Symbols and Vocab

I don't think my middle-level students really understand what the geometry markings mean. Last week I marked the legs of an isosceles triangle with tic marks to show that they were equal, and my students didn't understand what the tic marks meant. (Actually, they thought they meant the lines were parallel... "How can sides of a triangle be parallel??" I asked... At least they've learned not to trust their eyes with the figures we use.) In the future I'll need to spend more time being very explicit about what the different markings mean. If I stop writing the words out on handouts or on the board and just use the symbols, that should force them to create meaning for the symbols as well.

I think another part of the problem is that I haven't been going through the book in order. I've been organizing sections into my own units. My reasoning for this has been that chapters 1 and 2 have so much vocabulary. Students learn all the basic vocabulary for points, lines, planes, triangles, quadrilaterals, other polygons, circles, and angles. (And I'm sure there's more that I'm missing.) What's nice about spreading out the first two chapters, then, is that students don't have to learn so much vocabulary all at once. Additionally, I'm not forced to teach them about the parts of shapes twice. What a time saver, right?

The problem with spreading out this information is that the vocabulary and markings from future units are sometimes used within the current unit. For example, there are interesting questions about isosceles triangles that use the radii of circles. But since we haven't gotten to circles yet, I can't expect my students to understand how to solve these problems.

Maybe next semester I'll try going in order in the book and see which way works out better. I just need to come up with a way to introduce all that vocabulary without lecturing all class...