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Is there any word on when we can expect a geometry progressions for beyond grade 6?
Right now I am struggling with differences in grade 8 and the geometry course when it comes to transformations and volume formulas. For example, Grade 8 has the standard, “8.G.C.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems” and high school has “HS. GMD. A.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments”
Iunderstand what they are asking students to do is different for each standard. I am assuming that when you teach these volume formulas in grade 8, you want students to undersand the concept behind the formulas and know where they came from. How is the teaching going to be different for “students being able to give an informal argument for the formulas” in high school and having students know where the formulas come from in middle school? I realized that discussion may occur at higher level at high schoool since it lists some arguments and principles to use. Do those arguments have to be used, or will the understanding from middle school be enough to informally explain the formulas?
I also wonder the same type thing when it comes to tranformations. It seems 8th grade spends a lot of time working with tranformations and using transformations to show congruence. They even work with coordinates (8.G.3) The high school geometry standards include many standards that also have students experiment with transformations and use them to show congruence as well. I’m having a hard time picking up on how they are different, beyond the fact that things are “formalized” in the high school course. Can anyone help?
Your intuition is correct that the middle school geometry standards are more experiential and the high school ones more formal. In middle school students get a feeling for transformations and their properties by playing around with transparencies or dynamic geometry software. In high school they should be able to make arguments using the precise descriptions of transformations. Sorry that the geometry progression hasn’t come out yet; working on that.
As for the question about volume formulas, I would be inclined to take the Grade 8 standard fairly literally; it’s really just about knowing the formulas. Understanding where they come from and being able to give a formal derivation is significantly more advanced than that, which is why it is left till high school. I can see why some might find this interpretation unpalatable, but some formulas are quite simply beautiful and classical, and it doesn’t do any harm to appreciate them for a while without deep analysis (we do the same with art all the time).
I am also eagerly awaiting the Geometry Progressions. We begin our work overhauling HS Geometry this year (we are a little behind). I am hoping we will see the progression sometime in first semester. Will we? 🙂
Wu’s article is superb. It’s been my primary source as I rework my geometry class.
I have been reading Wu’s article on Geometry. I am unsure how heavily to rely on this work for guidance. For example, the elementary grades use an inclusive definition for trapezoids- according to Wu. I was consulting with a colleague about this shift. She wanted to see what guidance the progressions had on the matter, rather than trusting Wu’s interpretation of the matter. I looked at the K-6 Geometry progression and saw that Wu was in line with standards. I haven’t yet completed the entire article but am anticipating more such “new” ideas and would like a second source to consult. Also, I find the progressions are easier to consume than Wu.
The standards themselves do not specify which definition to use, but the progression does, as you point out. It probably makes sense for everybody to agree on this, and the progression is as close to an official interpretation as one can get, I suppose, since the progressions were written by members of the original Work Team.
I hope the 7–12 geometry progression will be out by the end of the summer. (That’s a hope, not a promise.) It will necessarily be shorter than Wu’s document; the progressions are not intended to spell out every point, but to provide some exegesis of the standards.
Any thoughts on Guershon Harel’s article that is essentially a response to Wu’s article?
I think highly of both thinkers, and have read both their writings on this, but don’t have a detailed comparison of their different interpretations of the geometry standards to throw out right now.
I think highly of both thinkers, and have read both their writings on this, but don’t have a detailed comparison of their different interpretations of the geometry standards to throw out right now.
Is there an update as to when the 7–12 geometry progression will be out?
Thanks!
Also wondering if there is an update on the middle school geometry progressions. Less specific questions, more general guidance.
Thank you!
Jen
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