This study explored preschool age and gender differences in help-seeking within the theoretical framework of scaffolded problem-solving and self-regulation (Bruner, 1986; Rogoff, 1990; Vygotsky, 1978; 1986). Within-subject analyses tracked changes in help-seeking among 62 preschoolers (34 boys, 28 girls, mean age 4.22 years) solving a challenging…

In this article we show how the Sudoku puzzle and the three simple rules determining its solution can be used as an introduction to proof-based mathematics. In the completion of the puzzle, students can construct multi-step solutions that involve sequencing of steps, use methods such as backtracking and proof by cases, and proof by contradiction…

This article analyzes latent variable models from a cognitive psychology perspective. We start by discussing work by Tuerlinckx and De Boeck (2005), who proved that a diffusion model for 2-choice response processes entails a 2-parameter logistic item response theory (IRT) model for individual differences in the response data. Following this line…

The relationship between emergent spatial understanding in different cognitive domains, including navigation and language, has rarely been studied using methods that allow for the examination of individual differences. In this study the authors explored emergent place learning and its relationship to early spatial language, namely prepositions, in…

This story is a chemical mystery with an emphasis on qualitative analysis, metallurgy, and gravimetric analysis. It is, as well, yet another article in the continuing series, created by Thomas Waddell and Thomas R. Rybolt, that presents a scientific problem in mystery format in the context of the popular and beloved characters of Sherlock Holmes…

In recent years, education quality and quality assessment have received a great deal of attention at Higher Education Institutions (HEIs) in Bangladesh. Most of the HEIs in Bangladesh face severe resource constraints and find it difficult to improve education quality by improving inputs, such as better infrastructure and modernized classroom…

An "n" x "n" chessboard is called deficient if one square is missing from any spot on the board. Can all deficient boards with a number of cells divisible by 3 be tiled by bent (or L-shaped) trominoes? The answer is yes, with exception of the order-5 board. This paper deals with the general problem plus numerous related puzzles and proofs…

We introduce a simple game made up of a board of coins on a triangular lattice. We then study the possibility of turning the board from one pattern of heads and tails to some other pattern. Given that a solution exists we find a precise answer to the number of solutions possible. We then generalize this to more complex boards with coins of many…

According to Thomas Kuhn, a significant part of "normal science" is the fact gathering, empirical work which is intended to illustrate an existing paradigm. Some of this effort focuses on the determination of physical constants such as the astronomical unit (AU). For Kuhn, normal science is also what prepares students for membership in a…

Generalizability theory was used to examine the generalizability and dependability of outcomes from two single-item Direct Behavior Rating (DBR) scales: DBR of actively manipulating and DBR of visually distracted. DBR is a behavioral assessment tool with specific instrumentation and procedures that can be used by a variety of service delivery…

The "N" queens problem is a classic puzzle. It asks for an arrangement of "N" mutually non-attacking queens on an "N" x "N" chessboard. We discuss a recent variation called the "N" + "k" queens problem, where pawns are added to the chessboard to allow a greater number of non-attacking queens to be placed on it. We describe some of what is known…

A major goal of education is to help learners store information in long-term memory and use that information on later occasions to effectively solve problems (Vockell 2010). Therefore, this author began to use the Rubik's cube to help students learn to problem solve. There is something special about this colorful three-dimensional puzzle that…

Concepts in mathematics are often universally applicable to other fields. A critical aspect for success in high school or college is the ability to transfer content knowledge from one discipline to another. This is especially true for material learned in the sciences and mathematics. Several studies have suggested that strong mathematical skills…

Students in introductory courses generally respond favorably to novel approaches to learning. To this end, I developed and used three crossword puzzles in spring and fall 2009 semesters in Introductory Soil Science Laboratory at Colorado State University. The first hypothesis was that crossword puzzles would improve introductory soil science…

Insight problem solving is characterized by restructuring. We hypothesized that the difficulty of rebus puzzles could be manipulated by systematically varying the restructurings required to solve them. An experiment using rebus puzzles varied the number of restructurings (one or two) required to solve a problem and the level at which the…