Articles · Stories · Curriculum
The thinking skills academics actually use — defining carefully, questioning assumptions, building from first principles — made accessible to everyone.
Explores what mathematicians have learned about the art of defining — how to choose good definitions, what makes one better than another, and why these skills matter far beyond mathematics.
15 min read
An overview of how mathematics education could develop general thinking skills through theory building — defining carefully, questioning assumptions, classifying, and constructing knowledge — rather than just teaching formulas and procedures.
12 min read
A practical guide to three classroom activities — the Podgon game, triangle theory building, and discrete geometry — that shift mathematics education from reproducing results to constructing knowledge.
15 min read
Fiction that develops critical thinking — stories that pose problems, invite definitions, and reward careful reasoning, for readers of all ages.
An ancient shepherd invents counting, place-value systems, and measurement — all to keep track of his herd of sheep, cattle, and the occasional dinosaur.
Ages 10+ · 4 parts
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Two friends debate whether squares are rectangles and humans are animals — discovering that classification systems are choices, not facts, and that some choices are better than others.
Ages 10+ · 4 parts
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Dr. Crivsola tries to understand the human body without dissection — using only observation, logic, and the scientific method of proposing models, testing predictions, and refining theories.
Ages 12+ · 4 parts
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A mother and son try to figure out who committed a neighbourhood murder using probability and Bayesian reasoning — with help from their cousin Glagalbagal.
Ages 12+ · 3 parts
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A definition-guessing game that develops skills in careful defining, counterexample reasoning, and precision of mathematical language.
Grades 6-10 · 4 documents
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Students build a theory of triangles by listing claims, constructing proof trees through assumption digging, and discovering definitions, axioms, and the structure of mathematical reasoning.
Grades 8-11 · 4 documents
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Students create finite-point worlds by choosing definitions and rules, then explore how concepts like straight lines, bisection, circles, and triangles behave when assumptions change.
Grades 8-11 · 4 documents
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