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
Tag: MyBooks
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
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
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
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
"Enrichment"
During my first ten years as a teacher, I worked in elementary schools. In addition to team teaching my own class (grade 3, then 4, then 5) I was a math specialist for grades K-5. The basic idea was that there was "normal" math (a lot of arithmetic, textbook-based), and there was "enrichment" math. I… Continue reading "Enrichment"
"A New Algebra"
About twenty years ago, along with Anita Wah, I wrote "A New Algebra", a paper for the Journal of Mathematical Behavior (JMB). It was an attempt to address what I saw as a crucial issue in secondary math education: on the one hand, the traditional Algebra 1 course was the gateway to any further work… Continue reading "A New Algebra"
Working with Pentominoes
Much of this information is outdated. See an updated post here. Didax just published my book Working with Pentominoes. It is geared to grades 4-8, though I use some of the content in high school. Pentominoes are a geometric puzzle, a staple of recreational mathematics. This is what they look like: You can read… Continue reading Working with Pentominoes
Algebra for all?
Mike:Before responding to your post let me go on with the train of thought I started last week in my post about All of high school math in one year?Teaching math to students who'd rather not be there is not anyone's idea of a good time. Can anything be done about that? One solution is… Continue reading Algebra for all?
Henri's Math Education Blog 