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Perpendicular bisector theorem
Under the assumptions of the Common Core, the triangle congruence criteria (SSS, SAS, ASA) are no longer postulates. Instead they are to be derived from transformational geometry. There are many consequences to this state of affairs, and I have written about it on this blog: one, two, three. I have developed bits of curriculum, which… Continue reading Perpendicular bisector theorem
Themed courses?
This is the third in a series of summer posts on big-picture planning for a math department. Previous installments: Pruning the Curriculum, and Mapping Out a Course. Today's post represents a further zooming out, to discuss my thoughts about how to organize content across courses. Of course, many if not most teachers are not consulted… Continue reading Themed courses?
Geoboard Triangles
One way to discover or apply the formula for the area of a triangle is to explore area on the geoboard. The initial activities should be along the lines suggested in my Geometry Labs Lab 8.4. (Free download.)After that, one can zero in on triangles, by asking a question like: "Find triangles of area 15."… Continue reading Geoboard Triangles
About Hints, the sequel
A few weeks ago, I wrote about the use of hints in the math classroom. I just reread that post, and stand by what I wrote. I admit that my very last sentence (in the PS) was perhaps a bit snarky, and I'll try to elaborate on it in this post.What is prompting me to… Continue reading About Hints, the sequel
Constant Sums, Constant Products
I just cleaned up an existing page on my Web site: Constant Sums, Constant Products, "an untraditional approach to traditional topics". This is a mega-unit, spanning content from middle school, all the way to what one might call "teachers' mathematics." Take a look at it on a summer day when you have a little time… Continue reading Constant Sums, Constant Products
New on my Web site
I usually mention any new material on my Math Education Page on this blog. Today's installment: three new pages, each of which links to several others.1. A new issue of my Math Education Newsletter, featuring links to recent blog posts, info on my summer workshops, and an update on what's new on my Web site.… Continue reading New on my Web site
Mapping Out a Course
A correspondent writes (I added the links): Our district is looking at revamping our year map and I would like to suggest a map that has the qualities of Algebra: Themes, Tools, Concepts (ATTC): particularly its ‘integratedness’ and how well it spirals through the topics. I’ve read on your blog about separating topics and lagging… Continue reading Mapping Out a Course
Online Collaboration
In 2008, I gave a talk about teacher collaboration at the Asilomar meeting of the California Math Council. It was well attended, and well received, but more than a few attendees told me that they had no one to collaborate with. They were the only math teacher at their school, or the only one teaching… Continue reading Online Collaboration
Pruning the Curriculum
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
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