Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

The National Council of Teachers of Mathematics has set ambitious goals for the teaching and learning of mathematics that include preparing students for both the workplace and higher education. While this suggests that it is important for students to develop strong mathematical competencies by the end of high school, there is evidence to indicate…

An investigation of these numbers is shown to give students an opportunity to make use of such mathematical skills as algebraic substitution, modular arithmetic, counting arguments, and mathematical induction. (MP)

Results of operations on the Pythagorean formula are interpreted pictorially to yield interesting art forms. (MP)

Four problems are given and discussed involving reflection about a line or the reflection properties of conic sections. Solutions are given. (MP)

Challenges traditional use of logic in the mathematics curriculum, indicating how it may be better used. Explicit suggestions and justification for placing inferential logic in high school geometry and relegating most of the sentential logic to algebra are provided. Overviews of both forms of logic are also provided. (JN)

Presents a mathematical puzzle that asks about "missing" area and leads to an exploration of the Fibonacci sequence as well as genuine inquiry in plane geometry connected to algebra. Discusses the inquiry, the concepts, the solution, and an extension that deepens all students' understanding of the connections between algebra and…

The effect of testing format on achievement was investigated. Statistical analysis indicated no significant differences between any of the four formats used. (MK)

Introduces a strategy for writing equations of graphs to help students and teachers build strong conceptual connections between the symbolic representations of algebra and the spatial representations of geometry. (Author/MKR)

A previous article argued that the tradition of teaching sentential logic in geometry should be challenged and suggested that sentential logic be moved to algebra and replaced by inferential logic. Specific inferential logic topics were also suggested. This article elaborates on the inference schemes suggested and describes general proof…

Rational points in the plane were defined as points having both coordinated rational. Students solved several problems linking rational points with lines, circles, and other geometric figures. (SD)

A particular shot on a pool table is analyzed using the concept of similar triangles, to introduce the equivalence of the "incident-reflection" principle and the "minimum-distance" principle. (CR)