Actionable companion · Assessment & reasoning
Learning with agency: A Theoretical Framework for a Mathematical Cognitive Model for Adaptive Learning Systems
AI-assisted editorial implementation guide, separate from the original research. Proposed actions are not claims or recommendations attributed to the source authors. No independent peer review of this guide is asserted.
Evidence and context
Title and abstract screening; stage labels describe reported settings, not verified numerical ages. Design labels require full-text appraisal. Reported stage(s): Secondary school. Verify the participant population and task before transferring the findings.
Original authors’ abstract, reproduced under the linked source license:
The emergence of artificial intelligence has made adaptive learning possible, but building an adaptive system requires a comprehensive understanding of students’ cognition. The cognitive model provides a crucial theoretical framework to explore students’ cognitive attributes, making it vital for learning assessment and adaptive learning. This study investigates 52 experts, including primary and secondary school teachers, mathematics education experts, and graduate students, based on the 16 cognitive attributes in the TIMSS 2015 assessment framework. Through an analysis of their attribute questionnaires, the Interpretive structural modeling (ISM) method is used to construct a five-level mathematical cognitive model. The model is then revised through oral reports and expert interviews, resulting in a final cognitive model ranging from “memorize” to “justify”. The cognitive model describes the relationship between different attributes in detail, enabling the development of adaptive systems and aiding in the diagnosis of students’ cognitive development and learning paths in mathematics.
What kind of evidence is this?
Intelligent tutoring & adaptive learning · Qualitative / mixed methods
Stage: Secondary school. Screening labels describe reported context and study-design language. They are not a risk-of-bias rating or proof of effectiveness for an age band.
Study methods · source passage
The cognitive model construction in this study involved two stages. In the first stage, 33 primary school mathematics teachers, 15 graduate students, and 4 mathematics education specialists in Shanghai were invited to evaluate the relationships between cognitive attributes from both practical and theoretical perspectives. They needed to judge the pair relationship between the 16 cognitive attributes in Table 1. In the second stage, six mathematics education professors were invited to revise the preliminary model, and a fourth-grade child was randomly selected to give an oral report to verify the efficacy of the cognitive model.
Limitations and uncertainty · source passage
Although this study offers a new approach to constructing cognitive models, there is still a significant amount left to explore. Firstly, it is important to note that the cognitive model of mathematical cognition developed in this study was solely constructed using interpretive structural modeling (ISM) and does not incorporate specific mathematical content. However, cognitive attributes, such as procedures, skills, strategies, and knowledge, are crucial in the problem-solving process. This includes not only procedures and skills but also knowledge. The vast system of mathematical knowledge is at the heart of mathematics education, and constructing a cognitive model that integrates knowledge content requires considerable time and effort. Therefore, mathematics educators and cognitive model researchers should continue to focus their efforts on this task. Secondly, while the cognitive model was built using various research approaches, the underlying data still rely on expert calibration, and the model’s rationality must be evaluated using longitudinal data from students. The cognitive model serves as the foundation for cognitive diagnosis, and cognitive diagnostic assessments can help refine the model further. As a result, cognitive diagnostic assessments can verify the validity of the mathematical cognitive model in the following stages of research. Thirdly, it should be noted that this cognitive model is exclusively suited to the context of mathematical problem-solving processes and has limited applicability to other domains. The cognitive attributes investigated in this study, such as compute, modeling, and classify, possess distinctive mathematical characteristics that diverge from the core competencies of other disciplines. Nevertheless, it is worth highlighting that some of these cognitive attributes are also relevant to other subjects, such as retrieve and classify, which hold crucial value in science education.
Design the system before the pilot
Document the learner model, mastery rule, hint sequence and adaptation signal. Compare adaptive routing with the same content in a non-adaptive sequence. Check whether early errors lead to persistent low-expectation pathways.
- Use common rubrics, blind scoring where feasible and a fresh unaided reasoning task. Document permissible assistance and avoid treating AI-detector scores as proof of misconduct.
A 90-day district pilot
- Days 1–15 · Appraise. Have the curriculum lead and a teacher read the methods and limitations. Record the study design, sample, comparator, outcomes and evidence gaps. Define a local question that the study can help inform.
- Days 16–30 · Design. Ask learners to attempt a problem unaided, compare an agent hint, explain a revision and verify the final reasoning against a trusted source. Make the permitted use explicit for each assignment. Name an accountable owner and set the baseline, success threshold and budget before implementation.
- Days 31–60 · Test. Start with a small voluntary cohort, preserve an accessible non-AI route and require teacher review. Use synthetic or de-identified examples; approve data handling and tool terms through district processes.
- Days 61–90 · Decide. Measure unaided transfer and delayed retention, calibration of confidence and the ability to identify an incorrect AI explanation. Record whether help-seeking becomes answer copying. Compare with baseline, document uncertainty and stop or revise if learning worsens, access is unequal or critical errors persist.
The board decision brief
Report the learning problem, evidence quality, participating population, total cost including review time, measured benefit, errors, access differences and remaining uncertainties. Make a dated recommendation to stop, revise or expand. A positive perception survey alone does not establish learning improvement.
Attribution and reuse
Siyu Sun; Xiaopeng Wu; Tianshu Xu. A Theoretical Framework for a Mathematical Cognitive Model for Adaptive Learning Systems. Behavioral Sciences (2023-05-12). https://doi.org/10.3390/bs13050406
Companion prepared 2026-10-30. Original authorship and DOI are preserved. The abstract is an attributed source extract; the implementation plan is new AI-assisted editorial material, offered under the same CC BY 4.0 license. This guide has not undergone independent peer review.