In typical school mathematics, students experience problem solving in different ways. Sometimes students learn about problem solving by being introduced to different strategies, such as making a table or drawing a picture. Other times, problem solving is presented as a context for applying previously learned mathematics skills and concepts.…

COVID-19 pandemic policies requiring disease testing provide a rich context to build insights on true positives versus false positives. Our main contribution to the pedagogy of data analytics and statistics is to propose a method for teaching updating of probabilities using Bayes' rule reasoning to build understanding that true positives and false…

This is the fifth in a series of statistical articles for mathematics teachers. In this article the authors discuss graphs for exploring relationships between one categorical variable and one numerical variable using stemplots and boxplots and between two numerical variables, using scatterplots and time series plots. [For "The Data Files 4:…

Visual elements such as graphs, tables, and diagrams are essential components of scientific writing. Although scientific writing textbooks and guides often contain information on how to design such visuals, little has been written on how to effectively discuss those visuals within the text. This article offers a novel heuristic for teaching…

This article presents a reflection on a teaching experience involving the use of the Brügner tangram, an interesting but little-known manipulative material. It details an activity conducted as part of an undergraduate mathematics education course for prospective primary school teachers. The main objective of this paper is to present the…

With the increased number of MOOC offerings, it is unclear how these courses are related. Previous work has focused on capturing the prerequisite relationships between courses, lectures, and concepts. However, it is also essential to model the content structure of MOOC courses. Constructing a precedence graph that models the similarities and…

Critical thinking is a skill that people must develop to navigate skillfully the information they receive through media channels. The cultivation of this skill must begin in the early stages of education and continue uninterrupted through the completion of academic training. For this reason, the search for tools to promote critical thinking in the…

In this work, we present an experimental approximation to the study of the phenomenon of radioactivity in secondary schools, taking as an analogy the process of release of carbon dioxide in a carbonated beverage. In this way, we intend to facilitate the approach to the mathematical formalism and to the graphical description of this phenomenon, as…

This article presents a task providing college students opportunities to build on their high school knowledge of trigonometry to explore parametric equations and inverse trigonometric relationships within a contextual learning ladder problem.

The ideal gas law, "PV = nRT," is one of the simplest physical laws in nature that is introduced to students as early as in high school and first year in college. In this equation, "P" stands for pressure, "V" is the volume, "n" is the amount expressed in mole, "T" is the temperature in Kelvin…

The authors take a mathematical journey into polygonal chains to provide an algorithm that will construct a closed polygonal chain where the lines intersect exactly an exactly an odd number of times.

In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…

It is said that a picture is worth a thousand words, but what about graphs? Although graphs have the potential to bring data to life, numerous studies show that learners struggle with graphical comprehension. Furthermore, many textbook examples on graphs are boring and appear meaningless to students. Students want to know more about something…

Several researchers have promoted reimagining functions and graphs more quantitatively. One part of this research has examined graphing "conventions" that can at times conflict with quantitative reasoning about graphs. In this theoretical paper, we build on this work by considering a widespread convention in mathematics teaching: putting…

Graphs about Us (GaU) is an activity for building classroom community within mathematics classrooms. Through the creation and analysis of graphical representations of data about the students' lives in and out of school, this activity aims to allow each student to feel seen and validated in the class, create shared knowledge of students'…