Assessing student learning traditionally involves determining whether students can solve a certain percentage of problems correctly, under the assumption that this achievement indicates they have the knowledge and understanding they need to progress to new topics. This article explores what teachers can learn from looking closely at student…

The inspection of mistakes can play a powerful role in an individual's learning process (Boaler 2015). The purpose of this article is to support the reader in selecting mistakes that can be leveraged to benefit the learning of all students. Specifically, the authors focus on "which" and "why": "which" mistakes to…

Thoughtful implementation of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) presents an opportunity for increased emphasis on the development of mathematical understanding among students. Granted, ascertaining the mathematical understanding of an individual student is highly complex work and often exceedingly difficult.…

Early elementary school students are expected to solve twelve distinct types of word problems. A math researcher and two teachers pose a structure for thinking about one problem type that has not been studied as closely as the other eleven. In this article, the authors share some of their discoveries with regard to the variety of…

More important than infusing courses and curricula with modern content is to give students the tools to use and understand mathematics--including some that does not yet exist. A curriculum organized around habits of mind tries to close the gap between what users and makers of mathematics do and what they say. These cross-journal articles are…

Too often the professional development provided for teachers of mathematics is a short-term, one-shot effort. Today's shrinking budgets, increasing class sizes, and growing demands on teachers' time present further challenges. For the past six years, staff development efforts in the author's district have focused on language arts with little…

This article describes five representations and the connections between and among them. It also describes how to use multiple representations to support students' mathematical understanding.

Presents responses to the Stair Skipping problem that appeared in the April, 2000 issue of this journal. (KHR)

The National Council of Teachers of Mathematics (NCTM) poses constructivist ideas in its "Principles and Standards for School Mathematics" (2000). NCTM supports mathematics instruction that takes a developmental perspective; starts and builds on what children know; and leads children to construct relational understanding, problem-solving…

Discusses planning instruction on the basis of children's thinking. First, individualize instruction by adjusting the value of the numbers used for individual children. Second, base problem presentation on the types of thinking prevalent in the class. Third, conduct some instruction in small groups. Fourth, suggest alternative strategies. Finally,…

This article proposes that student-written math riddles can provide worthwhile mathematical tasks that support the learning of important concepts as they engage and challenge children. It describes procedures for guiding students as they create math riddles for their classmates to solve.

Features responses to a problem that appeared in the February 2000 issue. (KHR)

Explores how children from kindergarten to 6th grade think about the same fraction problem and what that should mean for instruction. (Author)

Presents activities to incorporate Polya's four-step problem-solving process. (KHR)

Presents a sampler of statements from "Principles and Standards for School Mathematics" related to standards, goals, and activities for preschoolers. (Author)