This paper presents the importance of the visual expression of factor decomposition in regression analysis, which is particularly worthwhile for undergraduate students whose majors are not mathematics but social science. The conventional purpose of regression analysis is to examine specific hypotheses empirically. In particular, the statistical…

Recently, abstracted quantitative structures (AQS), a construct from quantitative reasoning, has been offered as a means to conceptualize and study mathematization during mathematical modeling. Extending this theoretical work, we provide empirical evidence that an intervention targeting participants' AQS can assist in aligning modelers' models…

Understanding math and the ability to use math in various situations can greatly contribute to a successful life. Different math skills are of importance for understanding and supporting math ability. In addition, math interest may influence math ability. We investigated the relationship between math conceptual and procedural skills, their…

Background: Problem-solving as a vehicle to develop independent thinking skills is mostly underestimated and is often either overlooked or not given adequate attention within the existing South African mathematics curriculum. Consequently, numerous learners often display limited skills or lack skills to adequately crack Mathematics problems by…

The concept of determinant plays a central role in many linear algebra concepts and is also applied to other branches of mathematics and science. In this study, we focus on the application of determinant and inverse matrix concepts, in solving systems of equations by a group of 116 in-service mathematics teachers who were studying the topic at a…

Understanding how environments influence learning requires attending not only to what is present but also to what is absent. In the context of mathematics learning, this means attending not only to problems that children encounter frequently in textbooks but also to ones that appear rarely. We present research in this article showing that students…

Understanding how environments influence learning requires attending not only to what is present but also to what is absent. In the context of mathematics learning, this means attending not only to problems that children encounter frequently in textbooks but also to ones that appear rarely. We present research in this article showing that students…

We engaged five mathematicians who conduct research in the domain of complex analysis or use significant tools from complex analysis in their research in interviews about basic concepts of differentiation and integration of complex functions. We placed a variety of constructivist, social-constructivist, and embodied theories in mathematics…

Previous research has investigated the representational translation practices of high school students, high school teachers, and college preservice teachers in various mathematical contexts including linear functions. Findings from qualitative research has frequently led to new notions about participant work and understanding. Many quantitative…

There has been a lack of research into conceptually teaching the structure of contextual problems to kindergarten students. This is despite the popularity of contextual problems and the difficulties that students have with them. This study focuses on creating a textless, image-based application that uses the Triplet Structure Model to teach about…

Knowing when students have the prerequisite knowledge to be able to read and understand a mathematical text is a perennial concern for instructors. Using text describing Newton's method and Vinner's notion of concept image, we exemplify how prerequisite knowledge influences understanding. Through clinical interviews with first-semester calculus…

The purpose of this research study was to understand how mathematics majors make sense of similar matrices, a linear algebra topic that is rich in internal and external connections, in a series of in-depth qualitative interviews in a technology-assisted (MATLAB) learning environment. The study was also an attempt to develop a cognitive theory in…

In many mathematics curricula, the notion of limit is introduced three times: the limit of a sequence, the limit of a function at a point and the limit of a function at infinity. Despite the use of very similar symbols, few connections between these notions are made explicitly and few papers in the large literature on student understanding of…

Nationally, student performance in math has been flat, and achievement gaps persist. And with a growing economy driven by industries in the science, technology, engineering, and math (STEM) fields, educators are tasked with instilling interest in and preparing students for college studies and careers that will supply these in-demand jobs. Now,…

In this article, we present a coding framework based on simultaneity and connections. The coding focuses on microlevel attention to three aspects of simultaneity and connections: between representations, within examples, and between examples. Criteria for coding that we viewed as mathematically important within part-whole additive relations…