I just uploaded a book of Polyomino Lessons to my Web site. The book first came out in 1986, and has long been out of print. It includes a wide range of puzzles and activities for middle and high school, mostly carried out on grid paper.Here are some solutions to one of the puzzles: One… Continue reading Polyomino Lessons
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Bay Area Circle for Teachers
I will present an overview of the mathematics and pedagogy of function diagrams at the Winter Workshop of the Bay Area Circle for Teachers, on Saturday, January 26, in Jack London Square in Oakland, CA. Function diagrams are also known as the parallel axes representation, and a computer version is sometimes called "dynagraph". There's a… Continue reading Bay Area Circle for Teachers
Manipulatives update
As larger publishers swallow smaller ones, educational materials with a smaller market tend to be removed from the market. As an author, I have been a victim of this economic reality for quite some time now. However today I have some good news on that front.My book Geometry Labs was originally published by Key Curriculum… Continue reading Manipulatives update
Integrating y=x^2
I added a new page to my Web site. It's a visual proof that the integral of y=x2 from 0 to b is indeed b3/3.Some interesting things about this proof:It was discovered by Jacob Regenstein, a high school student.It does not involve any algebraic manipulation.It shows a dramatic example of how integration increases the degree… Continue reading Integrating y=x^2
New Lesson
I posted a new lesson on my Web site: Comparing Cell Phone Plans. I wrote the lesson as part of a project I worked on with Amanda Cangelosi, an ex-colleague and currently a prof at the University of Utah. We were auditioning for a new online math lessons Web site. We did not make the… Continue reading New Lesson
Solving Inequalities
One topic that has nearly vanished from my teaching is the solving of inequalities "by hand". There are several reasons for that choice:The techniques are difficult to teach and difficult to learn, because they are so close to the ones for the solving of linear equations, but differ in one crucial case.It is difficult to… Continue reading Solving Inequalities
Using interactive geometry
This is the final post of my report on the Asilomar conference. (To read the whole set, start here.)I made a cameo appearance in my colleague Scott Nelson's presentation on how using computer software intelligently has made his Analytic Geometry course vastly more accessible. I loved his presentation. (If you teach in a member school… Continue reading Using interactive geometry
The third dimension!
This is another post about sessions I attended last weekend at the Asilomar Northern California CMC conference. (To read the whole set, start here.)Kevin Rees presented two variations on a classic volume optimization problem. In the traditional problem, you start with a square piece of cardboard, cut off congruent squares at the four corners, and… Continue reading The third dimension!
About Student-Created Problems
In my last post, I reported on Avery Pickford's exciting presentation at the Asilomar conference. The idea of student-created problems was thought-provoking — here are some thoughts it provoked.I have no doubt that pursuing student-created problems is worthwhile, but a skeptic may not be convinced by the argument that we should do this because it… Continue reading About Student-Created Problems
Student-Created Problems
This is the continuation of my report on last weekend's Asilomar conference. (Previous installment.)Avery Pickford's session was about student-created problems. You can read a summary on this blog (Without Geometry, Life is Pointless). Creating problems is, after all, what mathematicians do. Yes, they sometimes explore questions that have been posed by others, but even then,… Continue reading Student-Created Problems
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