Mathematics is used in the physical sciences to describe and model phenomena, resulting in a unique interface between mathematics and disciplines such as chemistry and physics. This paper focuses on themes emerging from a larger project that investigated how students understand and use mathematics in chemical kinetics, a field of study concerned…

In this article, a theoretically derived grid is presented combining Pólya's phases of the problem-solving process with the way in which teachers emphasize their students' strategic diversity in problem solving. It is used to categorize previous results from the literature. In an empirical part, the grid is also used to describe mathematics…

Arithmetic problem solving is a crucial part of mathematics education. However, existing problem solving theories do not fully account for the semantic constraints partaking in the encoding and recoding of arithmetic word problems. In this respect, the limitations of the main existing models in the literature are discussed. We then introduce the…

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…

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…

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…

Embedding mathematics in a relatable context has changed the way Christie Henderson's elementary students view the subject. In this article, Henderson discusses how presenting mathematics through a relatable context enables students to visualize the math and make a pictorial representation to aid them in solving it. When relevant and relatable…

Competence with fractions is foundational to acquiring more advanced mathematical skills. However, achieving competency with fractions is challenging for many students, especially for those with mathematics learning difficulties who often lack foundational skill with whole numbers. Teaching fractions is also challenging for many teachers as they…

The mathematical reasoning ability is one of the essential hard skills of a student, especially in solving everyday problems. In supporting the achievement of this mathematical reasoning ability, meaningful teaching materials are an essential part of keeping exciting and not dull a learning process. This study aimed to design and develop an…

This study investigated the role of the bar model method, a significant aspect of the Singapore mathematics curriculum, in the remediation of seventh-grade students' errors on algebra word problems. To accomplish this purpose, we first assessed students' errors on a written test involving algebra problems and identified ten students based on the…

Background: Adaptive expertise is a highly valued outcome of mathematics curricula. One aspect of adaptive expertise with rational numbers is adaptive rational number knowledge, which refers to the ability to integrate knowledge of numerical characteristics and relations in solving novel tasks. Even among students with strong conceptual and…

Background: In this cross-national study, Spanish, Finnish, and Swedish middle and high school students' procedural flexibility was examined, with the specific intent of determining whether and how students' equation-solving accuracy and flexibility varied by country, age, and/or academic track. The 791 student participants were asked to solve…

Quantitative reasoning is defined as reasoning about relationships between items, measurements of objects, and quantities rather than numbers. Both in the transition from arithmetic to algebra and in the problem-solving process, quantitative reasoning is seen as a critical instrument for the development of students' mathematical skills. In the…