Reversibility thinking carried out mentally in mathematical operations has an important role in the process of understanding concepts as it involves developing a thinking process from beginning to end and from end to beginning. This qualitative research aims to describe students' reversible thinking processes in solving algebra problems,…

This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students' behavior in these three stages of problem posing, especially focusing on investigating…

To help young students succeed in problem-based learning (PBL), researchers suggested investigating students' need for cognition (NFC), one's inclination to exert mental effort during learning. How one puts mental effort into a learning task is related to motivation. If motivated, students are more likely to engage in challenging tasks, put in…

In this study, a collaborative problem solving-based STEM course was implemented in a seventh-grade class. This study aimed to examine the effects of students' prior knowledge on their CPS-based STEM learning processes by using a mixed-methods approach. First, a lag sequential analysis was used to investigate individual cognitive and metacognitive…

In mathematics education, representations are used in place of mathematical structures, ideas, or relationships to concretize, transform, and represent them. When students interact with these representations, they engage in various cognitive activities such as thinking, reasoning, understanding, remembering, problem-solving, attention, and…

This study sought to understand how students activate number sense in determining the position of fractions on a number line and identify how the natural number bias and number sense influences students' thinking processes. The study utilized the Cognitive Task Analysis (CTA), involving four fifth-grade elementary students as the research…

Critical thinking is a fundamental competence in 21st-century education, particularly in mathematics, where students frequently encounter contradictory information that requires logical reasoning and reflective judgment. This study explores the stages of critical thinking among junior high school students when solving contradictory mathematical…

Open-ended learning environments (OELEs) support constructivist approaches to STEM learning. This promotes student engagement and facilitates a deeper understanding of STEM topics. Despite their benefits, OELEs can present significant challenges for novice learners. Recent studies have revealed the complex relationship between students' affective…

The ability of solving problems collaboratively has been increasingly significant. This research takes mathematics open-ended problems as the tasks and carries out collaborative problem solving with multi-machine video recording in the classroom environment aimed at 112 student pairs and 56 four-person student groups stemming from 224 students in…

This exploratory and descriptive study aims to theoretically promote the schema of pseudo-thinking processes in mathematical problem-solving by students. The participants in this study were 36 eighth graders and one math teacher. The researchers collected the data using tests and interviews. The results showed that the structure of pseudo-thinking…

Project-based learning (PBL) plays a critical role in fostering interdisciplinary integration within science, technology, engineering, and mathematics (STEM) education. However, its complexity often hinders students' ability to apply knowledge and solve problems, particularly in environments that lack psychological and cognitive support. This…

The purpose of this study is to investigate students' thinking of direct, inverse and nonproportional problems. Thirty two seventh grade students from three different government schools participated in this study. To collect the data, the participants were asked to solve 9 open-ended problems, including 3 direct, 3 inverse and 3 non-proportional…

Both sketching and self-explanation are widely believed to be effective for problem-solving in science learning. However, it is unclear which aspects of these strategies promote learning and how they might interact. Compared to a read-only baseline, we examined the impact of instructing 11-year-old students to solve science problems to sketch,…

In this study, it is aimed to determine the algebraic thinking habits of two eighth grade school students through the answers they gave in the process of solving mathematical problems. The algebraic habits of mind (ZCA) theoretical framework developed by Driscoll (1999) was used to reveal these thinking habits. The research design of this study is…

Mathematics pre-service teachers (PSTs) need opportunities to learn best practices in teaching mathematics, e.g., productive struggle. Productive struggle happens when students work through challenging problems that are not straightforward. This paper describes mathematics PSTs' engagement with productive struggle in a mathematics methods course.…