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Steinberg, Ruth M.; Empson, Susan B.; Carpenter, Thomas P. – Journal of Mathematics Teacher Education, 2004

In the context of U.S. and world wide educational reforms that require teachers to understand and respond to student thinking about mathematics in new ways, ongoing learning from practice is a necessity. In this paper we report on this process for one teacher in one especially productive year of learning. This case study documents how Ms. Statz's…

Descriptors: Inquiry, Educational Change, Case Studies, Mathematics Teachers

Peer reviewed

Carpenter, Thomas P. – Arithmetic Teacher, 1985

Research on the characteristics of individuals who have demonstrated a high level of ability in mathematics is presented. The importance of structure in mathematical thinking is stressed and implications for teaching are detailed. (MNS)

Descriptors: Cognitive Processes, Educational Research, Elementary Education, Elementary School Mathematics

Peer reviewed

Carpenter, Thomas P.; And Others – Mathematics Teacher, 1975

The results of the first report on the mathematical abilities of 13 and 17 year-olds by the National Assessment of Education Progress (NAEP) are summarized and interpreted. A similar article for elementary school mathematics appears in SE 514 769. (SD) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

Descriptors: Algebra, Geometry, Mathematics Education, Measurement

Peer reviewed

Carpenter, Thomas P.; And Others – Elementary School Journal, 1996

Suggests that children enter school with a great deal of informal intuitive knowledge of mathematics that can serve as the basis for developing much of the formal mathematics of the primary school curriculum. Describes a research-based model of children's thinking that teachers can use to interpret, transform, and reframe their informal or…

Descriptors: Addition, Cognitive Development, Cognitive Processes, Division

Peer reviewed

Carpenter, Thomas P.; And Others – Arithmetic Teacher, 1975

The results in the first report on the mathematical abilities of 9- and 13-year-old students by the National Assessment of Educational Progress are summarized and interpreted. A similar report on secondary school mathematics students appears in SE 514 760. (SD) Aspect of National Assessment (NAEP) dealt with in this document: Results…

Descriptors: Elementary Education, Elementary School Mathematics, Geometry, Mathematics Education

Peer reviewed

Carpenter, Thomas P.; And Others – American Educational Research Journal, 1989

Twenty first-grade teachers' use of knowledge from research about mathematical thinking of children was compared with that of 20 teachers who did not participate in an analysis of research. Implications for teacher education and practice are discussed. (SLD)

Descriptors: Children, Classroom Techniques, Cognitive Processes, Comparative Analysis

Carpenter, Thomas P. – 1979

The purpose of this paper is to identify how the theory and techniques of research in cognitive development can be applied to the study of learning and instruction in mathematics. Five basic research paradigms are characterized; major directions of research on number, measurement, geometry, and adolescent reasoning are identified. Most of the…

Descriptors: Cognitive Development, Educational Research, Elementary School Mathematics, Elementary Secondary Education

Peer reviewed

Carpenter, Thomas P.; And Others – Journal for Research in Mathematics Education, 1988

The study investigated children's ability to write number sentences for simple addition and subtraction word problems. The results suggest that open number sentences may provide mathematical symbolism that allows young children to build on informal strategies for presenting and solving simple word problems. (Author/PK)

Descriptors: Addition, Basic Skills, Educational Research, Elementary Education

Peer reviewed

Carpenter, Thomas P.; And Others – Arithmetic Teacher, 1980

The National Assessment of Educational Progress (NAEP) has completed its second mathematical assessment. This article focuses on the results from the second assessment of 9 year olds and 13 year olds; major results of the content areas are summarized and examples of the data are given to support the conclusions. (Author/MK) Aspect of National…

Descriptors: Achievement, Computation, Educational Assessment, Elementary Education

Carpenter, Thomas P.; Fennema, Elizabeth; Franke, Megan Loef; Levi, Linda; Empson, Susan B. – 1999

This book, with accompanying CD-ROMs, was written to help readers understand children's intuitive mathematical thinking and use that knowledge to help children learn mathematics with understanding. Based on more than twenty years of research, this book portrays the development of children's understanding of basic number concepts. Detailed…

Descriptors: Cognitive Processes, Concept Formation, Educational Strategies, Elementary Education

Peer reviewed

Carpenter, Thomas P. – Education and Urban Society, 1985

Children's solutions to simple word problems requiring addition or subtraction skills develop through four stages: (1) modeling with objects; (2) utilization of both modeling and counting strategies; (3) reliance on counting strategies; and (4) reliance on number facts. The current primary mathematics curriculum fails to capitilize on rich…

Descriptors: Arithmetic, Informal Education, Learning Processes, Mathematics Curriculum

Peer reviewed

Fennema, Elizabeth; Carpenter, Thomas P.; Jacobs, Victoria R.; Franke, Megan L.; Levi, Linda W. – Educational Researcher, 1998

Considers implications of the findings of the study by E. Fennema and others that boys in the primary grades use different mathematics problem-solving strategies than girls and suggests that equitable mathematics instruction may require specific attention to gender differences and underachieving groups. (SLD)

Descriptors: Elementary School Students, Equal Education, Learning Strategies, Longitudinal Studies

Peer reviewed

Carpenter, Thomas P.; And Others – Mathematics Teacher, 1981

Results of the second mathematics assessment of the National Assessment of Educational Progress (NAEP) are analyzed with regard to the performance of 13- and 17-year-olds on probability exercises. The results suggest that this area has been neglected in mathematics instruction. (MP)

Descriptors: Mathematical Concepts, Mathematics Curriculum, Mathematics Instruction, Probability

Peer reviewed

Carpenter, Thomas P.; And Others – Elementary School Journal, 1984

Conclusions about the performance of 9-, 13-, and 17-year-old students on mathematics exercises are reported and illustrated with exercises from the 1973, 1978, and 1982 National Assessment of Educational Progress. (RH)

Descriptors: Academic Achievement, Basic Skills, Blacks, Elementary Secondary Education

Carpenter, Thomas P.; Levi, Linda – 2000

This report describes a research project that investigated how to design instruction to help children take the step to generalizing and formalizing their knowledge into powerful abstract systems for representing and operating mathematical ideas. The studies build on existing research on cognitively guided instruction (CGI). The goal of this paper…

Descriptors: Algebra, Elementary Education, Mathematics Curriculum, Mathematics Instruction

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