This paper aims to broaden the scope of the construct concept image by addressing the mathematically oriented notion of "solution of an algebraic equation." The notion solution of an algebraic equation is not mathematical per se, but it is most prevalent in mathematical communications and in mathematics education. The paper describes…

Northern Norway's population comprises many different cultural groups. According to the Norwegian Education Act, education must give students insight into and a firm foundation in history and culture. This paper aims to present a proposal for how to start working with the creation of local rural mathematics curricula for which Sámi culture in…

As students transition from the calculus sequence to upper-level mathematics classes, many struggle to understand the purpose of proofs and how to produce them on their own. One tool students and mathematicians alike frequently use is examples to aid their understanding and production of proof. Using examples productively has been argued to be…

Elementary teachers are expected to teach all relevant material in all areas of the curriculum to their students. Even after completing excellent teacher preparation programs, these teachers often have little confidence teaching mathematics. In fact, many of these teachers have negative feelings toward mathematics from their own classroom…

The purpose of this quantitative comparative study was to examine differences in college-level math students' self-efficacy attributable to recent use of virtual reality (VR) learning environments and processes. The theoretical foundation for this study included connectivism, multi-dimensionalism and social cognitive theory, and self-efficacy…

Doors to other educational opportunities and future professions are closed when students have a low motivational profile in mathematics starting in elementary school and continue with an unchanged profile into high school (Lazarides et al., 2020). Students must learn how to increase their mathematical self-efficacy in order to increase their…

Through a social constructivist lens, this study looked at how paraprofessionals understand mathematics instructional content and associated pedagogical skills and explore an organization's current involvement of support staff in schools' mathematical classrooms. The setting for this bounded case study was two elementary schools contained in one…

Students' use of problem posing is an assessment tool for evaluating mathematical creativity, and it plays a substantial role in creative tasks. Integrating problem-posing tasks into a curriculum is beneficial for teaching and learning mathematics. The Photo-Math Project is an example of problem posing in terms of generating new problems. This…

Jordan canonical form (JCF) is one of the most important, and useful, concepts in linear algebra. Mathematics, physics, biology, science and engineering undergraduates often find the first application of real JCF in the discipline of differential equations (continuous models) to solving systems of differential equations. In this work, we apply…

Problem posing is an indispensable constituent of mathematical thinking, which makes it a requisite ability for students of all grades. Therefore, pre- and in-service teachers should carry out problem posing activities of high quality, and having them pose non-routine problems may be a good way to make this happen. In this context, this study…

The purpose of this study is to gain understanding of how secondary teachers conceptualize the relationships between mathematical modeling and problem solving. Eight secondary teachers participated in semi-structured, think-aloud individual interviews. Some conceptualizations include (a) modeling and problem solving are two distinct processes; (b)…

This paper is a part of a larger research study that we are conducting to develop a framework consisting of the data-driven best practices around teaching and learning algebra in K-12 classrooms. The purpose of this paper is to develop a usable definition for algebra interventions for the second stage of screening within the larger study, which…

Our study explores teaching practices that aim to promote students' learning to define an analytical object. A Calculus II instructor conducted a teaching experiment (TE) in which 11 students reinvented a formal definition of a limit over five class periods with the instructor's guidance. During the TE, the instructor's teaching practices were…

The study describes how the common representations are coordinated. I analyzed a popular geometry textbook using semiotics and a pragmatic approach to capture the variety of representations into categories and to use descriptive statistics to narrow the focus to the most common representations and coordinations. The major findings are: (1)…

In this theoretical paper, I use an empirically based example to illustrate particular design features of the Learning Through Activity (LTA) design framework and examine the impact of particular design principles. The LTA design framework is based on our elaboration of Piaget's construct of reflective abstraction. The example discussed here,…