The study investigated the impact of using Autograph software as a tool in teaching and learning of quadratic functions on gender performance in core Mathematics for Senior High School (SHS) students in Ghana. Non-equivalent quasi-experimental design was used. The population was all second year students in the Komenda-Edina-Eguafo-Abrem (KEEA)…

The development of urban students' mathematical proving ability is a goal of several curricula frameworks, including some located in the southern hemisphere. However, in achieving this goal, most curriculum frameworks do so from a Western worldview, which is characterized by competition and the role of the individual. The purpose of this study was…

A growing body of evidence suggests that non-symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non-numerical magnitudes not only share analog format but also form part of a general magnitude system raises…

This paper proposes a philosophical approach to the mathematical engagement involving students and a digital tool. This philosophical proposal aligns with other theories of learning that have been implemented in mathematics education but rearticulates some metaphors so as to promote insight and ideas to further support continued investigations…

The study investigated the effects of using the problem of the week in teaching (POWT) on teachers' learning and changes in knowledge and teaching skills, in algebraic thinking and algebra tasks, in the setting of a university mathematics education graduate program. The graduate students participated in learning POWT weekly in a mathematics…

The authors examined the implementation of written reflections in a Grade 4 mathematics classroom over the course of 8 weeks. Students in this case study engaged in a workshop modeled after Calkin's Writers' Workshop and within this workshop the use of writing as a reflective tool in mathematics was introduced. The authors explore how students…

This study investigates how students in England and Shanghai understand linear function. Understanding is defined theoretically in terms of five hierarchical levels: Dependent Relationship; Connecting Representations; Property Noticing; Object Analysis; and Inventising. A pilot study instrument presented a set of problems to both cohorts, showing…

This article describes a preservice teacher's imaginative exploration of completing the square through a process of reasoning and sense making. She recounts historical perspectives and her own discoveries in the process of completing the square. Through this process of sense making, she engaged with the content standard of completing the square to…

Price comparison is a functional mathematics skill involving purchasing, use of money, and budgeting, with the goal of selecting the best deal based on a person's financial resources (Browder, Spooner, & Trela, 2011). The operational definition of "price comparison" is to compare the magnitudes of the price numbers and then select…

This article draws on semi-structured, task-based interviews to explore secondary teachers' (N = 7) understandings of inverse functions in relation to abstract algebra. In particular, a concept map task is used to understand the degree to which participants, having recently taken an abstract algebra course, situated inverse functions within its…

This article reports on using open-response questions to reveal the level of, and change in, conceptual understanding of a small sample of Grade 11 learners of trigonometry in a South African high school. The investigation used learner response sheets in a regular classroom with the teacher as researcher. Combining the idea of concept image and…

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students' learning during graphing functions. However, the display of graphs of functions that students sketched by hand may…

The authors recently conducted a randomized controlled trial that showed a significant impact of teachers' lesson study, supported by mathematical resources, on both teachers' and students' understanding of fractions. The research and mathematical resources are described in the second part of this article. First the authors examine some of the…

Students in Norway and other countries experience vectors as a difficult topic. Four young skilled climbers, who all did well in mathematics at school, participated in the Vector Study (VS). They participated for free and each lesson lasted until the students decided it was over. The idea was to investigate how climbing may function as a basis for…