Instruction of multiplication facts has been and continues to be an essential part of mathematics curriculum for students in the intermediate grades with the majority of initial instruction at third grade. Teachers often comment that this is a topic that students struggle to master and that they frequently use fluency drills and fact flash cards…

The literature has shown that preservice elementary school teachers (PSTs) struggle to adequately attend to a number's multiplicative structure to determine divisibility. This study describes an intervention aimed at strengthening preservice and in-service teachers' procedural knowledge with respect to using a number's prime factorization to…

Reports show that only 40% of 4th-grade students are proficient in math and American students are failing to demonstrate proficiency in key areas of mathematics (National Center for Educational Statistics 2011). Improving students' fluency of basic math multiplication facts has been recommended as a way to increase math proficiency…

This article examines the importance of developing the notion of place value as a rate of ten. In exploring how to nurture this concept, the author looks at the role of the language of value, the problem types of multistep multiplication and addition along with measurement division, each with ten as an organizing unit, as well as strategically…

Mathematical argumentation and proof has long been identified with algebraization. Much literature discusses the relationship between the two, but with little specificity on how particular semiotic features in argumentation relate to coordination in early algebra. Further, there is a particular lack of research on this topic in the…

A multiple-baseline across participants design was used to investigate the effect of the Cover-Copy-Compare (CCC) intervention on multiplication-fact fluency for students with emotional and behavioral disorders (EBD). Although CCC is a well-researched intervention for mathematics, limited research has been conducted with students with EBD even…

Intending to improve the teaching and learning of the notion of mathematical proof this study seeks to uncover the kinds of flaws in postgraduate mathematics education student teachers. Twenty-three student teachers responded to a proof task involving the concepts of transposition and multiplication of matrices. Analytic induction strategy that…

In this paper we analyze the outcomes of a design experiment that sought to improve the multiplicative reasoning of 12-13 year-old learners across two schools in a South African context of low performance. Using a hybrid theoretical base in Realistic Mathematics Education, variation theory and analogical reasoning, a short-term intervention…

Competence with fractions is foundational to acquiring more advanced mathematical skills. However, achieving competency with fractions is challenging for many students, especially for those with mathematics learning difficulties who often lack foundational skill with whole numbers. Teaching fractions is also challenging for many teachers as they…

In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3 = 8), subtraction (e.g., 5 - 3 = 2), and multiplication (e.g., 5 × 3 = 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All…

This small study sought to determine students' knowledge of multiplication and division and whether they are able to use sets of bundling sticks to demonstrate their knowledge. Manipulatives are widely used in primary and some middle school classrooms, and can assist children to connect multiplicative concepts to physical representations.…

We examined the type of errors on multiplication and division computation problems of 326 rising fifth graders enrolled in four elementary schools in Northern Portugal. We further examined whether there was a difference in the number of errors across age and whether there was an association between students' performance on number knowledge and…

Mathematics teachers frequently provide concrete manipulatives to students during instruction; however, the rationale for using certain manipulatives in conjunction with concepts may not be explored. This article focuses on area models that are currently used in classrooms to provide concrete examples of integer and binomial multiplication. The…

This study analyzed the methods used to teach the multiplication of fractions in Turkish and American textbooks. Two Turkish textbooks and two American textbooks, "Everyday Mathematics" (EM) and "Connected Mathematics 3" (CM), were analyzed. The analyses focused on the content and the nature of the mathematical problems…

How do students cope with and make sense of polysemy in mathematics? Zazkis (1998) tackled these questions in the case of 'divisor' and 'quotient'. When requested to determine the quotient in the division of 12 by 5, some of her pre-service teachers operated in the domain of integers and argued for 2, while others adhered to rational numbers and…