the unit is always a regular-shaped region rather than irregular. The findings indicate the strong influence of the rectangular model often used in traditional mathematics textbooks on students' understanding of the whole. These findings support reforms in the teaching of fractions that include not only unit partitioning activities but also completing the whole using a variety of models. (Author) ED391660

Telese, J. A., & Kulm, G. (1995). Performance-based Assessment of At-risk Students in Mathematics: The Effects of Context and Setting. Pennsylvania Available in paper copy and microfiche. EDRS Price - MF01/PC03 Plus Postage. Contract no.: RE117E20049. A team of university and public school mathematics educators designed performance-based mathematics assessment tasks designed to align with the Texas Assessment of Academic Skills for 93 students who had been identified as at-risk in mathematics. Scenarios were developed based on four contexts: (1) familiar activity; (2) social issue; (3) hands-on; and (4) technology. Each context was administered in three settings: individually, aided by a proctor, and small group. The data analysis consisted of two repeated measures analyses of variance with context and setting, and content and setting as the main factors. The repeated measures were operations, concepts, or problem-solving scores. The results indicated that context was not significant, but content was significant. Setting was significant in both analyses. Generalizability studies (G-studies) were conducted to measure dependability of raters and students. The G-studies indicated that the six raters were dependable when assigning scores. The problem-solving domain was the most dependable knowledge domain rated and the concept domain was least dependable. An appendix provides scoring rubrics and sample questions. Thirteen tables and four figures. (Contains 48 references.) (SLD) ED382685

Thomas, C., & Others, A. (1993). Teacher to Teacher: You've Learned It When You Can Use It. Arithmetic Teacher v41 n2 p98-99 Oct 1993. Gives suggestions to help students generalize skills so that they can use them in a variety of situations inside and outside of the mathematics classroom. Addresses uses of ratio and proportion but suggestions are also applicable to other mathematical topics. (MLN) UMI Report/ISSN: ISSN-0004-136X EJ474914

Thomson, B. S., & Hartog, M. M. D. (1993). Activities To Teach Mathematics in the Context of Environmental Studies. Ohio Available in paper copy and microfiche. EDRS Price - MF01/PC07 Plus Postage. Contract no.: RI88062006. The National Council of Teachers of Mathematics' (NCTM) "Curriculum and Evaluation Standards" recommends that mathematical connections be made between mathematics and other disciplines. This book presents 35 activities for middle school students that integrate the teaching of mathematical concepts with environmental concepts. An introduction discusses the need for mathematical connections and provides the rationale for utilizing environmental studies as a context from which to learn mathematics. Each activity provides a reference for its source, the NCTM standards for middle school mathematics addressed by the activity, student objectives, background information, materials needed, procedures, methods for closure, and evaluation suggestions. The activities are grouped according to the following environmental concepts: (1) energy and natural resources; (2) plants and animals; (3) population description and growth; (4) solid waste disposal; (5) transportation; (6) water resources; and (7) weather and air. An index classifies the activities according to the NCTM Standards for grades 5-8. The eight curriculum standards addressed are: computation and estimation; patterns and function; algebra; statistics; probability; geometry; measurement; and number and number relationships. General standards addressed by the activities are problem solving, mathematical connections, reasoning, and mathematical communication. A summary discusses how the activities were chosen and encourages teachers to let students expand the context of the activities themselves by making the activities more relevant to local issues. (MDH) ED359052

Tirosh, D., & Stavy, R. (1992). Students' Ability to Confine Their Application of Knowledge: The Case of Mathematics and Science. School Science and Mathematics v92 n7 p353-58 Nov 1992. Reports a study to examine secondary school students' (n=200) responses to two figurally and spatially similar problems from mathematics and science that require different responses before and after instruction. Results indicated that most students gave the same response to both questions. Reasons for this pattern are discussed. (MDH) UMI Report/ISSN: ISSN-0036-6803 EJ458178

Tittle, C. K. (1992). Assessment Research in the Context of Practice. New York Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. Commemorating the work of Anne Cleary, the author considers the need for research on assessment in the practice context, provides an example of research in context, and proposes general areas of development for assessment research in the context of practice. Research has shown that effects of testing programs on practice are often not those that were intended. In addition, assessments are becoming more complex. These factors and the historical independence of test developers and measurement practitioners from educational practitioners make research in the context of educational practice extremely important. The development of the Mathematics Assessment Questionnaire (MAQ), a survey of students' thoughts and feelings about learning and doing mathematical word problems in classroom activity settings, illustrates research in the context of practice. A framework has been developed to describe teacher change using the MAQ assessment. Research in the context of practice will necessarily link more closely to research on teaching and learning in subject matter areas. To foster this integration, examples are needed of new organizational arrangements and research that makes explicit use of theories of teaching and learning. New procedures to extend and adapt assessment development are needed, as are criteria for evaluating the meaning and use of assessments in context. One table and one figure illustrate the discussion. (SLD) ED360385

Tittle, C. K., & Others, A. (1993). Assessment Theory and Research for Classrooms: From "Taxonomies" to Constructing Meaning in Context. Educational Measurement: Issues and Practice v12 n4 p13-19 Win 1993. Major changes in educational and psychological theories that have come about since the cognitive and affective taxonomies of educational objectives were published in 1956 and 1964 are traced. The changes emphasize the need to understand thinking in the context of students' beliefs and self-directed cognitions. (SLD) Report/ISSN: ISSN-0731-1745 EJ476856

Tobias, R. (1992). Nurturing At-Risk Youth in Math and Science: Curriculum and Teaching Considerations. Indiana Available in microfiche only. EDRS Price - MF01 Plus Postage. PC Not Available from EDRS. National Educational Service, P.O. Box 8, 1610 W. Third Street, Bloomington, IN 47402 ($19.95). Report/ISSN: ISBN-1-879639-20-3. The social environment of today has necessitated revision in educators' beliefs about what students are considered to be at risk of failing to complete their education with adequate levels of skills. This book addresses this issue in the areas of mathematics and science and is intended as a curriculum and teacher training accompaniment that can enhance mathematics and science proficiency among at-risk youth. The introduction defines at-risk students and identifies six common denominators of the educationally at risk. Six chapters, contributed by different educators, discuss different aspects of the issue. Chapter 1 presents data covering a period of approximately 7 years concerning mathematics and science proficiency of at-risk students. Chapter 2 discusses the activities of the Institute for the Advancement of Mathematics and Science in the preparation of teachers. Chapter 3 examines the teaching of mathematics through context. Chapter 4 explores other strategies and programs achieving positive results in working with at-risk students, such as the Science Skills Center and Computer Assisted Learning, both in Brooklyn, New York. Chapter 5 explores ways of raising students' self-confidence and self-esteem through creative mathematics and science teaching. Chapter 6 discusses the mathematical competencies expected of the at-risk learner as delineated by the National Council of Teachers of Mathematics in the "Curriculum and Evaluation Standards for School Mathematics." Recommendations for educational policymakers and classroom teachers with respect to assessment issues are given. Information about the authors is provided: Randolf Tobias, chapters 1, 4, and 5; Madeline Long and Lynne Conrad, chapter 2; Everard Barrett, chapter 3; and Eleanor Armour-Thomas, chapter 6. References are included with chapters. (MDH) ED351197

U

Uprichard, A. E., & Engelhardt, J. (1986). A Research Context for Diagnostic and Prescriptive Mathematics. Focus on Learning Problems in Mathematics v8 n1 p19-38 Win 1986. Future research initiatives on learning and instruction are considered to be of most worth if grounded in general systems theory and if multiple research methods are used. Discussed are an information processing theory and a theory for the structure and structuring of stored information. (MNS) EJ341868

V

________. (1985). Voluntary Service Overseas (VSO). Mathematics in School v14 n3 p30-33 May 1985. Describes a course designed to introduce trained teachers to some of the differences and difficulties they may encounter when teaching in a secondary school in a developing country as opposed to teaching in a British school. Language, lack of equipment, and cultural context are addressed. (JN) UMI EJ321572

Vacher, H. L. (1989). The Three-Point Problem in the Context of Elementary Vector Analysis. Journal of Geological Education v37 n4 p280-87 Sep 1989. This article presents a vector-analysis approach to the classical three-point problem in hydrogeology. Problem sets involving strike and dip, and ground water flow including computer programs (in BASIC) for their solution are given. (CW) UMI EJ403029

Van Den Heuvel-Panhuizen, M. (1994). Improvement of (Didactical) Assessment by Improvement of Problems: An Attempt with Respect to Percentage. Educational Studies in Mathematics v27 n4 p341-72 Dec 1994. Focuses on the role of mathematics problems in the development of better assessment and gives examples with respect to some key concepts and operations on percentage. Reports results from use of the problems with two seventh-grade classes. (33 references) (Author/MKR) UMI Report/ISSN: ISSN-0013-1954 EJ498210

Vasco, C. E. (1984). Learning Elementary School Mathematics as a Culturally Conditioned Process. Colombia Available in paper copy and microfiche. EDRS Price - MF01/PC03 Plus Postage. Mathematics is thought to be the most culturally independent of all academic subjects. "New Math" textbooks printed in the United States or Belgium were translated into Spanish and Portuguese with only minor variations in the story problems and are now taught in most Latin-American countries. Looking backwards, it was not different in past years in Colombia, where standard school textbooks copied each other in a chain going back to Spanish and Latin Renaissance arithmetics. The myth of mathematics as the universal language of science and the superficial image of mathematical truth as invariable and "a priori" structured in human reason, reinforced the stereotype of mathematics as a supra-cultural subject. The purpose of this paper is to (1) determine as accurately as possible the cultural dependence of the learning process in mathematics; (2) examine what is essentially right in the claim to universality in mathematics; (3) consider where the culturally specific aspects of mathematics are to be located, both theoretically and empirically; and (4) determine how they are to be used to develop a culturally adapted curriculum for elementary school mathematics. (JN) ED259910

W

Webb, N., & Yasui, E. (1992). The Influence of Problem Context on Mathematics Performance. Project 2.1: Alternative Approaches to Assessment in Mathematics and Science. California Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. Contract no.: R117G10027. Whether or not working with more realistic and lengthier problems during instruction would make students better able to solve similar problems on achievement tests was studied for 82 seventh graders (50 in the experimental condition and 32 in the control condition) in general mathematics classes at an urban middle school. The study also investigated whether different kinds of problems (short versus extended word problems) would promote different information about students' performance and problem-solving ability. Two seventh-grade classes were assigned to the experimental situation of realistic problems, and one classroom was assigned to the control condition of textbook problems. Experience with extended realistic problems did not give students an advantage on the posttest, and the lack of experience did not seem to be a disadvantage. Different kinds of word problems did reveal different information about problem-solving skills, but these differences were only found by coding specific errors. On extended word problems, some students misinterpreted the type of answers required, something that did not happen on short problems. On short problems, students sometimes omitted a type of item altogether. Further studies will be needed to measure these aspects of problem-solving ability. Three figures and 13 tables present study findings. There are 18 references, and 9 appendixes, each containing a table of additional data. (SLD) ED349331

White, L., & Frid, S. (1995). Contextual Perspectives of School Mathematics: What Determines Mathematical Understanding? Australia; Western Australia Available in paper copy and microfiche. EDRS Price - MF01/PC01 Plus Postage. Results of a study into secondary school students' and teachers' conceptions of what mathematics is and the purposes of school mathematics are outlined. A total of about 220 first year engineering students and 600 high school students in Australia were involved in the surveys while 40 students, 19 teachers, 2 career counselors, and 2 administrators were involved in interviews. Students and teachers held broad views of the content or discipline of mathematics, while their interpretations of mathematics within a wider sociocultural context reflected additional, influential, personally and socially derived factors: social status of mathematics, utility of mathematics, career aspirations, and interest or disinterest in mathematics. The role of the researcher in identifying such factors, as well as determining the focus of a research study and the perspective for analysis and interpretation, are examined. How mathematics means different things depending upon the context and an individual's interactions with an environment, including cognitive, social, and political contexts, are discussed. In addition, the role of mathematics in secondary education is questioned in relation to current curriculum movements in education. Contains 20 references. (Author/MKR) ED387344

Wilcox, S. K., & Others, A. (1992). Influencing Beginning Teachers' Practice in Mathematics Education: Confronting Constraints of Knowledge, Beliefs, and Context. Michigan Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. National Center for Research on Teacher Learning, 116 Erickson Hall, Michigan State University, East Lansing, MI 48824 ($6.75). This paper compares and contrasts cases of three beginning teachers, graduates of a teacher education program that included an intervention component designed to change prospective elementary teachers' knowledge and beliefs about mathematics education. The goal of the intervention (a sequence of three mathematics courses, a methods course, and a curriculum seminar) was to develop a more conceptual level of knowledge about mathematics itself and about the learning and teaching of mathematics. Each subject is described as both student and teacher of mathematics. Analysis focuses on ways in which knowledge and context influenced choices made by these novice teachers. Each new teacher faced responsibility for teaching multiple subject matter; deciding on the mathematical content children should have an opportunity to learn; creating mathematical tasks; and using instructional time given multiple and competing goals. Differences appeared in choices made in response to these issues. Choices were influenced by an interaction of views about knowledge and pedagogy and the degree to which context was perceived as a constraint. A question is raised regarding the nature of support required in the induction years if new teachers are expected to institute practices that are innovative and difficult to implement, questioned in traditional school settings, and unfamiliar to faculty, administrators, parents, and students. (Author/LL) ED343888

Wilson, B. (1981). Cultural Contexts of Science and Mathematics Education: A Bibliographic Guide. United Kingdom; England Not available from EDRS. Document Not Available from EDRS. Centre for Studies in Science Education, University of Leeds, Leeds LS2 9JT, England (no price quoted). Report/ISSN: ISBN-0-904421-10-4. Designed to help educators become aware of the fact that science and mathematics curriculum materials may be viewed as culture laden packages, this bibliography of over 800 references is international in scope. Regions selected for study are Australia and Papua New Guinea, Britain, the Anglophone countries of Africa, and China. (Only items published in English are included). The book contains nine chapters: (1) General References; (2) The Economic Context; (3) The Context of Language; (4) The Political Context; (5) The Religious and Philosophical Context; (6) The Social Context; (7) Cognitive Research; (8) The Curriculum; and (9) Three Case Studies. Three indexes, by author, by country, and by school subject, are also included. In addition the materials annotated are crossreferenced, both within chapters and between chapters. It is intended to be read by persons interested in the cultural context of school education and the influence of that context on the teaching and learning of science and mathematics. (PEB) ED201511

Y

Yen, W. M. (1979). The Extent, Causes, and Importance of Context Effects on Item Parameters for Two Latent-Trait Models. California Available in paper copy and microfiche. EDRS Price - MF01/PC02 Plus Postage. The extent, causes, and importance of context effects on item parameters for one- and three-parameter latent-trait models were examined. Items were taken from the California Achievement Tests Reading Comprehension and Mathematics Concepts and Applications subtests. The reading items were administered to 1,678 fourth-grade students, and the mathematics items were administered to 1,812 sixth-grade students. Context effects were measured by comparing the stabilities of item parameters obtained in the same context with the stabilities of parameters obtained in different contexts. Stability of item parameters was determined by testing the students twice with the same items. Changes in context were produced by changing the order of the items for the second test administration. Changes in context usually had substantial effects on the item parameters of both models, and to some extent these context effects appeared to be the result of the items' positions in the test booklets. Context effects appeared more important in item calibration than in item selection and in making predictions for single items than in making predictions or obtaining trait estimates with groups of items. (Author/MH) ED183567

Z

Zaslavsky, C. (1975). What is Math For? Urban Review 8 3 232-240. Foreseen for the future of school mathematics in the U.S. is an increased interest in developing interdisciplinary approaches to educating the individual, greater emphasis on learning by doing, and a search for the kind of mathematics that is relevant to our society. (Author/AM) EJ131952

Zaslavsky, C. (1991). World Cultures in the Mathematics Class. For the Learning of Mathematics v11 n2 p32-36 Jun 1991. Introduces a cultural perspective in the teaching of mathematics. Describes the mathematical practices of African peoples and of the indigenous peoples of the Americas in relationship with numbers and numeration, design and pattern, architecture, and games of chance and skill. (MDH) EJ445134

Contact Us

Enter feedback, comments, questions, or suggestions:

Email this page

Search

(Indexed quarterly)

positivepractices.com

WWW

Translations

Caution: Machine generated language translations may contain significant errors. Use with care.