Innovations in Science, Technology, Engineering, and Mathematics (STEM) are a cornerstone of the United States' economic prosperity, yet national and international assessments paint a poor picture of students' STEM competencies (reference 1; reference 2). These data have led to transformative approaches to improve STEM education including…

The use and understanding of mathematics is a crucial component of the physical sciences. Much work has been done in physics education research and science education more broadly to determine persistent difficulties with mathematics. This work has led to the development of numerous problem solving strategies aimed at helping learners approach…

This article concerns student sense making in the context of algebraic activities. We present a case in which a pair of middle-school students attempts to make sense of a previously obtained by them position formula for a particular numerical sequence. The exploration of the sequence occurred in the context of two-month-long student research…

In this response to Sternberg's (2017) feature article in this special issue, we identify and define a kind of closed-minded, dogmatic, self-serving thinking that is nowadays quite prevalent around the world but counterproductive in solving many social problems. We argue that overcoming such a mindset takes wisdom and creativity. We present some…

Suppose that there is an inexhaustible supply of $3 and $5 vouchers from the local supermarket. They may only be exchanged for items that cost an exact number of dollars made up from any combination of the vouchers. What is the highest amount not able to be obtained? This is an interesting problem in mathematical thinking and logic requiring only…

Clock Buddies is our favorite first-day-of-class activity. It starts as a nonthreatening icebreaker activity that helps students learn one another's names, but it soon asks students to find their own strategies for solving a real-world scheduling problem. Even highly math phobic students work with others and succeed. Students gain insight from…

A good understanding of ternary phase diagrams is required to advance and/or to reproduce experimental research in solid-state and materials chemistry. The aim of this paper is to describe the solutions to problems that appear when studying or determining ternary phase diagrams. A brief description of the principal features shown in phase diagrams…

Designers give themselves something to "react to" and they make it "rich." During design, what they react to can take many forms: a homepage wireframe, an Excel spreadsheet, building drawings, and a Tweet prototype. Using a phenomenological research design using an interactive methodology and multiple data collection methods,…

Students need lifelong skills to build their problem-solving capabilities for better understanding of the world and themselves. Working through design lessons allows them to directly apply thinking strategies and learning about facts, figures, and concepts while they are crafting meaningful ideas about the influence and social implications of…

The Dijkstra's algorithm is an algorithm that determines the shortest paths needed to go from a starting node to any node in a graph. In this article, the process and results of an activity that included route formation among the provinces in the Aegean region using Dijkstra's algorithm are shared. The activity was designed based on a mathematical…

The aim of the research is to describe the profile of problem solving ability of secondary student with high mathematical ability in learning based on realistic mathematics supported by ethnomathematics. The study is a descriptive qualitative research. The subject is a 7th grade student in a public secondary school at Semarang regency, Central…

The study aims to describe the ability of mathematical creative thinking on the aspects of fluency, flexibility, and originality in solving open-ended problem of Linear Equations with One Variable. The subjects are 7th grade students of one private junior high school in Surakarta, Central Java, Indonesia. The data was collected by the test,…

This article begins by describing a class scenario in which a teacher gives her students the L problem (Watanabe 2008), which involves finding the area of a composite figure. Her students inappropriately extend the area formula for rectangles (A = L x W) to composite figures by multiplying all given dimensions. After class, the teacher concluded…

Between two popular teaching methods (i.e., balance method vs. inverse method) for equation solving, the main difference occurs at the operational line (e.g., +2 on both sides vs. -2 becomes +2), whereby it alters the state of the equation and yet maintains its equality. Element interactivity occurs on both sides of the equation in the balance…

Collaborative biostatistics is the creative application of statistical tools to biomedical problems. The relatively modest literature about the traits of effective collaborative biostatisticians focuses on four core competencies: (a) technical and analytical; (b) substance-matter knowledge; (c) communication; and (d) problem solving and problem…