The golden ratio, one of the most beautiful numbers in all of mathematics, arises in some surprising places. At first glance, we might expect that a General checking his troops' progress would be nothing more than a basic distance-rate-time problem. However, further exploration reveals a multi-faceted problem, one in which the ratio of rates…

The Venn diagram is suggested as a graphical solution to conjunction fallacies and a modification of it is suggested to more fully communicate set relations.

Integers are sometimes used in physics problems to simplify the mathematics so the arithmetic does not distract students from the physics concepts. This is particularly important in exams where students should not have to spend a lot of time using their calculators. Common uses of integers in physics problems include integer solutions to…

Designers try to "enlist" whatever they can to help themselves arrive at high quality, novel and original designs. When stimuli are used for this purpose, usually provided at the onset of the design process, these stimuli, or sources, may have one of two effects: they may enhance the design search and contribute to a high-quality, creative design,…

"Who has been to Dairy Queen® and purchased a Blizzard?®" Ms. Bosetti asked her students. During the summer, Bosetti had seen many of her former and future students at the local Dairy Queen enjoying Blizzard desserts and wondered, "Which Blizzard size is the best value?" She used this context for a ratios and proportions task…

The Maker Movement is a community of hobbyists, tinkerers, engineers, hackers, and artists who creatively design and build projects for both playful and useful ends. There is growing interest among educators in bringing making into K-12 education to enhance opportunities to engage in the practices of engineering, specifically, and STEM more…

An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

The article reports on a small-scale short story writing project. It details the development of the project and shares the emerging findings. The aim of the project was to enhance the quality of students' writing while developing teachers' practice in the teaching of short story writing. The project team comprised the author and four secondary…

Sixty individuals representing staff from state departments of education, school districts, other countries, testing and testing-related companies, and other educational organizations participated in a forum on June 22, 2015 in San Diego, California, to discuss implementing accessibility frameworks for all students, including students in general…

Case study instruction is characterized by centering instruction around the use of hypothetical classroom dilemmas. It uses descriptive stories and invites students to discuss application of course material as they engage in hypothetical classroom problem-solving and teacher decision-making. Teaching is a complex profession that requires high…

This report summarizes the results of the 2013-2014 AISD teacher appraisal and related survey items with emphasis on areas of need for additional professional development.

This article describes how selected nonfiction science books can be read as mystery stories featuring people confronting problems, gathering evidence, tossing aside preconceived ideas when necessary, and finding solutions.

The dictionary definition of constraint is one-sided, solely restrictive. The problem-solving definition is two-sided. Constraints come in pairs. One retains its restrictive function, precluding something specific; the other directs search for its substitute. The paired constraint model is applied to both domain and classroom. I discuss the…

This paper discusses an alternative approach for developing problem solving experiences for students. The major argument is that students can develop their creativity by engaging in collaborative problem solving activities in which they apply a variety of mathematical methods creatively to solve problems. The argument is supported by: considering…

It is great to see how the sharing of ideas sparks new ideas. In 2011 Lyon and Bragg wrote an "Australian Primary Mathematics Classroom" (APMC) article on the mathematics of kitchen gardens. In this article the authors show how the kitchen garden may be used as a starting point for proportional reasoning. The authors highlight different…