Get a deeper understanding of teaching functions, 9-12 with our concise and comprehensive Go-To Guide. Based on "Developing Essential Understanding of Functions 9-12" and "Putting Essential Understanding of Functions into Practice 9-12," this summary distills the key concepts and ideas into a quick-reference guide that's…

The perfect guide to help you embed metacognitive approaches to your teaching. What is metacognition and how can you use it in your teaching? Metacognition -- being aware of our own ways of thinking -- is popular in education, but it is not always obvious how it links to teaching practice and how to teach it explicitly. This book translates…

This article describes several ways to connect probability to other topics within mathematics, over a range of year levels, and across the curriculum. It includes a description of common issues and misconceptions, and practical learning activities to address them.

To address student misconceptions and promote student learning, use discussion questions as an alternative to reviewing assessments. This article describes how using discussion questions as an alternative to going over the test can address student misconceptions and can promote student learning.

Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

The International Association for the Evaluation of Educational Achievement (IEA) Research for Education series represents a further effort by IEA to capitalize on it's unique datasets, so as to provide powerful information for policymakers and researchers. Each report focuses on a specific topic and is produced by a dedicated team of leading…

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…

The perpetuation of mathematical rules that expire (Karp, Bush, and Dougherty 2014; 2015), or rules that are taught in previous grades that no longer hold true, suggests that many secondary students harbor misconceptions from their elementary and middle-grades mathematics experiences as they progress to mathematics classes that are more…

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 ties between literacy and numeracy exist in the development of vocabulary and language for understanding mathematical concepts. Research indicates that explicit instruction in mathematics vocabulary supports success with mathematics problem solving (Biemiller 2009; Pierce and Fontaine 2009; Rubenstein and Thompson 2002) for native…

For decades, students have been encouraged to use "Please Excuse My Dear Aunt Sally" as a means of learning the order of operations. Teachers unfamiliar with the Aunt Sally mnemonic are perhaps more familiar with a mnemonic such as PEMDAS. Each mnemonic is intended to convey "parentheses, exponents, multiplication, division,…

Middle-grades teachers and students can have different perspectives on the value of discussing students' mathematical mistakes, despite various classroom evidence that such discussions can help foster strong conceptual understanding. Some teachers consider student mistakes to be an opportunity to correct errors in individual student thinking.…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) outlines ambitious goals for fraction learning, starting in third grade, that include the use of the number line model. Understanding and constructing fractions on a number line are particularly complex tasks. The current work of the authors centers on ways to successfully…

"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…

How can a simple dot--the decimal point--be the source of such frustration for students and teachers? As the author worked through her own frustrations, she found that her students seemed to fall into groups in terms of misconceptions that they revealed when talking about and working with decimals. When asking students to illustrate their thinking…