This inquiry presents two fine-grained case studies of students demonstrating different levels of cognitive functioning in relation to bilateral symmetry and reflection. The two students were asked to solve four sets of tasks and articulate their reasoning in task-based interviews. The first participant, Brittany, focused essentially on three…

This study is focused on identifying and describing the reasoning patterns of middle grade students when examining potentially similar figures. Described here is a framework that includes 11 strategies that students used during clinical interview to differentiate similar and non-similar figures. Two factors were found to influence the strategies…

This study aims at determining to what extent visuals contribute to success in non-routine problem solving process and what types of errors are made when solving with visuals. Comparative model was utilized for identifying the effect of visuals on student achievement, and clinical interview technique was used to determine the types of errors. In…

Critical thinking, problem solving, the use of tools, and the ability to consume and analyze information are important skills for the 21st century workforce. This article presents a qualitative case study that follows five undergraduate biology majors in a computer science course (CS0). This CS0 course teaches programming within a data-driven…

This article argues for a shift in how researchers discuss and examine students' uses of representations during their calculus problem solving. An extension of Zazkis, Dubinsky, and Dautermann's (1996) Visualization/Analysis-framework to include physical modes of reasoning is proposed. An example that details how transitions between visual,…

Research has been conducted on the role and importance of visualisation in many fields, including psychology, but very little has been done to extend its role to mathematics education in particular. Furthermore, much research has been done on the importance of critical thinking. However, to date not much has been done to clarify the fact that…

The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…

This study adds momentum to the ongoing discussion clarifying the merits of visualization and analysis in mathematical thinking. Our goal was to gain understanding of three calculus students' mental processes and images used to create meaning for derivative graphs. We contrast the thinking processes of these three students as they attempted to…

This mixed-method research attempted to clarify the role of visuospatial abilities in learning about mineralogy. Various sources of data--including quantitative pre- and postmeasures of spatial visualization and spatial orientation tests and achievement scores on six measures and qualitative unstructured observations, interviews, and field trip…

The main purpose of this study is to determine the strategies of using the generalizing patterns of the primary fifth grade students. The practice of this research is conducted on twelve students, which have high, middle and low success levels. Task-based interviews and students journals are used as the tools for data collection. For the analysis…