I have taught grades K-5, high school, future teachers, and working teachers, but I have never taught middle school, except for a couple of summer jobs some years ago. Nevertheless, my curriculum materials are widely used at that level, and maybe half the teachers I have worked with are middle school teachers.I just started a… Continue reading Middle School
Author: hpicciotto
Egyptian Fractions
I had a great time at the Julia Robinson Math Festival the weekend before last. Hundreds of kids attended, most of them girls, it seemed to me. The setup: many, many tables; at each table, one or two adult guides, and a math problem that combines access and depth. Students choose a table, and work… Continue reading Egyptian Fractions
The Geometry of the Parabola
Parabolas are a central topic in high school algebra classes, but, perhaps because of the rigid separation between algebra and geometry classes in the US secondary curriculum, we do not usually treat them as geometric objects. While most teachers are aware of some of the parabola's geometric properties, few of us are familiar with the… Continue reading The Geometry of the Parabola
Saturday workshop
I will present a workshop at the the Math Teachers' Circle in Palo Alto (at the American Institute of Mathematics.) The topic is area on a lattice, which we will explore on geoboards and dot paper. We will discuss "curricular" classroom applications (the Pythagorean theorem, simplifying radicals) as well as Pick's theorem and its proof,… Continue reading Saturday workshop
The Common Core
Now that I'm a freelance math education consultant and curriculum developer, I need to pay attention to the Common Core State Standards as they affect everything I do in my professional life. Merely listening to talks about the standards, and reading angry posts about them did not provide a lot of information. On the other… Continue reading The Common Core
A Curriculum Model
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
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
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