Research shows that though some students can easily find the correct solutions to the problem(s) at hand, the algorithms that these students create are not always ones that would, when implemented, produce the correct solution(s). Towards shedding light on this phenomenon, the present study explicates a mechanism--accounting for features of the…

Professionals working with individuals at risk for, or with, disabilities are required by federal legislation to select, implement, and formatively and summatively evaluate the effectiveness of evidence-based practices in typical settings. Although multiple resources related to graph construction and visual analysis are available in the…

Single-case research designs (SCRDs) are rigorous methods used to investigate the effects of interventions on socially important outcomes. A hallmark of SCRDs is repeated measurement of observable behavior presented in time-series graphs. The construction of time-series graphs can inflate Type I or Type II errors made via visual analysis. In the…

In this paper, we describe a framework for characterizing students' graphical reasoning, focusing on providing an empirically-based list of students' graphical resources. The graphical forms framework builds on the knowledge-in-pieces perspective of cognitive structure to describe the intuitive ideas, called "graphical forms", that are…

This article recounts the life of mathematician Leonhard Euler and discusses the use of Graph Theory in student learning.

Visual representations of data are widely used for communication and understanding, particularly in science, technology, engineering, and mathematics (STEM). However, despite their importance, many people have difficulty understanding data-based visualizations. This work presents a series of three studies that examine how understanding time-based…

This study aimed to examine the quality of the open-access GeoGebra applets for function transformations by attending to the opportunity to learn function transformations afforded by them. Guided by the variation theory, this study conceptualized the opportunity to learn function transformations as the opportunity to discern critical features of…

The well-known artificial intelligence-based chatbot ChatGPT-4 has become able to process image data as input in October 2023. We investigated its performance on the test of understanding graphs in kinematics to inform the physics education community of the current potential of using ChatGPT in the education process, particularly on tasks that…

The teacher's use of representations is a crucial aspect of instructional quality in mathematics education, given their pivotal role in facilitating mathematics learning. However, in our international research community, perspectives on what constitutes high-quality use of representations may vary. This cross-cultural study aims to explore whether…

Little research has examined specific instructional variables that influence the development and effectiveness of task-analysis instruction. We conducted two experiments using text-based task analyses to teach college students to create single-subject reversal design graphs. In Experiment 1, we tested the effects of presenting antecedent and…

This contribution explores the teaching of graph theory in the context of engineering education. We examine how teachers use collectively designed resources in terms of their backgrounds. After a literature review, we justify the choice to develop an analytical framework for studying the materials in terms of connections to be established in the…

This case study examines how material resistance (limitations posed by the physical world) and graph interpretation intersected during a high school biology investigation using digital sensors. We use an extended episode from a small group to illustrate how, in an inquiry-based unit, measuring near the resolution limit of a sensor caused scaling…

Mathematics seems abstract, difficult, and uninteresting to many students, which in turn reduces their interest in learning mathematics. It has been found that the use of ICT and meaningful contexts of problem-solving tasks can make learning mathematics more enjoyable and easier to understand for students. To increase students' interest in…

This study examined college calculus instructors' preferences in solving two calculus tasks to examine college calculus instructors' use of important cognitive roots in understanding derivatives of function. Our results showed that only one instructor consistently uses cognitive roots while other instructors either focus on algebraic methods or…

Incorporating technology into educational processes is increasingly necessary to address the complexities of contemporary learning environments. This study investigates the impact of Augmented Reality (AR) on the academic performance of third-grade students in the areas of graphs and geometry. A quasi-experimental design was employed, comparing a…