Researchers who have carried out studies pertaining to mental computation and everyday mathematics point out that adults and children reason intuitively based upon experiences within specific contexts; they use invented strategies of their own to solve real-life problems. We draw upon research areas of mental computation and everyday mathematics…

This commentary draws on the articles in this issue to underscore the importance of community engagement and districtwide capacity building as central to efforts to use data to inform accountability and choice, along with school and instructional improvement. The author cautions against treating data as an all-purpose tool absent adequate…

In organic chemistry, spatial reasoning is critical for reasoning about spatial relationships in three dimensions and representing spatial information in diagrams. Despite its importance, little is known about the underlying cognitive components of spatial reasoning and the strategies that students employ to solve spatial problems in organic…

Becoming a skillful prover is critical for success in advanced undergraduate and graduate mathematics courses. In this dissertation, I report my investigations of proof and the proving process in three separate studies. In the first study, I examined the amount of logic used in student-constructed proofs to help in the design of…

In complex problem solving domains, correct solutions are often comprised of a combination of individual components. Students usually go through several attempts, each attempt reflecting an individual solution state that can be observed during practice. Classic metrics to measure student performance over time rely on counting the number of…

In turbulent business environments, change is rapid, continuous, and unpredictable. Turbulence undermines those adaptive problem solving methods that generate solutions by extrapolating from what worked (or did not work) in the past. To cope with this challenge, organizations utilize trial-based problem solving (TBPS) approaches in which they…

The Likelihood-to-Act (LtA) survey and a mathematics test were used in this study to assess students' impulsive-analytic disposition in the context of mathematical problem solving. The results obtained from these two instruments were compared to those obtained using two widely-used scales: Need for Cognition (NFC) and Barratt Impulsivity Scale…

The aim of this research is to analyse relationship between intelligence areas and problem solving skills of the students of Faculty of Education according to multiple intelligences theory of Gardner. Research sample is composed of 311 (64.3% female, 35.7% male) students who attended the Faculty of Education. Research data has been collected…

In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…

A seminal study by Chi "et al." firmly established the paradigm that novices categorize physics problems by "surface features" (e.g., "incline," "pendulum," "projectile motion," etc.), while experts use "deep structure" (e.g., "energy conservation," "Newton 2," etc.). Yet, efforts to replicate the study frequently fail, since the ability to…

Artificial satellites are easily observed most nights when the weather is fine. The website called "Heavens Above" at www.heavens-above.com will help locate these satellites flying over one's location. It also includes how bright they will appear. The direction of travel of each satellite in the night sky also indicates the type of satellite. For…

According to an action-specific account of perception, the perceived speed of a ball can be a function of the ease to block the ball. Balls that are easier to stop look like they are moving slower than balls that are more difficult to stop. This was recently demonstrated with a modified version of the classic computer game Pong (Witt & Sugovic,…

After completing their introductory studies on thermodynamics at the university level, typically in a second-year university course, most students show a number of misconceptions. In this work, we identify some of those erroneous ideas and try to explain their origins. We also give a suggestion to attack the problem through a systematic and…

A well-known optimization problem is the Popcorn Box investigation, which involves a movie theater snack container. The problem has been tailored for classroom investigations by the Ontario Association for Mathematics Education. The exploration was designed for students in grades 9 through 12. A common strategy proposed for algebra students is to…

This reproduces, for fun, a conversation between three professors at the University of Illinois, that originated at a dinner party over a couple of bottles of good red wine.