At the school level statistics begins with exploratory data analysis, or EDA. Statistical learning goes on to include statistical inference, which will be discussed in the second part of this article. In this article, the author will talk about EDA and CODAP. EDA can be thought of as looking for patterns in data using graphs and simple statistics…

This article discusses a pedagogical technique for utilizing breakout rooms for small group discussions and synchronous drawing features in Zoom to create crowdsourced solutions to mathematical problems that involve graphing or visualization. Students begin with specific examples and then move quickly to the development of a more general…

Although there is much research exploring students' covariational reasoning, there is less research exploring the ways students can leverage such reasoning to coordinate more than two quantities. In this paper, we describe a system of covariational relationships as a comprehensive image of how two varying quantities, having the same attribute…

Inferential reasoning is an integral part of science and civic society, but research shows that it is a problematic domain for many people. One possibility for a more accessible approach to inferential reasoning is to use randomization tests via computer simulations. A case study was conducted with primary preservice teachers after they had passed…

We are all fascinated by loops and their formation in space. When a line cuts itself, it forms an intersection point and creates a space. This is an experimental study done by analyzing several loops, forming a concrete formulation by visualizing the patterns observed, and then proving the formulations proposed using the known standard…

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…

At the undergraduate level, the composite motion of simple harmonic vibrations has always been the main content of physics as well as several other scientific disciplines. Many textbooks tell us clearly that when the frequency ratio [omega][subscript 1]/[omega][subscript 2] of two perpendicular vibrations is simple integer ratio n[subscript…