Designing an Interactive Problem‑Solving Platform to Guide Students Step‑by‑Step
This article outlines a design for an educational platform that uses Polya's problem‑solving steps—understand, plan, execute, check—to provide timed hints, scoring based on time and hint usage, and competitive or cooperative modes that encourage autonomous learning and assessment.
Idea: By setting appropriate problems and answers, maximize student autonomy in solving problems. The solving process follows Polya’s steps: understand, plan, execute, check. When students encounter doubts at any step, provide targeted hints and evaluate their answers to resolve issues.
Design: Use Polya’s problem‑solving table as source of questions for each step.
Method 1.0: Left side shows the problem, right side has a hint button; students click for hints when needed.
Method 1.1: Add a timer that starts when a problem is opened; hints become available after a set time.
Method 1.2: Scoring rules based on solving time and hint usage; longer time or more hints lower the score, with weighting for relevance.
Method 1.2.1: “Discrimination” rule – higher‑level students have higher expectations; low‑level tasks yield lower scores for advanced students.
Method 1.3: PvP mode – students compete on the same problem or set, scores based on speed.
Method 1.3.1: Cooperative PvP – two‑team collaboration, final score assigned.
Model Perspective
Insights, knowledge, and enjoyment from a mathematical modeling researcher and educator. Hosted by Haihua Wang, a modeling instructor and author of "Clever Use of Chat for Mathematical Modeling", "Modeling: The Mathematics of Thinking", "Mathematical Modeling Practice: A Hands‑On Guide to Competitions", and co‑author of "Mathematical Modeling: Teaching Design and Cases".
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