Discusses how students construct their own understanding of mathematics as they discover and then learn it in class. Presents Krystal's method to subtract mixed numbers that her peers adopt and name for her. (ASK)

Describes first grade students' mathematical investigation of the number of spots on a cheetah. The exploration of counting and estimation strategies that grew from the investigation gives evidence that mathematicians come in all ages. (ASK)

Describes a student project that enables students to experience problem-solving strategies and construct their own understandings of the problem-solving strategies by researching the problem-solving process itself, uncovering and defining strategies that they can subsequently use to solve problems, and exploring the impact that attitude has on…

Provides examples of student work on a problem which shows that students solve problems in several different ways. Discusses challenges to the teacher that might result from problems such as these. (ASK)

Reviews an alternative patterning approach and highlights the difficulties it can present when students lack the requisite skills and knowledge of processes. Describes how this approach can be used to introduce elementary algebraic ideas and offers recommendations for establishing these important understandings. (ASK)

Presents a set of tasks using a child's invented strategy and a nonstandard algorithm to illustrate one way to facilitate the development of mathematical and pedagogical dispositions. (ASK)

Computation activities focusing on speed and accuracy do not provide children with the opportunity to learn or develop their own mental computation strategies. Sets out some goals and ideas for teaching mental computation and introduces a card game for helping children compute mentally. (ASK)

The 16 units of this book are designed as textbook supplements to encourage students to think mathematically and as mathematicians. Each unit begins with an orientation session which raises general concerns that always occur within mathematical exploration. This is followed by a short, original text in which a mathematician creates a particular…

This book offers ideas to enrich instruction and help teachers explore the intrinsic beauty of math. Through dozens of examples from arithmetic, algebra, geometry, and probability, the symmetries, patterns, processes, paradoxes, and surprises that have facilitated generations of great thinkers are revealed. Activities include: (1) The Beauty in…

Discusses the importance of revisiting problems to encourage children to amplify their mathematical thinking and for teachers to note developmental growth and patterns among learners. Describes experiences with a classic problem that was revisited several times. (ASK)

This book is a compatible instructional component to any algebra textbook and was developed by University of Hawaii under the Dwight D. Eisenhower Mathematics and Science Education Improvement Act. The tasks align with the content and instructional approach used in daily classes that emphasize standards-based teaching and learning. The tasks…

The first section of this guide contains detailed instructions on how to stage a Microscopic Explorations Festival and an overview of learning station activities that can be used during such an event. The main section of this guide provides concise instructions for setting up each of the festival stations. For each station there is an overview,…

This publication is designed for families with young children ages four through eight. It aims to help families acquire methods and materials through which to make mathematics more accessible for all students. Special focus is placed on those students from groups that are not traditionally well-represented in mathematics: students of color, girls,…