This article discusses a set of tasks that introduce dilations using nonstandard figures, incorporating snippets of classroom conversations as students try to make sense of the specified tasks, to show how they progress in their understanding. The authors provide a theoretical foundation for the tasks and discuss the pedagogical implications for…

In this paper, we highlight examples from school mathematics in which invariance did not receive the attention it deserves. We describe how problems related to invariance stimulated the interest of both teachers and students. In school mathematics, invariance is of particular relevance in teaching and learning geometry. When permitted change…

Sixty four preservice teachers taking a mathematics methods class for middle schools were given 3 math problems: multiply a three digit number by a two digit number; divide a whole number by a fraction; and compare the volume of two cylinders made in different ways from the same rectangular sheet. They were to a) solve them, explaining their…

Presents a geometric problem and illustrates four different ways to solve it: (1) a synthetic approach; (2) a coordinate approach; (3) a vector approach; and (4) a transformation approach. (KHR)

Presented is a method for solving certain types of problems, with the goal of piquing students' interest in studying affine geometry, which underlines the method. (MNS)

Discussed is an application of number theory to cryptology that can be used with secondary school students. Background on the topics is given first, followed by an explanation for use of the topic. (MNS)

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 considers how the algebra curriculum in secondary mathematics might be reformulated by rethinking both the content of algebra and the approaches to teaching and learning algebraic concepts. It considers how the concept of function can be made a central theme of the algebra curriculum and further suggests that computer software, when…

This guide is designed to help classroom teachers implement the Alabama Course of Study: Mathematics K-12. It is inclusive also of the objectives tested by the Stanford Achievement Tests and the Alabama Basic Competency Tests. One characteristic of the curriculum guide is that it clearly states what students should learn in each grade level. These…