Computational thinking (CT) has the potential to enhance learning when integrated into mathematical classroom activities. Teachers are being asked to include CT concepts in their core disciplines; however, there is an open question as to how best to equip teachers to integrate CT into their practice. Oftentimes teacher candidates enter math and…

Guessing, for Pólya, is an important way of getting an initial handle on a mathematical problem. An argument can be made to place guessing in any one of the first three steps of the four-step approach to problem solving as described in "How to Solve It" (Pólya 1945). It could be a part of understanding the problem, devising a plan, or…

The ubiquity of the subject of percentages in our everyday life demands that math teachers and pre-service math teachers demonstrate a profound knowledge and thorough understanding of the concept of percentages. This work, which originated from one specific lesson in an 8th grade math class, studies the conceptual understanding and problem-solving…

The intention of the present study was to see the improvement of students' intuitive skills. This improvement was seen by comparing the Realistic Mathematics Education (RME)-based instruction with the conventional mathematics instruction. The subject of this study was 164 fifth graders of elementary school in Palembang. The design of this study…

A possible contributing factor to students' difficulty in learning advanced mathematics is the conflict between students' "natural" learning styles and the formal structure of mathematics, which is based on definitions, theorems, and proofs. Students' natural learning styles may be a function of their intuition and language skills. The purpose of…

Presents a way of using counterintuitive mathematics problems to help keep students actively involved in mathematics education. (KHR)

This submission contains the Proceedings of the 2009 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at York University in Toronto, Ontario. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group…

Jean Louis Nicolet is a Swiss teacher of mathematics who found his subject so fascinating that he was puzzled as to why so many pupils could not share this enjoyment in their studies. He came to a conclusion which is now supported by the results of psychological research into the learning process: he suggested that the mind does not spontaneously…

Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…

What people mean by randomness should be taken into account when teaching statistical inference. This experiment explored subjective beliefs about randomness and probability through two successive tasks. Subjects were asked to categorize 16 familiar items: 8 real items from everyday life experiences, and 8 stochastic items involving a repeatable…

The learning difficulties that students experience with fractions begin immediately when they are shown fraction symbols with one numeral written above the other and told that the "top number" is called the numerator and the "bottom number" is called the denominator. This introduction to fractions will usually include a few visual diagrams to help…

Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)

This paper discusses a radically different set of assumptions to improve educational outcomes for disadvantaged students. It is argued that disadvantaged children, when exposed to carefully organized thinking-oriented instruction, can acquire the traditional basic skills in the process of reasoning and solving problems. The paper is presented in…