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Learning with agency: Mathematics intelligent tutoring system for learning multiplication and division of fractions based on diagnostic teaching

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.

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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): Age / stage not established. Verify the participant population and task before transferring the findings.

Original authors’ abstract, reproduced under the linked source license:

Abstract A one-on-one dialogue-based mathematics intelligent tutoring system (ITS) for learning multiplication and division of fractions was developed and evaluated in this study. This system could identify students’ error types and misconceptions in real-time by using a block-based matching method. The adaptive dialogue-based instruction was supported by a response-driven tutoring model, which was constructed based on the diagnostic teaching methodology. Instructional strategies including provoking cognitive conflict, problem simplification and representational teaching were used in the tutoring model of the system. Effectiveness of the math ITS in remedial instruction was evaluated through a quasi-experimental study. The participants of the study were 66 sixth graders chosen from central Taiwan. They were divided into an experimental group of 35 and a control group of 31. One week after the pretest, the experimental group received 2-h one-on-one instruction via the math ITS, while the control group took a 2-h conventional teacher instruction with the same teaching content in the classroom. All participants took a post-test within 2 days after the remedial instruction. The results showed that the experimental group using the math ITS significantly outperformed the control group. Further analysis indicated that the math ITS had a significant effect on the lesser-performing group (the lower 75% in the pretest score). In addition, a usability and user experience survey showed that students were willing and likely to learn mathematics using the dialogue-based math ITS. Keywords: Adaptive instruction, Diagnostic teaching, Dialogue-based, Mathematics intelligent tutoring system, Multiplication and division of fractions

What kind of evidence is this?

Intelligent tutoring & adaptive learning · Comparative / pre-post study reported

Stage: Age / stage not established. 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

Figure 2 shows the quasi-experimental design of this study (Huang, 2018). Before the experiment, the tutoring corpus of the ITS was built by collecting students’ item responses from a paper-and-pencil test, categorizing expectation/misconception response patterns, and setting up tutoring scripts. Because the experiment in this study focused on remedial instruction, all students learned the tutoring materials in the ITS, and in the pilot study, students could finish these tasks within two hours, so the experimental intervention time was set at two hours. The pretest was held one week before the remedial instruction. After the pretest, the participants from the experimental group received two hours of one-on-one instruction via the math ITS, while those in the control group received two hours of traditional remedial instruction. When students in the experimental group used the ITS, they were guided by the tutor agent to finish the learning course by themselves without mathematics teachers. For both groups, the remedial instruction was held within one week after the pretest, and the teaching content was the same. Then, within two days of the remedial instruction program, all participants took a post-test in an equivalent form. The participants from the experimental group answered a questionnaire concerning the usability of and their user experience with the math ITS. All statistical analyses of the collected data were performed using SPSS version 22.

Limitations and uncertainty · source passage

Despite these advantages, there are still some limitations and barriers to overcome. In the current design of the math ITS, learners must input their responses and answers using a keyboard and mouse. This is time-consuming and inconvenient, particularly for learners unfamiliar with computers, which may cause learners to become impatient. In addition, the course content taught in this study was fraction arithmetic, focused on checking and correcting computation procedures and answers. However, complex word problems can often be solved using various calculating patterns. In addition, there are always multiple steps in a calculation, and sometimes a sequence of calculations can be treated in a different order. Furthermore, when dealing with multiplication and division, there are various forms of mixed fractions. For these reasons, it was difficult to include in the system all possible patterns of learners’ responses.

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

  1. 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.
  2. Days 16–30 · Design. Treat the paper as background evidence until its population is verified in the full text. Do not assign an age-specific intervention or extend adult results to children. Name an accountable owner and set the baseline, success threshold and budget before implementation.
  3. 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.
  4. Days 61–90 · Decide. Extract the participant ages or education stage, recruitment, task and comparator before selecting a local pilot. If these cannot be established, retain the paper for design discussion rather than age-band efficacy claims. 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

Shu-Chuan Shih; Chih-Chia Chang; Bor-Chen Kuo; Yu-Han Huang. Mathematics intelligent tutoring system for learning multiplication and division of fractions based on diagnostic teaching. Education and Information Technologies (2023-01-10). https://doi.org/10.1007/s10639-022-11553-z

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.