"Mathematical Thinking: From Assessment Items to Challenging Tasks" is a compilation of 36 problem-based lessons that encourage students to engage in productive struggle and deep thinking. Its 36 full-length lessons for grades 2-8 are each inspired by an actual test item from the National Assessment of Educational Progress (NAEP).…

Multiple-choice testing is an educational reality. Rather than complain about the negative impact these tests may have on teaching and learning, why not use them to better understand your students' true mathematical knowledge and comprehension? Maryann Wickett and Eunice Hendrix-Martin show teachers how to move beyond the student's answer--right…

The new Common Core State Standards for Mathematics have been formulated to provide students with instruction that will help them acquire a thorough knowledge of math at their grade level, which will in turn enable them to move on to higher mathematics with competence and confidence. "Hands-on Activities for Teaching the Common Core Math…

This article, which describes integrating virtual manipulatives with the teaching of probability at the elementary level, puts a "virtual spin" on the teaching of probability to provide more opportunities for students to experience successful learning. The traditional use of concrete manipulatives is enhanced with virtual coins and spinners from…

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…

In many mathematics classes, students are asked to learn via the discovery method, in the hope that the intrinsic beauty of mathematics becomes more accessible and that making conjectures, forming hypotheses, and analyzing patterns will help them compute fluently and solve problems creatively and resourcefully (NCTM 2000). The activity discussed…

Examples are given of problems which can be solved pictorially, thus aiding in the general development of geometric intuition and in developing some of the basic ideas of probability. (MP)

Presents an activity related to probability in order to answer a question based on the English football league. The question is "What is the probability that the FA Cup Final will be between the same two teams that played in the previous tournament?". (ASK)

Presents student responses to the "The Darts, Anyone?" problem that appeared in the May, 1999 issue of this journal. The problem concerned finding possible scores on dart rings. (KHR)

Describes a personal problem solving-inquiry journey, working on a problem suggested by an activity on probability observed in a junior primary classroom. Presents reflective thoughts about the mathematical and pedagogical lessons to be learned from this journey. (ASK)

This book contains 40 lessons in problem solving divided into five chapters. Chapter 1 contains several lessons in which solutions are derived through investigation of numerical patterns. Chapter 2 contains lessons in which problem-solving situations are presented in a graphical context. It also includes two lessons in which students construct…

The probability of selecting two matching socks is discussed. (MNS)

Presents a problem of triangular tiles that involves counting and probability. Includes instructor guiding questions. (KHR)

Presents a word problem designed to encourage students to create systematic methods for counting and develop probability concepts. Involves sharing eight cookies between three people. (KHR)

Advantages and disadvantages of common ways to justify the answer to a probability problem are discussed. One explanation appears superior to the others because it is easy to understand, mathematically rigorous, generalizes to a broader class of problems, and avoids the deficiencies of the other explanations. (MNS)