Please post questions in the forums

If you have questions about the standards, please click on the Forums tab above and post them in the appropriate forum. There are forums for each K–8 domain and high school conceptual category, and a general forum for questions that do not fit in any of these.

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New Illustrative Mathematics website, with K–5 blueprints

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.

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When the Standard Algorithm Is the Only Algorithm Taught

Standards shouldn’t dictate curriculum or pedagogy. But there has been some criticism recently that the implementation of CCSS may be effectively forcing a particular pedagogy on teachers. Even if that isn’t happening, one can still be concerned if everybody’s pedagogical interpretation of the standards turns out to be exactly the same. Fortunately, one can already see different approaches in various post-CCSS curricular efforts. And looking to the future, the revisions I’m aware of that are underway to existing programs aren’t likely to erase those programs’ mutual pedagogical differences either.

Of course, standards do have to have meaningful implications for curriculum, or else they aren’t standards at all. The Instructional Materials Evaluation Tool (IMET) is a rubric that helps educators judge high-level alignment of comprehensive instructional materials to the standards. Some states and districts have used the IMET to inform their curriculum evaluations, and it would help if more states and districts did the same.

The criticism that I referred to earlier comes from math educator Barry Garelick, who has written a series of blog posts that aims to sketch a picture of good, traditional pedagogy consistent with the Common Core. The concrete proposals in his series are a welcome addition to the conversation math educators are having about implementing the standards. Reading these posts led me to consider the following question:

If the only computation algorithm we teach is the standard algorithm, then can we still say we are following the standards?

Provided the standards as a whole are being met, I would say that the answer to this question is yes. The basic reason for this is that the standard algorithm is “based on place value [and] properties of operations.” That means it qualifies. In short, the Common Core requires the standard algorithm; additional algorithms aren’t named, and they aren’t required.

Additional mathematics, however, is required. Consistent with high performing countries, the elementary-grades standards also require algebraic thinking, including an understanding of the properties of operations, and some use of this understanding of mathematics to make sense of problems and do mental mathematics.

The section of the standards that has generated the most public discussion is probably the progression leading to fluency with the standard algorithms for addition and subtraction. So in a little more detail (but still highly simplified!), the accompanying table sketches a picture of how one might envision a progression in the early grades with the property that the only algorithm being taught is the standard algorithm.

The approach sketched in the table is something I could imagine trying if I were left to myself as an elementary teacher. There are certainly those who would do it differently! But the ability to teach differently under the standards is exactly my point today. I drew this sketch to indicate one possible picture that is consistent with the standards—not to argue against other pictures that are also consistent with the standards.

Whatever one thinks of the details in the table, I would think that if the culminating standard in grade 4 is realistically to be met, then one likely wants to introduce the standard algorithm pretty early in the addition and subtraction progression.

Writing about algorithms is very difficult. I ask for the reader’s patience, not only because passions run high on this subject, but also because the topic itself is bedeviled with subtleties and apparent contradictions. For example, consider that even the teaching of a mechanical algorithm still has to look “conceptual” at times—or else it isn’t actually teaching. Even the traditional textbook that Garelick points to as a model attends to concepts briefly, after introducing the algorithm itself:

Brownell et al., 1955

Brownell et al., 1955

This screenshot of a Fifties-era textbook is as old-school as it gets, yet somebody on the Internet could probably turn it into a viral Common-Core scare if they wanted to. What I would conclude from this example is that it might prove difficult for the average person even to decide how many algorithms are being presented in a given textbook.

Standards can’t settle every disagreement—nor should they. As this discussion of just a single slice of the math curriculum illustrates, teachers and curriculum authors following the standards still may, and still must, make an enormous range of decisions.

This isn’t to say that the standards are consistent with every conceivable pedagogy. It is likely that some pedagogies just don’t do the job we need them to do. The conflict of such outliers with CCSS isn’t best revealed by close-reading any individual standard; it arises instead from the more general fact that CCSS sets an expectation of a college- and career-ready level of achievement. At one extreme, this challenges pedagogies that neglect the key math concepts that are essential foundations for algebra and higher mathematics. On the other hand, routinely delaying skill development until a fully mature understanding of concepts develops is also a problem, because it slows the pace of learning below the level that the college- and career-ready endpoint imposes on even the elementary years. Sometimes these two extremes are described using the labels of political ideology, but I have declined to use these shorthand labels. That’s because I believe that achievement, not ideology, ought to decide questions of pedagogy in mathematics.

Jason Zimba was a member of the writing team for the Common Core State Standards for Mathematics and is a Founding Partner of Student Achievement Partners, a nonprofit organization.

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Common Core Math Parent Handouts by Tricia Bevans and Dev Sinha

In the transition to the Common Core, we have focused more on supporting teachers and administrators, through tools to help improve their own understanding and to help work more fruitfully with their students.   But parents can also use help in this transition.  They have many legitimate questions and concerns such as having difficulty in helping their child with homework or wondering how the Common Core is designed to support their child’s mathematical development.    As parents ourselves we certainly empathize with others who are looking for clear, accessible knowledge.
We have written these parent handouts at the link below to help begin conversations which address these questions and concerns.  They are meant to be used for example at curriculum nights for parents.  We limit ourselves to one page of discussion and one page of an example (mostly taken from Illustrative Mathematics) at each grade, both for ease of use and so as to not overwhelm people with too much information at first.  Locally, we have been involved in discussions of deeper learning opportunities for parents, with these handouts as a starting point.
Click here for the document.
Edit:  Some people have asked for this document in a Spanish translation.  If you want to translate the document we would be happy to share the Spanish version here.
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Fall Virtual Lecture Series from Illustrative Mathematics

Welcome back to school! This fall Illustrative Mathematics will be offering our second Virtual Lecture Series, this one focuses on the theme:

Working with Number in the Elementary Classroom

The following lectures are scheduled in the series on Thursday nights from 7-8pm Eastern on Adobe Connect.  Watch them live with the ability to ask questions, or watch the recordings at any time:

September 25, 2014 Linda Gojak, Immediate Past President, National Council of Teachers of Mathematics, Director, The Center for Mathematics Education, Teaching, and Technology, John Carroll University “Using Representations to Introduce Early Number and Fraction Concepts”

October 23, 2014 Dona Apple, Mathematics Learning Community Project, Regional Science Resource Center, University of Massachusetts Medical School “Supporting students’ conceptual understanding about number through reasoning, explaining and evidence in both their oral and written work”

November 20, 2014 Brad Findell, The Ohio State University

December 11, 2014 Francis (Skip) Fennell, Professor of Education McDaniel College, Past President NCTM “Fractions Sense – It’s all about understanding fractions as numbers (and this includes those special fractions – decimals!) – use of representations, equivalence, comparing/ordering and connections”

January 22, 2015 Susan Jo Russell, TERC: Mathematics and Science Education and Deborah Schifter, Education Development Center (EDC) “Operations and Algebraic Thinking in the Elementary Grades”

Sign-up here!

This school year we will offer two series. In the fall we are featuring “Working with Number in the Elementary Classroom” and this spring we will offer “Incorporating Mathematical Practices into the Middle and High School Classroom.” The intended audience for these series is classroom teachers, district and state mathematics specialists, and mathematics coaches. The five hour long sessions will include 40 minutes of presentation from national experts on Adobe Connect, followed by 20 minutes of Q&A. The sessions will also be recorded for participants that are not able to join in person. The cost to virtually attend each series is $150.

Here is a flyer to circulate among friends that might be interested or to post in the staff room!  Hope to see you there.

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Learning about the standards writing process from NGA news releases. Take 2.

About a year ago I noticed there was a lot of misinformation being spread about the process for writing the standards, so I came up with the brilliant idea of pointing people to the historical source documents that chronicled the process: the NGA press releases about the Common Core during 2009–2010. That will solve the problem, I thought; people will just read the press releases and figure it out. Boy was I ever wrong. In this post I’ll try to give a clearer timeline of the process. Along the way I’ll point out the involvement of testing organizations, since I think that one of the reasons the misinformation has survived for so long is a narrative, compelling to some, that the testing industry dominated the process. (Spoiler alert: they didn’t.)

First, here is the list, with an additional one from July 2009 that I missed last time (which has been the source of much confusion):

Notice that there seem to be duplicate announcements of the Work and Feedback Group and duplicate releases of the standards. What’s going on here is that there were two documents. First, in summer of 2009, the people listed in the July 2009 release worked on the document that was announced in September of 2009. That document, which was actually entitled College and Career Readiness Standards for Mathematics, was confusingly referred to as Common Core State Standards in the title of the September 2009 press release. If you take a look at it you will see that it is a draft description of what students should know by the end of high school.

Subsequently, as described in the November 2009 press release, a new process with new groups was started, to produce “K–12 standards.” These were to be a set of grade level recommendations that described a pathway to college and career readiness. For the K–12 process, there were about 50 people on the Work Team and about 20 people on the Feedback Group for mathematics, representing a wide range of professions, including teachers, mathematicians, policy makers, and one representative each from College Board and ACT … none representing for-profit providers of assessments. The members of this group are listed in a linked pdf in the press release.  This is the document that was released for public comment in March 2010, as described in the March 2010 press release, and released in final form as the Common Core State Standards on 6 June 2010, as described in the final press release.

As you can see from the list of members, I chaired the Work Team for the second document. Within the work team there was a smaller writing team consisting of myself, Jason Zimba, and Phil Daro (who had all been involved in the summer 2009 document, Phil Daro as chair for mathematics). We based the standards on narrative progressions of particular mathematical topics across grade levels that were solicited from the Work Team. We circulated many drafts to the Work Team, the Feedback Group, the 48 participating states, various national organizations such as AFT and NCTM, and, in March 2010, the public (see the March 2010 release). I personally made sure that we responded to and made considered decisions about all of the voluminous feedback we received.

When you hear people claim that “the standards were written by the testing industry,” they are probably referring to the first document, because of the greater involvement of College Board and ACT. Both organizations, along with Achieve, which was also represented, had conducted research into the requirements of college and career readiness. (All are non-profits, by the way.) The problem is that some people refer to the first document in a way that suggests they are talking about the second document (i.e., the actual K-12 standards adopted by states). That is an error and a misleading one.

The two documents are different in nature, of course, since one of them is just a picture of an endpoint while the other is a progression. Feel free to compare them. One influence of the first document on the second is that in the first document you can see the first draft of what became the Standards for Mathematical Practice. And the topic areas listed in the first document evolved into the high school conceptual categories in the second. All this evolution happened under the processes for the second document, with input from the various groups described above.

I think the second document is the work of the 70-odd people listed as the Work Team and Feedback Group in the November 2009 press release. But, just for fun, I put the teams for the two documents together and counted how many of them came from ACT and College Board (no other testing organizations were represented). It comes to a total of 81 people with 7 from ACT and College Board, about 9%. So even with this interpretation the claim that the process was dominated by the testing industry is false.

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Drawings in the Common Core

There’s been a lot of talk recently about the Common Core and drawings. I won’t get into the politics of that here—that’s for my other blog—but, politics aside, there is an important question of interpretation, and possible misinterpretation, of the standards here. Let’s look at the wording of standards that talk about drawings.

Continue reading

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6–8 Elaborations of the Practice Standards

Here is the grades 6–8 elaborations document for the practice standards. As usual, please comment in the forums.

[corrected version added 5/6/2014]

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Problem with RSS Feed for Forums Fixed

The link to the RSS feed for the forums (on the right of this page) was broken. I’ve fixed it now. You might not have noticed (I didn’t for a while) because it was simply not updating. So if you are using an RSS reader to follow the forums, you should delete your old feed and add the new url. If you don’t understand this message, ignore it!

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K–5 Elaborations of the Practice Standards

Illustrative Mathematics, with the assistance of Mary Knuck, Deborah Schifter, and Susan Jo Russell, has been working on developing grade band elaborations of the Standards for Mathematical Practice. Here is a draft of the K–5 document.

As usual, please comment by starting a new thread in the forums. I’ve created a new forum for the practice standards there.

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Virtual Lecture Series! (and we’re back from a rocky end of year)

Are you interested in engaging with national experts around mathematics education without the travel, hassle, and costs associated with attending a conference? Introducing Virtual Lecture Series, brought to you by Illustrative Mathematics. Virtual Lecture Series bring together top speakers from around the country for a series of talks, as well as time for questions and answers, giving you a chance to learn and interact with experts without leaving your classroom or office. Illustrative Mathematics will be offering a variety of Virtual Lecture Series on different themes.

Our first Virtual Lecture Series will meet around the theme: Preparing and Facilitating Engaging Professional Development for Teachers around the Common Core, on the last Wednesday of the month at 7pm Eastern/4pm Pacific from January through May. The intended audience for this series is district and state mathematics specialists as well as teacher leaders. The five hour long sessions will include 40 minutes of presentation from national experts on Adobe Connect, followed by 20 minutes of Q&A. The cost to virtually attend the entire series is $150 which includes access to the following presentations:

January 29th: Diane Briars, President Elect of NCTM, Topic: Effective Instructional Practices to ensure all your students are “Common Core Ready”
February 26th: Bill McCallum, Lead writer of the CCSSM, Topic: Preparing K-12 Teachers for the Pathway to Algebra
March 26th: Mary Knuck, Arizona Department of Education Retired, Topic: Math Talks
April 30th: Ashli Black, NBCT and Cal Armstrong, Math Teacher Leader, Topic: Involving Teacher Leaders in Preparing and Facilitating Professional Development
May 28th: James Tanton, Mathematician and Author of Thinking Mathematically! Topic: Instilling a Love of Mathematics

Also the blog is back from a rough time over the new year.  Sorry if you had trouble with any of the posts or forums, we were not as quick as we could be in renewing the domain.  Let us know if you continue to have trouble accessing anything.

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