In XVII century, presumably between 1637 and 1638, with a note in the margin of Diophantus' "Arithmetica", Pierre de Fermat stated that Diophantine equations of the Pythagorean form, x[superscript n] + y[superscript n] = z[superscript n], have no integer solutions for n > 2, and (x, y, z) > 0. Of this statement, however, Fermat…

Many students struggle to grasp the concept of limits, leading to persistent learning obstacles. This study employed a didactical design research (DDR) approach involving 56 mathematics education students at Universitas Khairun, divided into two groups. Data from tests, interviews, and teaching interventions revealed three key obstacles:…

This study reviews the literature on error patterns in mathematics among students with mathematics difficulty. We analyzed and synthesized the findings from 17 studies, focusing on the characteristics of error analysis studies, the mathematics topics examined, and the specific error patterns identified. The results revealed the following: (a) the…

In this paper, we describe our extension of the action, process, object, schema (APOS) theory to capture the complex interplay of mathematics and physics. We do this in the context of the 2D heat equation. We describe a hypothetical learning trajectory of the 2D heat equation, a preliminary genetic decomposition that stresses the conceptual…

It is agreed that algebra has an important role in physics, particularly through handling symbols. A lot of previous research has focused on how mathematics is used in physics from perspectives where mathematics is taken for granted, and not addressing potential differences of mathematics in the physics classroom and in the mathematics classroom.…

Authors Chepina Rumsey and Jody Guarino continue their advocacy for math-curious classrooms, building on their work in Nurturing Math Curiosity With Learners in Grades K-2. They argue that curiosity not only engages students but also invigorates them to reason and develop a conceptual understanding of grade-level mathematical ideas. Dive into…

This study examined whether elementary children's executive functions (EFs) moderated associations between observed autonomy-supportive and controlling parenting during math homework help and children's math achievement and anxiety 1 year later. In total, 170 parent-child dyads completed a second-grade assessment (M[subscript age] = 8.02), and 111…

A teacher of mathematics knows mathematics as a teacher and as a mathematician. Whilst the existing research on teacher knowledge contributes to our understanding of the ways of knowing mathematics as a teacher, little is known about ways of knowing mathematics as a mathematician. Guided by the conceptual framework of mathematical practices (MPs)…

Functions and graphs are fundamental mathematical concepts in mathematics and are vital to helping students comprehend the relationship between variables and other advanced topics in higher-level mathematics. Research has shown that students continually possess misconceptions and inaccurate thinking about functions and function representations.…

This study investigated the impact of Process-Oriented Guided Inquiry Learning (POGIL) approach in the proficiency level of Grade 9 students along quadratic functions. It employed a quasi-experimental design with a qualitative approach. Two groups with 40 students each from Saint John Berchmans High School Incorporated were considered as the…

The stereotype of math being male-typed prevails among most Western societies. This math-gender stereotype is associated with math-gender misconceptions, which are scientifically incorrect specific theories about girls' math abilities (e.g., girls inherently think less systematically and thus have less math ability than boys). Teachers may…

The aim of this pilot study is to evaluate the relevance of the use of history in mathematics education. This paper presents an experiment carried out in France with sixth-grade students (n=108) in which an ancient number system is used, an approach that is commonly suggested in French sixth-grade textbooks but has previously been unassessed.…

Attention to the disconnection between culture and mathematics has been addressed then and now (Wilder (in: Graves et al., Proceedings of the international congress of mathematicians, American Mathematical Society, 1950; Liu in Taiwan Journal of Mathematics Education, 8:79-88, 2021b). Recently, studies, workshops, and contests about an approach to…

Effective initial teacher education will develop preservice teachers' disposition towards mathematics and the teaching of mathematics, alongside their mathematical and pedagogical content knowledge. This paper reports on a case study of eight students who participated in an optional mathematics course for preservice primary teachers. Analysis of…

Mathematics plays many roles in physics and physics education. While these roles have previously been extensively discussed in the physics education research community, no systematic picture of the multifaceted considerations has yet been formed. To gain a comprehensive overview of the previous studies on the topic, we conducted a systematic…