Here is a twopager on benchmarks for choosing a curriculum attuned to the Standards for Mathematical Practice written by Al Cuoco of EDC that came out of a workshop they had. I thought it might be a good stimulus for discussions about how to implement the practice standards. Comment away!
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Unfortunately I think there will be many districts that will quickly adopt textbooks that claim they align to the CCSS especially at the K – 6 level where many teachers are not math specialists. At this point many of our educators need professional development to help better understand teaching practices and align with the mathematical practices of the CCSS. I will be sharing the article with my district to let them know simply adopting a CCSS aligned textbook is not the fix. If anyone could direct me in the way of inspiring professional development for NYS K – 8 teachers of mathematics in transitioning to the CCSS I would truly appreciate it!!
I especially liked the section of “General purpose tools.” There are two similar topics I would like to bring up for discussion. I have known very few students who could explain why crossproducts were equivalent. Most of my new students seem to enjoy using cross products and want to cross multiply every time they see two fractions! About six years ago I stopped using cross products and switched to using reciprocals, which students can readily see are equivalent. This method connects beautifully with multipicative identity and equality as they eliminate denominators to solve equations. They can continue to use reciprocals with more complicated rational equations; however, as the students gain experience eliminating denominators, they begin using cross products without being taught because they “see” a cross product as they are eliminating two denominators.
Another issue that I have resolved is regarding students not knowing whether to add, subtract, or multiply exponents. Instead of teaching the “laws of exponents,” I require prime factorizations for the entire unit, using worksheets that gradually progress in difficulty. In this way, the meaning of the notation is deeply engrained and they begin to envision the laws as they predict the results of their prime factorizations.
Would like to second Lane on “General purpose tools.” Is it possible to elaborate and explicitly include gradeappropriate statements into progression documents?
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