Compare problems are the most difficult type of word problems among primary school students, especially inconsistent problems, when the relational term is not consistent with the arithmetic operation required for the solution. The present study examines whether different methods help students successfully solve them and how these approaches…

The study of loops and spaces in mathematics has been the subject of much interest among researchers. In Part 1 of "The Theory on Loops and Spaces," published in the "Mathematics Teaching Research Journal," introduced the concept and the basic underlying idea of this theory. This article continues the exploration of this topic…

This paper proposes a three-step approach to develop knowledge graphs that integrate textbook-based target knowledge graph with student dialogue-based knowledge graphs. The study was conducted in seventh-grade STEM classes, following a collaborative problem solving process. First, the proposed approach generates a comprehensive target knowledge…

Discrete mathematics and mathematical modelling, along with the educational discourse surrounding these, have many connections. However, ways that the educational discourse on discrete mathematics can benefit from the inclusion of examples of mathematical modelling and the accompanying discussion are currently under-researched. In this paper, we…

The objective of this work is to show an educational path for combinatorics and graph theory that has the aim, on one hand, of helping students understand some discrete mathematics properties, and on the other, of developing modelling skills through a robust understanding. In particular, for the path proposed to middle-school students, we used a…

In the context of scholarly and scientific discourse, students often have to deal with graphic-visual modes of communication, which requires their ability to comprehend and utilize inscriptions, that is, scientific visual representations, to convey information effectively--what we call graphical literacy. Despite its pivotal role for training…

Graphs are an important component in physics laboratory reports. We have noticed that our students have difficulty selecting the "scale" and the "starting value" for an axis while generating graphs on graph paper. Recommendations concerning convenient scales and starting values are found in textbooks, laboratory manuals, and…

The literature reports that students have difficulties connecting different meanings, multiple representations of the derivative, and performing reversibility processes between representations of f and f'. The research goal is to analyze the mathematical connections that university students establish when solving tasks that involve the graphs of f…

Many students persistently misinterpret histograms. Literature suggests that having students solve dotplot items may prepare for interpreting histograms, as interpreting dotplots can help students realize that the statistical variable is presented on the horizontal axis. In this study, we explore a special case of this suggestion, namely, how…

A group of eighth-graders was presented with a two-day lab exploring graph theory as an enrichment experience. With the school's winter break looming, students were weary of solving linear equations, and this topic was intended to inject some new life into the classroom. In addition to learning about a completely new topic, they would be exposed…

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…

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…

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…

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

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…