The last remaining progression, the quantity progression, is here. Comments in the forums welcome!

# Catching up

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.

# Geometry Progression Grades 7 to High School

It’s been a while coming, but here is the draft Geometry Progression for Grades 7 to High School. As usual, please make comments and corrections in the relevant forum.

# Illustrative Mathematics Session at the Joint Mathematics Meeting

Illustrative Mathematics organized a special session at the Joint Mathematics Meeting on January 7, 2016 in Seattle, WA called *Essential Mathematical Structures and Practices in K-12 Mathematics*. Here is a description of the session:

The mathematics curriculum in the US has been shaped by myriad forces over the years, including the competition for market share among publishing companies, economic realities of school districts’ purchasing power, the ease with which teachers can deliver the material, traditional expectations of what mathematics classroom work should look like, and so on. Surprisingly absent from these forces is the nature of the discipline of mathematics itself. The focus of this special session was on identifying and describing the essential mathematical structures of the K-12 curriculum, as well as the key mathematical practices in the work of mathematicians that should be mirrored in the work of students in K-12 classrooms.

- Up first was Susan Addington, who spoke about Essential Mathematical and Cognitive Structures in K-5 Mathematics: Where They Come From and Where They Go. (Link to slides.)
- Next, Jim Madden spoke about An Historical Perspective of Proportion, Ratio and Measurement. (Link to slides.)
- Then Kristin Umland asked, What Do We Mean by Proportionality? (Link to slides.)
- Maggie Cummings and Hugo Rossi spoke about The Emergence of Essentiality from Educator-Mathematician interactions in context. (Link to slides.)
- Then Cody Patterson spoke about Functions, Rates, and Quantitative Reasoning: From Proportionality to Exponential Growth. (Link to slides.)
- Bill McCallum wrapped up with a talk entitled, From the ark of history to the arc of reasoning. (Link to slides.)

# Transformations and triangle congruence and similarity criteria

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.

# Yesterday’s post on the Noyce-Dana essays

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.

# Essays from the Noyce-Dana project: clarifying the mathematical underpinnings of secondary school

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.

# Having trouble posting comments?

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.

# The confusion over Appendix A

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.

# 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.