The design of interactions among peers plays a key role in collaborative learning. Various strategies have been applied to assist learners in collaborating and creating a continuous effort to construct and maintain shared knowledge, such as utilizing a concept map as a representational tool during discourse. Some previous studies have revealed its…

The purpose of this research study was to understand how linear algebra students in a university in the United States make sense of subspaces of vector spaces in a series of in-depth qualitative interviews in a technology-assisted learning environment. Fourteen mathematics majors came up with a diversity of innovative and creative ways in which…

Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with…

This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to regression and correlation analysis to increase student understanding of the concepts and methods in elementary statistics courses and in courses at the college algebra/precalculus level that…

This paper utilizes concept mapping as a tool for conscious and deliberate knowledge building in mathematics and its extension to algorithms. Currently, alleged defects in mathematics education are obvious: instead of conceptual elaboration, everyday praxis relies on routine computations that are likely to lead into alienated concepts with weak…

Rational number understanding is a critical building block for success in more advanced mathematics; however, how rational number magnitudes are conceptualized is not fully understood. In the current study, we used a dual-task working memory (WM) interference paradigm to investigate the dominant type of strategy (i.e., requiring verbal WM…

Multiple reports highlight the increasingly quantitative nature of biological research and the need to innovate means to ensure that students acquire quantitative skills. We present a tool to support such innovation. The Biological Science Quantitative Reasoning Exam (BioSQuaRE) is an assessment instrument designed to measure the quantitative…

The current study investigated college students' content knowledge and cognitive abilities as factors associated with their algebra performance, and examined how combinations of content knowledge and cognitive abilities related to their algebra performance. Specifically, the investigation examined the content knowledge factors of computational…

The study we report here examines parts of what Chevallard calls the "institutional" dimension of the students' learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To…

The purpose of this study was to assess algebra and geometric prerequisites skills as incorporated into the Applied Calculus Optimization Problem (ACOP) solution. The difficulties that students encounter in applying algebraic and geometric prerequisites at the early stages of the ACOP solution were identified. The study analyzes errors related to…

College students (n=32) in their first abstract algebra course were asked to list elements and find the product of 2 elements in the dihedral group D4. Most students found solutions using a combination of visual approaches and analytic strategies. Proposes an alternative model, the Visualizer/Analyzer model, which assumes visualization and…