We explored the mediating role of prior knowledge on the relation between intelligence and learning proportional reasoning. What students gain from formal instruction may depend on their intelligence, as well as on prior encounters with proportional concepts. We investigated whether a basic curriculum unit on the concept of density promoted…

Visuospatial thinking is considered crucial for understanding of three-dimensional spatial concepts in STEM disciplines. Despite their importance, little is known about the underlying cognitive processing required to spatially reason and the varied strategies students may employ to solve visuospatial problems. This study seeks to identify and…

A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…

Subgoal learning, a technique used to break down problem solving into manageable pieces, has been used to promote retention and transfer in procedural domains, such as programming. The primary method of learning subgoals has been passive, and passive learning methods are typically less effective than constructive methods. To promote constructive…

According to Geary's evolutionary approach, humans are able to easily acquire primary knowledge and, with more efforts, secondary knowledge. The present study investigates how primary knowledge contents can facilitate the learning of formal logical rules, i.e., secondary knowledge. Framing formal logical problems in evolutionary salient contexts…

In support of efforts to foreground functions as central objects of study in algebra, this study provides evidence of how secondary students use trigonometric functions in contextual tasks. I examined secondary students' work on a problem involving modeling the periodic motion of a Ferris wheel through the use of a visual programming environment.…

Purpose: The purpose of this paper is to illustrate how associationism mistakenly assumes that direct experience is possible; that is, there is expectation-free observation and association without prior expectation. Thus, associationism assumes that learning involves the absorption of information from the environment itself. However, contrary…

This research targets children's informal strategies and knowledge of fractions by examining their ability to create, interpret, and connect representations in doing and communicating mathematics when solving fractions tasks. Our research group followed a constant comparative method to analyze clinical interviews of children in grades 2-6 solving…

The demand for Information Systems (IS) graduates with expertise in Structured Query Language (SQL) and database management is vast and projected to increase as "big data" becomes ubiquitous. To prepare students to solve complex problems in a data-driven world, educators must explore instructional strategies to help link prior knowledge…

Solving new problems can be made easier if one can build on experiences with other problems one has already successfully solved. The ability to exploit earlier problem-solving experiences in solving new problems seems to require several cognitive sub-abilities. Minimally, one needs to be able to retrieve relevant knowledge of earlier solved…

Context: A concept map is a graphical and cognitive tool that enables learners to link together interrelated concepts using propositions or statements that answer a posed problem. As an assessment tool, concept mapping reveals a learner's research skill proficiency and cognitive processing. Background: The identification and organization of the…

Although the characteristics of PBL (problem focused, student centered, self-directed, etc.) are well known, the components of a problem-based learning environment (PBLE) and the cognitive scaffolds necessary to support learning to solve different kinds of problems with different learners is less clear. This paper identifies the different…

Contemporary theories of Human Causal Induction assume that causal knowledge is inferred from observable contingencies. While this assumption is well supported by empirical results, it fails to consider an important problem-solving aspect of causal induction in real time: In the absence of well structured learning trials, it is not clear whether…

An understanding of proof does not start in a high school geometry course. Rather, attention to logical reasoning throughout a student's school experience can help the development of proof readiness. In the spirit of problem solving, the author has begun to use some Japanese logic puzzles other than sudoku to help students develop additional…

This study examined whether familiarity with content influences performance on conditional reasoning problems of the form P implies Q independently of ease of generation of specific examples of "Q and not-P." Results indicated that increased content familiarity resulted in higher performance levels. (Author/JAZ)