The Malaysian educational system tends to take a clear instructionally-focused approach to the teaching of mathematics. This means that many students gain a good procedural command of areas of mathematics. This paper explores one outcome of a teaching experiment in which one area of mathematics (differentiation) was taught in a radically different…

The major idea in this paper is the formulation of a theory of three distinct but interrelated worlds of mathematical thinking each with its own sequence of development of sophistication, and its own sequence of developing warrants for truth, that in total spans the range of growth from the mathematics of new-born babies to the mathematics of…

This research report presents a study of the work of agronomy majors in which an extension of linear models to non-linear contexts can be observed. By linear models we mean the model y=a.x+b, some particular representations of direct proportionality and the diagram for the rule of three. Its presence and persistence in different types of problems…

In this work we show some activities designed with a First Year group of the Mathematics Degree to give the graphic register back its mathematical status and promote its use on the part of the students. In particular, we have chosen the topic related to improper integration to reinforce the use of this register by the students. [For complete…

The current education reform efforts place greater emphasis on conceptual understanding and focus attention on teacher preparation, especially on the adequacy of teachers' mathematical knowledge of the material they will be teaching. This paper discusses the responses of 20 prospective elementary and special education mathematics specialists to…

The author of this paper submits that humans have a natural inquisitiveness; hence, mathematicians (as well as other humans) must be active in learning. Thus, we must commit to conjecture and prove or disprove said conjecture. Ergo, the purpose of the paper is to submit the thesis that learning requires doing; only through inquiry is learning…

There has been a long held perception that the field of mathematics is more appropriate for males than for females. The construct, mathematics as a male domain, has been considered a critical variable in explanations for females' under-representation in the most demanding mathematics subjects offered at school and higher education, and in related…

This document provides a preliminary report of the study Gateways To Advance Mathematical Thinking (GAMT) run by Educational Development Center, Inc. (EDC). The study was designed to see what types of reasoning students who have recently completed a linear algebra course apply to problems in algebraic thinking. Student interviews were used as the…

It is not complex to teach the algorithm for multiplying fractions so that children can multiply numerators and denominators to arrive at correct answers. However, it is a challenge to teach so that students build understanding of multiplication of fractions, extending what they have already learned about fractions and about multiplication of…

Noting that young children often need many experiences with a mathematical concept before they fully understand the concept, this annotated bibliography lists children's books for presenting mathematical concepts within a context and details activities that extend the text as a way to engage children in hands-on mathematical learning experiences.…

Whole numbers written in spiral or triangular patterns with spaces occupied by prime numbers blocked in produces interesting visual patterns. Described is a game based on these patterns that may be played at many different levels. (JP)

Number sequence patterns for counting boundaries of familiar figures are extended to higher dimensions. (JP)

Results indicated that females in the retention index treatment retained significantly more than females in either the choice or fixed group, while males in the choice treatment retained more than males in the other groups. (Author)