We offer a new angle to explain the comprehension of mathematical infinity. We use Action-Process-Object-Schema (APOS) theory to explore the construction of different aspects of the cognitive Object related to this notion. We focus our attention on different ways of interacting with infinity, and how to act on infinite entities. Our aim is to shed…

A solid foundation in mathematics is beneficial not only for individuals' concurrent and later academic achievement, but also for future career success and financial stability. Rational number knowledge plays a pivotal role in mathematical success, yet it is often regarded as a challenging area to grasp comprehensively. The dissertation aims to…

This qualitative study aimed to examine: (1) the manner in which kindergarten children and first graders make sense of the term "area" regarding optimization problems; (2) how this manner is manifested in their decision-making and "STEAM" (science, technology, engineering, art and math) skills; and (3) how kindergarten children…

In this paper, a learning progression for geometric transformations is developed based on research that demonstrates the importance of viewing transformations as functions of the plane. The 5 levels of the progression reflect a student's evolving understanding of transformations as functions and their evolving understanding of the domain of these…

The phenomenon of insight is frequently characterized by the experience of a sudden and certain solution. Anecdotal accounts suggest that insight frequently occurs after the problem solver has taken some time away from the problem (i.e., incubation). However, the mechanism by which incubation may facilitate insight problem-solving remains unclear.…

Often, students who solve fraction tasks respond in ways that indicate inadequate conceptual grounding of unit fractions. Many elementary school curricula use folding, partitioning, shading, and naming parts of various wholes to develop children's understanding of unit and then nonunit fractions (e.g., coloring three of four parts of a pizza and…

This paper describes five growth points in linking representations of function developed from a study of secondary school learners. Framed within the cognitivist perspective and process-object conception of function, the growth points were identified and described based on linear and quadratic function tasks learners can do and their strategies…

Teachers across all grade levels agree that problem solving and reasoning are areas of weakness in students. Assessments among U.S. students indicate that these weaknesses persist (NCTM 2014) in spite of repeated calls that date back more than thirty years for increased problem solving, reasoning, and sense making in our schools. The NCTM is…

Over the last number of years, opportunities to learn in higher education for people with intellectual disabilities have increased. Consequently, this subgroup of students is gradually becoming part of an increasingly diverse college community. Because learning varies across different individual cultures and systems of higher education, our…

Even though reflective symmetry is heavily embedded in the everyday, learners continue to experience challenges when they mathematize concepts from this informal/everyday context. In this article we argue that symmetry exists in nature, it can also be symbolized algebraically and it can be abstracted into the world of axioms and theorems. We…

There were two purposes in the study. One was to explore the cognitive activities during spatial problem solving and the other to probe the relationship between spatial ability and science concept learning. Twenty university students participated in the study. The Purdue Visualization of Rotations Test (PVRT) was used to assess the spatial…

Students with language-based learning disabilities demonstrate learning challenges that must be addressed to enable them to succeed academically. Some of these students have difficulty with the process of organizing their thoughts about information acquired and expressing them in the form of an explanation, both of which are critical to effective…

Visualizations are an increasingly important part of scientific education and discovery. However, users often do not gain knowledge from them in a complete or efficient way. This article aims to direct research on visualizations in science education in productive directions by reviewing the evidence for widespread assumptions that learning styles,…

Recent studies show that a new strategy called differential-associative processing is effective for learning related concepts; however, our knowledge about differential-associative processing is still limited. Therefore the goals of the present study are to assess the duration of knowledge that is acquired from using differential-associative…

Students in the Science, Technology, Engineering, and Mathematics (STEM) fields are confronted with multiple external representations (MERs) in their learning materials. The ability to learn from and communicate with these MERs requires not only that students comprehend each representation individually but also that students recognize how the…