Having a deeper understanding of division derived from multiple models is of great importance for teachers and students. For example, students will benefit from a greater understanding of division contexts as they study long division, fractions, and division of fractions. The purpose of this article is to build on teachers' and students'…

During the semester break, 36 second-grade students accessed a set of resources and completed a series of online math activities focused on the application of the model method for arithmetic in two contexts 1) addition/subtraction and 2) multiplication/division. The learning environment first modeled and then supported the use of a scripted series…

Pratham's "Read India" initiative is a large-scale intervention to improve basic learning and arithmetic among children in primary school. It was started almost 10 years ago and has evolved considerably over time. Currently, this initiative uses two strategies. The first strategy is to work directly with village communities and local…

Much has been written about the value of concrete manipulatives for supporting students' mathematics learning. This is particularly true for the domain of fractions and decimals. Understanding of decimal place-value is seen as critical for students' mathematics learning. To understand decimals, students need first to have a solid understanding of…

Action research (AR) is defined by Macintyre to be: "an investigation, where, as a result of rigorous self-appraisal of current practice, the researcher focuses on a problem,or a topic or an issue which needs to be explained, and on the basis of information, plans, implements, then evaluates an action then draws conclusions on the basis of…

At the heart of the recent focus on mathematics has been an increased emphasis on developing students' "number sense." Ironically, although growing as a force in the education literature, number sense has not been clearly defined for teachers. Teachers need specific support in understanding how to develop number sense in students, to…

Appropriate concrete and pictorial models allow students to construct meaning for rational numbers and operations with the numbers. To develop deep understanding of rational number, sixth through eighth graders must experience a variety of models (NCTM 2000). Since 1979, personnel from the Rational Number Project (RNP), a cooperative research and…

Assessment is a common task in education that has many varied purposes. One of these is the use of assessment data to make decisions about instructional planning. This article presents a framework for how to use assessment data to plan instruction. It also provides some background on terminology of assessment for instructional planning,…

The game presented in this article provides for students' development of the use of models, benchmarks, and equivalent forms to judge the size of fractions in a motivational and flexible way.

This article uses one of the authors' classroom experiences to explore how teachers can create technology-rich learning environments that support upper elementary students' mathematical understanding of algebra and number and operations. They describe a unit that presents a common financial problem (the use of credit cards) to engage sixth graders…

This article discusses two sequences of activities that were developed to support middle school students' and preservice teachers' construction of algorithms for dividing fractions. One sequence is intended to promote understanding of the common-denominator algorithm; the other sequence is intended to promote understanding of the…

Algebraic reasoning stands as a formidable gatekeeper for students in their efforts to progress in mathematics and science, and to obtain economic opportunities (Ladson-Billings, 1998; RAND, 2003). Currently, mathematics education research has focused on algebra in order to provide access and opportunities for more students. There is now a growing…

In this article, the author believes that a visual image of the number system is helpful to everyone, especially children, in understanding what is, after all, an abstract idea. The simplest model is the number line, a row of equally spaced numbers, starting at zero. This illustrates the continuous progression of the natural numbers, moving to the…

Multiplication, division and fractions are "hotspots" for students in the middle years with many students experiencing difficulty with these concepts. Arrays effectively model multiplication and help children develop multiplicative thinking and learn multiplication facts. In this article the authors show how an open-ended array problem…

This article challenges the traditional model for teaching computation in the primary grades. It describes a model in which students are encouraged to invent and use alternative computation procedures.