Successful mathematical problem-solving relies on choices about how best to represent and solve problems. In this article, a range of methods and strategies are presented for solving a single mathematical problem, including novel methods posed by in-service teachers at one Australian university. The variety of problem-solving strategies rely on…

In fact, ever since Seymour Papert (famous in his later years for constructionism, a learning theory that married conceptual constructivism with concrete experience) created Logo programming, many schools have been coding using Logo, the educational computer programming software that has the famous 'turtle' on the computer screen. Importantly,…

The two-stroke engine is an engineering marvel that has been incorporated into many aspects of modern-day life. While many seek to eliminate the two-stroke, others seek to revive this simple and effective power plant, aiming to make it more environmentally friendly and fuel-efficient. If successful, improvements could be far-reaching and…

Today, children of all ages experience rigorous career preparation as part of their education. School systems strive to implement mandated standards to help students excel in standardized testing and gain necessary skills for future job opportunities. In this worthwhile pursuit, many creative school programs such as art and music are deemed…

Le Châtelier's principle is used as a basis to derive an expression to calculate solution pH during titrations that involve only strong acids and strong bases. Central to this model are the reaction quotient and a re-equilibration term that represents the extent of neutralization during a titration. Unlike the method traditionally taught to…

We discuss teaching and learning situations that surfaced when computer programming and mathematics were brought together in a course where students write computer code to explore mathematics problems. Combining programming and mathematics creates a rich ecosystem which, on top of traditional mathematics activities (writing solutions, proofs,…

An important but challenging problem-solving technique in introductory mechanics is that of using "tilted axes." For inclined plane and centripetal motion problems, using axes that are aligned relative to the ramp direction or the radial direction (rather than the horizontal and vertical) yields equations that are conceptually more…

Chemical engineering problems often involve the solution of systems of nonlinear algebraic equations (NLE). There are several software packages that can be used for solving NLE systems, but they may occasionally fail, especially in cases where the mathematical model contains discontinuities and/or regions where some of the functions are undefined.…

The paper concerns an important but underappreciated genre of algorithmic puzzles, explaining what these puzzles are, reviewing milestones in their long history, and giving two different ways to classify them. Also covered are major applications of algorithmic puzzles in cognitive science research, with an emphasis on insight problem solving, and…

Literacy coaches are more effective when they have a clear plan for their collaborations with teachers. This article provides details of such a plan, which involves identifying a problem, understanding the problem, deciding what to do differently, and trying something different. For each phase of the problem-solving model, there are key tasks for…

At the root of problem solving, Tishman and Clapp assert, is a sense of agency. The impetus to engage with a problem starts with a sense that it's possible to reshape something by directing one's actions purposefully. The authors--who participated in a long-term project observing how the "maker movement" is being implemented in…

Herein, we present an experience-based learning approach that uses the COVID-19 pandemics knowledge about virus spread and epidemics to establish an analogy between a simple epidemics model--the SIR model (susceptible--infected--removed), and a second-order autocatalytic reaction with subsequent catalyst deactivation. Our approach provides a…

The case study described in this article focused on a topic of real national concern, landslides, which can trigger sudden and tragic environmental problems and bring considerable loss of life. Landslides occur in many parts of Thailand, for example on mountain slopes, areas eroded by water or areas with rock degradation (Department of Mineral…

Descriptions of mathematical thinking have an extended lineage. Sometimes accurate and sometimes not, sometimes misinterpreted and sometimes not, characterizations of mathematical thought processes have inspired and at times misled people interested in designing or framing mathematics instruction. Challenges the field faces in conceptualizing…

Because polarization and demonization of the "other" are increasingly prevalent in today's America, there are limited opportunities for deep and informed engagement across lines of difference, particularly on college campuses. "Bridging the Gap: Dialogue across Difference" (BTG) is a 2-3 week January term immersive experience…