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How I would teach geometry were I not using a school-approved teaching series:
-There are only three shapes in all the world, and thus, only three formulas for area that you ever have to memorize: triangles, rectangles, and circles. Two-dimensional, three-dimensional, area, volume- doesn’t matter. There are only three shapes.
Really, once you realize that a triangle is just a rectangle cut in two equal pieces, there are only two formulas.
I remember hating geometry in high school because it seemed like a bunch of arbitrary formulas to put numbers into. Then I took 4 semesters of Calculus and realized that knowing those formulas was completely and utterly ridiculous(which is why Calculus will always be the best of the maths). I hate this series and the way it acts like throwing a bunch of variables around is somehow making it easier for students to understand how to find area, and written by a non-math guy who I don’t think understands geometry and relationships between shapes nearly as well as he thinks he does.
Sigh. I should write my own math book/theory on how to teach math. Then I can stop dealing with actual students and go into the business of telling other teachers how they’re doing it wrong. Mmm…