This "Math Snacks" intervention measured 741 fifth grade students' gains in conceptual understanding of core math concepts after game-based learning activities. Teachers integrated four "Math Snacks" games and related activities into instruction on ratios, coordinate plane, number systems, fractions and decimals. Using a…

As teachers we are encouraged to contextualize the mathematics that we teach. In this article, Belinda Beaman explains how she used the weather as a context for developing decimal understanding. We particularly enjoyed reading how the students were involved in estimating.

Taking as the point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following five pairs of 7th grade students as they progress in algebraic discourse during 24 months, from their informal algebraic talk to the formal algebraic discourse, as taught in school. Our analysis follows changes that…

The mission of German special schools is to enhance the education of students with Special Educational Needs in the area of Learning (SEN-L). However, recent studies indicate that students with SEN-L from special schools show difficulties in basic arithmetical operations, and the development of basic mathematical skills during secondary special…

Teaching experiments have generated several hypotheses concerning the construction of fraction schemes and operations and relationships among them. In particular, researchers have hypothesized that children's construction of splitting operations is crucial to their construction of more advanced fractions concepts (Steffe, 2002). The authors…

The maturation of multiplicative thinking is key to student progress in middle school as rational number, ratio, and proportion concepts are encountered. But many students arrive from the intermediate grades and falter in developing this essential disposition. Elementary students have historically learned multiplication and division as operation…

This article reports on an ethnographic study of a 10-year-old's pursuit of school-based mathematics across school and home to suggest that participating in school-based mathematics is a cross-setting phenomenon in at least 2 ways. First, I illustrate how accomplishing school-based mathematics literally extends into the home and how individuals…

In a previous article of the same journal, we have discussed the interrelations of students' beliefs and self-efficacy beliefs for the use of representations and their respective cognitive performance on the learning of fraction addition. In the present paper, we confirm a similar structure of cognitive and affective factors on using…

Interactions between conceptual and procedural knowledge influence the development of mathematical competencies. However, after decades of research, these interrelations are still under debate, and empirical results are inconclusive. The authors point out a source of these problems. Different kinds of knowledge and competencies only show up…

The purpose of this technical report is to describe a research study exploring students' cognitive processing while solving problems related to division of fractions. Four students were interviewed using verbal protocol techniques with the intention of better understanding their cognitive processing when dividing fractions. Information gained from…

In this technical report, we describe the development of cognitive diagnostic test items that form the basis of the diagnostic system for Project DIVIDE (Dynamic Instruction Via Individually Designed Environments). The construct underlying the diagnostic test is division of fractions. We include a description of the process we used to identify the…

Created by teachers for teachers, the Math Academy tools and activities included in this booklet were designed to create hands-on activities and a fun learning environment for the teaching of mathematics to the students. This booklet contains the "Math Academy--Dining Out! Explorations in Fractions, Decimals, and Percents," which teachers can use…