Arithmetic fluency is regarded as a foundational math skill, typically measured as a single construct with pencil-and-paper-based timed assessments. We introduce a tablet-based assessment of single-digit fluency that captures individual trial response times across several embedded experimental contrasts of interest. A large (n = 824) cohort of…

This paper seeks to answer the question: How does the handling of the contradictions that emerge in activities of initial mathematics teacher education contribute to the learning of geometric knowledge when pre-service teachers and the teacher educator solve geometric construction problems with GeoGebra? A dialectical-materialist approach is used…

Background: Empirical studies have revealed students' development of computational thinking (CT) and mathematical thinking (MT) during programming-based mathematical problem-solving, highlighting specific CT concepts or practices that serve as learning goals or outcomes. However, implementing programming-based mathematics instruction requires…

This essay extends beyond the characteristics and discourse of word problems to, more generally, school mathematical problem-solving and the implications entailed by a predominant paper-and-pencil mode of learning and instruction since the modern era of education. Contrasting what I call "one-handed" (with paper-and-pencil) with…

This study explores high school students' and their mathematics teachers' mathematical discourses on the equal sign and variables in the classroom context. The participants in this case study were ninth graders and their mathematics teachers. The data were analyzed in terms of participants' routines, specifically ritual and explorative routines in…

In this portfolio, I reflect on my efforts to provide professional development targeted to support teachers during the launch phase of their mathematics teaching, to elicit and respond to student ideas and experiences. I grounded my study in research on ambitious teaching practices for launching complex mathematical tasks using problem-based…

Fostering a culture of professionalism is the work of all stakeholders in a school and can be influenced by participating in self-selected professional development. Professionalism is a trait among teachers that has garnered significant attention within mathematics education. Central to the principle of professionalism is the recognition that…

The aim of the exploratory method research centered on the presence of mathematical tools in STEM through three main questions: Is mathematics an essential tool in the field of STEM? Can mathematics complete projects solely with mathematical and digital tools? Does understanding mathematical modeling affect STEM teaching? A better understanding of…

Operations Research (OR) is a branch of applied mathematics that deals with optimization problems arising from different real contexts. The solving process of its problems is based on the construction and resolution of mathematical models, showing the possible connections between mathematics and the real world. Nevertheless, OR is not typically…

Students' difficulties in differentiating the direct proportion and inverse proportion problems cause interference. Proactive interference is the error that occurs when old information (concept of direct proportion) interferes with new information (concept of inverse proportion). In solving the problem of inverse proportion, students often use the…

The National Council of Teachers of Mathematics (NCTM) emphasizes the teaching of "Big Ideas" in mathematics. This study focuses on the part-part-whole (PPW) relationship as a crucial aspect of word problem solving involving addition and subtraction. This study, conducted in the United States, evaluated the effects of conceptual…

This work is the result of a master's investigation in Brazil, which discusses the teaching of the parabola in the initial training of mathematics teachers. Our theoretical framework addresses the relationship between intuition and the dialectics of the theory of didactic situations, which supports the analysis of the results of this study Its…

This study examines the solutions of 34 kindergarten children as they create equal groups from n bottle caps, where n was equal to 8, 9, 22, and 23. For each n, children were asked to find as many different solutions as possible. The number of solutions they found, i.e., children's fluency, as well as the strategies used to create equal groups,…

The aim of this study is to reveal the mathematical literacy skills of seventh grade students according to the PISA Mathematical Literacy Framework. In the study, a special case study from qualitative research methods was used. The participants of the study were 25 seventh grade students studying in the middle school of a public school in Giresun…

Contributing to research on undergraduate students' thinking about problem solving tasks, the present study reports on students' reasoning about two initial-value problems i.e. first-order linear ordinary differential equations with initial conditions. A qualitative analysis of task-based interviews and work written by 34 students revealed that…