In the continual pursuit of classroom learning effectiveness, researchers and educators aim to develop strategies that improve student performance and learning. One such strategy is to create academically homogeneous environments where students are grouped into classes based on their preconceived academic ability. The research team tests this…

Despite longstanding efforts in the K-12 STEM education community to create meaningful mathematical experiences across disciplines, mathematics continues to be a siloed subject which is tracked based on ability. With an increasing number of high-achieving students enrolling in Algebra I in Grade 7 or earlier, there is a need for research on the…

This paper offers instructional interventions designed to support undergraduate math students' understanding of two forms of representations of Calculus concepts, mathematical language and graphs. We first discuss issues in students' understanding of mathematical language and graphs related to Calculus concepts. Then, we describe tasks, which are…

Epidemiological models have enhanced relevance because of the COVID-19 pandemic. In this note, we emphasize visual tools that can be part of a learning module geared to teaching the SIR epidemiological model, suitable for advanced undergraduates or beginning graduate students in disciplines where the level of prior mathematical knowledge of…

This study explores university students' understanding of the relationships between formal definitions of the limit of a function and the limit of a sequence in terms of the accumulation point in a technology-enhanced collaborative learning environment. The participants of this study are 17 prospective mathematics teachers. The data are collected…

In this paper, we assess the pedagogical approaches we employ in our US-based undergraduate mathematics courses during the COVID-19 pandemic. Our goal is to share anecdotal evidence on the use of math journals, oral exams, and learning portfolios in the synchronous online mathematics classroom. We reflect on our experience using artifacts of…

Student multimodal writing has gained attention in the teaching and learning of mathematics with the anticipation that these assignments will benefit student engagement and learning in a variety of ways. This study investigates students' perceptions of learning in a post-secondary calculus course, which contained four multimodal writing…

The goal of the paper is to pay attention to some important techniques and approaches including adequate designations as a tool for unambiguous understanding and a key to success in solving problems, vivid visual images as a mnemonic techniques, and special formulas as a universal tool for solving typical problems, when teaching medical students…

This study investigated how problem-solving videos can be used in video-mediated professional learning to support secondary preservice mathematics teachers (PMTs) in developing teacher knowledge for noticing student thinking in the context of the derivative concept in calculus. A model of the trajectory of PMTs' noticing was constructed as six…

This paper examines the Torricelli law for the flow of liquid from a small drain hole in a container. It shows how the system can be modelled using either a traditional calculus-based approach or a non-calculus step-wise computer method appropriate to the background of the student group. An experiment to measure the head of out-flowing liquid as a…

This study presents a bibliometric analysis of research on mathematics education from 1980 through 2020. The purpose of the study is to provide scientific data on the distribution pattern of mathematics education journals, the most prolific authors, countries, institutions, current research topics, potential international collaboration, and…

This research deals with a possible use of history of mathematics in mathematics education. In particular, history can be a fundamental element for the introduction of the concept of integral through a problem-centred and intuitive approach. Therefore, what follows is dedicated to the teaching of mathematics in the last years of secondary schools,…

The paradigm shift from traditional didactic instruction to technology-enriched teaching and learning environments significantly benefits learners. Educational technology can visualize abstract mathematical concepts contextually and graphically and allow learners to actively construct this knowledge. This study aims to ascertain the efficacy of a…

How should our students think about external forcing in differential equations setting, and how can we help them gain intuition? To address this question, we share a variety of problems and projects that explore the dynamics of the undamped forced spring-mass system. We provide a sequence of discovery-based exercises that foster physical and…

We describe the use of student-generated video content to assess students' engagement with, and understanding of, problem-solving skills. In this framework, students are tasked with using technology to create videos that show them working through, and explaining solutions to, challenging calculus exercises. The videos are then posted online,…