Background/purpose: This study aims to analyze students' ability to solve differential calculus problems in relation to their prior mathematical knowledge (PMK). Materials/methods: A qualitative research design method was employed. Participants in this study were 103 third-semester students at the university enrolled in the Differential Calculus…

Background/purpose: This study investigates the effectiveness of Problem-Based Learning (PBL) integrated with scaffolding in enhancing problem-solving skills among students with varying levels of prior knowledge. The main objective is to determine how scaffolding, when combined with PBL, can support students in developing stronger problem-solving…

Word problems are frequently taught in shallow contexts, where students primarily use procedural knowledge to solve problems and struggle to transfer their learning to real-life situations. This study examines how extra-mathematical knowledge and motivation may enhance the learning process. The study involved 345 fifth-grade students (51.2% male)…

Graph theory allows the student to work on problems that require imagination, intuition, systematic exploration, conjecturing, and reasoning. It implies that mathematical investigation skill is essential to be proficient in Graph Theory. In this study, we conduct empirical research that deals with associational research. There were 97 students…

In numerical cognition research, the operational momentum (OM) phenomenon (tendency to overestimate the results of addition and/or binding addition to the right side and underestimating subtraction and/or binding it to the left side) can help illuminate the most basic representations and processes of mental arithmetic and their development. This…

Nowadays, mathematics teachers in K-12 strive to promote their students' mathematical knowledge and computational thinking (CT) skills. There is an increasing need for effective CT-embedded mathematics learning material and a better understanding of students' views toward them. In this work, we present the results of a research study, which…

Background: During their university studies, student teachers are equipped for the teaching profession in various domains of knowledge and practice. In addition to learning pedagogic skills for practice purposes, they also expand their knowledge of the subjects that they will teach. In mathematics teacher education, one important principle is that…

Computational thinking is acknowledged as an essential competency for everyone to learn. However, teachers find it challenging to implement the existing learning approaches in K-12 settings because the existing approaches often focus on teaching computing concepts and skills (i.e., programming skills) rather than on helping students develop their…

The aim of this study was to examine the relationship between common classroom help-seeking determinants (achievement goals, self-efficacy, prior knowledge, gender, and help-seeking perceptions) and help-seeking behaviors online (hint use percentage, latency of help seeking, answer attempt percentage, feedback level percentage, and seeking help…

We report on a research study conducted within a transition-to-proof course for mathematics majors at a large public university. Within the course, students explored famously unproven conjectures and reflected on how their perspectives of mathematics changed through this exploration (if at all). In this report we share students' takeaways from the…

When presented with a problem in mathematics class, students often function as problem performers rather than problem solvers (Rigelman 2007). That is, rather than understanding the problem, students focus on using an operation to complete it. Students' tendencies to act as problem performers can prevent them from suggesting problem-solving…

Psychologists and mathematics educators have long viewed flexibility as critical to students' mathematical development. In this paper, we focused on the multidimensional nature of flexibility to better understand how preference, knowledge, and use of effective methods for solving algebra problems are related. In Study 1, we identified…

In our study, 32 German and Swiss 8th/9th-grade classes of lower-secondary school worked with their teacher on the same proving problem. The sample belongs to the Swiss-German study "Quality of Instruction, Learning Behavior and Mathematical Understanding". Our data analyses relate to the teachers' approaches to generating a specific…

This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students…

The current project, Exploring Math Education Relations by Analyzing Large Data Sets (EMERALDS) II, is an attempt to identify specific Common Core State Standards procedural, conceptual, and problem-solving competencies in earlier grades that best predict success in algebraic areas in later grades. The data for this study include two cohorts of…