Research into didactics of calculus has maintained a long-standing interest in students' grasp of the relations between definite integrals and areas. This study comes to contribute to this line of research by unpacking how students use the concept of area to find definite integrals. Specifically, we focus on mathematical situations where the…

Engaging in the construction and interpretation of graphs is a complex process involving concerted activation of context-specific cognitive resources. As students engage in this process, they apply fine-grained, intuitive ideas to graphical patterns: graphical forms. Using data involving pairs of students constructing and interpreting graphs, we…

Through galleries of graphs and short filmstrips, this paper aims to sharpen students' eyes for visually recognizing continuous functions. It seeks to develop intuition for what visual features of a graph continuity does and does not allow for. We have found that even students who can work correctly with rigorous definitions may not be able to…

This work is devoted to exploring proof abilities in Graph Theory of undergraduate students of the Degree in Computer Engineering and Technology of the University of Seville. To do this, we have designed a questionnaire consisting of five open-ended items that serve as instrument to collect data concerning their proof skills when dealing with…

We describe and evaluate a method to mitigate unwanted student collaborations in assessments, which we recently implemented in a second-year undergraduate mathematics module. The method requires a list of specific pairs of students to be prevented from collaborating, which we constructed based on the results of previous assessments. We converted…

Using a mixed methods approach, we explore a relationship between students' graph reasoning and graph selection via a fully online assessment. Our population includes 673 students enrolled in college algebra, an introductory undergraduate mathematics course, across four U.S. postsecondary institutions. The assessment is accessible on computers,…

A growing body of literature suggests manipulating some graphing conventions can affect visual analysis and adherence to graphing conventions varies widely in single case design publications. Yet use of graphing conventions by the wider population of behavior analysts is largely unexplored. The current study examined relations among types of…

This case study investigated the development of prospective mathematics teachers' technological pedagogical content knowledge (TPACK) in graphical data displays with (VM) within the context of a microteaching lesson study (MLS). This research investigated how five participants integrated technology and implemented a lesson plan aimed to teach…

Inverse and injective functions are topics in most college algebra courses. Yet, current materials and course structures may not afford students' conceptual understanding of these important ideas. We describe how students' work with digital activities, "techtivities," linking two different looking graphs that represent relationships…

Adapting interventions based on learner progress is paramount to the effectiveness of interventions in special education and applied behavior analysis. Although there is some research on effective methods for training practitioners to make general instructional decisions (e.g., modify an intervention) based on graphed performance data, research on…

Background and Context: Source code plagiarism is a common occurrence in undergraduate computer science education. Many source code plagiarism detection tools have been proposed to address this problem. However, such tools do not identify plagiarism, nor suggest what assignment submissions are suspicious of plagiarism. Source code plagiarism…

Background: The purpose of this paper is to do a cross-sectional analysis to evaluate the impact of the Coronavirus Disease 2019 pandemic on Dental Match Residency statistics from the year 2019-2023. Methods: The Dental Match Residency statistics available from the Dental Match website were analyzed from years 2019-2023 to evaluate the impact of…

Visual inspection of single-subject data is the primary method for behavior analysts to interpret the effect of an independent variable on a dependent variable; however, there is no consensus on the most suitable method for teaching graph construction for single-subject designs. We systematically replicated and extended Tyner and Fienup (2015)…

The necessity for students to clarify their own cognitive structure and the amount of their knowledge mastery for self-reflection is often ignored in building the student model in the adaptive model, which makes the construction of the cognitive structure pointless. Simultaneously, knowledge forgetting causes students' knowledge level to fall…

This study investigates undergraduate STEM students' interpretation of quantities and quantitative relationships on graphical representations in biology (population growth) and chemistry (titration) contexts. Interviews (n = 15) were conducted to explore the interplay between students' covariational reasoning skills and their use of disciplinary…