What makes this book interesting and important is the detailed attention it gives to a subject
area exemplifying the essence of mathematics, and one that has yet to receive sufficient …

Theories of adult reasoning propose that reasoning consists of two functionally distinct
systems that operate under entirely different mechanisms. This theoretical framework has …

In this paper we describe two episodes of instructional interaction, in which examples are
used in order to help students face their misconceptions. We introduce the notions of pivotal …

Planning for instruction is an important and integral part of the complex activity of teaching.
Learning how to plan for instruction continues to challenge teacher educators, who seek …

In this article we investigate how preservice elementary school (K–7) teachers understand
the concept of prime numbers. We describe participants' understanding of primes and …

Lesson play is a novel construct in research and teachers' professional development in
mathematics education. Lesson play refers to a lesson or part of a lesson presented in …

In Sect. 1, after discussing how proof at the tertiary level is different from proof at the school
level, we discuss transitions from secondary to undergraduate level and from undergraduate …

When a topologist colleague was asked to teach remedial geometry, he used Schaum's
Outline of Geometry and also wrote proofs on the blackboard. One day a student, who was …

Acknowledging students' difficulty in generalizing in general and expressing generality in
particular, we assert that the choice of examples that learners are exposed to plays a crucial …

Mathematical language and its uses by learners and teach-ers has attracted the interest of
many mathematics educators. However, despite significant attention to specific terminology …