Simplifying equations via assumptions is integral to the "engineering method." Algebraic scaling helps in teaching the engineering skill of making good assumptions. Algebraic scaling is more than a pedagogical tool. It can create a solution where one was not possible before scaling. Scaling helps in engineering proper design…

Even when using mixed-ability grouping--grouping students so that students with a range of mathematical thinking work together--there is potential to position some students as more capable than others. In this article, the authors describe two approaches to mixed-ability grouping, providing examples of how teachers using those approaches describe…

Dimensional comparison theory (DCT; Möller & Marsh 2013:Psychological Review, 120(3), 544-560), first formulated 10 years ago, describes individuals' internal comparison processes applied between different areas of their lives. Dimensional comparisons explain the seemingly counterintuitive phenomenon that students' verbal and mathematical…

As our world becomes more complex, the skills learned in humanities classes supply our students with the flexibility needed to be successful in a rapidly changing world. Building off this idea, I wanted to take the conversation into a specific area, mathematics. Using a specific case study, I will show the importance of having a strong mathematics…

Graded Troubleshooting (GTS) is a powerful routine that teachers can use easily to engender students' metacognitive thinking and boost their understanding of mathematics concepts and procedures. This article describes a new GTS activity designed to prompt students to efficiently exploit worked examples when asked to diagnose erroneous examples…

Eddie Woo discusses the importance of problem solving in mathematics education. He points to the need for teachers to carefully consider the approaches they use to best support the growth of problem-solving abilities in students.

Students with autism spectrum disorder (ASD) are included in the general education classroom more often than ever before. Despite mathematical strengths and early success, these students experience poor outcomes (academic and employment) compared to their typically developing peers. The language of mathematics increases in complexity, use, and…

This activity provides students with opportunities to practice addition strategies and explore probability in this adaptation of the classic probability game Greedy Pig. To play, you will need a 6-sided dice, a number chart, and a brown counter to represent the mouse, and a yellow counter to represent the cheese. The game is suitable for two or…

This article describes an exercise for a physical laboratory experiment designed to enable physical geography students to practice transferable quantitative skills through inquiry-based learning. The exercise is a deliberately simplified physical model of storm-driven coastal overwash typical of low-lying coastal barrier systems. The experiment…

The purpose of this paper is to propose an effective learning environment for the initial stages of mathematical learning. Basic numerical skills and the objects and actions that trigger those skills are conceptualized as a mathematics-learning environment. We discuss numerical learning mechanism and the basic skills and environments we use to…

The aim of this article is to buid a Guide to the Analysis of Probability Textbook Lessons for secondary education (students aged 12-14), using the framework of Didactic Suitability. The facets, components and indicators of the didactic suitability construct are applied to categorize and organize didactic-mathematical knowledge on teaching and…

The mathematical modeling process is also a powerful way to teach students the meaning of data. In mathematical modeling, students are collecting data to answer a question. Data collection is the means to an end and not the end in itself. The author was looking for an engaging way to introduce his third-grade mathematics class to the skill of…

In this paper we follow a hypothetical mathematician who is working on a problem that is eventually solved. We treat this problem as if it were difficult for the mathematician. In following the mathematician's work, we note both what she does and what she doesn't do in the process. By the latter, we consider the times when progress is not being…

The COVID-19 public health emergency has been characterized by an abundance of data in the form of numbers and charts. Although these data are readily available, there have been challenges associated with their interpretation--exacerbated by generally low numeracy rates. Consequently, people may underestimate the speed at which the disease spreads…

This essay examines how line graphs functioned as markers of status and authority in early 20th-century America, distinguishing intellectual elites from ordinary citizens. Despite education reformers' efforts to democratize functional thinking and graphical representation in the first decades of the century, line graphs retained their position as…