Felix Klein's notion of "double discontinuity" between university mathematics and secondary school mathematics has persisted in mathematics teacher education. Situating this study in Hong Kong, we investigated three prospective secondary teachers' experiences in higher education and secondary mathematics classrooms, including their…

The current meta-analysis quantifies the average effect of worked examples on mathematics performance from elementary grades to postsecondary settings and to assess what moderates this effect. Though thousands of worked examples studies have been conducted to date, a corresponding meta-analysis has yet to be published. Exclusionary coding was…

This paper reports on concept images of 38 secondary school mathematics prospective teachers, regarding the evenness of numbers. Written assignments, individual interviews, and lesson transcripts uncover salient, erroneous concept images of even numbers as numbers that are two times "something" (i.e., "2i" is an even number),…

This paper explains teaching modern geometry for schools using software called Surfer and converting the algebraic surfaces into Batik motifs as one example of teaching mathematics with the integration of STEAM. Typical algebraic surfaces known in schools were, for example, cylinders and spheres which are identified as traditional geometry in this…

The transition from school to university is a challenging process for many students which is reflected in high dropout and low examination success rates during the first year at university. Qualitative studies have found hints that students' beliefs play an important role during the transition. Due to their dialectic nature with cognitive as well…

The use of the algebraic method for solving word problems is a challenging topic for secondary school students. Students' difficulties are usually associated with extracting the problem's network of relationships between quantities and with formalizing these relationships into algebraic language in a problem model. Both sources can coexist and…

This article presents a task providing college students opportunities to build on their high school knowledge of trigonometry to explore parametric equations and inverse trigonometric relationships within a contextual learning ladder problem.

Work in teacher noticing has captured to what extent teachers notice students' thinking on paper and pencil tasks and technology tasks, yet no one study has considered how the same group of teachers notices across task types. This study used Jacobs et al.'s (Journal for Research in Mathematics Education, 2010, 41(2), pp: 169-202.) professional…

The study discussed here aims to describe students' understandings of the definition of a mathematical function, which was achieved through a pilot case study of clinical interviews with four participants -- two ninth graders and two twelfth graders. The participants were recruited from the same urban public high school in the northeast of the…

For the first time in 32 years, the national average scale score in mathematics dropped by seven points across the country in grades four and eight, according to the latest results of the National Assessment on Educational Progress (NAEP). The 2022 results in mathematics were staggering, in which "math performance fell for the first time in…

This study investigated in-service teachers' conceptualization of the pure imaginary number, within the Cartesian form, "a" + "ib" where "a" and "b" are real numbers and "i" is the imaginary unit. As part of a larger design-based research study, in which a professional development (PD) program was…

Providing students with opportunities to build, and test and revise ideas, can help them develop critical thinking and problem-solving skills. In this article, the authors describe how core measurement and geometry concepts were embedded within a "Model It!" task. They replicate an industry-based, interdisciplinary problem, but only…

In Ireland, Initial Teacher Education [ITE] standards require all teachers to possess an adequate level of numeracy themselves in order to teach for numeracy learning across the school curriculum. This paper reports on a study that investigated 204 pre-service post-primary teachers' numeracy capabilities. Analysis of questionnaire data from…

In this "Perspective on Practice," we describe an application of recommendations made in "Formative Assessment in Secondary ­Mathematics: Moving Theory to Recommendations for Evidence-Based Practice" (Kenney et al., 2022), which was recently published in this journal. The authors made recommendations for mathematics teacher…

The study evaluates the Mythematix prototype, an innovative adaptive e-learning system designed specifically to enhance secondary school students' understanding and proficiency in mathematics. Utilizing a mixed-methods approach, it combines qualitative and quantitative research methodologies to thoroughly assess students' perceptions and…