Earticle

This study focuses on the activities in which learners engage when they construct and enter their mathematical problem solutions as text in a generative artificial intelligence environment that is used as a digital resource in mathematics education. To this end, direct intervention in the mathematical content of the solutions presented by the research participant was intentionally avoided, and the role of the AI was restricted to providing feedback that supported the review and improvement of logical structure. This study employed a qualitative approach to analyze the entire process through which a pre-service teacher entered a previously solved mathematical problem solution as text in a ChatGPT environment, using paper-based solutions, screen-recording data, and post-task interview responses as data sources. The findings revealed that pauses, revisions, and reorganizations were repeatedly observed throughout the process of entering a completed solution into ChatGPT. This suggests that the pre-service teacher’s solution was not merely transcribed but was continuously adjusted and reorganized during the text-entry process, and that the ChatGPT environment functioned as a digital resource prompting the learner to reflect on and logically justify the solution.his study

This qualitative case study explores how calculation-dependent beliefs and control failures manifest in low-achieving high school students during definite integral problem-solving. Following the 2015 Revised Mathematics Curriculum, which introduces definite integrals through procedural definitions, students often prioritize formulaic computation over conceptual understanding. Using Schoenfeld’s framework (Resources, Heuristics, Control, and Beliefs), the study analyzed two low-achieving students.Findings revealed that calculation-dependent beliefs led to significant control failures, such as skipping analysis/planning and jumping directly to formulas without verifying signs or interval conditions. This resulted in errors like confusing displacement with distance. However, pedagogical intervention through graph visualization acted as a meta-cognitive mediator. Visualization prompted students to reorganize resources—identifying signs, interval splits, and symmetry—thereby activating self-monitoring and strategy revision. The study concludes that visualization is not merely a visual aid but a critical pedagogical tool that lowers entry barriers and provides external standards for self-regulation, helping low-achieving students transition from mechanical execution to structural understanding.

This study explored how three second-grade middle school students approached real-life contextual word problems, using Schoenfeld’s (1985) problem-solving framework of resources, heuristics, control, and beliefs. A qualitative case study design was adopted. The students’ problem-solving processes were video-recorded and analyzed through transcripts and follow-up interviews. Although all three students were aware of the mathematical knowledge needed to solve the problems, clear differences appeared in how they organized their knowledge, chose and applied strategies, monitored their work, and viewed problem solving. These differences became especially evident in a high-level task that required students to check and adjust their strategies. The findings suggest that success in solving real-life contextual word problems depends not only on what students know, but more importantly on how they use that knowledge. Heuristics guide the use of resources, control regulates the process, and beliefs support or constrain these actions. Therefore, students’ errors or unrealistic responses should not be seen simply as cognitive weaknesses, but as the result of interactions among these problem-solving components.

The purpose of this study is to investigate how individual students' heuristics and control actions contribute to the formation of group-level control during collaborative mathematical problem solving. To achieve this, the researcher observed two ninth-grade students solving an unstructured quadratic function task involving a drone’s trajectory using a "think-aloud" method. The analysis, based on Schoenfeld’s framework, revealed that while individual students actively utilized metacognitive control—such as questioning the use of conditions and setting strategic goals—these actions were not stably organized into effective group-level control, often leading to repetitive interruptions or regressive discussions. The findings provide two key pedagogical implications: (a) effective group-level control requires a pre-established collective consensus on fundamental problem premises, such as coordinate settings and variable interpretations; (b) individual self-questioning does not automatically scale to group-level control without specific social interaction mechanisms to bridge the two. Finally, this study suggests further research to explore the specific instructional conditions and discourse structures that facilitate the transition of individual metacognitive questions into stable group-level control actions.