This paper is a practical how-to guide to help you start using active learning or to have greater success and more fun with it. We categorize active learning techniques as Think, Pair, Share, Composite, Group, Move, or Lead and discuss how to implement activities in each category, along with advice on creating engaging, effective, and equitable…

Proof comprehension is an important skill for students to develop in their proof-based courses, yet students are rarely afforded opportunities to develop this skill. In this paper, we describe two implementations of an activity structure that was developed to give students the opportunity to engage with complex proofs and to develop their proof…

In a pre-service mathematics methods class I taught, in which we mathematized political districting (first horizontally, then vertically), student questions led to engaging mathematics, in particular, the development of a new number sequence.

We describe the components and implementation of an activity for multivariable calculus featuring applications to the field of chemistry. This activity focuses on the isobaric thermal expansion coefficient found using partial differentiation of the volume of an ideal gas with respect to temperature as pressure is held constant. Broader goals of…

In this paper, we draw on our recent research to inspect again some of the theoretical perspectives we have been using to analyze data and to characterize teaching-learning in university settings. We focus particularly, within a sociocultural perspective on Activity Theory and the construct the "Teaching Triad," seeking to embed the…

Academic institutions dedicate a substantial effort to ensure the academic success of their students. At the course level, teachers recommend learning paths (RLPs) for students to guarantee the achievement of their learning outcomes. In terms of performance, these kinds of approaches are deemed more effective than others based uniquely on…

Creativity and collaboration are key components of a mathematician's work, and thus in the preparation of future mathematicians, undergraduate mathematics courses should aim to develop students who can effectively work collaboratively and creatively with one another. Despite this need, research on mathematical creativity has primarily investigated…

This paper details an integrated inquiry-based mathematics and science method course for preservice teachers designed around STEM problem-based learning. It documents how problem-based learning (PBL) activities supported PSTs' envisioning of equitable approaches for diverse children. The overarching research question was: "How did preservice…

This study aims to prepare an educational program based on integrating Science, Technology, Engineering and Mathematics (STEM) to develop students' mathematical thinking skills. It also aims to provide proposals that could have a major role in rebuilding some of the general features on which mathematics curricula can be built according to the STEM…

This article presents a reflection on a teaching experience involving the use of the Brügner tangram, an interesting but little-known manipulative material. It details an activity conducted as part of an undergraduate mathematics education course for prospective primary school teachers. The main objective of this paper is to present the…

In this dissertation, I report results from a study that investigated the impact of students' engagement in a series of tasks in an introductory proof course that was designed to stimulate their learning of reading strategies to support their comprehension of mathematics proofs. Specifically, I investigated the impact of the design of five…

Students encounter difficulties in understanding integral because the concept of integral requires the usage of theorems, formulas, daily life practices, and interdisciplinary approaches. From this point of view, in this study we examine the effects of a teaching process consisting of modelling activities on understanding the definite integral…

Integration is an important, albeit difficult, goal of science and mathematics education. This paper presents a framework and a research design proposal to identify preservice teachers' (PSTs) integration performance of science and mathematics (IPoSM). It also presents the classification of PSTs' level of integration in each phase of a…

This introduction presents Active Learning Methodology, surveying its history, main existing tools and supporting evidence, with an emphasis on mathematics and higher education, in particular engineering studies. This work is part of the DrIVE-Math project, developing innovative mathematical teaching strategies in engineering studies.

We believe that developing cultural competencies can help students learn mathematics and conversely that learning mathematical content can help students learn about themselves and others. Using frameworks introduced by Rendón (2009) and Gutiérrez (2018), we present a five-part bundle of activities for undergraduate differential equations course…