The student's criterion for being diagnosed with MLD (Mathematics Learning Disabilities) can be classified as low arithmetic skills and poor working memory. The goal of this research is to understand students' process of thinking through the Polya stages when tackling arithmetic problems, as it has been expounded by Dr. Polya For students who have…

This qualitative descriptive study was designed to address the deficiency in early math literacy skills, specifically those related to multiplication fact fluency, in early elementary students. More specifically, this study was designed to gather research and data to provide understanding of the mathematical curriculum instruction used in…

Mathematics learning within the context of videogames is an increasingly important area of study that has not yet fulfilled its promise of powerfully contextualized and transformative learning. This research served to begin pushing the boundaries of the field by relying upon cutting edge mathematics education research on fractions and the best…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

After being introduced to the distributive law in meaningful contexts, students need to extend its scope of application to unfamiliar expressions. In this article, a process model for the development of structure sense is developed. Building on this model, this article reports on a design research project in which exercise tasks support students…

In many Canadian schools the acronym BEDMAS is used as a mnemonic to assist students in remembering the order of operations: Brackets, Exponents, Division, Multiplication, Addition, and Subtraction. In the USA the mnemonic is PEMDAS, where 'P' denotes parentheses, along with the phrase "Please Excuse My Dear Aunt Sally". In the UK the…

Children learn to find answers when multiplying two whole numbers (e.g., 3 × 7 = 21). To this end, they may repeatedly add one number (e.g., 7 + 7 + 7 = 21). But what meanings do they have for multiplication? The authors address this issue while sharing an innovative, playful task called Please Go and Bring for Me (PGBM). Drawing on the…

A large number of students demonstrate difficulty acquiring and retaining math facts highlighting the need for early math intervention. This study used a single-case cumulative acquisition design to examine the differential effectiveness and efficiency of three drill interventions, incremental rehearsal (IR), incremental rehearsal with visual…

Curriculum-based measurement (CBM) tools are increasingly administered through technology-based modalities such as computers and tablets. Two studies were conducted to examine whether students perform similarly on paper-based and tablet-based math fact probes. Ten students completed 1-min addition or multiplication math probes using a single-case…

Elementary standards include multiplication of single-digit numbers and students advance to solve complex problems and demonstrate procedural fluency in algorithms. The ability to illustrate procedural fluency in algorithms is dependent on the development of understanding and reasoning in multiplication. Development of multiplicative reasoning…

This study investigated preservice middle school mathematics teachers' (PSTs) understanding of proportional and nonproportional relationships and their abilities to differentiate these relationships from each other. The PSTs' abilities to interpret and represent proportional and nonproportional situations and solution strategies were also…

In this chapter, I propose a stance on learning fractions as multiplicative relations through reorganizing knowledge of whole numbers as a viable alternative to the Natural Number Bias (NNB) stance. Such an alternative, rooted in the constructivist theory of knowing and learning, provides a way forward in thinking about and carrying out…

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…

The number sequences describe a hierarchy of students' concepts of number. This research uses two defining cognitive structures of the number sequences--units coordination and the splitting operation--to model middle-grades students' abilities to write linear equations representing the multiplicative relationship between two unknowns. Results…

This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…