Hot off the presses is the *K-8 Publishers’ Criteria for the Common Core State Standards for Mathematics*, written by the three lead authors of CCSSM: Phil Daro, Bill McCallum, and Jason Zimba. According to a post in Bill McCallum’s blog, the HS version, as well as revisions to the K-8 document, is due to be published early next year.

Erik Robelen has written an article about the K – 8 document in Education Week. In the article, he included comments from a conversation with Jason Zimba about the document. He closed the article by stating: “There is far more covered in the publishers’ criteria than I can possibly address in this blog post. So, take a look for yourself, Dear Reader. I expect to be back with more analysis and feedback later, once folks out in the field have a chance to digest this.”

This blog post is my first attempt at making sense of the document from the standpoint of why a classroom teacher would want to peruse it. So, dear reader, take what you will from this post and I encourage you to check out the document yourself.

We all have heard the “mile wide, inch deep” description of the U.S. mathematics curriculum and the push in the CCSSM for fewer topics, especially in K – 5, with deeper understanding of each topic. This new document has established criteria for publishers to use as they create new materials that mirror the basic tenets of CCSSM. In response to the adoption of the standards, many publishers have developed supplementary materials that highlight what to leave out or what to add in. The general results that I have seen from this process are non-tesselating jigsaw puzzles, held together with duct tape.

Hopefully, in the next few years, we will see quality material that does indeed reflect the focus, coherence and rigor that is at the heart of the CCSSM change. Rather than waiting for textbook companies to come to our rescue, I am increasingly (or rather primarily) using the web as a place to find cutting edge resources. This blog has evolved due to the fact that I needed to find a way to organize the plethora of good quality free online resources.

The supposed advantage to a text book series or program is that the teacher doesn’t have to search for good materials. The materials have supposedly been vetted by the expert authors of the program. In my experience, though, I have found very few programs that are a complete fit for myself or my students. (Full disclosure: I am no longer in the classroom. I taught HS math for 16 years, followed by 9 years as a principal, primarily in the elementary grades, and have been an independent K-12 math consultant for the past 3 years.)

Textbooks are expensive and quickly become outdated. My (humble) opinion is that a wiser way for schools to spend taxpayer’s money is to provide students and teachers 1-to-1 access to technology. Then be purposeful about training teachers and students in the use of the technology to learn math, or ELA, or history, or science, or art, or music…I still think we need them moving around in PE rather than learning it from a computer. I could use a little bit more of that myself!

So, now that you know my bias, I will highlight pieces of the 24-page document that teachers may want to take note of. This overview is longer than I initially planned, so peruse it at your convenience. The target audience for this review are the people who make decisions about what is taught in a classroom on a day-to-day basis. This is the classroom teacher. My recommendation for classroom teachers is to use this criteria as a guide to what goes on in your classroom. If it is also used by publishers as they develop resources, then so much the better.

Pages 1 – 5 provide the background of why these criteria are being published and clarifying what is meant by focus, coherence, and rigor. Anyone who has been attending introductory PD sessions on CCSSM will have at least heard this information. Page 3 has a summary table with a short description of Focus, Coherence, and Rigor. I especially like that they highlighted the three aspects of rigor: (1) conceptual understanding, (2) procedural skill and fluency, and (3) applications.

Page 6 lists several ways that the criteria can be used:

- Informing purchases and adoptions
- Working with previously purchased materials
- Reviewing teacher-developed materials and guiding their development
- Professional development

It is recommended that the criteria for *focus* be attended to first. ”By attending to focus, coherence and rigor may realistically develop. Failing to meet any single focus criterion is enough to show that the materials in question are not aligned to the Standards.”

At the bottom of page 6 is a hint that the writers are trying to think creatively at what is considered a “resource”, which I will interpret to mean that a text book series is not the only answer. The bold italics are mine and are meant, of course, to highlight my bias! “The standards do not dictate the acceptable forms of instructional resources – to the contrary, they are a ** historic opportunity to raise student achievement through innovation**. Materials and tools of very different forms can meet the criteria that follow, including workbooks, multi-year programs, and targeted intervention….

*. Digital materials offer substantial promise for conveying mathematics in new and vivid ways and customizing learning. In a digital or online format, diving deeper and reaching back and forth across the grades is easy and often useful.*

**This also includes digital or online materials and tools**

**Focus and coherence can be greatly enhanced through dynamic navigation – though, if such capabilities are used poorly, focus and coherence could also be greatly diminished.**Starting on page 7 are the “Criteria for Materials and Tools Aligned to the Standards”. Below are the headings. Each heading is followed by details about that criterion. Criteria # 1 – 6 address the **Content Standards**. Criteria # 7 – 10 address the **Practice Standards**.

### Criteria that address the Content Standards:

**1. Focus on Major Work: In any single grade, students and teachers using the materials as designed spend the large majority of their time, approximately three-quarters, on the major work of each grade. **On page 8 is a table that lists the progress in each grade level to Algebra I. The table does not use the phrase “major work” and the * blurb at the bottom of the page indicates that the two assessment consortia (PARCC and SBAC) have designated “major work” for each grade level. Here is a link to a pdf from Engage NY that highlights the Major and Supporting CCSSM Clusters K – HS.

**2. Focus in Early Grades: Materials do not assess any of the following topics before grade level indicated. **A table lists the following topics and the grade in which they are first introduced: Probability (Gr. 7) Statistical Distributions (Gr. 6), Similarity, Congruence, Geometric Transformations (Gr. 8), and Symmetry (Gr. 4). Isn’t it nice to be told to take some things OUT?

**3. Focus and Coherence through Supporting Work: Supporting content does not detract from focus, but rather enhances focus and coherence simultaneously by engaging students in the major work of the grade. **Go back to the link under #1 above that lists the major and supporting clusters. My interpretation of this criterion is that the supporting clusters are used to provide examples to illustrate the concepts in the major clusters.

**4. Rigor and Balance: Materials and tools reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by **

**a. Developing students’ conceptual understanding of key mathematical concepts**

**b. Giving attention throughout the year to individual standards that set an expectation of fluency.**

**c. Allowing teachers and students using the materials as designed to spend sufficient time work and engaging with applications, without losing focus on the major work of each grade.**

**5. Consistent Progressions: Materials are consistent with the progressions in the Standards.**

**a. Basing content progressions on the grade-by-grade progressions in the Standards**

**b. Giving all students extensive work with grade-level problems**

**c. Relating grade level concepts explicitly to prior knowledge from earlier grades.**

Here is a link to Bill McCallum’s blog *Tools for the Common Core*. Go to the Tools bar at the top and then click Progressions Documents for the Common Core. Click on “Products” and you will see a list of the documents. They all say “Draft” on them, but for the most part, according to Bill McCallum, they are complete. The story behind the Progressions Documents (per Bill McCallum) is that they were the original documents that guided the writing of CCSSM. After the final draft of the CCSSM, the progressions documents were revised to reflect the finished product. I find the documents extremely informative, but they are a bit of a dry read.

**6. Coherent Connections: Materials foster coherence through connections at a single grade, where appropriate and where required by the Standards, by:**

**a. Including learning objectives that are visibly shared by CCSSM cluster headings, with meaningful consequences for the associated problems and activities.**

**b. Including problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.**

### Criteria that address the Content Standards:

**7. Practice-Content Connections: Materials meaningfully connect content standards and practice standards. **

**8. Focus and Coherence via Practice Standards: Materials promote focus and coherence by connecting practice standards with content that is emphasized by the Standards.**

**9. Careful attention to Each Practice Standard: Materials attend to the full meaning of each practice standard.**

**10. Emphasis on Mathematical Reasoning: Materials support the Standards’ emphasis on mathematical reasoning, by:**

**a. Prompting students to construct viable arguments and critique the arguments of others concerning key grade-level mathematics that is detailed in the content standards.**

**b. Engaging students in problem solving as a form of argument.**

**c. Explicitly attending to the specialized language of mathematics.**

### Additional Criteria

Following the 10 criteria listed above, the authors have included two additional sections. First is a discussion of the importance of having a **consistency and alignment between what students learn in math class and what they learn in science and technical subjects.** This is important especially in middle and high school when students take a “math” course and a “science” course and perhaps a “tech ed” course and each teacher approaches the same topic in a different way. The recommendation is for science and technical subjects to have an understanding of how CCSSM approaches algebra and statistics. A table is included for guidance.

The final section is entitled** “Indicators of quality in instructional materials and tools for mathematics.” ** This section focuses on choice of problems, products, pacing, teacher materials, use of manipulatives, visual design, and support for English Language Learners.

Their last suggestion for print material may irritate some readers, since Japanese textbooks are held up as a model.

“A textbook that is focused is short. For example, by design Japanese textbooks have less than one page per lesson. Elementary textbooks should be less than 200 pages, middle and secondary less than 500 pages.”

Since I am not a fan of most textbooks to start with, the suggestion to at least make them short is a step in the right direction. However, I still think that 500 pages is a bit of an overkill. They must have been bowing to pressure when they came up with that number.

### Appendix

The appendix includes an essay by the three CCSSM authors, entitled “The Structure is the Standards”, which uses a shattered Grecian urn metaphorically as a reminder that the standards should be taught as a whole structure, not as individual bullet points.

On pages 22 – 24 is a template for judging curriculum materials. On three pages, each of the ten criteria are listed and summarized, with a place for notes, and check boxes for evaluating the material.

As stated earlier, this summary has taken much longer than I expected, but I’m glad I charged through it so I can use it in my work the schools. I hope someone in the blogosphere can use this summary to help them decide whether to or how to use the document. As for myself…I’m headed out to the garden!