Learning to name and notice students' mathematical strengths is a challenging process requiring time and multiple iterations of practice for prospective teachers (PTs) to adopt. Mathematics teacher educators (MTEs) can approximate and decompose the complex practice of naming and noticing students' mathematical strengths so PTs learn to teach…

School students of all ages, including those who subsequently become teachers, have limited experience posing their own mathematical problems. Yet problem posing, both as an act of mathematical inquiry and of mathematics teaching, is part of the mathematics education reform vision that seeks to promote mathematics as an worthy intellectual…

Listening to students' mathematical thinking is one of the reform-minded visions of mathematics teaching. Examines how a mathematics letter exchange between grade 4 students provided an occasion for prospective teachers to learn about students' mathematical thinking and examine their interpretive practices. (Contains 26 references.) (Author/ASK)