This paper highlights the new enhancements of the Halomda platform designed to improve students' learning and exam preparation. The new features include a Graph Plotter, Algebraic Calculator and Context ChatGPT Recommended Key Guidelines. The use of these features is demonstrated though a working example of solving a double integral, illustrating…

The action of hammering a nail into wood is examined in terms of the force, momentum and energy required. Some unexpected experimental results are also presented.

This paper is a continuation of an earlier discussion in this journal about adhering to principles of mathematics while presenting function graphs in physics. As in the previous paper, the importance of the vertical line test was examined, this paper delves more in-depth, and it pinpoints a need for presenting graphs with a continuous rate of…

Nomographs (or nomograms, or alignment charts) are graphical representations of mathematical relationships (extending to empirical relationships of data) which are used by simply applying a straightedge across the plot through points on scales representing independent variables, which then crosses the corresponding datum point for the dependent…

The Java software jBar consists of a graphical user interface that allows the user to customize and assemble an included script for R. The scripted R pipeline calculates means and standard errors/deviations for replicates of numerical bivariate data and generates presentations in the form of bar graphs. A two-sided Student's t test is carried out…

Linear functions are an essential part of school and university education. Nevertheless, this topic is challenging for many students--especially in STEM topics. In this article, we contribute to the understanding of learning difficulties in the context of mathematical and physical problems. Here, we present the results of an eye-tracking study on…

It is widely acknowledged that communicating mathematical thinking is complex, difficult, and often messy. In this article, the authors explore how mathematical thinking is communicated, providing examples of strategies for teachers and students to use in the mathematics classroom.

Whether selection processes contribute to group-level disparities or merely reflect pre-existing inequalities is an important societal question. In the context of observational data, researchers, concerned about omitted-variable bias, assess selection-contributing inequality via a kitchen-sink approach, comparing selection outcomes of…

In this paper, we introduce and discuss a construct called "graphical forms," an extension of Sherin's symbolic forms. In its original conceptualization, symbolic forms characterize the ideas students associate with patterns in a mathematical expression. To expand symbolic forms beyond only characterizing mathematical equations, we use…

In working with the youngest learners, drawing from their own lived experiences to inform mathematics instruction is a critical piece for engaging with as well as supporting students in mathematizing their world (NAEYC and NCTM 2002, 2010; NCTM 2020). In the interaction described in this article, four-year-old children used mathematics to examine…

A quantitative approach to social network analysis involves the application of mathematical and statistical techniques and graphical presentation of results. Nonetheless--as with all sciences--subjectivity is an integral aspect of network analysis, manifested in the selection of measures to describe connection patterns and actors' positions (e.g.,…

Introductory physics students often express fears regarding graphical vector addition. To ameliorate student trepidation of possibly making a mistake when moving the second vector to its new position at the head of the first vector before being added, as is most often advised by physics teachers, an alternative method is detailed here. This subtly…

In this study, based on the analysis of a teaching experiment with middle school students, we propose a framework for describing meanings of a point represented on a plane in terms of multiplicative objects in the context of graphing. We classify those meanings as representing: (1) non-multiplicative objects; (2) quantitative multiplicative…

In this report, we present how one prospective elementary teacher (PT) engaged in the Ant Farm Task, which we designed to investigate PTs' reasoning about coordinate systems. We highlight the cognitive resources the PT drew upon in solving the task via the establishment of a Cartesian coordination and consider educational implications. [For the…

Theories of discourse argue that comprehension depends on the coherence of the learner's mental representation. Our aim is to create a reliable automated representation to estimate readers' level of comprehension based on different productions, namely self-explanations and answers to open-ended questions. Previous work relied on Cohesion Network…