Building Student Capacity for Mathematical Thinking and Reasoning: An Analysis of Mathematical Tasks Used in Reform Classrooms

American Educational Research Journal - Tập 33 Số 2 - Trang 455-488 - 1996
Mary Kay Stein1, Barbara W. Grover2, Marjorie Henningsen1
1Learning Research and Development Center, University of Pittsburgh
2Ohio University

Tóm tắt

This article focuses on mathematical tasks as important vehicles for building student capacity for mathematical thinking and reasoning. A stratified random sample of 144 mathematical tasks used during reform-oriented instruction was analyzed in terms of (a) task features (number of solution strategies, number and kind of representations, and communication requirements) and (b) cognitive demands (e.g., memorization, the use of procedures with [and without] connections to concepts, the “doing of mathematics”). The findings suggest that teachers were selecting and setting up the kinds of tasks that reformers argue should lead to the development of students’ thinking capacities. During task implementation, the task features tended to remain consistent with how they were set up, but the cognitive demands of high-level tasks had a tendency to decline. The ways in which high-level tasks declined as well as factors associated with task changes from the set-up to implementation phase were explored.

Từ khóa


Tài liệu tham khảo

Anderson LM, 1989, Knowledge base for the beginning teacher, 101

10.1086/461535

Brown CA, 1993, Paper presented at the Annual Meeting of the American Educational Research Association

Carpenter T, 1988, Integrating research on teaching and learning mathematics, 2

Cohen DK, 1990, Effects of state level reform of elementary-school mathematics curriculum on classroom practice

10.3102/00346543053002159

10.1207/s15326985ep2302_6

10.1080/03626784.1984.11075917

Fitzgerald W, 1986, Middle grades mathematics project: Factors and multiples

Grouws DA, 1992, Handbook of research on mathematics teaching and learning

Grover BW, 1993, Paper presented at the Annual Meeting of the American Educational Research Association

Henningsen M, Journal for Research in Mathematics Education

10.3102/00028312030002393

Kitcher P, 1984, The nature of mathematical knowledge

10.1017/CBO9781139171472

10.3102/00028312027001029

10.1086/461534

Mathematical Association of America, 1991, A call for change: Recommendations for the mathematical preparation of teachers of mathematics

Meyer C, 1983, Make it simpler: A practical guide to problem solving in mathematics

National Council of Teachers of Mathematics, 1989, Curriculum and evaluation standards for school mathematics

National Council of Teachers of Mathematics, 1991, Professional standards for teaching school mathematics

National Research Council, 1989, Everybody counts

Newman D, 1989, The construction zone: Working for cognitive change in school

10.3102/0013189X018005009

QUASAR Documentation Team., 1993, The QUASAR teacher background questionnaire summary report on selected items

Romberg TA, 1992, Handbook of research on mathematics teaching and learning, 49

Schoenfeld AH, 1992, Handbook of research on mathematics teaching and learning, 334

Schroyer J, 1986, Middle grades mathematics project: Mouse and elephant

Shavelson R, 1986, Handbook of research on teaching, 3, 50

Silver EA, 1985, Teaching and learning mathematical problem solving: Multiple research perspectives

10.1177/0042085996030004006

Smith MS, 1993, Paper presented at the Annual Meeting of the American Educational Research Association

Stein MK, 1989, Paper presented at the Annual Meeting of the American Educational Research Association

Stein MK, 1993, Paper presented at the Annual Meeting of the American Educational Research Association

Stein MK, Educational Research and Evaluation

Stein MK, 1996, Paper presented at the Annual Meeting of the American Educational Research Association

Stodolsky S, 1988, The subject matters: Classroom activity in mathematics and social studies

Systat 5 for the Macintosh. [Computer program]1989Evanston, ILSystat

Williams S, Elementary School Journal

Wittrock MC, 1986, Handbook of research on teaching, 297

Thông tin
Thông tin xuất bản

American Educational Research Journal

Tập 33 Số 2

455-488

Thông tin tác giả