My retirement is finally kicking in, and for the first time things have slowed down a bit. I'll have a chance to organize the math materials in my basement, and who knows, maybe even take up some genuine retiree sorts of activities.
However, my summer is going to be intense, as usual. I'll be offering four workshops for grades 6-12 math teachers. (See below.)
Until then, I'll try to continue writing blog posts and adding stuff to my Web site! Read on for some possibly useful links.
PS: If you live in the Bay Area, you may be interested in attending a meeting of the #mtbosBA, Saturday Feb 6, 2-5pm in San Francisco. Topics: 'Using Desmos', and 'Mathematical Habits of Mind'. Professional development for math teachers, by math teachers! More info and RSVP here. Free!
Here are links to posts on my Math Education Blog that you might find interesting.
If you are so moved, you may comment on the posts, and/or subscribe to the blog.
All classes are heterogeneous: some students pick up new math ideas faster, some slower. As it turns out, we as teachers can do something about this. I offer a few practical suggestions, and answer frequently asked questions, in this blog post. If all your students learn math at the same rate, you need not read it.
12th Grade Math Options
A rambling post about traditional and especially non-traditional 12th grade electives. The non-traditional options include two advanced electives I have taught over many years ("Infinity", and "Space".) And one overview of essentials in secondary school math, organized as a one-year course. (The latter is intended for students who did poorly in math up to that point, and want to be ready for community college.) Find links to all that here.
More on Hints
In past newsletters (May, Nov) I linked to blog posts about hints. Probably because hints are such a central part of classroom interaction, the conversation about this topic continues. I present two arguments that appear to contradict each other, and yet are both valid. Read about it here.
I continue to write about transformational geometry, both on my Web site and on my blog. Here are the latest additions, largely based on work I developed over many years for my Space course.
Isometries of the Plane
This is a packet of worksheets for students in grades 11-12, or teachers. It goes a bit further and deeper than required by the Common Core, and can be combined with other material on my Transformational Geometry page to create a solid advanced unit for a precalculus or elective course.
Only Four Kinds of Isometries
This is the epic proof of the Fundamental Theorem of Isometries: given any two congruent figures in the plane, one is the image of the other in a single reflection, rotation, translation, or glide reflection. In other words, any rigid motion must be one of these four. The piece is mainly intended for teachers and curriculum developers, but it also serves as a teachers' guide for parts of the above packet. The argument is supported throughout with interactive GeoGebra applets, which can be downloaded and used in the classroom. Read it here.
Much of the above includes the use of the glide reflection. Alas, that transformation is not well known. I don't mind its omission from the Common Core, as it really is not a core concept. But it is essential if you want to be able to even state the Fundamental Theorem of Isometries, or if you want to explore symmetry in depth, e.g. in the figure below. I wrote two blog posts on this: Glide Reflections and Congruence, and Glide Reflections and Symmetry.