Actionable companion · Learning design & outcomes
Learning with agency: Developing a cognitive model of solid geometry based on Interpretive Structural Modeling method
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:
Abstract With the advancement of science and artificial intelligence, education is experiencing significant innovation. The adaptive learning system is emerging as a promising approach to achieving personalized learning. The cognitive model plays a crucial role as the fundamental rationale behind the adaptive learning system. Currently, there is no uniform and highly operational method for constructing cognitive models. This study adopts Interpretive Structural Modeling (ISM) as the foundational approach for constructing a cognitive model of solid geometry. Based on literature and expert opinions, 17 cognitive attributes of high school solid geometry were identified. Subsequently, a questionnaire survey involving 40 experts was conducted to establish the contextual relationships among these attributes. Applying the ISM method resulted in a seven-level model. This model was then revised based on expert opinions to create the final cognitive model, revealing three primary paths within the domain of high school solid geometry. This paper contends that the use of the ISM method for constructing cognitive models is effective and objective. The resulting cognitive model unveils the content structure of high school solid geometry, and provides an innovative perspective on the construction of cognitive models. Keywords: Online learning, Adaptive learning system, Cognitive model, Interpretive structural modeling (ISM), Mathematics education
What kind of evidence is this?
Intelligent tutoring & adaptive learning · Survey / observational study
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.
Limitations and uncertainty · source passage
This study applies ISM method to construct a cognitive model of high school solid geometry. There are some limitations in this study. Firstly, the attribute determination in this study was completed through the literature review and expert opinions. However, although it is less subjective than traditional methods, there is still subjectivity within, so further research is needed to verify whether these attributes are comprehensive and accurate in covering solid geometry. Secondly, while the model obtained in this study is based on specific knowledge content and possesses a certain degree of practicality, further analysis is necessary to ascertain its applicability in an adaptive learning system. The utility of the cognitive model obtained in this study can be further verified by using structural equation modeling and cognitive diagnostic assessment in future large-scale assessments.
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.
- Specify a measurable learning objective, a comparator and a task without tool assistance before adopting a system.
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
Heyang Zhang; Xiaopeng Wu; Mingyue Ju. Developing a cognitive model of solid geometry based on Interpretive Structural Modeling method. Heliyon (2024-02-24). https://doi.org/10.1016/j.heliyon.2024.e27063
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.