Many research on primary school children in Malaysia indicate an over reliance on the written symbols representation (Munirah, 2001; Parmjit, 2005; Munirah& Noor Azlan, 2002; Chinappan & Ambigapathy, 2009; Mohini & Jacinta, 2010). This is a cause for concern as researchers draw strong connections between the representations children use and their understanding (Lamon, 2001). Janvier (1987) desc...

Observations of apparently random phenomena are commonplace in science. However, randomness and Christian belief are often seen as incompatible, both by naturalists and by theists. This article argues that the scientific concept of randomness and the historic Christian understanding of God’s nature are compatible. It argues that the existence of randomness cannot be settled scientifically; neve...

We argue that visual, analogical representations of mathematical concepts can be used by automated theory formation systems to develop further concepts and conjectures in mathematics. We consider the role of visual reasoning in human development of mathematics, and consider some aspects of the relationship between mathematics and the visual, including artists using mathematics as inspiration fo...

The gestures children spontaneously produce when explaining a task predict whether they will subsequently learn that task. Why? Gesture might simply reflect a child's readiness to learn a particular task. Alternatively, gesture might itself play a role in learning the task. To investigate these alternatives, we experimentally manipulated children's gesture during instruction in a new mathematic...

In the search for principles of pattern generation in complex biological systems, an operational approach is presented that embraces both theory and experiment. The central mathematical concepts of self-organization in nonequilibrium systems (including order parameter dynamics, stability, fluctuations, and time scales) are used to show how a large number of empirically observed features of temp...

We have come a long way and finally are about to study calculus. Many of you might have taken some courses in the past where you learned a number of formulas to calculate the derivatives and integrals of certain functions. The purpose of this course, however, is not to memorize these formulas mindlessly. Rather, our goals are to understand the mathematical concepts underlying such formulas and ...

Vygotsky posed a variety of meaningful ideas for education in his short life. This paper focuses on everyday concepts and mathematical concepts or scientific concepts from his theory, reorganizing these ideas according to a new idea of sublated concepts. Using a series of interviews from a third grade fraction class in Japan, the paper discusses how everyday and mathematical concepts arise out ...

1) The facility with numbers and calculations, 2) The art of avoiding unnecessary calculations, 3) Memorizing formulas and theorems, 4) Understanding and finding proofs, 5) Solving problems with well-described procedures, 6) Solving problems for which there are no well-described procedures, 7) Understanding abstract mathematical concepts, 8) Creating new mathematical concepts, and clarifying an...

This mixed-methods study investigates the effects of student attitudes and behaviours on the outcomes of learning mathematics with computer tools. A computer tool was used to help students develop the mathematical concept of function. In the whole sample (N = 521), student attitudes could account for a 3.4 point difference in test scores between individuals on a 10-point scale. General attitude...

Recent studies have suggested that educators should avoid concrete instantiations when the goal is to promote transfer. However, concrete instantiations may benefit transfer in the long run, particularly if they are “faded” into more abstract instantiations. Undergraduates were randomly assigned to learn a mathematical concept in one of three conditions: generic, in which the concept was instan...