Imagine it a lot prettier with stick figure examples.
I don't differentiate between these three very well (at all) with my students. The always insightful Grace also pointed out to me that it helps the teacher differentiate the three types of activities. Often a teacher calls something "group work" but what it really is just students working in parallel. It's one of those "no duh" moments I always have when I walk into someone else's classroom.
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Addendum: Something I forgot to mention in my last post. Mission HS is experimenting with Geometry for every 9th grader regardless of whether or not they even took Algebra in 8th grade. During the class they emphasize the algebra components within geometry, mainly working with the coordinate plane, graphs, and solving equations. As sophomores, students then go back to either taking Algebra or Advanced Algebra.
They had a whole bunch of interesting reasons. They felt students could use a fresh start and didn't need their math history to haunt them into high school. Geometry itself is so different that perhaps students who hadn't had success in math would find something in geometry. Their freshman courses were heavily skewed along racial lines. The standard math sequence is screwy anyway since you'd be better off doing Advanced Algebra (Alg II) immediately after Algebra instead of having a year off with Geometry.
I'm curious to follow up next year. Last year I wrote about how inspiring the group of math teachers are and nothing I saw changes my opinion. I really don't know if Geometry for all ninth graders is a good idea. Someone in California politics thought Algebra for every 8th grader was a good idea. But they're willing to stick their necks out and experiment and do what they believe is the right thing.
PS - Mission is the school featured in the article Everything You've Heard About Failing Schools is Wrong.
I think Geometry for kids who haven't had Algebra 1 is doable, as long as the teacher is prepared to teach a little bit of "bootcamp" equations at the beginning of the year to get everyone at least familiar with the idea of equations and finding an unknown. I agree with the whole idea that Geometry is a fresh start, but without at least a good idea of what "x" is and how to solve basic equations like 2x + 3 = 19, it's not easy for a student to focus on the geometry concepts that can already be daunting enough. It puts those kids with weak algebra at somewhat of a disadvantage, I think, simply because they'll have to learn two things at the same time. In that sense, I'm not sure it would necessarily serve the purpose of rescuing those kids from the fear of math...
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