Introducing, and thereafter teaching calculus to senior secondary, early college and
university students, at the expense of algebra and geometry, is causing half-baked calculus …

When students learn a calculus construct, both a concept image as well as a concept
definition is imprinted in their mind, and because of it, concrete and real-life examples …

1991] THE TEACHING OF MATHEMATICS 627 cp (a) o cp (b)= cp (a* b) for all a, b in G. If
that is true, then cp (G) will be a subgroup of A (G). Conversely, if cp (G) is a subgroup of A …

The interest in producing this book arose out of a concern for the education of graduate
students and young researchers in mathematics education. A few years ago, as a result of …

The concept image consists of all the cognitive structure in the individual's mind that is
associated with a given concept. This may not be globally coherent and may have aspects …

The present study builds on earlier work by Meyer and Land (2003) which introduced the
generative notion of threshold concepts within (and across) disciplines, in the sense of …

Advanced Mathematical Thinking has played a central role in the development of human
civilization for over two millennia. Yet in all that time the serious study of the nature of …

A threshold concept can be considered as akin to a portal, opening up a new and previously
inaccessible way of thinking about something. It represents a transformed way of …

How Humans Learn to Think Mathematically describes the development of mathematical
thinking from the young child to the sophisticated adult. Professor David Tall reveals the …

... that the subject involves two disciplines, psychology and mathematics, and would require,
in order to be treated adequately, that one be both a psychologist and a mathematician …