This qualitative research study uses middle-grades students' numerical reasoning to model their symbolic representations of the relationship between two multiplicatively related unknowns on an algebra task. Students in sixth grade through ninth grade participated in clinical interviews that assessed their numerical reasoning using the Number…

Among the problems identified at Technical and Vocational Education and Training (TVET) colleges, low achievement in mathematical subjects is the most prominent one. This paper documents a qualitative case study undertaken at TVET College in Gauteng with the purpose of exploring the National Certificate Vocational (NC(V)) Level 4 students' errors…

Mathematics teacher candidates enter teacher education with knowledge that could support or limit their learning. It is therefore important to gain insights of this knowledge to inform teacher education. This paper offers such insights for prospective mathematics teachers' initial knowledge of problem solving (PS) for teaching at the beginning of…

This study reports a secondary analysis from a randomized control trial study conducted with third graders with mathematics difficulty (MD; N = 75). We used simple linear regression to investigate whether students' performance on a word-problem vocabulary assessment predicted their performance on a measure of word-problem solving. Additionally, we…

This paper explores the impact of a tailored working memory training program on the mathematics achievement of secondary school students in Myanmar. While previous studies have investigated the relationship between working memory and mathematics, this study focuses on a context where computerized training programs are limited. Twelve Grade 8…

Taylor series play a ubiquitous role in calculus courses, and their applications as approximants to functions are widely taught and used everywhere. However, it is not common to present the students with other types of approximations besides Taylor polynomials. These notes show that polynomials construed to satisfy certain boundary conditions at…

This paper presents results of a study aimed at describing and discussing evidence/features of advanced algebraic thinking processes. To achieve these objectives, we analysed the written production of students enrolled in engineering courses working on mathematical modelling tasks related to differential equations. Our guiding question was as…

This article aims to illustrate how the collective resolution of routine mathematical tasks can give rise to uncertainties, fostering and supporting a rich and authentic mathematical activity. While solving routine tasks may not typically be classified as problem-solving, the research presented in this paper shows that, at the collective level,…

The ability to solve geometric construction problems is justly regarded as an essential component of mathematical culture. The dynamic, general nature of objects provided by dynamic geometry systems allows the development of intuitive methods for solving construction problems. The core mathematical concept underlying this approach is the loci…

Research Findings: Children are increasingly using touchscreen technologies at home, which has become a recurring feature within their classroom too. Research has investigated the potential effect of using computer-based tests to assess pupils' performance rather than traditional paper tests. An agreement has still not been formed about the impact…

The importance of mathematical problem posing has been acknowledged by many researchers. In this theoretical paper, we want to capture different meanings and aspects of problem posing by approaching it from three different levels: (1) by comparing definitions, (2) by relating it to other constructs, and (3) by referring to research and teaching…

As a distinct mode of mathematical representation and communication, geometry diagrams are both signs that represent abstract geometric concepts and visual images that offer graphical-spatial properties. Dynamic geometly environment offers a wide range of tools for its users to create and interact with geometry diagrams. In this paper, I propose a…

We present our analysis of 254 Calculus I final exams from U.S. colleges and universities to identify features of assessment items that necessitate qualitatively distinct ways of understanding and reasoning. We explore salient features of exemplary tasks from our data set to reveal distinctions between exam items made apparent by our analytical…

Quadratic modeling problems are commonplace in high school mathematics courses; they typically situate quadratic patterns of change and their corresponding parabolic graph within real-world contexts. Traditional approaches to this type of problem lend themselves to making connections across different representations (e.g., Garofalo and Trinter…

Creativity has been identified as a key characteristic that allows students to adapt smoothly to rapid societal and economic changes in the real world. However, Chinese students appear to perform less well in mathematical problem-solving and problem-posing abilities, which are strongly connected to mathematical creativity. Mathematical modelling…