Articles
Ideas, derivations and stories from the classroom
Blog posts on education, learning and teaching, written for parents and teachers. In-depth articles on pure mathematics.
Blog
Blog articles
On how children learn and how teachers teach: pedagogy, classroom ideas and practical tips for school and home.
- AI, School and Your Child: What Is Your Role?
- We Are Not Teaching Mathematics. We Are Teaching Studenting.
- Gamify the Problem: Teaching Mathematics Through Puzzles and Play
- Ask Questions, Not Doubts: Small Words That Shape Mathematical Thinking
- One-Shot or Short: Two Shops and Four Solve-Keepers of the Pedagogy Market
- Why I Started Getting Bored While Teaching?
- A Smart Strategy for Maxima-Minima in Calculus
- Rhombus, Attention Residue, Doubts: A Teacher’s Dilemma
- The Art of Derivation: A Path to Mathematical Clarity
- Exploring Voronoi Diagrams
- Mahaviracharya’s Series: Deriving the Sum of Squares in Natural Numbers
- Mathematics of Chhappan Bhogas (56 Dishes) in Indian Cookery
- Optimizing Math Learning: Three Essential Steps
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PDF articles
In-depth PDF articles
Pure mathematics, written in depth. Each article takes one problem or idea and works it through to the proof. They open as PDFs in Google Drive.
Stirling Numbers and Bell Numbers: Counting Partitions, Cycles and Equivalence Relations
How many equivalence relations does a set have? Count its partitions: Stirling numbers, Bell numbers and Dobinski’s formula.
Open PDF →One Definition, Three Curves: Common Properties of Conic Sections
One focus–directrix law, SP = e·PM, proves the shared properties of the parabola, ellipse and hyperbola at once.
Open PDF →Frégier’s Theorem in Coordinate Geometry: Proofs, Formulas, and Problem Solving
Chords making a right angle at a conic concur at a fixed point on its normal.
Open PDF →Checking Differentiability by using Continuity of Derivative
A quick, reliable test for differentiability at a point, with its limits.
Open PDF →Unifying Trigonometric Finite Products and Sums
From roots of unity to logarithmic derivatives: one method for many classic results.
Open PDF →Uncoupling the Circle: Lucas’s Problème des Ménages
Solving the ménage problem with inclusion–exclusion.
Open PDF →Why Functional Symmetry and Term-by-Term Comparison Fail to Prove the Riemann Hypothesis
Where a tempting line of argument breaks down.
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