Counting problems have applications in probability and computer science, and they provide rich contexts for problem solving. Such problems are accessible to students, but subtleties can arise that make them surprisingly difficult to solve. In this paper, students' work on the Groups of Students problem is presented, and an important issue related…

Researchers are currently investigating how calculus students understand the basic concepts of first-year calculus, including the integral. However, much is still unknown regarding the "cognitive resources" (i.e., stable cognitive units that can be accessed by an individual) that students hold and draw on when thinking about the integral. This…

Teachers continue to face the challenge of identifying efficaciously gifted students' learning capacity in its multiple forms. While most educators acknowledge its multidimensional characteristics, the protocols used to identify it are frequently evaluated as unnecessarily restrictive. This study investigates an assessment tool that could…

International trended assessments have long attempted to provide instructional information to educational researchers and classroom teachers. Studies have shown that traditional methods of item analysis have not provided specific information that can be directly applicable to improve student performance. To this end, cognitive diagnosis models…

This article reports on an investigation with first year undergraduate Product Design and Management students within a School of Engineering and Applied Science. The students at the time of this investigation had studied fundamental engineering science and mathematics for one semester. The students were given an open ended, ill-formed problem…

This study used participant observation to explore students' thinking when learning the concept of factorial functions. First-year university students undertaking a mathematics methodology course were asked to find the number of ways in which five people could sit around a circular table with five seats. Using grounded theory as a qualitative…

The aim of the study is to conceptualize the technology-aided mathematical modelling process in the frame of cognitive modelling perspective. The grounded theory approach was adopted in the study. The research was conducted with seven groups consisting of nineteen prospective mathematics teachers. The data were collected from the video records of…

The purpose of the present study was to test the efficacy of a modified cognitive strategy instructional intervention originally developed to improve the mathematical problem solving of middle and high school students with learning disabilities (LD). Fifth and sixth grade general education mathematics teachers and their students of varying ability…

Two independent studies were conducted to examine the relationship of problem solving styles to parenting styles. Both studies used VIEW: An Assessment of Problem Solving Style and the Parental Authority Questionnaire (PAQ). Study 1 included 173 adults recruited using Mechanical Turk and Study 2 included 131 adults recruited using Qualtrics. Data…

Test results from the Program for International Student Assessment (PISA) reveal that Shanghai students performed less well in solving interactive problems (those that require uncovering necessary information) than in solving analytical problems (those having all information disclosed at the outset). Accordingly, this study investigates…

This research explores solutions and challenges pertaining to a child's development of self-efficacy. After working with fifth grade students in a public education setting, Inoticed an increased reliance on teachers for both creative and procedural directions. This paper explores research of educators who examine the internal and external factors…

Mathematical processing associated with solving short geometry problems requiring logical inference was examined among students who differ in their levels of general giftedness (G) and excellence in mathematics (EM) using ERP research methodology. Sixty-seven male adolescents formed four major research groups designed according to various…

Multiple studies have shown benefits of problem-solving prior to instruction (cf. Productive Failure, Invention) in comparison to direct instruction. However, students' solutions prior to instruction are usually erroneous or incomplete. In analogy to "guided" discovery learning, it might therefore be fruitful to lead students…

Our aim in this article is to elaborate the role of training in representational change theory (RCT), particularly in terms of Ohlsson's (2011) spread of activation explanation (named "redistribution theory"), and to develop novel training manipulations that effect the re-encoding mechanism proposed by RCT (Ohlsson, 1992). Two…

Theories of mind are implicitly embedded in educational research. The predominant theory of mind during the latter half of the twentieth century has focused primarily on the individual mind in isolation, context-free problem-solving and mental representations and reasoning, what we refer to as "cognitivism." Over the last two decades, CS…