How Middle School Students Can Build Simple Decision Models for Choosing a Laptop

1. Students' Models Are Effective

Comprehensive evaluation models are important mathematical tools for scoring and ranking multiple alternatives. Classic methods such as TOPSIS, entropy weighting, and Analytic Hierarchy Process are beyond the curriculum of middle‑school students, but everyday decisions—choosing a university, rating tourist sites, or selecting a candidate—are typical evaluation problems.

Mr. Wang teaches mathematical modeling on Saturdays in a suburban school. His current laptop is too heavy, and he wants to purchase a new notebook priced around 5,000 CNY. Design a mathematical model to help him choose the most suitable computer.

Eight‑grade students proposed several simple models:

Screening model: sequentially eliminate options that do not meet criteria, keeping the last remaining one.

Rank‑sum method: rank each laptop on every indicator, sum the ranks, and select the smallest total.

Rank‑product method: similar to rank‑sum but multiply the ranks and choose the smallest product.

Weighted rank‑product: after ranking, multiply each rank by a weight reflecting the indicator’s importance (smaller weight for more important indicators when using a “smaller‑is‑better” scheme).

Other methods (not detailed).

2. Good Models Can Be Further Improved

After students present solutions, teachers and students reflect on them, leading to a progressive refinement process:

Initial idea: devise a model that considers multiple factors.

Model 1: rank and sum to obtain a composite score.

Reflection 1: explore alternative aggregation methods.

Model 2: rank and multiply to obtain a composite score.

Reflection 2: incorporate indicator importance.

Model 3: add weighted terms to account for importance.

…

This iterative discussion deepens students’ understanding of modeling and encourages further improvement.

3. Guiding Students Beyond the Basics

Once students have solved the problem, teachers can use the shortcomings of their models as a springboard to introduce more advanced techniques such as Analytic Hierarchy Process or entropy‑weight methods for handling subjective weights.

4. Summary

For beginners in mathematical modeling, teachers should respect students’ ideas, encourage complete solutions, and, based on students’ reflections, gradually introduce new modeling concepts.