The complexity in understanding the [epsilon-delta] definition has motivated research into the teaching and learning of the topic. In this paper I share my design of an instructional analogy called the Pancake Story and four different questions to explore the logical relationship between [epsilon] and [delta] that structures the definition. I…

Answering a call by the "Common Vision" for instructional material to "establish stronger connections with other disciplines" and "work with professional-level technology tools," the present article shows how various aspects of fitting circles to data fit in existing courses from basic calculus to advanced calculus.

This article covers how a computer algebra system (CAS) "wxMaxima" can be explored for teaching single-variable and multivariable calculus to Korean digital natives. We present several examples where "wxMaxima" can handle calculus problems easily, not straightforwardly but still successfully with some human intervention, and…

Teaching and learning Calculus concepts and procedures, particularly the definite integral concept, is a challenge for teachers and students in their academic careers. In this research, we supplement the analysis made by different authors, applying the theoretical and methodological tools of the Onto-Semiotic Approach to mathematical knowledge and…

The fields of quantitative and covariational reasoning boast a wide range of powerful theoretical tools, which are described carefully in the literature. Less frequent and explicit attention, however, has been paid to writing down detailed, practical guidance for operationalizing these theoretical constructs. Some guidance is provided by…

Given the challenge of visualizing the main constructs of two-variable functions and their differential and integral calculus, it is essential to consider instructional resources' use and perceived potential to contribute to students' understanding. This case study considers how four instructors selected and used digital and physical resources in…

Assembly Bill 1705 (AB 1705) seeks to strengthen students' completion of the first STEM Calculus course for Science, Technology, Engineering, and Math (STEM) programs across the California Community Colleges. The law sets new standards for students' placement and first math enrollment to ensure STEM students begin in transfer-level coursework that…

This technical appendix accompanies the report, "Preparatory Pathways and STEM Calculus Completion: Implications of the AB 1705 Standards." The appendices contain a full methods section and multivariate analyses that augment the descriptive analyses presented in the report. Together, these analyses examined a cohort of more than 37,000…

This paper presents a case study conducted by two universities seeking to explore Open Education Resources (OER) in their precalculus course. Students not only gained access to their textbook for free on the first day of class, but also Lumen OHM, an online mathematics assessment platform. The majority of students involved in the study were…

Helping students reach a clear understanding of the cause-and-effect relationship between changes in parameter and the graph of an equation is the focus of the activity outlined in this article. The behavior of phase shifts has been regarded as counterintuitive for many people, and often, because of this, conflict between student intuition and…

Mathematics teacher questioning plays a significant role in students' learning. Research has persisted in analyzing teacher questioning from a cognitive perspective. Considering teaching as a relational practice, we explored teacher questioning from cognitive and affective perspectives. Data comprises 14 video-audio recordings, field notes,…

This note presents a derivation of Viète's classic product approximation of pi that relies on only the Pythagorean Theorem. We also give a simple error bound for the approximation that, while not optimal, still reveals the exponential convergence of the approximation and whose derivation does not require Taylor's Theorem.

Students use a variety of resources to make sense of integration, and interpreting the definite integral as a sum of infinitesimal products (rooted in the concept of a Riemann sum) is particularly useful in many physical contexts. This study of beginning and upper-level undergraduate physics students examines some obstacles students encounter when…

Undergraduate calculus instruction is a contributor to racialized and gendered trends of STEM persistence and disidentification with mathematics. However, the nature of instruction that promotes equitable learning opportunities for disrupting such negative outcomes and experiences among historically marginalized populations is underexplored. To…

The home confinement that was imposed to reduce and control the spread of COVID-19 pandemic led educational systems to implement changes in many school activities. Teachers moved to remote teaching and relied on digital apps to present and discuss learning activities with their students. Likewise, they looked for new routes and means to follow up…