Proportionality can be considered among the most important mathematical notions in the middle school math curriculum (grades 5 to 8). It is the capstone of elementary arithmetic, number, and measurement concepts, and at the same time one of the most elementary understandings one needs for more advanced mathematics. Understanding proportionality is…

Mathematization is a critical competency in the modelling process. This study aims to elicit prospective mathematics teachers' mathematizing through the analysis of their solution approaches to a modelling problem related to the bales of straw. This study was conducted with 75 fourth-year prospective mathematics teachers (PMTs) enrolled in a…

Although culturally responsive mathematics teaching is important, post-secondary education for preservice teachers (PTs) does not typically lead to learning opportunities for them to use mathematics to recognize the roles of social agents. To address this issue, we created a culturally responsive mathematical modeling task in which we invited PTs…

Mathematics is an essential subject in schools, helping develop cognitive skills such as critical analysis, logical reasoning, and problem-solving. However, academic achievement in mathematics often declines, with some students having difficulty understanding mathematical ideas. Many factors influence mathematics achievement, including students'…

An alternating treatments design was used to analyze the effects of concrete and virtual manipulatives on the duration and number of correctly solved linear equations by three middle school students with cognitive disabilities. Participants physically manipulated algebra tiles to solve an equation during the concrete manipulative condition. During…

This investigation explores the relationship between the use of digital pencil and mathematical problem-solving accuracy among 1,530 students with learning disabilities (LD) and 25,400 general education (GE) peers from the 2017 digital National Assessment of Educational Progress mathematics assessment. The term "digital pencil" in this…

This investigation explores the relationship between the use of digital pencil and mathematical problem-solving accuracy among 1,530 students with learning disabilities (LD) and 25,400 general education (GE) peers from the 2017 digital National Assessment of Educational Progress mathematics assessment. The term "digital pencil" in this…

Challenge: The Hodgkin-Huxley membrane conductance model has been featured in biomedical engineering (BME) curricula for decades. A typical BME assignment might require students to apply the relevant equations and parameters to model the generation of action potentials; however, there is opportunity for students to build and explore both…

In this paper, we finish describing the project and the experimentation of "Ricerca Operativa Applicazioni Reali" (ROAR; in English, Real Applications of Operations Research), a three-year project for higher secondary schools. ROAR is composed of three teaching units addressed to grades 10, 11, and 12, respectively. To improve students'…

Collaborative problem-solving (CPS) has been one of the essential core skills for future students. However, we found that there are many studies on the evaluation of collaborative problem-solving skills, but there is little studies on the subject areas based on which collaborative problem-solving skills have been evaluated. The three-dimensional…

In this paper, we present an empirical study carried out in a country where STEM education does not have a tradition, and the content and didactics of mathematics are typically studied separately from the content and didactics of biology. In that context, we focus on analogies in the conceptual structure of mathematics and biology, and study how…

This paper reports a two-year research project studying Indonesian primary and secondary teachers' mathematics-related beliefs (MrB) and mathematical problem-solving knowledge for teaching (MPSKT). In the first year, a quantitative study involving 80 primary teachers, 70 lower secondary school, and 55 upper secondary schools from four districts in…

This study embarks on the question in the title with the construct of epistemological status, which pertains to the solver's satisfaction with the way and the degree to which their solution had fulfilled their intellectual and psychological needs in a particular problem situation. The construct is used to hypothesize that a solver's decision to…

This study aimed to determine the cognitive process employed in problem-solving related to the concept of area conservation for seventh graders. Two students with different mathematical ability were chosen to be the subjects of this research. Each of them was the representative of high achievers and low achievers based on a set of area…

In mathematical activities and in the analysis of mathematics teaching-learning processes, "objects," "signs", and "representations" are often mentioned, where the meaning assigned to those words is sometimes very broad, sometimes limited, other times intuitive, allusive, or not completely clear. On the other hand, as…