generaleducators
Why Assumptions Matter More Than Answers
A deep dive into assumption digging — the process of tracing any claim back through its chain of justifications to the foundational assumptions.
11 min read
Articles
Thirteen articles on theory building and academic thinking — from classroom practice to curriculum design to conversations at home.
Audience:
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parents
How to Have Mathematical Conversations at Home
A practical guide for families, offering concrete conversation starters that develop careful thinking habits through natural, low-pressure mathematical discussions at home.
12 min read
parents
Your Child's Math Homework Is Missing Something Important
Written for parents, this article explains the gap between knowing math formulas and understanding why they work, and argues that the habit of asking 'why' is one of the most valuable skills.
10 min read
educators
Three Activities That Change How Students See Mathematics
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
educators
What Happened When We Let Students Build Their Own Math
A detailed account of implementing a nine-session theory building course with thirty students across two schools in Pune — what worked, what did not, and what students said they valued.
12 min read
educators
What Does It Actually Look Like to Teach This Way?
An honest account of the facilitation challenges in running a theory building classroom — knowing when to intervene, handling productive struggle, and managing group dynamics.
13 min read
educators
How to Teach Proof Without Two-Column Proofs
Critiques the two-column proof format and proposes a tree representation that makes logical structure, hidden assumptions, and gaps in reasoning visible.
12 min read
educators
Theory Building: The Missing Piece in Math Curricula
Analyses how major curriculum frameworks already call for reasoning and argumentation, yet classroom practice falls short — and argues that theory building offers a concrete way to close that gap.
12 min read
generaleducators
From Geometry to Ethics: One Framework for Thinking Across Disciplines
Shows how the thinking tools of mathematical theory building appear in structurally similar forms in science and ethics, making the case for a transdisciplinary approach.
13 min read
generaleducators
Why Being Wrong Should Be Celebrated in School
Argues that errors in mathematical reasoning are among the most valuable learning opportunities when handled well in the classroom.
12 min read
generaleducators
What Happens When You Change the Rules of Geometry
Describes what happened when students were asked to do geometry in a world with only six points, discovering that changing the rules changes the truths.
13 min read
generaleducators
The Art of Defining: Why Most Arguments Are About Words, Not Facts
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
generaleducators
What If Math Class Taught You How to Think, Not Just How to Calculate?
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