Graphing functions is an important topic in algebra and precalculus high school courses. The functions that are usually discussed include polynomials, rational, exponential, and trigonometric functions along with their inverses. These functions can be used to teach different aspects of function theory: domain, range, monotonicity, inverse…

Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…

A mysterious conflict of solutions emerged when a group of tenth- and eleventh-grade students were studying a seemingly ordinary problem on combination and probability. By investigating the mysterious "conflicts" caused by multiple randomization procedures, students will gain a deeper understanding of what it means to perform a task…

The implementation of the Common Core's Standards for Mathematical Practice can pose a challenge to all teachers of mathematics but especially to preservice teachers. These standards require teaching in a way that often differs from what preservice teachers have experienced as learners. Standard 1--"Make sense of problems and persevere in…

Shapedoku is a new type of puzzle that combines logic and spatial reasoning with understanding of basic geometric concepts such as slope, parallelism, perpendicularity, and properties of shapes. Shapedoku can be solved by individuals and, as demonstrated here, can form the basis of a review for geometry students as they create their own. In this…

The kinematics teaching strategy is a teaching method that stimulates kinesthetic intelligence and thus offers students an unconventional approach for exploring mathematical ideas through movement. This article describes how to use the kinesthetic approach to introduce radian measure. The article includes detailed descriptions of easy-to-use…

Lessons given to a group of mathematically talented eleventh and twelfth graders enrolled in a problem-solving course that provided practice in applying the heuristic strategy of working backward are detailed. Special attention was given to the process of formulating generalizations that represent large problem classes. (MP)

Features activities for advanced second-year algebra students in grades 11 and 12. Introduces three random variables and considers an empirical and theoretical probability for each. Uses coins, regular dice, decahedral dice, and calculators. (ASK)

Discussed are trends in performance across the last three National Assessment of Educational Progress (NAEP) mathematics assessments for students in grades 7 and 11, and reports on indicators of instructional activity. The results suggest that achievement in mathematics has taken a modest upturn in the 1980s. (MNS)