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Learning and teaching with understanding.
A Longitudinal Study of Learning to Use Children's Thinking in Mathematics Instruction
This study examined changes in the beliefs and instruction of 21 primary grade teachers over a 4-year period in which the teachers participated in a CGI (Cognitively Guided Instruction) teacher…
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Thinking Mathematically : Integrating Arithmetic and Algebra in Elementary School
This unit provides opportunities for students to extend their ways of thinking about addition and subtraction to problems with larger numbers. Students use their prior knowledge of addition and skip…
Using Knowledge of Children’s Mathematics Thinking in Classroom Teaching: An Experimental Study
This study investigated teachers’ use of knowledge from research on children’s mathematical thinking and how their students’ achievement is influenced as a result. Twenty first grade teachers,…
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Children's Mathematics: Cognitively Guided Instruction
how the Cognitively Guided Instruction approach can help support mathematical to children's mathematical thinking and use this as a basis for instruction. In anticipation of the new edition of…
Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics
We argue that reform in curriculum and instruction should be based on allowing students to problematize the subject. Rather than mastering skills and applying them, students should be engaged in…
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Children's Conceptual Structures for Multidigit Numbers and Methods of Multidigit Addition and Subtraction.
Researchers from 4 projects with a problem-solving approach to teaching and learning multidigit number concepts and operations describe (a) a common framework of conceptual structures children…
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The Acquisition of Addition and Subtraction Concepts in Grades One through Three.
Children's solutions to simple addition and subtraction word problems were studied in a 3-year longitudinal study that followed 88 children from Grades 1 through 3. The children were able to solve…
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Professional development focused on children's algebraic reasoning in elementary school
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…
Capturing Teachers’ Generative Change: A Follow-Up Study of Professional Development in Mathematics
This study documents how teachers who participated in a professional development program on understanding the development of students’ mathematical thinking continued to implement the principles of…
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