Researchers are currently investigating how calculus students understand the basic concepts of first-year calculus, including the integral. However, much is still unknown regarding the "cognitive resources" (i.e., stable cognitive units that can be accessed by an individual) that students hold and draw on when thinking about the integral. This…

There is widespread concern about the reduction in the number of students in Australia studying calculus-based mathematics courses in the final year of secondary education. Over the last 20 years in New South Wales, we have seen a dramatic increase in the number of students studying general mathematics in place of calculus courses. The concern…

This article describes an activity that incorporates measurement in order to lead students to discover and explore fundamental concepts of calculus. Students are provided with an experientially real starting point involving measurement and are encouraged to engage in mathematical discussions in a low-stakes environment. I describe the activity as…

This article explores one segment of an extended research and development project that was conducted to better understand the ways online teacher professional development can support teachers' development of deep and connected mathematical understandings. In particular, this article discusses teachers' understandings of the concept of…

The purpose of the present action research study is to describe a hands-on activity model, named the Constructed Scaffold Model (CSM), used in an Advanced Placement Calculus class in a southeastern United States suburban high school. Data were collected over an 8-week period during the spring 2017 semester. The teacher-researcher developed a…

The purpose of this study was to investigate the effect of a calculus system that was designed using an adaptive dynamic assessment (DA) framework on performance in the "finding an area using an integral". In this study, adaptive testing and dynamic assessment were combined to provide different test items depending on students'…

The flipped classroom approach has recently gained prominence in education. However, a review of previous studies shows that the relationship associated with gender difference, student perceptions and learning outcomes has still remained unexplored, and there has been little discussion regarding flipped classroom environment. To fill this gap,…

The increased use of videos in mathematics courses means that direct instruction, traditionally part of class lectures, now often occurs outside of the classroom. Although students come to class with some baseline level of understanding, instructors lose opportunities to assess students' understanding of content as it is seen for the first time.…

A short series of practical classroom mathematics activities employing the use of a large and publicly accessible scientific data set are presented for use by students in years 9 and 10. The activities introduce and build understanding of integral calculus and trigonometric functions through the presentation of practical problem solving that…

In light of the recent growing interest in conceptual learning and teaching of calculus, and especially with the focus on using technological environments, our study was designed to explore the learning processes and the role played by multiple-linked representations and by interactive technological environment in objectifying the accumulation…

California Assembly Bill (AB) 705 authored by Irwin and passed on October 13, 2017, requires colleges to "maximize the probability that a student will enter and complete transfer-level coursework in English and math within a one-year timeframe" and use high school background data in placement processes. To implement this new law and…

This study addresses a longstanding question among high school mathematics teachers and college mathematics professors: Which is the best preparation for college calculus-- (a) a high level of mastery of mathematics considered preparatory for calculus (algebra, geometry, precalculus) or (b) taking calculus itself in high school? We used a data set…

These proceedings are a written record of the research presented at the 42nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Mazatlán, Mexico, virtually beginning May 27, 2021 and in-person June 2-6, 2021. The conference was originally scheduled to take place…

In this paper we outline the main tenets of the commognitive approach and we exemplify its application in studies that investigate the learning and teaching of mathematics at university level. Following an overview of such applications, we focus on three studies that explore fundamental discursive shifts often occurring in the early stages of…

In this paper, I discuss one of the most distinguishing features of Jamshid al-Kashi's pedagogy from his "Key to Arithmetic", a well-known Arabic mathematics textbook from the fifteenth century. This feature is the multiple paths that he includes to find a desired result. In the first section light is shed on al-Kashi's life…