Multiple external representations (MERs) are central to the practice and learning of science,
mathematics and engineering, as the phenomena and entities investigated and controlled in …

This chapter arose from the need to introduce researchers, including Master and PhD
students, to design-based research (DBR). In Sect. 16.1 we address key features of DBR …

In this theoretical article, we take an exercise to be a collection of procedural questions or
tasks. It can be useful to treat such an exercise as a single object, with individual questions …

In this article students' understanding of trigonometric functions in the context of two college
trigonometry courses is investigated. The first course was taught by a professor unaffiliated …

“Transition” from one state to another (eg, from childhood to adulthood) is a process of
change. Within an educational context change happens everywhere (or at least it should do …

Mathematics Education Research Centre University of Warwick, UK For several years I have
been working with Eddie Gray and others on the ways in which we conceptualize different …

A comment on'Three worlds and the imaginary sphere\Inglis, 23 (3): Even though a theory
of'three worlds' has been developing for just over two years, it is still under con-struction. A …

This paper considers mathematical abstraction as arising through a natural mechanism of
the biological brain in which complicated phenomena are compressed into thinkable …

Two questions are asked that concern the work of teaching high school geometry with
problems and engaging students in building a reasoned conjecture: What kinds of …

The transition to formal mathematical thinking involves the use of quantified statements as
definitions from which further properties are constructed by formal deduction. Our quest in …