It's not surprising that rainbows have received a great deal of attention: in textbooks, in magazines, and on the web. They are, after all, beautiful, fascinating, occasionally awe-inspiring, even a little mysterious. They are an almost perfect blend of natural beauty and simple physics. Has everything that can be said about rainbows already been…

Traditional visualization in meta-analysis uses forest plots to illustrate the combined treatment effect, along with the respective results from primary trials. While the purpose of visualization is clear in the pairwise setting, additional treatments broaden the focus and extend the results to be illustrated in network meta-analysis. The…

Integration of content areas allows students to deepen and transfer knowledge. An area that allows for an organic integration of STEM content is through combining mathematics with science instruction. This paper describes how we integrated a lesson coupling flower structure with data representation in a Year 3 classroom. The lesson occurred over…

The Earth's oceans are home to a diverse array of life, from large marine mammals to microscopic organisms. Among the most important are the marine phytoplankton, which comprise the basis of marine food webs, and also produce a large percentage of the Earth's oxygen through photosynthesis. Although the vast majority of phytoplankton are essential…

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…

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.

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…

In this paper, we provide an overall perspective on the teaching and learning of discrete mathematics. Our aim is to highlight what research has been conducted in this area and to connect it to existing research ideas for future work. We begin by characterizing discrete mathematics and its role in the school curriculum, highlighting themes,…

One way to develop a cross-curricular lesson is to select the most common mathematical formulas used in science and carefully develop and implement tasks that allow students to make connections between the mathematical representations and theoretical/physical science concepts. The slope-intercept formula, which is used to study relationships…

This article explains how explorations into the quadratic formula can offer students opportunities to learn about the structure of algebraic expressions. In this article, the author leverages the graphical interpretation of the quadratic formula and describes an activity in which students derive the quadratic formula by quantifying the symmetry of…