How can students achieve an understanding of multiplication that allows them to go beyond recall to explain their thinking? Author and mathematics education professor Juli Dixon introduces a program that teachers can seamlessly integrate into existing mathematics instruction. Learn six tactics to help you shift from an anxiety-producing,…

The purpose of this mixed-methods study was to measure the impact of a sequential use of manipulatives and visual models on third-grade students' multiplication fluency, math attitudes, and fact retention. According to results of this study, there was significant evidence that the students who gained a conceptual understanding of multiplication…

This article explores the role that gestures play in the development of mathematical understanding. Using Pirie Kieren's (1994) notion of image making and Lunney Borden's (2011) idea of verbing mathematics, we share two examples of how students respond to teacher requests to demonstrate what they know about arrays.

Developing multiplicative reasoning is an important milestone for elementary school students, which influences their learning of later mathematical concepts (Hackenberg and Tillema 2009). For children to conceptually understand multiplication, one should move beyond merely counting by ones to dealing with composites (twos, fives, etc.) and other…

The reduced interest of students in learning mathematics and consider mathematics to be a difficult subject to become a serious problem in Indonesia, especially in one of the provinces in Indonesia, namely in Lampung. The purpose of this study was to determine the effectiveness of the demonstration method assisted by Multiplication Board props to…

Multiplicative reasoning is essential for students' engagement with various mathematical concepts. Although the field's understanding of children's multiplicative concepts has grown over the past 30 years, relatively few studies have examined the development of multiplicative concepts with whole numbers, and even fewer have studied this phenomenon…

The purpose of this action research was to evaluate the implementation of technology integration with multiplication concepts (i.e., repeated, arrays, and decomposing numbers) for struggling third grade mathematics students. This study incorporated the use of virtual manipulatives and student think-aloud recordings to measure students' conceptual…

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…

"That was the day I decided I was bad at math." Countless times, preservice and in-service teachers make statements such as this after sharing vivid memories of learning multiplication facts. Timed tests; public competitive games, such as Around the World; and visible displays of who has and has not mastered groups of facts still…

The Common Core State Standards for Mathematics (CCSSM) call for an in depth, integrated look at elementary school mathematical concepts. Some topics have been realigned to support an integration of topics leading to conceptual understanding. For example, the third-grade standards call for relating the concept of area (geometry) to multiplication…

Formative instruction on multiplication primarily focuses on rote memorization. This leads to factual fluency, but also develops a narrow view of multiplication and hinders the development of conceptual understanding. Theory and research recommend the concurrent development of conceptual understanding and factual fluency during the initial stages…

This study presented sets of 15 multiplication facts to each of 4 third-grade participants. The items were presented by an iPod each session three times at three different time delays. When mastery was achieved on a set (80% correct across 3 consecutive sessions), the participant moved on to a new set. Generalization probes were administered…

This paper is a report on the results of a 3-year teaching experiment conducted in Ithaca, New York, introducing students to the concepts of multiplication, division, and ratio as a trio, and to ratio and proportion in a project-based curriculum with heterogeneous grouping. Fractions were introduced as a subset of ratio and proportion. The paper…