# Mathematics design

Mathematical literacy develops when learners mathematize a problem that feels
real. Shopping comparison, route estimation, evidence from data, geometric
design and random phenomena are contexts; a bare exercise with a person's name
is not.

The task must require learners to identify quantities and relationships, solve
or model, and communicate with an equation, diagram, table, graph, symbol or
reasoned explanation.

Stage arcs:

- primary 1–3: 情境问题 → 操作感知 → 建立表象 → 练习表达;
- primary 4–6: 真实问题 → 抽象列式 → 策略比较 → 反思表达;
- junior high: 情境问题 → 数学抽象 → 推理求解 → 模型解释 → 迁移;
- senior high: 真实情境 → 数学化 → 建模求解 → 论证反思 → 拓展.

Task design for compulsory-education “三会”:

- mathematical eyes: identify what can be quantified and which quantities
  relate;
- mathematical thinking: abstract, infer, model, ask why the representation
  works and compare another route;
- mathematical language: make the result inspectable in a diagram, expression,
  table, graph or precise explanation.

Non-negotiables: one authentic mathematizable problem; at least one strategy
comparison; a visible mathematical representation; and computation serving the
problem rather than an isolated drill.

Typical misconceptions: choosing an operation from a keyword; obtaining a
correct expression but being unable to explain its meaning; treating the first
method as the only method. Build the activity and quiz distractors from these.

The transfer task changes the numbers, constraints or context surface while
preserving the mathematical structure, and still asks learners to represent
and justify.