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Teachers' knowledge and its impact.
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…
Teacher Learning in Mathematics: Using Student Work to Promote Collective Inquiry
The study describes teachers' collective work in which they developed deeper understanding of their own students' mathematical thinking. Teachers at one school met in monthly workgroups throughout…
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Keeping It Complex
We analyze a particular pedagogy for learning to interact productively with students and subject matter, which we call “rehearsal.” Our goal is to specify a way in which teacher educators (TEs) and…
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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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Teacher Questioning to Elicit Students’ Mathematical Thinking in Elementary School Classrooms
Cognitively Guided Instruction (CGI) researchers have found that while teachers readily ask initial questions to elicit students’ mathematical thinking, they struggle with how to follow up on student…
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Cognitively Guided Instruction: A Knowledge Base for Reform in Primary Mathematics Instruction
In this article we propose that an understanding of students' thinking can provide coherence to teachers' pedagogical content knowledge and their knowledge of subject matter, curriculum, and…
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A Longitudinal Study of Gender Differences in Young Children’s Mathematical Thinking
One area in which gender differences in mathematics have been studied minimally deals with strategies used to solve mathematical problems. The limited evidence available suggests that there may be…
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