This study examined a 6-week intervention in which fourth grade students either played fluency games or used pictorial flashcards to develop fluency with their basic multiplication facts. Students who played fluency games showed more growth than the pictorial flashcards, but an analysis of variance showed that there was no statistically…

Responsive teaching requires teachers to have knowledge of children's thinking. Prospective teachers need support in developing such knowledge because they often enter teacher preparation programs with fragile mathematical knowledge and anxiety about teaching mathematics to children. We designed a learning trajectory-based intervention to support…

This study aims to develop a conceptual framework regarding practitioner knowledge and describe how one mathematics teacher generates her practitioner knowledge based on the framework. The characteristic of this framework is a combination of static and dynamic aspects of knowledge based on the teacher's perception and interpretation. The research…

The aim of this study was to examine the proportional reasoning skills of seventh-grade students before and after the implementation of STEM activities involving proportional and non-proportional relationships. Case study, one of the qualitative study methods, was used in the research. The data for the study was obtained from eight students. Seven…

The aim in the current study is to examine the conceptualizations of zero in arithmetic operations among students with learning disabilities (LD) and no learning disabilities (N-LD). The similarities and differences in the understandings of students with LD and N-LD of zero in arithmetical operations will be discussed. The study is a multiple case…

Fluent recall of basic facts is essential to the development of more complex math skills. Therefore, failure to develop fluency with basic facts may impede the development of these skills. The present study used a between-group experimental design to investigate whether a basic facts fluency program, implemented within a self-regulated learner…

Two-hour long developmental teaching interviews were conducted with each of 14 sixth grade students, ages 11-12. The purposes of the interviews were to investigate how students solved arrangement problems (APs), and how their solutions of these problems differed from their solution of Cartesian product problems (CPPs). The 14 students represented…

Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…

The purpose of this study is to explore preservice teachers' (PTs') ability to implement multiple strategies using standard algorithms and alternative strategies and to investigate their conceptual knowledge of decimal operations. There were 37 PTs who participated in this study, all of whom attended a mathematics course in the K-8 Teacher…

Skills and understanding of operations with negative numbers, which are typically taught in middle school, are crucial aspects of numerical competence necessary for all subsequent mathematics. To more swiftly and coherently develop the field's understanding of how to foster this critical competence, we need shared measures that allow us to compare…

In this study, we explored the insights that Chinese primary mathematics teachers gained into their students' mathematical understanding from using classroom assessment techniques (CATs). CATs are short teacher-initiated targeted assessment activities proximate to the textbook, which teachers can use in their daily practice to make informed…

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…

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…

In this article, we use a two-dimensional assessment to examine the experimental impacts of a mathematics learning trajectory-oriented formative assessment program on student strategies for problems involving multiplication and division. Working from the theory that the development of students' multiplicative reasoning involves improvements in…

This study examined whether students were reaching automaticity with single digit multiplication facts. A fourteen question interview was used to collect data. The first three questions asked the student basic information about themselves and their current math teacher. The next seven questions were math facts. The math facts chosen for the…