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Siegler, Robert; Carpenter, Thomas; Fennell, Francis; Geary, David; Lewis, James; Okamoto, Yukari; Thompson, Laurie; Wray, Jonathan – What Works Clearinghouse, 2010
This practice guide presents five recommendations intended to help educators improve students' understanding of, and problem-solving success with, fractions. Recommendations progress from proposals for how to build rudimentary understanding of fractions in young children; to ideas for helping older children understand the meaning of fractions and…
Descriptors: Mathematics, Problem Solving, Young Children, Elementary Education
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Jacobs, Victoria R.; Franke, Megan Loef; Carpenter, Thomas P.; Levi, Linda; Battey, Dan – Journal for Research in Mathematics Education, 2007
A yearlong experimental study showed positive effects of a professional development project that involved 19 urban elementary schools, 180 teachers, and 3735 students from one of the lowest performing school districts in California. Algebraic reasoning as generalized arithmetic and the study of relations was used as the centerpiece for work with…
Descriptors: Faculty Development, Algebra, Mathematical Logic, Thinking Skills
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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
Romberg, Thomas A., Ed.; Carpenter, Thomas P., Ed.; Dremock, Fae, Ed. – Lawrence Erlbaum Associates (Bks), 2005
The research reported in this book provides reliable evidence on and knowledge about mathematics and science instruction that emphasizes student understanding--instruction consistent with the needs of students who will be citizens in an increasingly demanding technological world. The National Center for Improving Student Learning in Mathematics…
Descriptors: Teaching Methods, Science Instruction, Mathematics Instruction, Mathematics Education
Carpenter, Thomas P.; Franke, Megan Loef; Levi, Linda – 2003
This book is designed to help teachers understand children's intuitive problem solving and computational processes and to figure out how to use that knowledge to enhance students' understanding of arithmetic. This book provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what…
Descriptors: Algebra, Arithmetic, Elementary Education, Mathematics Activities
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
Carpenter, Thomas P.; Levi, Linda; Farnsworth, Valerie – In Brief, 2000
"In Brief" focuses on K-12 mathematics and science research and implications for policymakers, educators, and researchers seeking to improve student learning and achievement This brief highlights the learning gains of 240 elementary students involved in a long-term study in Madison, Wisconsin and their remarkable ability to reason with arithmetic…
Descriptors: Abstract Reasoning, Algebra, Arithmetic, Educational Change
Fennema, Elizabeth; Sowder, Judith; Carpenter, Thomas P. – 1999
This chapter builds on the idea that classrooms that promote understanding can and do exist. Elaborating upon this idea the question is raised, "In what ways can many more classrooms be developed so that all students have the opportunity to learn with understanding?" The construction of classrooms that promote understanding is dependent upon…
Descriptors: Classroom Environment, Educational Research, Elementary Secondary Education, Instructional Effectiveness
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 H. – Music Educators Journal, 1971
Descriptors: Course Content, Course Evaluation, Educational Television, Elementary Education
Carpenter, Thomas H. – Educational Technology, 1971
The purpose of this article is to consider, first, some of the implications of using the videotape recorder in the television studio for in-school music instruction...and, second, some of the present-day practices of using smaller videotape recorders in the classroom and teaching studio for individualized instruction." (Author)
Descriptors: Educational Television, Individualized Instruction, Microteaching, Music Education
Carpenter, Thomas H. – 1969
A review of literature germane to the subject helps provide an introduction to this study whose object is to identify the trends and practices that have occurred in television teaching of music from the late 1940's to the present. Other purposes of the study are to categorize and analyze the content and developing program formats of current…
Descriptors: College Curriculum, Communications, Educational Media, Educational Television
Carpenter, Thomas P. – 1971
First-grade students' understanding of several basic measurement processes was examined. Twenty randomly selected students from five first-grade classes in two different schools were individually examined on 11 measurement tasks. Seven of the tasks were adapted from items reported in the Gal'perin and Georgiev study, designed to test understanding…
Descriptors: Cognitive Development, Conservation (Concept), Elementary School Mathematics, Geometric Concepts
Carpenter, Thomas P. – 1971
The major purpose of this study was 1) to investigate the development of the concept of a unit of measure and the coordination of unit size and the number of units 2) to relate this development to the development of conservation and 3) to determine the role of equivalence and nonequivalence relations in certain conservation and measurement…
Descriptors: Age Differences, Analysis of Variance, Children, Cognitive Measurement
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Carpenter, Thomas P. – 1972
Reported is a study of the development of conservation and measurement concepts, with reference to certain task factors which may affect performance. A group of 129 first and second graders were given a test of conservation and measurement consisting of five problem types crossed with three transformation types. The problems all involved moving…
Descriptors: Conservation (Concept), Elementary School Mathematics, Grade 1, Grade 2
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