The above map is an attempt at a curriculum development model. Traditional pedagogy stays at the top, as it is based on the belief that skills practice and teacher explanations are sufficient to build student understanding. Understanding acquired this way, plus the skills, allow the student to apply the ideas.Would that it were that simple.In… Continue reading A Curriculum Model
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Inscribing Geoboard Squares in Polyominoes
Draw a polygon following grid paper lines. No crossings, no holes — in other words, a polyomino.Now try to inscribe a square in it, with all its vertices at lattice points on the perimeter of the polyomino. Here are two examples: Conjecture: it is impossible to draw a polyomino that does not have such… Continue reading Inscribing Geoboard Squares in Polyominoes
Proving Pick’s Formula
Pick's formula is a way to find the area of a geoboard polygon by counting interior pegs and boundary pegs. Students can discover the formula by doing some experimenting under teacher guidance (see Geometry Labs 8.6 or Algebra: Themes, Tools, Concepts 4.12.) I have used this in the classroom for decades, because it is such… Continue reading Proving Pick’s Formula
Another "K-12 Unsolved" Problem
In a recent post, I mentioned a problem posed in 1917, which remains unsolved and which lends itself to use in K-12 education:Consider an n by n lattice. Is it always possible to choose 2n points in it so that no three points are in a line? Today, I present a related unsolved problem I… Continue reading Another "K-12 Unsolved" Problem
Asilomar Report, Part 2
Read about my morning at the Asilomar meeting of the California Math Council here.My afternoon was taken up with function diagrams. First, I attended Martin Flashman's presentation on this topic, then I made my own presentation, and finally I had dinner with Martin. (If you know nothing about function diagrams, read no further. Or find… Continue reading Asilomar Report, Part 2
Algebra: Themes, Tools, Concepts and the Common Core
Way back in the early 90's, I co-authored the textbook Algebra: Themes, Tools, Concepts (ATTC) with Anita Wah. It failed to become a best-seller, in part because while the lessons work well with students, the book is not very easy for teachers to manage. Still it's a good book. We have continued to use different… Continue reading Algebra: Themes, Tools, Concepts and the Common Core
Summer Workshops
I'll be teaching four workshops in June, at the Urban School of San Francisco's Center for Innovative Teaching. I just posted the info here. Some changes from past years:I've broken up my Geometry workshop, which used to be three or four days, into two chunks, two days each. The first (Hands-On Geometry) will be based… Continue reading Summer Workshops
Asilomar report, Part 1
Once again, I had a great time at the Asilomar conference of the California Math Council. Here are some notes from the first two sessions I attended.Scott Farrand (of Cal State Sacramento) and UC Davis's Rick West's presentation "Diophantine Equations Can Hide Geometric Surprises" was a fun way to start the day.Think of two whole… Continue reading Asilomar report, Part 1
No Three on a Line
In a recent post, I mentioned K-12 Unsolved, the project I'm involved in that aims to publicize 13 unsolved math problems, in the hope that an appropriate version of each problem will find its way into K-12 classrooms. One problem we looked at was posed by Henry Dudeney in 1917. Here is the problem: Consider… Continue reading No Three on a Line
Geoboards and Dot Paper
If you are familiar with my curricular creations, you know that I often use the geoboard as a microworld to introduce interesting problems and important concepts. This is in line with my call for a tool-rich pedagogy. (A geoboard is a square lattice pegboard on which students use rubber bands to create and investigate geometric… Continue reading Geoboards and Dot Paper
Henri's Math Education Blog 