A couple of years ago, I recommended a few books on complex instruction, an approach to teaching that was refined by a group of teachers in a Bay Area public school nicknamed "Railside", as it sits "on the wrong side of the tracks." My recommendation was based not on reading the books, but on my… Continue reading Math for Equity
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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
Geometric Series
... geometric in more than one way! Start with a right triangle ∆ABC, with hypotenuse AB = 1, and AC = b.Draw a parallel to AB through C.Draw a circle centered at C, with radius b.Label the intersection of the line and the circle D.Drop a perpendicular from D to line AC, intersecting it at… Continue reading Geometric Series
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
Make These Designs
Among the activities I have developed, "Make These Designs" is among the most popular. Students enjoy it, and teachers appreciate how it can be used as an engaging introduction to, or interesting review of, an important topic: graphs of linear functions, and the parameters m and b in y=mx+b.When electronic graphing first came onto the… Continue reading Make These Designs
Proportional Relationships
One good thing about the Common Core middle school standards is the emphasis on proportional relationships, and the fact that they are approached in a multidimensional way. In addition to "set up a proportion and solve it", which is probably the most common way to teach this, the standards propose multiple representations and a variety… Continue reading Proportional Relationships
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