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…

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…

Technology has the potential to make complex and abstract mathematical ideas more accessible to students, especially to those who have difficulties with challenging curricular concepts (NCTM 2000, NCTM 2008). What one sometimes forgets is that technology is a tool and, like any tool, can be used productively only in the hands of a skilled…

Quite a bit of the arithmetic in elementary school contains elements of algebraic reasoning. After researching and testing a number of instructional strategies with Irish third graders, these authors found effective methods for cultivating a relational concept of equality in third-grade students. Understanding equality is fundamental to algebraic…

Ms. Beyer's first graders have been working for several weeks on solving problems that encourage the use of such multiple representations as ten frames and number lines. The class is using Math Trailblazers, a National Science Foundation-supported elementary school math curriculum developed to reflect recent reform efforts in mathematics…

Effectively teaching mathematics to speakers of other languages requires teachers to recognize, validate, honor, and support the math that these students have already learned before entering a U.S. classroom. To do so, they must become aware of procedures, types of math instruction, and students' current performance levels. They should be…

Learning mathematics has traditionally been thought of as a sequential progression. Children learn to count to 10, then to 20, and then to 100. They learn to add without regrouping and then with regrouping. The authors teach addition before multiplication and the two-times table before the six-times table. They usually teach division as a separate…

This article describes how first graders' sense of number can be developed through the perspective of measurement. (Contains 5 figures.)

Discusses the concept of equality, which is a crucial idea for developing algebraic reasoning in young children. Explores young children's understanding and misconceptions about the "equals" sign, and relates the experiences one teacher had helping children better understand the sign. (ASK)

This article shares activities that fourth, fifth, and sixth graders can enjoy as they discover relationships among fractions, decimals, and percents, including the 100-penny chart. (MKR)

Discusses how the misuse of symbols, specifically "=", can impede mathematical understanding. Concludes that teachers should help students learn the appropriate meanings for symbols. (ASK)

Illustrates the use of representation of equality, perimeter and area, measurement, and data in the mathematics classroom. (KHR)