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.

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…

Understanding educators' networks can inform the field of school psychology by offering insight into how the structure of social relationships supports the implementation of school-based programs. However, the difficulties of collecting and modeling network data remain barriers to using network methods in school psychology. To overcome these…

If the goal is to move beyond the shape of the graph to consider the dynamic aspects of functions, students need to explore dynamic representations of functions. To address this, the authors combined the use of a dynamic representation of function with the instructional routine, Which One Doesn't Belong? [WODB]. In this article, they briefly…

Quadratic modeling problems are commonplace in high school mathematics courses; they typically situate quadratic patterns of change and their corresponding parabolic graph within real-world contexts. Traditional approaches to this type of problem lend themselves to making connections across different representations (e.g., Garofalo and Trinter…

Helping students reach a clear understanding of the cause-and-effect relationship between changes in parameter and the graph of an equation is the focus of the activity outlined in this article. The behavior of phase shifts has been regarded as counterintuitive for many people, and often, because of this, conflict between student intuition and…

In this paper, we aim to show strategies for improving graph interpretation skills at middle and high school students using OZOBOT® BIT, a small and relatively low-cost programmable robot which had been used to teach programming to young children. OZOBOT's speed can be controlled by drawing lines with colour codes, as well as through a visual…

The lesson presented here provides a multifaceted inquiry-based opportunity to develop a deep grasp of Archimedes' principle. It was originally developed for high school teachers as part of their training in the basic structure of the Next Generation Science Standards. There are numerous demonstrations illustrating Archimedes' principle, many of…

Students often struggle with the relationship between mathematical graphs and the data they represent. To truly understand types of evolutionary selection, students need to be proficient with several different skills in math, science, and literacy contexts. With math, students must be able to identify variables, design appropriate graphs based on…

The lesson set in this article describes an introductory learning experience using wildlife camera-based citizen science projects hosted on Zooniverse (http://www.zooniverse.org). Wildlife camera projects were chosen due to the charisma of the study organisms, student engagement while looking at images, ease of access to projects, ease of teaching…

Despite holding wide-ranging experiences with constant velocity and non-zero acceleration, students wrestling with physical science concepts struggle to demarcate the two distinct characteristics of motion. In fact, this prior experience and loose familiarity with associated terminology often act as an obstacle toward a deep and robust…

Too often, high school algebra students encounter topics in a discrete, disconnected fashion. In the authors' first years of teaching, they found students to be adept at solving problems they were currently studying; for instance, they could solve quadratics during a quadratics unit. Too often, however, students struggled with that same content…

Nitrogen- or phosphorus-based fertilizers, used in agriculture, can run off into nearby waterways during periods of heavy rain or high flow and cause harmful blooms (Paerl et al. 2016), low oxygen (Joyce 2000), and decreased biodiversity (Sebens 1994). Studies of the effects wetlands can have on water and habitat quality (Verhoeven and Meuleman…

Understanding the relationship between energy and temperature can be challenging, but it is crucial to developing an understanding of the underlying mechanism behind climate change. In this article, the authors review the development of a unit that focuses on the relationship between energy, greenhouse gases, aerosols (a suspension of fine solid…

Graphing functions is an important topic in algebra and precalculus high school courses. The functions that are usually discussed include polynomials, rational, exponential, and trigonometric functions along with their inverses. These functions can be used to teach different aspects of function theory: domain, range, monotonicity, inverse…