Background: Specialized content knowledge (SCK) is a type of mathematical content knowledge specifically needed for teaching. This type of knowledge, although serving as a critical component for preservice teacher education, is often challenging to develop with preservice elementary teachers (PTs). The purpose of this study is to investigate PTs'…

Deaf students face problems in mastering multiplication facts. This study aims to identify the effectiveness of Magic Finger Teaching Method (MFTM) and students' perception towards MFTM. The research employs a quasi experimental with non-equivalent pre-test and post-test control group design. Pre-test, post-test and questionnaires were used. As…

To understand relationships between students' fractional knowledge and algebraic reasoning in the domain of equation writing, an interview study was conducted with 12 secondary school students, 6 students operating with each of 2 different multiplicative concepts. These concepts are based on how students coordinate composite units. Students…

This case study examined how a teacher's choice of numbers used in tasks designed to foster students' construction of a scheme for reasoning in multiplicative situations may afford or constrain their progression. This scheme, multiplicative double counting (mDC) is considered a significant conceptual leap from reasoning additively with units of…

This study examined pre-service elementary teachers' change in their understanding of fraction operations while taking a mathematics methods course. Specifically, their explanations and justifications for common algorithms for multiplication and division of fractions were coded using an existing framework (SOLO; Biggs, 1999) for the assessment of…

This project built on previous research showing that insufficient numbers of children reach expected levels of achievement in mathematics. Maori, Pasifika, and students from lower decile schools are particularly disadvantaged. Young children should be given equitable opportunities to develop their mathematical thinking, particularly in all…

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…

Many learners struggle to make the transition from addition and subtraction to multiplication and division, which hampers further progress in mathematics. In this article, I present a case study of one learner who struggled to attain fluency in multiplication by seven. The purpose of this study was to identify and explain how previous…

This study reports the case of a patient (AG) whose main calculation problem was with multiplication that was severely affected at all levels including that of conceptual knowledge. In contrast AG's problems with addition, subtraction and division were much less conspicuous and just involved the use of procedures. For all these latter operations,…

Of the four mathematical operators, division seems to not sit easily for many learners. Division is often described as "the odd one out". Pupils develop coping strategies that enable them to "get away with it". So, problems, misunderstandings, and misconceptions go unresolved perhaps for a lifetime. Why is this? Is it a case of "out of sight out…

One of the challenges of learning ratio concepts is that it involves intensive quantities, a type of quantity that is more conceptually demanding than those that are evaluated by counting or measuring (extensive quantities). In this paper, we engage in an exploration of the possibility of developing reasoning about intensive quantities during the…

Experts think in patterns and structures using the specific "language" of their domains. For mathematicians, these patterns and structures are represented by numbers, symbols and their relationships (Stokes, 2014a). To determine whether elementary students in the United States could learn to think in mathematical patterns to solve…

Designing and developing games for learning is a difficult endeavor. Educational game designers must not only make an engaging and motivating game, but must also ensure that learning takes place as a result of gameplay. Educational researchers have sought to define design principles in order to lessen the difficulty involved with game design. In…

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…

Developing pre-service teachers' (PSTs') knowledge of pedagogical practices can be particularly challenging within university classrooms. Teacher educators are well placed to provide PSTs with theoretical perspectives on pedagogical practices; what is particularly challenging, however, is linking theory with practice and developing PSTs' breadth…