Rich mathematical modeling activities are crucial to giving students agency and making mathematics meaningful. Proportional reasoning and transitional algebraic reasoning are the primary topics in the prealgebra curriculum, so a need exists for meaningful modeling activities using proportional reasoning in addition to geometric modeling. In…

Although many factors affect students' mathematical activity during a lesson, the teacher's selection and implementation of tasks is arguably the most influential in determining the level of student engagement. Mathematical tasks are intended to focus students' attention on a particular mathematical concept and it is the careful developing and…

How can geometry teachers design great tasks that allow students to make connections among interrelated concepts and expand their geometric reasoning skills? Many curricular materials provide problems for students to apply a single geometric concept. However, these problems do not always promote reasoning opportunities for students, because…

If students are going to develop reasoning and thinking skills, use their mathematical knowledge, and recognize the relevance of mathematics in their lives, they need to experience mathematics in meaningful ways. Only then will their mathematical skills be transferrable to all other parts of their lives. To promote such flexible mathematical…

Traditionally, a considerable part of teaching and learning algebra has focused on routine practice and the application of rules, procedures, and techniques. Although today's computerized environments may have decreased the need to master algebraic skills, procedural competence is still a central component in any mathematical activity. However,…

Constructivism has constituted a predominant philosophical trend in mathematics education, but its implementation in the classroom has proven to be "far more difficult than the reform community acknowledges". This difficulty may be due in part to administrative cultures that might insist on more procedural types of instruction aimed at testing, in…

Provides classroom suggestions for combining numerical, algebraic, and geometric techniques with the understanding of a simple method for computing square roots. Historical origins of the method illustrate the debt owed to ancient minds living in what are now India, Pakistan, Iraq, and Egypt. (Author/NB)

Describes teaching about proofs in college-level mathematics courses. Presents typical questions that students raise while studying proofs and offers possible answers to these questions. (ASK)

Presents a logical reasoning problem pivotal to the novel "Harry Potter and the Sorcerer's Stone" and discusses it at two levels. (Author/NB)

Presents a discovery activity that connects mathematics and the world of entertainment. Combines geometric transformations with a calculator's DRAW, MATRIX, and PRGM features to generate visual reinforcement of mathematical concepts. (Author/NB)

Introduces human graphing by having students standing on certain coordinates instead of points plotted in ink. Includes teacher tips for success and possible graphing explorations. (KHR)

Describes an activity in which students examine bicycle chain-rings, cogs, and gear ratios as a means of exploring algebraic relationships, data collection, scatter plots, and lines of best fit. (KHR)

Presents a mathematics activity that introduces proof by contradiction in a nonformal setting. This activity has the added benefit of helping students gain a greater understanding of the electoral college. (ASK)

Guides students through the process of designing a window. Allows them to use technology and a variety of representations while maximizing and minimizing the dimensions based on cost and light. Includes activity sheets. (Author/NB)

Describes an activity, The Spaghetti Problem, that shows how statistics could be used to introduce many topics in the secondary mathematics curriculum. (KHR)