Cover, Copy, Compare (CCC) has been shown to be an effective intervention at improving single-digit multiplication fluency within the academic intervention literature. The application of the three-term contingency trial embedded within CCC provides the intervention with several key components of evidence-based interventions. Given that teachers…

The learning of basic facts, or the sums and products of numbers 0-10 and their related differences and quotients, has always been a high priority for elementary school teachers. While memorization of basic facts has been a hallmark of elementary school, current recommendations focus on a more nuanced development of fluency with these facts.…

The subject of this study is to investigate if, and to what extent the performance of third-grade students' multiplication fact proficiency differs in a hybrid learning setting as compared to in-person instruction. These differences were questioned by researching if there was a change in student proficiency due to the instructional modality, if…

While an abundance of evidence-based mathematics interventions are available to support students' mathematics fluency, research suggests that they are not often implemented within schools. Moreover, national data suggests that most students in the United States are not meeting grade level expectations in mathematics. This underperformance coupled…

This formative study of a multiplicative reasoning (MR) intervention explored the intervention's potential for improving the ability of third-grade struggling students' ability to reason with multiplicative concepts and procedures. The feasibility of the study was examined in a school setting before a randomized control trial was conducted.…

This paper explores Year 3 Irish students' problem-solving strategies when responding to a skyscraper growing pattern problem. Students' strategies reveal their understandings of multiplicative thinking, pattern, and algebraic reasoning. The version of the growing pattern lesson was that a 'teaching through problem solving' approach was taken,…

The researchers conducted a qualitative case study to describe the teaching and learning of a third grade student with a learning disability as he worked on multiplicative tasks with a tutor. The student's strategies, at participatory and anticipatory levels of understanding, were analyzed to inform instructional decisions we made to support the…

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 shift from additive to multiplicative thinking is challenging for students. A professional learning program was developed that focused on an identified area of need by teachers, namely multiplicative thinking. Program content focused on concepts underpinning multiplicative thinking, pedagogical approaches, challenging tasks, and application to…

Early years mathematics textbooks are support material for teachers and learners as they contain visual representations which communicate and clarify mathematical concepts. In this paper, we report on the types and functions of visual representations of multiplication and division in South African early years mathematics textbooks. There seems to…

The Akita approach is the guideline in learning that responds to rapid changes in the 21st century. This research aimed to determine the effectiveness of learning management based on the Akita approach in accordance with the criteria efficiency of 75/75 and to explore the index of effectiveness of learning management pursuant to the Akita…

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.

The authors define two mathematical cognitive verbs which are fundamental to the development of mathematical thinking and reasoning. They distinguish between 'describing' and 'explaining' in relation to doing mathematics, rather than using them interchangeably.

The importance of fostering in students the requisite language to understand what is being communicated and how to communicate their understanding requires educators to conceptualize themselves as teachers of language and content. It is possible to engage in activities of the mathematics classroom and through that participation engage in language…