Students encounter mathematics word problems as early as kindergarten and continue to see them throughout their schooling experience. Schema instruction with an attack strategy can support students to successfully navigate word-problem solving. Schemas help students categorize word problems by similar characteristics. To better support students…

How can students achieve an understanding of multiplication that allows them to go beyond recall to explain their thinking? Author and mathematics education professor Juli Dixon introduces a program that teachers can seamlessly integrate into existing mathematics instruction. Learn six tactics to help you shift from an anxiety-producing,…

In this article, the authors argue that teachers need to possess appropriate understanding and diverse pedagogies to successfully move learners from additive to multiplicative thinking. Herein, they offer five pedagogical strategies that teachers can use to help students make this transition. Some of the challenges of learning multiplicative…

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The…

This paper describes results from a case study about how a primary pre-service teacher (PST) used curriculum materials (CMs) when planning for a mathematics lesson during her final practicum. The data is drawn from a doctoral study (in progress) and results show how the PST initiated an active process of searching for and sifting through CMs on a…

Efficient visualizations of computational algorithms are important tools for students, educators, and researchers. In this article, we point out an innovative visualization technique for matrix multiplication. This method differs from the standard, formal approach by using block matrices to make computations more visual. We find this method a…

This document includes instructional tips on: (1) Building on students' informal understanding of sharing and proportionality to develop initial fraction concepts; (2) Helping students recognize that fractions are numbers that expand the number system beyond whole numbers, and using number lines to teach this and other fraction concepts; (3)…

Instruction of multiplication facts has been and continues to be an essential part of mathematics curriculum for students in the intermediate grades with the majority of initial instruction at third grade. Teachers often comment that this is a topic that students struggle to master and that they frequently use fluency drills and fact flash cards…

Three-in-a-Row Lucky Numbers is an engaging, enjoyable, mathematically meaningful, game-based activity involving dice and a hundred chart, which can be used to introduce students to multiplication. The game provides a mechanism for students to explore the structure of multiplication, experiment with the distributive property, and begin to…

In this article, Jason Taff shares an approach that he presented to advanced seventh-grade prealgebra students. He begins by summarizing some of the shortcomings of equating the order of operations concept with the PEMDAS (often rendered mnemonically as "Please Excuse My Dear Aunt Sally") procedure with the hope of helping teachers at…

Productive struggle leads to productive classrooms where students work on complex problems, are encouraged to take risks, can struggle and fail yet still feel good about working on hard problems (Boaler, 2016). Teachers can foster a classroom culture that values and promotes productive struggle by providing students with challenging tasks. These…

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…

The "Making Meaning for Operations Casebook" was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The twenty-nine cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation of specific…

The connections the "Next Generation Science Standards" ("NGSS") creates between science content and practices to literacy and mathematics are especially beneficial at the elementary level. In this article, the authors present a series of lessons a second-grade teacher taught within a thematic unit that integrated standards…

The author wants her students to see any new mathematics--fractions, negative numbers, algebra--as logical extensions of what they already know. This article describes two students' efforts to make sense of their conflicting interpretations of 1/2 × -6, both of which were compelling and logical to them. It describes how discussion, constructing…