The ability to solve linear equations sets students up for success in many areas of mathematics and other disciplines requiring formula manipulations. There are many reasons why solving linear equations is a challenging skill for students to master. One major barrier for students is the inability to interpret the equals sign as anything other than…

Although high-fidelity digital models of human anatomy based on actual cross-sectional images of the human body have been developed, reports on the use of physical models in anatomy teaching continue to appear. This article aims to examine the common features shared by these physical models and analyze their educational value based on the…

The teaching of mathematics in Singapore continues, in most cases, to follow a traditional model. While this traditional approach has many advantages, it does not always adequately prepare students for University-level mathematics, especially applied mathematics. In particular, it does not cultivate the ability to deal with "non-routine…

The Lithuanian Informatics Olympiads (LitIO) is a problem solving programming contest for students in secondary education. The work of the student to be evaluated is an algorithm designed by the student and implemented as a working program. The current evaluation process involves both automated (for correctness and performance of programs with the…

Various studies suggest that covariational reasoning plays an important role on understanding the fundamental ideas of calculus and modeling dynamic functional events. The purpose of this study was to investigate a group of mathematics teachers' covariational reasoning abilities and predictions about their students. Data were collected through…

Spatial ability tasks appear on many intelligence and aptitude tests. Although the construct validity of spatial ability tests has often been studied through traditional correlational methods, such as factor analysis, less is known about the cognitive processes involved in solving test items. This study examines the cognitive processes involved in…

Most treatments of indirect effects and mediation in the statistical methods literature and the corresponding methods used by behavioral scientists have assumed linear relationships between variables in the causal system. Here we describe and extend a method first introduced by Stolzenberg (1980) for estimating indirect effects in models of…

Many educators believe that mathematical investigation involves both problem posing and problem solving, but some teachers have taught their students to investigate during problem solving. The confusion about the relationship between investigation and problem solving may affect how teachers teach their students and how researchers conduct their…

This module was initially developed for a course in applications of mathematics in biology. The objective of this lesson is to investigate how the allele and genotypic frequencies associated with a particular gene might evolve over successive generations. The lesson will discuss how the Hardy-Weinberg model provides a basis for comparison when…

The 3 most often-used performance measures in the cognitive and decision sciences are choice, response or decision time, and confidence. We develop a random walk/diffusion theory--2-stage dynamic signal detection (2DSD) theory--that accounts for all 3 measures using a common underlying process. The model uses a drift diffusion process to account…

Upper primary school children often routinely apply proportional methods to missing-value problems, even when it is inappropriate. We tested whether this tendency could be weakened if children were not required to produce computational answers to such problems. A total of 75 sixth graders were asked to classify 9 word problems of three types (3…

Problems on the dynamics of changing mass systems often call for the more general form of Newton's second law Fnet = dp/dt. These problems usually involve situations where the mass of the system decreases, such as in rocket propulsion. In contrast, this experiment examines a system where the mass "increases" at a constant rate and the net force…

Problem-based learning (PBL) is an instructional approach that is organized around the investigation and resolution of problems. Problems are neither uniform nor similar. Jonassen (1997, 2000) in his design theory of problem solving has categorized problems into two broad types--well-structured and ill-structured. He has also described a host of…

We examine the Stark effect (the second-order shifts in the energy spectrum due to an external constant force) for two one-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z greater than 0 and V(z) = [infinity] for z less than 0) and the symmetric linear potential…

Students who are deaf or hard of hearing are increasingly being educated in regular education classrooms along with their typical hearing peers. Establishing educational environments that address their unique needs is essential for their success. Response to intervention (RtI), as it is being implemented in the United States, provides a framework…