A few weeks ago, I led a workshop on taxicab geometry at the San Jose and Palo Alto Math Teacher Circles. Taxicab geometry is based on redefining distance between two points, with the assumption you can only move horizontally and vertically. So the taxicab distance from the origin to (2, 3) is 5, as you… Continue reading Taxicab geometry
Author: hpicciotto
Polyarcs
My early forays as a curriculum developer date back to my days as a K-5 math specialist in the 1970's. A key insight of my young self was that activities intended for students were that much more worthwhile if they were also interesting to me. I learned to view with suspicion activities that were boring… Continue reading Polyarcs
April: in the streets!
Taxicab Geometry I will be leading workshops on taxicab geometry at the AIM Math Teachers Circles next week. Here is the announcement:Please join us for math and dinner with Henri Picciotto (www.mathedpage.org)!The topic will be Taxicab Geometry. Many concepts in geometry depend on the idea of distance: the triangle inequality, the definition of a circle, the value… Continue reading April: in the streets!
Geoboard Problems for Teachers
At the San Francisco Math Teachers' Circle yesterday (March 4, 2017), we explored four "teacher-level" geoboard problems (All can be adapted for classroom use.) Here is a brief report, including some spoilers, I'm afraid. Pick's Formula It turns out that the area of a geoboard polygon can be figured out by counting the lattice points… Continue reading Geoboard Problems for Teachers
Calculation
Many students have weak arithmetic skills. Many teachers blame this on calculator use, but it is just as likely that the real reason lies elsewhere. For one thing, the teaching of arithmetic traditionally does not involve developing any understanding, so the learning is shallow and fragile. For another, students correctly feel that mindless arithmetic is… Continue reading Calculation
Geometry Boot Camp!
I will offer two workshops this summer (2017), at the Head-Royce School in Oakland, CA. Sign up for either or both! June 26-27: Hands-On Geometry (grades 6-10) June 28-30: Transformational Geometry (grades 8-11) If the times or locations don't work for you, I can offer a workshop for your school or district. Contact me directly.… Continue reading Geometry Boot Camp!
Comparing two approaches
Much can be said in defense of practice exercises, but when all is said and done, very few students develop deep understanding from routine practice. For example, compare these two approaches to the area of a trapezoid. Approach 1The teacher says: ”The area of a trapezoid is given by the formula h(b1+b2)/2, where h is… Continue reading Comparing two approaches
Algebra Manipulatives
A middle school teacher writes: Just a little note and question about Lab Gear. I have been having so much fun with my students using Lab Gear again this year. The 3D-ness of it totally blows the other (cheaper) algebra tiles that I used last year out of the water! I have heard this often… Continue reading Algebra Manipulatives
Yet More on Homework
This is part of a multifaceted strategy to teach heterogeneous classes. Read about it in this article: Reaching the Full Range.A correspondent writes, presumably in response to my lagging homework concept:I love your approach and a lot of the details. I guess my only immediate reservation would be the necessity for homework. A lot of U.S.… Continue reading Yet More on Homework
Time and Tide
This is my yearly report on the Asilomar conference of the California Math Council, Northern Section. Because I was presenting three times, I didn't end up attending as many sessions as I would have liked. As always at Asilomar, I enjoyed hanging out with my ex-colleagues, running into friends, and meeting the occasional fan of… Continue reading Time and Tide
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