This study examined the metacognitive knowledge of Finnish comprehensive school students and explored whether grade-based differences in metacognitive knowledge exist among 6th, 7th and 9th graders. Integrating qualitative (declarative, procedural, conditional) and contextual (person, task, strategy) frameworks, the research aims for a…

This study explores the self-efficacy and problem-solving skills of middle school mathematics students. The students -- 111 9th graders who were studying a unit for the analysis of function -- were given mathematics instruction that was based on either dynamic or static visualization. Findings revealed a positive impact of instruction that was…

Algebra I encompasses several topics that serve as a basis for students' subsequent mathematics courses as they progress in school. Some of the key topics that students struggle with is solving linear equations and algebraic word problems. There are several factors that may contribute to this ongoing struggle for students such as the structure of…

Sixty (35 girls) ninth graders were assessed on measures of algebraic reasoning and usage of visual and symbolic representations (with a prompt for visual use) to solve equations and inequalities. The study grouped visual representations into two categories: arithmetic-visual, which entailed the use of real-world objects to represent specific…

In this paper, we describe an experiment in using history to work on problem-solving and the relationship between arithmetic and algebra. The students involved attended the first year of the Italian upper secondary school (grade 9). The original sources we used are problems from Italian treatises on arithmetic and algebra that appeared in the…

Developing self-regulated learning (SRL) skills among young adolescents is crucial for lifelong learning, and teachers play a vital role in fostering these skills. Problem-solving is a key SRL skill; however, both learners and teachers encounter challenges during the problem-solving process and in evaluating its incorporated strategies. To tackle…

This study describes students' learning obstacles in solving early algebra problems requiring functional thinking ability. To reach this aim, qualitative research was conducted in this study. Participants of this study were 39 ninth graders and a mathematics teacher at one of the lower secondary schools in Bandung, Indonesia. The data were…

This study explores the effectiveness of GeoGebra in enhancing students' understanding of vectors in mathematics education. The research compares traditional teaching methods with the application of GeoGebra to determine its impact on conceptual and procedural knowledge acquisition. Vectors are often challenging for students to grasp due to their…

To solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving…

This study aims to investigate affordances of models and modelling in design projects in technology education. To learn more about affordances when working with models and modelling, four Swedish technology teachers were interviewed using a narrative approach. Despite a small number of informants data were rich, containing detailed descriptions of…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

This article analyses the impact of the role and significance of the virtual laboratory on ninth-grade lyceum students' attainment of more-in depth scientific knowledge and improved practical skills in the physics topic area of electromagnetism. Pedagogical experiments were conducted at the Baku European Lyceum. The results show that the virtual…

Mathematical modeling is a challenging and creative process. If one considers only interim or final solutions to modeling problems or interviews modelers afterward, often only their "explicit" models are accessible -- those expressed in work products or evinced in verbal and written reflections. The inner world of tacit knowledge and its…

Despite national curricula and instructional reforms calling for collaborative problem-solving skills (CPS), however, there is an absence of a theory-laden model showing how to effectively construct CPS for science learning. We therefore developed and validated a simulation-based CPS model that exploits its constructs, sequences, and causal…

This study aimed to describe and compare the students' fluency, flexibility, and originality in solving non-routine problems in the Palembang context. They were depicted from the student's fluency, flexibility, and originality of solving the horizontal and vertical mathematization forms. This qualitative study employed. The subjects of this study…