This is part of a multifaceted strategy to teach heterogeneous classes. Read about it in this article: Reaching the Full Range.In a previous post, I discussed the benefits of "lagging homework". These included extending student exposure to new ideas, which benefits everyone: stronger students get the forward motion they want and need, and students who… Continue reading One Should Separate Related Topics!
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"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"
More on Homework
In response to my previous post, Mike Thayer asks: "What's your take on no homework at all? " Most learning happens in class, and one should not overdo homework. Too much homework only antagonizes kids and in most cases, it does not help their learning. On the other hand, a small amount of homework is… Continue reading More on Homework
Lagging Homework
This is part of a multifaceted strategy to teach heterogeneous classes. Read about it in this article: Reaching the Full Range.One concept which has been extremely popular every time I've offered my workshops is "lagging homework". The idea is to completely separate tonight's homework from today's class work. I tend to assign homework about ideas… Continue reading Lagging Homework
Reimagining High School Math: Sharing
I am teaching a workshop in San Francisco, June 20-21, on "reimagining high school math".Support materials are on the workshop participants' Web site.Participants: please use the comments below to share ideas, resources, and questions. --Henri
Visual Algebra: Sharing
I am teaching a Visual Algebra workshop in San Francisco, June 17-19.Support materials are on the workshop participants' Web site.Over the past couple of decades, there has been a trend to teach algebra to younger and younger students. That could actually be a good thing. But unfortunately, that has been interpreted as teaching the traditional… Continue reading Visual Algebra: Sharing
Transformational Geometry, cont’d.
As I mentioned in a recent post, I will be one of the presenters at the Bay Area Math Project's summer workshop on Transformational Geometry. As part of preparing for this, I went through my notes, and compiled a sort of syllabus of the relevant lessons from my Space course. Symmetry and transformations are the… Continue reading Transformational Geometry, cont’d.
Embracing Contraries
In 1983, Peter Elbow, a professor at Stony Brook University, wrote a profound article about teaching. It was titled "Embracing Contraries in the Teaching Process" and was published in College English, Volume 45, Number 4. The article was very important for me. It helped me clarify my thinking about education — even though Elbow is… Continue reading Embracing Contraries
Intelligent sequencing vs. external mandates
Some time ago, Mike Thayer posted a comparison of Algebra 1 and Geometry as they are experienced in the classroom. He concluded that since geometry is so much more real to students, and lends itself to interesting connections, perhaps it should be taught first.In response, I suggested that moving specific topics up and down the… Continue reading Intelligent sequencing vs. external mandates
Symmetry in Spain
My wife had a conference in Spain, so we built a vacation around that. It turns out that Spain is a fun place to visit: great art, great food, and well, great math. For example, you can buy a book about the golden ratio from a news kiosk on the street: Unlike us as a… Continue reading Symmetry in Spain
