[Sarah Stevens]

It won’t be easy but you should find your answers in this progression written by Dr. Hung Hsi Wu. It is difficult reading but mathematically beautiful! https://math.berkeley.edu/~wu/CCSS-Geometry_1.pdf

Also, Dr. Zal Usiskin has written Geometry texts using this approach which can be ordered off Amazon: http://www.amazon.com/gp/product/067345956X?psc=1&redirect=true&ref_=oh_aui_detailpage_o02_s00

Finally, I had the pleasure of meeting Dr. Usiskin at the annual NCTM conference and he confirmed that this tiny little book is another great resource. http://www.amazon.com/gp/product/0866514651?psc=1&redirect=true&ref_=oh_aui_detailpage_o05_s00

In regards to your question, it is possible to do rigorous proofs of triangle congruence using rigid transformations. From reading Wu, you will see that a reflection along the perpendicular bisector will guarantee to carry one point to another. Then a reflection across the angle bisector will guarantee to take one side to another. Then it’s simply am matter of proving that the vertex opposite that side must be at the same location. To wrap my head around these proofs, I got a box of patty paper and worked on the transformations until I understand why one triangle was guaranteed to be concurrent with another. It really is quite a powerful tool.

[Sarah Stevens]

Hi! I am just following up and wondering if anyone has any thoughts on my question. I am planning for some Geometry PD this summer and would like to know if these perspectives are above the scope of the standards.

Thanks!
Sarah

[Sarah Stevens]

Let met try again. It doesn’t link to the article but to his blog. When you click on the link in the blog, it will download a word document with his thougths. http://steveleinwand.com/we-reallly-need-to-revise-the-9-12-common-core-math-standards/

If this link doesn’t work, you can go to steveleinwand.com and navigate to the blogs. It is the second blog back from the most recent.

[Sarah Stevens]

Hi again! I recently came across this blog post by Steven Leinwand addressing many of the frustrations I have about the high school standards. http://steveleinwand.com/we-really-need-to-revise-the-9-12-common-core-math-standards/#comment-10434

I definitely feel like the high school standards are too broad. It is frustrating when my K8 co-workers talk about how focused the standards are and I have to clarify that the High School standards do not share the same focus. For us, there is more. Are there plans to revise the High School Standards. Many states have 7 year adoption cycles for standards so they are beginning the process of re-adopting standards. I fear if the states undertake revisions in isolation, we will lose the combined force we gained when math classes were the same across the country.

[Sarah Stevens]

There was a similar question in the 6-8 Number System strand, which Bill replied to. You can find it here. http://commoncoretools.me/forums/topic/simplifying-radicals-2/

[Sarah Stevens]

Hi! Have you read the Geometry progression for K-6. I know your question is specific to 3rd grade but you might find your question answered by reading the entire document. It can be found here http://commoncoretools.files.wordpress.com/2012/06/ccss_progression_g_k6_2012_06_27.pdf

Also, you might look in the K6 Geometry section of this forum. I often find I am not the first to have a question and, therefore, can find an answer there.

Hope this helps!

[Sarah Stevens]

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.

[Sarah Stevens]

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? 🙂

[Sarah Stevens]

I continued searching and a local university professor directed me towards “Teaching Mathematics in Grades 6-12: Developing Research-Based Instrucitonal Practices” by Randall Groth (I purchased it from Amazon). I am still waiting for it to arrive but I read chapter 8 of this book and have a much clearer understanding of the functions-based approach. In the second paragraph he defines the functions based approach. “In general, a functions-based approach asks students to form their own theories about how the values of quantities depend on the values of other quantities.” The book is steeped in research and really highlights the reasons behind some of the decisions in the Common Core. For example, I found myself wondering about the standard A.REI.11. I had never considered teaching solving equations in this way. The book highlights a study that found students with multiplie strategies at their disposal (including  the functions-based approach) are the most successful while students who rely only on algerbraic manipulations are the least successful. I knew the CCSS were research based but it really helped me to read a little about instructional decisions and the studies behind them. I hope the rest of the book is as good as this one chapter!

I also purchased the Essential Understandings: Functions book from NCTM and found it filled in additional blanks and might be more digestable for teacher PD.

[Sarah Stevens]

First, thank you for expanding my question from specific to general. You raised issues I didn’t even know we had yet!  I have been researching a functions based approach to algebra and have read the NTCM book Essential Understanding- Functions, the functions progression, and a few internet sources. I still feel like this type of organization is eluding a firm seat in my knowledge base and would like to learn more. Can you direct me to any good resources? I have done google searches on “functions approach to algebra” and get back a limited number of applicable hits. Are their alternate phrases that will expand my search?

Thanks again for taking the time to answer questions and help us navigate the waters!

Sarah

[Sarah Stevens]

Thanks for bringing our attention to these items. I found a wealth of information in the PARCC document but the SBAC document only has grade 11. Am I missing it?

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