The role of mathematical modelling pertains several disciplines, both STEM and non-STEM, and various fields: education, academy, work, everyday and social life. Despite its importance, it is not uncommon to see university students facing difficulties with the use of Mathematics to create models, even when mathematical entities that play a role in…

Math anxiety is widely considered a potential barrier to success in STEM. Current thinking holds that math anxiety is directly linked to avoidance of and underperformance in STEM domains. However, past evidence supporting these claims is limited in important ways. Perhaps most crucially, it is possible that math anxiety predicts STEM outcomes…

The historical, traditional mathematics classroom of students sitting in rows receiving information from the teacher and working individually was still prevalent in the 21st century. Many teachers had resorted to student-centered activities to engage passive students, but the minimal progress of math achievement of United States students denoted a…

In this methodological paper, I present an enactivist approach to study how a student becomes coherently aware within a mathematics classroom, observing on the basis of my own observations of the learning of the students, acknowledging myself as part of the context, engaging with features of what I am seeing, demonstrating how through the…

Realistic Mathematics Education (RME) relies on the pedagogy of guided reinvention, in which opportunities for learning are created through the teacher's orchestration of whole-class mathematical discussion towards a specific goal. However, introducing an RME approach to students who are accustomed to traditional teaching requires a substantial…

Background: Many students solving quantitative problems in science struggle to apply mathematical instruction they have received to novel problems. The few students who succeed often draw on both their mathematical understanding of the equation and their scientific understanding of the phenomenon. Understanding the sensemaking opportunities…

Symbols are a cornerstone of the written language of mathematics and mathematical sciences. However, variations in their use pose a constant challenge to students. This paper reports data from first year undergraduate students studying mathematics, statistics and/or physics collected using surveys and interviews. It became clear that multiple uses…

Several new approaches to calculus in the U.S. have been studied recently that are grounded in infinitesimals or differentials rather than limits. These approaches seek to restore to differential notation the direct referential power it had during the first century after calculus was developed. In these approaches, a differential equation like dy…

Based on an experiment carried out with 10- to 11-year-old pupils, this paper questions the place of imagination in a class activity using the history of mathematics. The study focuses on three groups of pupils who were offered three variants of the same activity based on base-60 counting (our time measurement system inherited from the…

Inquiry into the teaching and learning of mathematics is a central aspect of the work of both the mathematics teacher and the mathematics education researcher, yet there are profound differences between the practices and processes underlying educational inquiries within each community. These differences are known to hinder implementation of…

The study explored the verb clauses and thematic development evident in curriculum materials and in transcripts of teachers planning lessons using the materials. A central argument is that though teacher characteristics influence the ways they plan lessons with curriculum materials, the materials themselves influence teachers' planned lessons via…

The goal of this note is to obtain the area enclosed between a parabola and two tangent lines using visual arguments. The first step that we have to follow, in order to do that, is noticing that the area between a parabola and a tangent line only depends on the leading coefficient of the quadratic function of the parabola. Finally, the…

With mathematics education dominated by practices of standardized test alignment, the quest for mathematical understanding is adrift despite so much talk about the importance of STEM subject matters. To add to the confusion there has long been worries among educators about any curricular programs or instructional practices that can be labeled…

This study is an investigation of the possible relationship between clinical interview skills and teacher noticing. In a multiple case study, video-recordings of pre-service teachers' (PSTs') mathematical clinical interviews and their written critiques of a mathematics lesson were examined using qualitative content analysis. Findings suggest that…

Parents and caregivers can use the activities in this report to help youth learn to solve algebra problems using different strategies. Knowing different strategies for solving algebra problems may help your child approach algebra problems with confidence. Children could apply the most appropriate strategy for a particular problem or could try a…