New Draft of NBT Progression

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.

Modeling Progression, Take 2

After talking to some teachers at PCMI on Tuesday and hearing from my fellow standards writer Jason Zimba I decided to do a quick fix on the modeling progression. The previous version ventured into territory that has been discussed on this blog: the different possible meanings of the word “model.” I decided this could be confusing, so edited it down so that it now sticks to the meaning of the word as used in the standards. The new version is here.

Progressions preface and introduction, and updates to Algebra and Functions

A a couple of things today. First, a a draft of the front matter for the Progressions, including an introduction explaining the sources of evidence, organization, and terminology for the standards. It also lists the members of the work team that produced the Progressions, who have been sadly unacknowledged until now. I would like in particular to call attention to the work of our editor, Cathy Kessel, who is also an occasional contributor to this blog.

Second, thanks to work of Al Cuoco, we have updated versions of the Algebra and Functions Progressions.

Draft of Modeling Progression

Isn’t summer wonderful? This has been sitting on my desk for a while, waiting to be typeset. Some teachers at PCMI this summer needed it for their c-TaP projects, so I finally got to it. As always, this is still only a draft. Please leave comments in the appropriate forum.

[Edited 4 July 2013. Please go here for the latest draft.]

Draft progressions on high school Algebra and Functions

I’m pleased to be able to give you the draft progressions on Algebra and Functions. These progressions are somewhat different from the K–8 progressions. Since the high school standards are not arranged into courses, the progressions are really more like descriptions than progressions; they are not in any particular curricular order. Furthermore, because each one covers a topic that occupies a large part of the high school curriculum, it gives less detail about how each standard might be addressed or how different standards might be arranged into various different curricular implementations.

Comments as always are welcome in the relevant forums: Algebra or Functions.