Teachers intuitively recognize the importance of metacognition but may not be aware of its many dimensions. Mr. Martinez explores the varieties of metacognitive skills and then offers suggestions for cultivating them in learners of all ages. (Contains 4 endnotes.)

We sometimes teach our students a method of finding all integral triples that satisfy the Pythagorean Theorem x[squared]+y[squared]=z[squared]. These are called Pythagorean triples. In this paper, we show how to solve the equation x[squared]+ky[squared]=z[squared], where again, all variables are integers.

For most teachers, more important than supplies and a spacious classroom is a happy learning environment in which each child feels welcome and safe. That is why it is so dismaying that according to one recent study, 43% of students worry about going to the restroom for fear of encountering a bully. The same study reported that a child is bullied…

This article discusses divisibility tests for any prime number.

We discuss a research-based theoretical framework based on affect as an internal representational system. Key ideas include the concepts of meta-affect and affective structures, and the constructs of mathematical intimacy and mathematical integrity. We understand these as fundamental to powerful mathematical problem solving, and deserving of…

This article discusses the art of storytelling as a means of introducing new mathematics topics. Telling a mathematically based story can be a break from the routine and can serve as literary mnemonics full of mental imagery that helps students recall in problem-solving steps. The authors provide a certain story that has been tried by several…

The understanding and a liking towards mathematics can be very effectively developed in students by allowing them to find out the solutions for any basic problem or simulations, which are basically mathematical reenactments of nearly or completely hypothetical situations. The nontransitive relation of Efron's dice or the assignment of numbers in a…

Specific examples are used to discuss assessment, an integral part of mathematics instruction, with problem posing and assessment of problem posing. General assessment criteria are suggested to evaluate student-generated problems in terms of their quantity, originality, and complexity.

This is a case study of a conflict management intervention in two secondary schools in post-apartheid South Africa. The feature of the intervention that we examine is the use of play as an educational strategy. The literature attests that play can facilitate change by allowing learners freedom to change their behaviour and opportunities to explore…

Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…

Problem Based Learning (PBL) has proven to be a highly successful pedagogical model in many educational fields, although it is comparatively uncommon in technical education. It goes beyond the typical teaching methodology by promoting student interaction. This paper presents a PBL trial applied to an undergraduate Digital Electronics course in the…

This study examines the effects of representational movement on long-term retention and recollection of academic content. The researcher hypothesized that students who used representational movement to elaborate on their understanding of chemical equations would demonstrate improved long-term ability to solve chemical equations. The study…

Chinese characters are used in both Chinese and Japanese writing systems. When literate speakers of either language experience problems in finding or understanding words, they often resort to using Chinese characters or "kanji" (i.e., Chinese characters used in Japanese writing) in their talk, a practice known as "brush talk" ("bitan" in Chinese,…

Students struggling with mathematics may benefit from early interventions aimed at improving their mathematics ability and ultimately preventing subsequent failure. This guide provides eight specific recommendations intended to help teachers, principals, and school administrators use Response to Intervention (RtI) to identify students who need…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…