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
Author: hpicciotto
Reasonable Acceleration
In previous posts, I expressed my concern about hyper-acceleration, the foisting of ever more advanced math topics on ever younger students. After illustrating some of the problems with that trend, I suggested a strategy for teachers to resist it. In this final post in the series, I will unpack one ingredient in that strategy: reasonable… Continue reading Reasonable Acceleration
Deeper, Not Faster
Hyper-acceleration
In some schools and communities teachers face a tremendous push for hyper-acceleration of certain students. As I mentioned in my previous post the pressure comes largely from parents, but they are often supported by students and administrators. Many parents believe that hyper-acceleration will help their child's college applications. Many students' self-image is intimately related to… Continue reading Hyper-acceleration
Acceleration
This is the first of a series of posts on the topic of acceleration. I have combined them and edited them into one article on my Web site. Read it there!I remember one student who managed to take my Geometry class in 9th grade even though (unbeknownst to me) she had already taken a traditional… Continue reading Acceleration
the function dance!
A friend on Google+ posted this image:<a href="data:<img alt="" border="0" src="data:I have often performed "the cubic dance" (see above!) for my students. I've also often asked them to "air graph" various functions.One complication is the fact that left and right are reversed for the person watching you, and while I try to perform things "backwards"… Continue reading the function dance!
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
Sum of the angles
New animation: Sum of the Angles in a Triangle. This is in the genre of "proofs without words", but of course its pedagogical power comes from students and teacher actually using words to discuss what happens.--Henri
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
