A correspondent writes:We emphasize the idea that students should approach problems in multiple ways. This has caused me to wonder about patterns. For example:students might conclude that 3^0=1 because of the pattern 3^4=81, 3^3=27, 3^2=9, 3^1=1orwhen the second difference is constant, students will conclude that the function is quadraticorwhen a function is concave up, the… Continue reading Patterns
Tag: Arithmetic
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
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
Crowd-Sourcing
Well, not much of a crowd, because not many people read this blog. Still... I created four worksheets of sorts, each one consisting of a short title and images of a dozen circles. Each circle is divided pizza-like into slices, as in the example above. The four titles: Angles, Fractions, Time, and Percents/Money. Here is… Continue reading Crowd-Sourcing
March 19 in Palo Alto
Once again, I will be presenting function diagrams to a math circle for teachers, this time for the American Institute of Mathematics Circle for Teachers. This will happen on March 19, at 340 Portage Ave. Palo Alto, from 5:00 to 8:00 p.m. There is no charge, and in fact a free dinner is provided. Here… Continue reading March 19 in Palo Alto
All of high school math in one year?
In my previous post, I responded to Michael Thayer's comments about my Mathematics Overview. In this post I will respond to Mike's proposal for a one-year course to replace all of high school math.Mike and I largely agree about the failings and shortcomings of traditional curriculum and pedagogy, but I don't agree with his solution.… Continue reading All of high school math in one year?
More on the Mathematics Overview
In his Hyperbolic Guitars blog, Michael Thayer writes:I've been mulling over the one-year course idea some more. And what to my wondering eyes did appear (thank you, @tieandjeans) but this really spectacularly well-thought-out and well-organized course outline created by Henri Picciotto. It's got everything, really, that I'd love to see in the course I'd proposed, and it… Continue reading More on the Mathematics Overview
Mathematics Overview
I have written an outline of one possible version of the foundational topics of secondary school math, covering key concepts usually taught in grades 7 to 10. The idea was to write a one-year review course for seniors who have had trouble with math up to that point, but still intend to go to a… Continue reading Mathematics Overview
Fraction Arithmetic
[I posted an edited version of this post, including an approach to the division of fractions, here.]If you are familiar with my Web site, you probably know my interest in visual representations of algebraic ideas. The seed for this was probably planted during my decade as an elementary school teacher, where I learned about visual… Continue reading Fraction Arithmetic
Henri's Math Education Blog 