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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
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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
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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
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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
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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
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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
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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
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
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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
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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
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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
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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
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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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
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