In my decades as math department chair, I learned that if you want to teach for understanding, you need to approach important topics repeatedly, and from different points of view. This includes different representations of concepts, and different learning tools to get at them. One reason for this is that since students have different backgrounds,… Continue reading Pruning the Curriculum
Tag: Technology
Getting Help
In my last post, I described a problem I encountered more than twenty years ago, and my recent attempt at solving it. The problem: Partition the numbers from 1 to 2n into pairs, so that the sum of the numbers in each pair is a perfect square. For what numbers is this possible? I decided… Continue reading Getting Help
I’ve Got a Problem!
Many, many years ago, I saw this problem somewhere:Arrange the whole numbers from 1 to 18 into nine pairs, so that the sum of the numbers in each pair is a perfect square.I liked the problem, and included it in a book I co-authored (Algebra: Themes, Tools, Concepts, following lesson 5.5). In the Teacher's Edition,… Continue reading I’ve Got a Problem!
Geometry of the Parabola
Parabolas are a central topic in high school algebra classes, but, perhaps because of the rigid separation between algebra and geometry classes in the US secondary curriculum, we do not usually treat them as geometric objects. While most teachers are aware of some of the parabola's geometric properties, few of us are familiar with the… Continue reading Geometry of the Parabola
Summer Workshops, 2015
I'll be teaching four workshops this summer, in two new locations: Seattle, and Waltham, MA (which is a half-hour West of Boston.) If you've meant to attend my workshops in the past, but couldn't make it to San Francisco, New York, or DC, perhaps these venues are more convenient for you? There will be no… Continue reading Summer Workshops, 2015
Geometric Construction, continued
Readers of this blog probably realize that I'm very much into geometric construction. This is in part related to my general interest in puzzles, in and out of the classroom. (In my other life, I construct cryptic crosswords.) My first math education publications were books of geometric puzzles for grades K-10. My pentomino puzzle books stayed… Continue reading Geometric Construction, continued
Asilomar Report: Think First
I attended the California Math Council meeting last Saturday. This post is a report on one talk I attended. It was given by Scott Farrand, a prof at Cal State University Sacramento. (I also reported on one of his talks last year.)This year's talk was called "Think First", which can be interpreted a few ways,… Continue reading Asilomar Report: Think First
One More Pythagorean Proof
I added a third dynamic proof of the Pythagorean theorem on my Web site. It is better-looking, but more difficult to justify than the previous two. You can see all three, starting here. For a brief discussion of how you might use these in the classroom, see this post. --Henri
Pythagorean Proofs
I just added a second dynamic geometry proof of the Pythagorean theorem on my Web site.Both are proofs "without words", which in reality means that you should use them to generate discussion. Indeed, many words are needed for students to fully grasp what they see, but the words should not come exclusively from the teacher.… Continue reading Pythagorean Proofs
Interactive Whiteboards
Some years ago, I wrote about interactive whiteboards (IWBs), in response to a passionate anti-IWB opinion piece I stumbled upon. The author of that piece objected to IWBs on multiple grounds, some of them legitimate. But I disagreed with his main point, which was to counterpose IWBs to student-centered pedagogy. To me, those are not… Continue reading Interactive Whiteboards
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