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…

The purpose of this study was to identify and characterize the pedagogical content knowledge (PCK) held by secondary mathematics preservice teachers. Task-based interviews were conducted to determine whether evidence of PCK exists in preservice teachers and, if so, what form that evidence took. Participants included preservice teachers near the…

First-year STEM students often interpret academic challenges as diagnostic of belonging. Studies demonstrate that a social-belonging intervention helps undergraduates reframe belonging uncertainty as temporary and universal. We implemented this intervention with first-year engineering majors. In Study 1 (N = 284), we analyzed data from engineering…

Females are underrepresented in all levels of physics, while a simultaneous need exists to increase the physical science workforce pipeline. A review of current literature found exposure to more advanced pSTEM courses might influence students to pursue those career-fields, however enrollment in Advanced Placement (AP) Physics remains…

Almost 70% of college students in California are required to take at least one remedial education course in mathematics or English, and of those students, only 40% continue to succeed in their educational goals of transfer or receiving a degree ("Student Success Scorecard," n.d.). Corequisite support remediation is an alternative to…

This study examines the perceptions of first-year, mathematics graduate teaching assistants (GTAs) participating in a six-week summer course designed to deepen their knowledge of collegiate mathematics teaching practices before being assigned to instruct undergraduate students in the subsequent fall semester. Through hybrid deductive-inductive…

This is an exploratory study considering instructional methods in mathematics education. The study examined misconceptions arising from selected assignments undertaken by sixty-five students. The students were attending a calculus mathematical course unit on limits of functions, in different academic areas offered at selected tertiary institutions…

In calculus courses, instructors often use the end-of-section problems in a textbook in homework assignments or other course assessments. As a result, these problems influence the teaching and learning of calculus. In this study, we examine the levels of cognitive demand of these problems in a mainstream calculus textbook and classify them within…

We present adaptable activities for models of drug movement in the human body -- pharmacokinetics -- that motivate the learning of ordinary differential equations with an interdisciplinary topic. Specifically, we model aspirin, caffeine, and digoxin. We discuss the pedagogy of guiding students to understand, develop, and analyze models,…

In this work we critically examine a mnemonic designed for the pedagogy of first-order ordinary differential equations. The particular mnemonic takes the form of the SHIELDS acronym. We perform a critical analysis on mnemonics, outlining some of their benefits and limitations from the literature. As a result, we propose a general mnemonic model…

The present study explores students' understanding of calculus-based kinematics (henceforth, CBK), in which argumentation is taken as the sequence of the modes of fostering reasoning and problem-solving. The investigation stresses the importance of arguments students bring to the learning situation of CBK and recognizes the active construction of…

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…

The purpose of this mixed-methods study was to explore how undergraduate students in an applied calculus course used the written curriculum (i.e., textbook, online homework system, and previous exams). The study design included three phases: (a) an online survey, (b) individual observations, and (c) student interviews. Students' survey responses…

The calculus concepts of concavity and inflection points are critical for a complete understanding of quantities' behavior, making them important topics of research for those interested in the intersections of STEM disciplines. This study seeks to provide insight into this area by reporting on trends in students' concept projections of these…