Basic multiplication fact fluency is an expected outcome of most third grade classrooms throughout the United States. Students need to know their multiplication facts. This statement does not seem to be under question; it is more about how will students learn their multiplication facts. The purpose of this study was to investigate the use of…

This case study examined competence in two third-grade classrooms where teachers centered children's mathematical thinking in instructional decision-making. Offering a synthesis of sociocultural characterizations of competence, and drawing from a variety of data sources including classroom video, student work and assessments, and teacher…

This paper reports on 13 Grade 3 students' approaches to partitive and quotitive division word problems. Of particular interest was the extent to which students drew on their knowledge of multiplication to solve division problems. The findings suggest that developing a relationship between multiplication and division is more significant than…

This paper reports on 13 Grade 3 students' approaches to "Equivalent groups" and "Times" as "many" multiplicative word problems. The findings are part of a larger study relating to children's development of multiplicative thinking. Of particular interest was the extent to which task level of difficulty influenced…

Learning the concept of perimeter and area is not easy for students in grade 3 of primary school. A common mistake is that students think that if the area is the same, the perimeter also has to be the same. It is difficult for them to understand that for a given area, there are many possibilities of perimeter and vice versa. When student are not…

This article proposes a taxonomy of strategies for single-digit multiplication, then uses it to elucidate the nature of the learning tasks involved in multiplication. In preceding work, it has generally been assumed that much of children's strategy development is driven by changes in their general conceptual capabilities relating to number. In…