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The note on p.3 allows for competing definitions of trapezoids (whether or not parallelograms are considered as such). While there are benefits to that at the higher level, even to the point of treating triangles as a limiting case of trapezoids, it seems that in K-12, particularly at the elementary level this ambiguity may result in more problems than benefits. I’ve seen schools using three different textbooks at the same level. So, transferring from class to class may require re-learning, not to mention changing districts of states. Given that it should not be difficult to introduce the more inclusive definition in college, if needed, should the exclusive definition be used for K-12?
Well, if I had to pick just one, I would pick the inclusive one. But this problem is not going to be solved in this forum, I think. Maybe as textbooks start to align more to the common core they will also come up with some common agreements on this sort of thing.
I checked with one of the progressions writers. The second to last paragraph of the sidenote on p. 3 can be revised to read:
“These different meanings result in different classifications at the abstract level. According to T(E), a parallelogram is not a trapezoid; according to T(I), a parallelogram is a trapezoid. At the analytic level, the question of whether a parallelogram is a trapezoid may arise, just as the question of whether a square is a rectangle may arise. At the visual or descriptive levels, the different definitions are unlikely to affect students or curriculum.”
That does still seem to leave a lot of years when differences in definitions might affect curriculum. However, given that classification only occurs in a few grades, my guess would be that the different definitions would affect curriculum in grades 3 to 5 and statements of theorems in high school (just how many would need to be checked—and it’s possible that students might create their own). Obviously, that’s not good if definitions change during those grades, but it’s better than having fluctuating definitions affecting all of K–12. And certainly students who happen to be curious should have their questions answered in consistent ways, so one would hope to have this issue mentioned in teachers manuals and professional development.
I am getting ready to begin teaching a grade 3 geometry unit and all the materials I have found use the exclusive definition. The definition needs to be clarified since third grade has only two geometry standards and one is about 2-D attributes. The inclusive definition will totally change the image that our students now recognize as a trapezoid. It will include all squares, rectangles, parallelograms, and rhombi.
Is PARCC aware of the discrepancy in terms?Yes, PARCC is using the inclusive definition, see here:
https://www.parcconline.org/sites/parcc/files/ES%20Table%20Geometry%20EOY%20for%20PARCC_Final.pdf
I sure wish that they had used the exclusive definition, since every text book that I have ever worked with does, but so be it. Does anyone know what SBAC has chosen for their definition?
I don’t see an SBAC definition, but my guess is they are likely to agree with PARCC. It is the more common sense definition from a mathematical point of view.
I don’t see an SBAC definition, but my guess is they are likely to agree with PARCC. It is the more common sense definition from a mathematical point of view.
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