In this brief article, the author illustrates the flaws of FOIL (multiply the First, Outer, Inner, and Last terms of two binomials) and introduces the box method. Much like FOIL, the box method can become easy to use. Unlike FOIL, however, the box method is a more direct and visible link to using the distributive property to determine area, a…

This paper provides an overview of John Dewey's ecological psychology and his basic concepts: experience, inquiry, and habit. The concept of habit, which is particularly relevant in understanding problem-solving strategies, is further explicated on the basis of Gross's (2009. "A Pragmatist Theory of Social Mechanisms." "American…

This article presents theoretical and empirical support for a data-driven instructional coaching approach and emerging evidence for the contributions of an online platform in operationalizing, assessing, and facilitating the implementation of key coaching actions for both research and practice. The contributions of an online platform in guiding…

Issues in society such as immigration and racial inequality threaten to derail classroom discussions. Likewise, issues in higher education such as general education (GE) reform threaten to obstruct faculty committee discussions. We want students to engage in classroom discussions through a comprehensive exploration of issues, ideas, and events…

This working group continues to develop a research program on the practice of launching mathematical tasks and its resulting impact on learners. Our research agenda contains two strands of inquiry exploring (1) theory and framework building concerning effective launches and (2) empirical examination of the link between launching and opportunities…

The solution of problems and the provision of proofs have always played a crucial part in mathematics. In fact, they are the heart and soul of this discipline. Moreover, the use of different techniques and methods of proof in the same mathematical field, or by combining fields, for the same specific problem, can show the interrelations between the…

One way to ease the solution of physics problems is to visualize the situation. However, by visualization we do not mean the pictorial representation of the problem. Instead, we mean a sketch for the solution of the problem. In this paper a new approach to solving physics problems, based on decomposing the problem into with and without gravity, is…

This paper uses the lens of a calculus student to examine different solutions to a weekly puzzler from the radio show "Car Talk," hosted by Tom and Ray Magliozzi. The puzzler describes an automobile that is traveling 75 miles per hour and is 75 miles from its destination. The trip is completed by traveling 1 mile at 75 miles per hour, 1…

Educators often hear about the need for students to be more creative, more free-thinking, and more exploratory throughout projects and class assignments. This article will highlight the importance of creating and implementing an open-classroom environment where students are confident in their ability to ask questions and capable of exploring a…

This article focuses on one common type of many different classroom discussions, open-strategy sharing (OSS), because it offers a starting point for teachers new to mathematical discussions. The goal of an OSS discussion is to explore multiple possible ways to solve a single mathematical task. Students share strategies, listen to others'…

It is critical for mathematics tasks to provide students with the opportunity to engage actively in reasoning, sense making, and problem solving so that they develop a deep understanding of mathematics. Learning mathematics while solving a problem can be like entering a dark room with a single small light. The objects are in the shadows, difficult…

Using the Teach to Lead process and drawing on their own study of how teachers can lift their social-emotional skills, three elementary teachers in Connecticut created a plan to work with fellow teachers to increase everyone's camaraderie and regularly problem solve together. When their school closed to in-place learning, they pivoted to find ways…

Mathematics and technology serve the health sciences as demonstrated in this article, cowritten by one of our calculus students. Creating a lesson based on dosing an antibiotic allows teachers and students to see the immediate value of high school calculus and technology.

Universal Design for Learning (UDL) is an approach to pedagogy, curriculum, and assessment grounded in the learning sciences and neuroscience. In this article, the author proposes a mathematical version of UDL called UDL Math. She describes three classrooms that include students with disabilities in meaningful mathematics and explores how the…

A small project of STEAM education called "Innovation for Love and Care" was implemented in a local secondary school in Hong Kong. Four seventh-grade students participated from November 2020 to February 2021. The project aims to integrate humanism into the traditional STEAM curriculum, to stimulate the students' innovation in a…