New animation: a geometric representation of completing the square. In this post, I present one way to use it as part of an algebra curriculum.Many secondary school teachers figure that the derivation of the quadratic formula by completing the square can be shown to students, but have little hope of any understanding. They… Continue reading Completing the Square
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New Practical Advice Document
Some time ago, I wrote about various techniques for extending student exposure to concepts, without allowing one's class to bog down. (See this post, and follow the links therein.) One key ingredient of this strategy is "lagging homework." The basic idea is that today's homework should not be about today's class work. It should be… Continue reading New Practical Advice Document
Pythagorean animation
Check out a GeoGebra animation I just posted: the Pythagorean theorem.It bears much discussion, as students are not likely to spontaneously make out its significance. One way to present it to a class is to first go through the whole thing on a projector, then go back through it slowly, discussing the meaning of each… Continue reading Pythagorean animation
Ripples
Math curriculum ideas expand outward from their originators, like ripples in a pond. In pre-Internet days, it was great to see teachers using photocopies of photocopies of photocopies of worksheets I created, such as "Make These Designs." Nowadays, of course, people can always download and print a fresh copy. One day at an NCTM meeting,… Continue reading Ripples
More Algebra Book Fan Mail
I have some good news for the users of the online version of Algebra: Themes, Tools, Concepts (ATTC, the textbook I co-authored with Anita Wah): all the ATTC PDFs are now searchable, and many of the files are smaller than they used to be. (See below for links.)Amanda Cangelosi, a Mathematics instructor at the University… Continue reading More Algebra Book Fan Mail
area of a parallelogram
I posted a GeoGebra animation that suggests the formula for the area of a parallelogram defined by two vectors: <img alt="" height="200" src="data: <img alt="" height="200" src="data:--Henri
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
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 