In 2000, the "National Council of Teachers of Mathematics" recommended that Algebra Standards, "instructional programs from prekindergarten through grade 12 should enable all students to use mathematical models to represent and understand quantitative relationships." In this article, the authors suggest the "Balance"…

This article describes how in early mathematics learning, young children are often asked to recognize and describe visual patterns in their environment--perhaps on their clothing, a toy, or the carpet; around a picture frame; or in the playground equipment. Exploring patterns in the early years is seen as an important introduction to algebraic…

This article presents a sequence of learning activities that lead to using the area model of multiplication to understand the distributive property (DP). The connection between area and multiplication is an important one, both for algebraic thinking and for geometry, as indicated in two of the critical areas for the third grade in the Common Core…

Parents can positively impact children's learning of mathematics. To productively engage families in the learning process, teachers must support such interpersonal relationships. The author describes the investigative work of a group of teacher candidates as they sought to attain such understanding. Eighteen preservice teachers, who were…

An operational understanding of the equal sign can hinder learning its relational meaning. After providing examples that illustrate the folly of expecting students who know the operational meaning of the equal sign to intuit the sign's relational meaning, this article provides teachers with strategies that will help them effectively introduce…

As students progress through elementary school, they encounter mathematics concepts that shift from additive to multiplicative situations (NCTM 2000). When they encounter fraction problems that require multiplicative thinking, they tend to incorrectly extend additive properties from whole numbers (Post et al. 1985). As a result, topics such as …

Mrs. Fisher's class was learning about arithmetic functions by pretending to operate real-world "function machines" (Reeves 2006). Functions are a unifying mathematics topic, and a great deal of emphasis is placed on understanding them in prekindergarten through grade 12 (Kilpatrick and Izsák 2008). In its Algebra Content Standard,…

Recent documents suggest that all students, even young children, should have opportunities to engage in reasoning and proof (CCSSI 2010; NCTM 2000, 2006, 2009). One mathematical practice that is central to reasoning and proof is making conjectures (CCSSI 2010; NCTM 2000; Stylianides 2008). In the elementary grades, "formulating conjectures…

"Strategy sharing" is a certain type of discussion that centers on students' ideas and occurs when children present different approaches to problems and provide information about how they solved the problem (Wood, Williams, and McNeal 2004). A teacher may orchestrate a strategy-sharing discussion to achieve one or more of the…

In the course of transitioning from classroom teacher to math instructional coach, Tara Zuspan identified critical themes and lessons she had learned. She focused her efforts on building relationships, partnering with the principal, understanding the process of change, and providing teachers with opportunities to collaborate. These intentional…

Math games can be powerful tools in helping students achieve automaticity in basic addition and related subtraction facts if both teachers and students use them purposefully. According to the National Council of Teachers of Mathematics (NCTM 2000), developing a solid mathematical foundation is essential for every child in prekindergarten through…

This is a story about teachers engaging in mathematics teacher leadership. The focus is on the teachers' learning, and the purpose is to illuminate the process. The setting is a semester-long graduate class called Teacher Leadership in Mathematics Education, and the characters are elementary and middle school teachers. Those in this group…

It is not surprising, as research has shown, that fractions are one of the most difficult of the elementary school math topics to teach and learn in ways that are meaningful. The authors reference a work by James Hiebert, "Mathematical, Cognitive, and Instructional Analyses of Decimal Fractions" (1992), that mathematical concepts should…

To challenge students' reasoning and to align with a physical fitness unit that students were studying, teachers and authors, Scott Frye and Signe Kastberg adapted a ratio comparison problem from Susan Lamon, "Ratio and Proportion: Connecting Content and Children's Thinking," (1994) to include athletes and doctors who share…

Textbooks, as well as classroom instruction, tend to present estimation as a stand-alone exercise, ignoring that "the process of estimation depends on the situation itself as well as the estimator." When taught this way, estimation is stripped of its power to help students judge the reasonableness of answers and make sense before,…