Mathematization is critical in providing students with challenges for solving modelling tasks. Inadequate assumptions in a modelling task lead to an inadequate situational model, and to an inadequate mathematical model for the problem situation. However, the role of assumptions in solving modelling problems has been investigated only rarely. In…

In our modern world, we are inundated and grapple with data daily. As mathematicians, we are often more comfortable discussing the behavior of functions presented analytically, in contrast with the data-driven or tabular presentations of functions ubiquitous in our culture. This paper introduces an entry-level course, Mathematical Modeling and…

The activity described in this paper is based on the idea that reading an introductory undergraduate mathematics text is similar to reading instructions. I want my students to think about how to read when the goal is to learn to complete a task. I give them written instructions for doing a card trick and ask them to complete the trick. The…

This study aimed to determine the effect of learning with reversible problem-solving approach on prospective-math-teacher students' reversible thinking. Using experimental research design, the study involved 65 prospective math teacher students as respondents (35 experimental, 30 control). Experimental class implemented a learning with reversible…

We present an algorithm for solving the time-dependent Schrödinger equation that is based on the finite-difference expression of the kinetic energy operator. Students who have some knowledge of linear algebra can understand the theory used to derive the algorithm. This is because the finite-difference kinetic energy matrix and the Hückel matrix…

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…

Teaching mathematics requires a wide range of knowledge, including types of mathematical knowledge specialized to the work of teaching. Because specialized content knowledge is a form of professional knowledge, it is important to emphasize in professional preparation. In this paper, we present results comparing the performance of prospective and…

We report on a study focused on identifying how the notion of "the mathematician" is constructed in lower secondary Mexican mathematics textbooks. To conduct the study, we adopted a Foucauldian approach that allows us to identify the way in which the notion of the mathematician is constructed but also to delineate the possible effects…

Rapid automatized naming (RAN) is associated with children's arithmetic performance, which is multifactorial by nature and consists of arithmetic fluency, arithmetic procedure, and word problems. Yet, it is unclear whether RAN can predict all key aspects of arithmetic skills independently and what cognitive mechanisms may explain this relation.…

Researchers and reformers across multiple areas of scholarship have challenged the idea of mathematics as fixed, politically neutral, and value-free. Ethnomathematics has brought attention to the mathematical practices of particular cultural groups that differ from Western ways of mathematical understanding. These practices raise the following…

Exponential functions are an integral component of the secondary mathematics curriculum with which students struggle. Inherent difficulties students have had around the topic of exponential functions suggested a need for thinking about and examining the teaching and learning related to this content. This study presented the mathematical ideas made…

Quantitative Reasoning (QR) is essential for today's students, yet most higher education institutions have not effectively addressed this issue. This study investigates students' quantitative reasoning in STEM and Non-STEM math pathways using a non-proprietary, NSF grant-funded instrument, the Quantitative Literacy & Reasoning Assessment…

The aims of this research was to find the effectiveness of learning devices based on realistic mathematics education, as well as improving mathematic spatial ability and motivation of SMP Negeri 2 Pulo Bandring students' grade IX. This research is a development research using the Dick & Carey development model. The results of the analysis of…

Students' approaches to learning are heavily researched in higher education and are of particular concern in the field of mathematics where many students have been found to struggle with the transition to university mathematics. This article outlines a mixed methods study which sought to describe undergraduate mathematicians' approaches to…

Many research studies have sought to explain why NCTM's vision for mathematics classrooms has not had greater impact on everyday instruction, with teacher beliefs often identified as an explanatory variable. Using instructional exchanges as a theoretical construct, this study explores the influence of teachers' institutional positions on the…