Sources of individual differences in scientific problem solving were investigated. Participants representing a wide range of experience in geology completed tests of visuospatial ability and geological knowledge, and performed a geological bedrock mapping task, in which they attempted to infer the geological structure of an area in the Tobacco…

The opportunities for meaningful classroom learning activities are everywhere. In this article, we explain some of the little known, widespread, horrific issues associated with one aspect of the pet trade. By the time they reach high school age, many students have personally experienced the end result of the deplorable business practices on which…

Martin Gardner wrote about a coin-flipping trick, performed by a blindfolded magician. The paper analyses this trick, and compares it with a similar trick using three cups flipped in pairs. Several different methods of analysis are discussed, including a graphical analysis of the state space and a representation in terms of a matrix. These methods…

The revelation effect is a change in response behavior induced by a preceding problem-solving task. Previous studies have shown a revelation effect for faces when the problem-solving task includes attractiveness ratings of the faces. Immediately after this problem-solving task participants judged faces as more familiar than without the…

A mixed-method exploratory approach was employed to examine the relationship between epistemological beliefs and quality of thinking when participants first thought about an ill-structured problem alone, and then with another person in a dyad. The results showed that there was not a systematic connection between epistemological beliefs and…

This paper reports on a study that introduces and applies the "K[subscript 5]Connected Cognition Diagram" as a lens to explore video data showing teachers' interactions related to the partitioning of regions by axes in a three-dimensional geometric space. The study considers "semiotic bundles" (Arzarello, 2006), introduces "semiotic connections,"…

We use a concept of framing to explain 3 cases in which participants initially lacked mutual understanding but then achieved significant mutual understanding. The cases were all consistent with a pattern of "positional framing" that includes a human participant who is inquiring, which we call a "listener", and a "source", which may be another…

In mathematics learning, word problems always include sufficient information; however, in everyday situations, people sometimes encounter problems with insufficient information. Previous studies suggest that people cannot successfully handle word problems with insufficient information because they believe a word problem has only one answer and…

How many ways may one climb an even number of stairs so that left and right legs are exercised equally, that is, both legs take the same number of strides, take the same number of total stairs, and take strides of either 1 or 2 stairs at a time? We characterize the solution with a difference equation and find its generating function.

Spatial reasoning, a crucial skill for everyday actions, develops gradually during the first several years of childhood. Previous studies have shown that perceptual information and problem solving strategies are critical for successful spatial reasoning in young children. Here, we sought to link these two factors by examining children's use of…

Open-ended problem solving is a central skill in engineering practice; consequently, it is imperative for engineering students to develop expertise in solving these types of problems. The complexity of open-ended problems requires a unique set of skills. The purpose of this qualitative study was to investigate the approaches used by engineering…

"What do you do with the remainder when you divide?" Mrs. Thompson asked her third-grade students. They replied with such comments as, "You can't share that, because they won't be equal!" and "It's not going to come out even because you can't do that!" These answers were consistent with third- and fourth-grade student performance in a pretest and…

This paper describes a forward approach to an inverse problem related to detecting the nature of geological substrata which makes use of optimization techniques in a multivariable calculus setting. The true nature of the related inverse problem is highlighted. (Contains 2 figures.)

Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new…

This article presents a new contract negotiation and drafting exercise designed for undergraduate and graduate business students in a business law or legal environment of business survey course. Structured as an asset purchase and sale agreement involving a small business with intangible social media and intellectual property assets in a…