There are no separate female and male face shape calculators, but selecting your gender will personalize some aspects of the face shape calculator. Which is why this WODB lesson is nice: in this noisy shape naming logic space, you’ve created a little quiet tent where just one distinction is considered at the students pace – and it makes sense to them.Whether you're male or female, the face shape calculator will determine your face shape in a jiffy. It will be appealing for some students, but for others it’s going to be a real turn-off. It could all be a nice logical exercise, if we hadn’t muddied the waters to start with, and hadn’t got quite so many names we wanted to teach. And a square is a rhombus that’s a rectangle.
And by the way “diamonds” are rhombuses actually. Then we say, after years of this kind of thing, well, squares are rectangles too. And thinking about it, it’s not just the structure of the shape naming logic that’t the problem, teachers that make it hard work for students too. Thanks Kristin – that Chris Lusto post was very entertaining. It is all in aid of making theories tidy, so there are no annoying exceptions, but it fits poorly with everyday life. The other thing is the idea of degeneracy, where a point is a degenerate circle, that is, a circle with zero radius.A triangle in which the sum of the lengths of two of the sides is equal to the length of the third side is degenerate, you get a line segment ! This idea of degeneracy is as hard for older,serious math students to get hold of as is the square/rectangle. Likewise “circle” as a definition is a special case of “ellipse”. One is the idea of “special case”, where one says “square” is a special case of “rectangle”, and so squares fit the definition of “rectangle”. There are two things in mathematics concerned with the classification and description problem (well, probably more than two, if we get into mathematical logic!!). Delightful, and very thorough, especially the topological bit. I just read the two posts and the comments. Thank you Christopher! All of these years of trying to settle that rhombus vs diamond debate settled right here with great conversation all around! And because it didn’t have five sides, not a diamond either. “Could we call this a rhombus?” They said no because the sides weren’t equal, so not a rhombus. I pointed to the kite and asked about that one, since it has four sides. They were really confident in making the rule that the quadrilateral one had to be a rhombus and the pentagon was the diamond. We came back and they seemed to agree we couldn’t call them both a diamond because of the number of sides. I had them turn and talk to a neighbor while I listened to them.
I saw a few thinking that may be a great idea.
“Can we call both of them a diamond?” I asked. Students explained that the lower right actually looks like a real diamond and the rhombus doesn’t now that they see them together. “Yesterday you were calling this rhombus a diamond, what changed your mind?” Funny how quickly they abandoned their idea from yesterday, so I reminded them….they were not getting off the hook that easy ) Another classmate added on and said the lower left “may not have a name but it is kite-shaped and looks like it got stuck in a tree sideways.” I asked the class what they thought about the names we had on the board and it was a unanimous agreement on all of them. Because I knew at the end of our talk I wanted to ask about the diamond vs rhombus, I wrote the names on the shapes. The next student said the lower left was the only one “that didn’t have a name.” When I asked him to explain further, he named the square, rhombus, and diamond. It started with a student saying the square didn’t belong because it is the only one that doesn’t look like a diamond. Honestly, I was surprised names didn’t come up as one of the first things. Here are pictures of the SMARTboard after our talk:Īfter great discussions around number of sides, rotations, decomposition and orientation, they finally got to the naming piece. Of course I had to pop into the same classroom today and try it out! The lower right was so obviously a diamond to me that I was curious to see if students saw the same thing and if it changed their reasoning about the rhombus as a diamond. Which one doesn't belong? (Diamond edition)
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