The last remaining progression, the quantity progression, is here. Comments in the forums welcome!
The site was down for a few hours today because of a malware attack, but I think we have it fixed now.
I took the opportunity to catch up on comments in the forums; I was way behind! Thanks to all those who responded to readers’ questions. I will try to stay more on top of it. One of the things that has been keeping me busy is our work on grades 6–8 curriculum for Open Up Resources. It is being piloted this year, so that link is still password protected, but stay tuned!
Also, I am close to finishing up the Quantity Progression, the last one not yet done.
While we are all waiting eagerly for the geometry progression I thought people might be interested in this article by Henri Picciotto and Lew Douglas on a transformational approach to the criteria for triangle congruence and similarity. There is also lots of other good stuff on Henri’s transformational geometry page.
I don’t think the normal notifications went out about this, so I’m adding this to let people know about the collection of essays about secondary mathematics that I posted yesterday.
In 2008–2009 Dick Stanley and Phil Daro, with the help of Vinci Daro and Carmen Petrick, convened a group of mathematicians and educators to write essays clarifying the mathematical underpinnings of secondary school mathematics in the United States. At the urging of Dick Stanley I am publishing these essays here.
Some people are getting a message that comments have been closed if they try to post a comment on a post. I don’t generally close comments, so this is an error. I haven’t figured out how to fix it, but if this happens to you please send me an email.
A number of people have gotten in touch with me recently about Appendix A, so I wanted to clarify something about its role. States who adopted the standards did not thereby adopt Appendix A. The high school standards were intentionally not arranged into courses in order to allow flexibility in designing high school courses, and many states and curriculum writers have taken advantage of that flexibility. There was a thread about this on my blog 3 years ago, and there is a forum on the topic here.
Appendix A was provided as a proof of concept, showing one possible way of arranging the high school standards into courses. Indeed, on page 2 of the appendix it says:
The pathways and courses are models, not mandates. They illustrate possible approaches to organizing the content of the CCSS into coherent and rigorous courses that lead to college and career readiness. States and districts are not expected to adopt these courses as is; rather, they are encouraged to use these pathways and courses as a starting point for developing their own.
States will of course be constrained by their assessments. But Smarter Balanced consortium does not have end of course assessments in high school, leaving states and districts free to arrange high school as they choose. And although PARCC does have end of course assessments, they do not follow Appendix A exactly. See the footnote on page 39 of the PARCC Model Content Framework , which says
Note that the courses outlined in the Model Content Frameworks were informed by, but are not identical to, previous drafts of this document and Appendix A of the Common Core State Standards.
Furthermore, there are plenty of states not using either the PARCC of SMARTER Balanced assessments.
I hope this helps clear things up.
Here the almost final draft of the Progression on Number and Operations in Base Ten, K–5. It incorporates many changes in response to comments here on this blog and elsewhere.
In addition to numerous small edits and corrections, and some redrawn figures, here are some of the more significant changes:
- The sidenote with glossary entry for algorithm was moved to first instance of “algorithm” together with some text on notation for standard algorithm (this piece is a revision of a paragraph that was in the main body of the previous version).
- Section on Strategies and Algorithm: The 2 old paragraphs were deleted and 3 new paragraphs were inserted. Reason: the new paragraphs give an overview of the organization of the NBT standards for strategies and algorithms explaining that students see efficient, accurate, and generalizable methods from the beginning of their work with calculation and that there is a progression from strategies to algorithms: for addition and subtraction (with whole numbers in K to Grade 4; and generalization to decimals in Grades 4 to 6), for multiplication (Grades 3 to 5) and division (Grades 3 to 6) with whole numbers, then decimals.
- The balance of emphasis on “special strategy” vs “general method” in the earlier progression has been shifted in this draft in the direction of general methods..
- Mathematical practices section was revised to focus more on the centrality of the SMPs, illustrating progression from strategy to algorithm and following the structure of the sections on computations, and strategy and algorithm.
As usual, please comment in NBT thread in the Forums.
Illustrative Mathematics has a new look today. There’s a video explaining some of the new features on the Illustrative Mathematics Facebook page. One big new feature is the course blueprints. At the moment we just have K–5 blueprints. We’ll be adding more content to those and also adding high school and middle school blueprints over the next few months. I’ve made a forum here for people to comment and ask questions about them.