The purpose of this study was to explore the variations in students' achievement on computational fluency assessments and variations in strategies for solving computation problems. Computational fluency was defined as a student's ability to compute flexibly, accurately, efficiently, and appropriately. Seven- and eight-year-old students completed…

In that current study, pattern conversion ability of 25 pre-service mathematics teachers (producing figural patterns following number patterns) was investigated. During the study participants were asked to generate figural patterns based on those number patterns. The results of the study indicate that many participants could generate different…

The issue of this article is to identify and discuss what conditions may be necessary to build into tasks to make it likely for students to be involved in an algebraic Learning Activity inspired by Davydov. Data from a pilot study was used in which a group of students (N = 28) in grade 1 (7-year-olds) were invited to participate in discussions and…

A mathematical investigation (MI) encapsulates the reform movement in mathematics education by addressing content and process simultaneously and providing a novel opportunity for students to develop thinking skills and good mental habits. However, introducing MI to teachers and students who are used to routinised teaching approaches and…

In this report we examine students' perceptions of the implementation of carefully designed curriculum materials (called modules) in linear algebra courses at three different universities. The curricular materials were produced collaboratively by STEM and mathematics education faculty as members of a professional learning community (PLC) over…

The analysis of pre-service teachers' concept images can provide information about their mental schema of fractal dimension. There is limited research on students' understanding of fractal and fractal dimension. Therefore, this study aimed to investigate the pre-service teachers' understandings of fractal dimension based on concept image. The…

This study is part of a larger study investigating the subject matter knowledge and pedagogical content knowledge of Hong Kong prospective mathematics teachers, the relationship between the knowledge of algebraic operation and its inverse, and their teaching competency. In this paper, we address the subject matter knowledge and pedagogical content…

We analyze the results of a study conducted for the purpose of assessing the viability of an alternative starting point for teaching fractions. The alternative is based on Freudenthal's insights about fraction as comparison. It involves portraying the entities that unit fractions quantify as always being apart from the reference unit, instead of…

This paper reports the findings of an evaluative study of an initiative, in its sixth year of implementation, enhancing the learning and teaching of mathematics in 20 disadvantaged secondary schools in KwaZulu-Natal (KZN), South Africa, twenty years after democracy. Findings highlight the importance of initial and ongoing professional development…

Many teacher education programs are criticized for their failure to prepare pre-service teachers to utilize and transfer their knowledge of content and educational principles into authentic classroom teaching. Studies also consistently report that pre-service teachers' ability to identify what is noteworthy about a mathematics classroom situation…

In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students' intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are able…

While it is well recognized that students are prone to difficulties when performing linguistic-to-algebra translations, the nature of students' difficulties remain an issue of contention. Moreover, the literature indicates that these difficulties are not easily remediated by domain-specific instruction. Some have opined that this is the case…

Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After…

Professional development (PD) programs often evaluate their impact on teachers' learning by assessing teachers either individually or in groups. The goal of this paper is to illustrate the variety of paths teachers might follow as a result of working in groups within online PD settings. Data are drawn from a PD program for grades 5-9 mathematics…

Students start to memorize arithmetic facts from early elementary school mathematics activities. Their fluency or lack of fluency with these facts could affect their efforts as they carry out mental calculations as adults. This study investigated participants' levels of brain activation and possible reasons for these levels as they solved…