One major task of the geometry teacher is to get your students to transition from recognizing geometric figures by “looks” to recognizing geometric figures by definition. I’ve found my students saying things like “a rhombus is a sideways diamond,” or “a trapezoid is the funny shaped one,” or “what do you mean ‘what’s a rectangle?’, it’s a rectangle!” Today everyone was stumped when I asked them to draw a rectangular rhombus, “If you wanted us to draw a square Mr. Follett, why didn’t you just ask!?”

Getting our students to a level of precision where they can say “yes, that’s a trapezoid because it has only one set of parallel sides” may seem trivial but it reflects a level of mathematical precision which has a profound effect on thinking. Our students can now move away from the “it is because it is” sort of line of argument to “it is because….” So we stop falling prey to persuasion with no “meat” and begin to think critically about the things which influence us and the things we believe.

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I hope this will be of interest to everyone interested in the history of geometry or in teaching the subject:

http://www.independent.co.uk/news/uk/home-news/stonehenge-builders-had-geometry-skills-to-rival-pythagoras-834313.html

A way to get past this might be exercises with a bunch of identical figures that “look like” something (a rectangle, maybe), but only a few of them have the congruence/angle markings that mean they have to be a rectangle.

On another note, teaching geometry well is really, really hard.

I love it. Being a 5th grade teacher we have to work with identifying the 2d and 3d shapes. I’m going to have to make sure that I hold my kids accountable for identifying the shapes by definitions.