The development of the mathematical concept of the infinite, through the reflections that arise from personal notions and perceptions and the analysis of some ideas of Galileo and Cantor, invites us to investigate the relationship between intuition and formalization for the understanding of the said concept. This paper aims to observe and describe…

Our study explores teaching practices that aim to promote students' learning to define an analytical object. A Calculus II instructor conducted a teaching experiment (TE) in which 11 students reinvented a formal definition of a limit over five class periods with the instructor's guidance. During the TE, the instructor's teaching practices were…

We conducted a collective case study investigating two college algebra students' graph reasoning and selection on an online assessment. Students completed the assessment during individual, semi-structured interviews, as part of a broader validation study. The assessment contained six items; students selected Cartesian graphs to represent…

Researchers have recommended using tasks that support students in reasoning covariationally to build productive meanings for graphs, rates of change, exponential growth, and more. However, not many recent studies have been done to identify how students reason when engaging in covariational reasoning tasks in undergraduate precalculus courses. In…

Prior to the COVID-19 pandemic, the university educational system in Nigeria largely employed traditional, face-to-face classroom approaches for teaching. This study examines how mathematics lecturers adapted to online teaching in response to COVID-19 restrictions. A mixed methods approach was used to obtain both qualitative and quantitative data…

The aim of this study is to characterize ways of reasoning and arguing that first year university mathematics students exhibit in problem-solving activities from a course that emphasizes the importance of formulating conjectures and the search for different ways to support or validate them. The use of a Dynamic Geometry System in the…

In this study, I present how eight U.S. college calculus instructors with different patterns of inquiry practices used instructional situations to frame instructional tasks for introducing derivatives graphically to students. During four interviews, the instructors proposed up to eight tasks for introducing derivatives physically, graphically,…

This research contributes to the need to identify and expand learning environments that encourage undergraduate students to develop collaborative work skills and apply their classroom knowledge to solve real-world problems. Using qualitative methods, we examine the effects of the interaction between two teams of students when solving a…

This article describes the results of an investigation based on a Models and Modeling Perspective [MMP]. We present the evolution of the models built by university students when solving a model development sequence designed to promote their learning of the exponential function. As a result, we observed that students' thinking was modified,…

Instructors manage several tensions as they support students to engage in mathematical disciplinary practices such as defining, conjecturing, and proving. These tensions include honoring students' contributions while simultaneously apprenticing students to following mathematical norms. I present a case study of a teacher-researcher in a laboratory…

Recently, abstracted quantitative structures (AQS), a construct from quantitative reasoning, has been offered as a means to conceptualize and study mathematization during mathematical modeling. Extending this theoretical work, we provide empirical evidence that an intervention targeting participants' AQS can assist in aligning modelers' models…

Student engagement is an impactful component of student experience in mathematics classrooms and can shape academic and affective outcomes. The measurement of engagement in classroom settings has been limited to self-report measures or observational frameworks which privilege verbal participation. By conducting a microanalysis of two students'…

Machine learning is a powerful method for predicting the outcomes of interactions with educational software, such as the grade a student is likely to receive. However, a predicted outcome alone provides little insight regarding how a student's experience should be personalized based on that outcome. In this paper, we explore a generalizable…

In the mathematical community, two notions of "function" are used: the set-theoretic definition as a univalent set of ordered pairs, and the Bourbaki triple. These definitions entail different interpretations and answers to mathematical questions that even a secondary student might be prompted to answer. However, mathematicians and…

The purpose of this study was to help undergraduate STEM students at a Hispanic-serving institution make connections between calculus and physics content and their lives using a utility-value intervention. As part of either a Calculus II or a calculus-based Newtonian Physics course, 471 undergraduate students were randomly assigned to either read…