NCTM11 – Common Core

I went to three different sessions today about Common Core.  Two of the three sessions I was at were packed solid – the third was in Hall F and wasn’t anywhere near as packed. This is definitely one of the things teachers want to know about this year – or at least it seems that way by the attendance at sessions on Common Core.

I started off at Learning Progressions and the Common Core State Standards that was done by Bradford Findell of the Ohio Department of Education. Of the three sessions, this was the one I got the least out of and I left it early to head to stop at the exhibits before heading to see Arne Duncan speak. Friday was my most solid day of sessions. Most of what Findell talked about I already knew – he reviewed the nomenclature and organziation of the Common Core State Standards (CCSS – which corrected to CUSS the first time I tweeted from my phone and I thought that was amusing and telling).

Most of Findell’s presentation was on the progressions – sequence of increasing sophistication in understanding and skill within an area of study. The first he touched upon was the Learning Progression – how learning grows in an area. This is based on research on student learning. He spent the least amount of time on this progression.

The second progression is the Standards Progression – analyzing where kids are supposed to come from and are headed. This is built into the standards. CCSS Math does not support this easily, however there are standards progressions that are being put out by the CCSS writers here and it is written by Bill McCallum (see info later on). Ohio and some states also have done Standards Progressions and you can find Ohio’s CCSS resources here.

The third progression is Task Progression and Findell spent the most time talking about this. Task Progression is afforded by tasks. A rich mathematical task can be reframed or resized to serve different mathematical goals (and the goals might lie in different domains). It also has multiple entry points. He then spent the rest of the time I was there going through a task involving a fixed area and changing perimeter.  I have seen something like this before and left after I pretty much came to the conclusion that I had seen all the new stuff I was going to out of this session.

The second Common Core session I attended was presented by William McCallum from The University of Arizona and Zalman Usiskin from The University of Chicago (and UCSMP). They split the time and presented their viewpoints on the CCSS. The video from this session can be found at the NCTM website here and you can also find the video from the Arne Duncan address/question and answer there as well.

Bill McCallum spoke first. His powerpoint is here. McCallum was on the committee that wrote the CCSS.  He began and ended his talk talking about the idea of the original 1989 NCTM standards as being a jigsaw puzzle and that the CCSS was putting the pieces of the puzzle together. He did this huge analogy to Keats’ ‘Ode to a Grecian Urn’ that I had a really hard time following.

He then went into the design features of the CCSS. The first thing he talked about was the word “understand” and how it was in many of the standards. He did say that single standards don’t take place in a single lesson or day and that any lesson can and should cover several standards. He also talked about balance but I didn’t get a chance to write much on that in my notes.

McCallum did say that they needed to make decisions to get rid of the “mile wide inch deep,” especially in K-8. There is less emphasis on data and more emphasis on number and operations in K-8. They also moved away from universal strands K-12 that state standards had and focused on domains with a beginning and end.

As far as high school goes, Reasoning and Sense Making is the focus. Want to focus on the application of the mathematics. Seeing structure in expressions is a theme throughout High School mathematics. They did not divide HS mathematics into courses but into themes. They also wanted to embed the NCTM process standards (originally from the 1989 doc) so they could be taken seriously. They are now the Standards for Mathematical Practice and they should be assessed. (see more on this later – 3rd CCSS presentation)

There is also coherence in CCSS – “flows” in the standards that are multi-grade. If you look at his slides, you’ll see what he means and it also shows up in some of the Ohio Department of Education CCSS information. McCallum feels that mathematics comes together – it pulls things together that may seem different at first. There is also coherence in the standards since the domains are also tied together.

There are two websites he recommended: Progressions and the Illustrative Math Project. The Illustrative Math Project site is not up yet but will be shortly. Also on the list of resources were the Common Core Tools blog mentioned earlier and the NCTM sample Reasoning and Sense Making tasks.

Next up was Zalman Usiskin. He emailed me his powerpoint he used and I have it here. He started off quite quickly and you could tell he was fired up about his viewpoint on the CCSS. He started off by saying that when standards documents come without associated high stakes tests, creativity is inspired and it gives stepping off points for curricula. When standards documents come with associated high stakes tests, it is like a road with no turn offs and it stifles creativity. He implied but did not out and out say that CCSS is the latter, not the former.  Usiskin feels that CCSS is a mandated national curriculum.

He then went through several assumptions (read his powerpoint), some true, some not true in his opinion. He did make the point that in the last 20 years, we have made substantial, unprecedented gains in several measures such as the NAEP and SAT (see the powerpoint for stats). He did say that students are not the same as 20 years ago and that all indicators show that we are doing better than we were 20 years ago.

The next section of the presentation Usiskin went through (briefly) what he felt were the positive points and (in more detail) the negative points of CCSS. Take the time to read through the powerpoint to see what they are – especially the negatives that are spelled out pretty well.  The biggest ones that caught my attention was that there is a total disregard for technology K-12 and emphasis on paper and pencil and that there is an overloading of material in 6th grade. I have not looked at the CCSS K-12, only really 9-12 and those things were surprising to me. Usiskin feels that CCSS brought curricula back to a world that doesn’t exist and that many algorithms are out of date.

One of his biggest concerns he expressed here was that the CCSS is being used word-for-word to develop standardized tests that will be given beginning in 2014-2015. CCSS was not developed with enough time or consideration to public reactions – they were rather rushed in his opinion. CCSS has never been tested with students anywhere either. He feels that the flaws need to be corrected – the most glaring ones immediately, the rest at a set revision (possibly beginning in 2015 for implementation in 2020). He also wants high level test created that are not destructive.

The ending of his presentation (which I ended up missing to head to another session) was his recommendations for fixing CCSS. There were six of them and they are explained in detail in his power point. This presentation from both sides was excellent and if you have the time to watch it, I would recommend it.

I had rushed out of the end of Usiskin’s talk to head to a 3 pm session that wasn’t what I expected. So I decided to pop in on former NCTM president Hank Kepner’s talk on the NCTM Perspective on Common Core. Well, really, it’s Kepner’s perspectives. After having heard McCallum’s and Usiskin’s perspectives, I found Kepner’s to be somewhat of a middle ground but leaning toward Usiskin’s point of view. Kepner mentioned many “cautions” (his word) about the CCSS. I’m not going to blog about all my notes from Kepner, but I am going to hit what I feel are things that haven’t already been said.

Kepner’s main emphasis was on the Standards for Mathematical Practice. He even had us repeat the whole name for them several times. It is a small part of the CCSS but Kepner feels they are the most important part of them. He even made the point that the governors signed on to them as standards and may not have really realized they did that.  Basically, he was saying that the content standards aren’t enough. We have to do the Standards for Mathematical Practice also. Simply teaching more mathematics content is not the answer.

We need to address students’ lack of engagement. This is the greatest problem in math classrooms. Kepner reported that the most challenging problem reported by US teachers of Algebra 1 is unmotivated students. As we phase in CCSS we must include Standards of Mathematical Practice in all aspects of implementation. New curricula should include tasks addressing the Standards of Mathematical Practice and professional development systems should expand instructional strategies. Kepner also reminded us that we shouldn’t just do problem solving on Fridays – we should be doing it daily.

Multiple representations are important. There are prerequisite knowledge and skills in other domains needed for student learning for progression. The example he showed was for fractions.

The success of CCSS depends on the ability of teachers to assist students in learning the specified “fewer” standards at grade level and in using them extensively in subsequent situations forever. The point Kepner was making here was that even though there are fewer standards (which we wanted), many things are only taught once and students are expected to remember them once it’s been taught for the remainder of their K-12 math experience. To me, that means vertical discussions have to happen and there has to be communication as to what is being taught when. It also means that everyone has to teach what is in the CCSS or it won’t work. Mr. Smith can’t decide that he only has 2 years left so he’s going to keep teaching what he has been for 28 years.

Kepner spent a lot of time talking about assessment. There are two consortiums that are driving the assessment on CCSS – PARCC (used to be Achieve) and Smarter Balanced Assessment Consortium.  The states are split 50-50 between them and they are not required to be members of any consortium. Kepner feels there are states that may opt out of some parts of assessments due to costs (the performance based assessments – they are expensive to grade).

Both consortiums are working on building assessment pathways to college and career readiness for all students. There will still be one test at HS as there is now and the 3rd-8th tests as now. Achieve wants end of course exams in addition, Smarter Balanced doesn’t seem to be heading that way. The second thing the consortiums are diong is creating high quality assessments. PARCC is creating quarterly tests that you would give each quarter to your students. They are promising quick grading and return to teachers so that they are more useful to school. I believe that these results only go to the schools and are not reported out. Kepner’s concern with this is it creates a lock step curriculum and he feels it is contradictory to CCSS. He also stated it seems to be dictate when we teach what.

Smarter Balanced also is looking at the same idea but instead of them being 1st quarter, 2nd quarter, etc, they would have modules around key topics for “quarterly” assessments.

PARCC also has in its plans to create model instructional units and content frameworks. This really concerned Kepner because the assessors would be creating the curricula and he didn’t feel that was good.

As far as high school and the CCSS, there is a substantive need to unpack many of the standards to clarify how sub-constructs develop and build. CCSS is weak on getting students to be career ready. Kepner also talked about Appendix A. It is in the document, but not in the document. It was done very quickly. Kepner told us it is not mandated. I added the bold here because I think states and subsequently high school teachers are treating it as such. Appendix A is examples and we need to look at it and offer feedback to our states and CCSS. He also suggested we go back and read the Summing Up from March which talks about traditional (Alg-Geom-Alg 2) versus integrated possibilities.

Kepner feels that the pathways lists are not as important as the focus, the coherence, and the connections(his emphasis) that support a student’s learning and mathematical maturity. We need to look at how the ideas are developed and do it thoughtfully. We should also include a strategic use of technology. Kepner said the CCSS are silent on technology due to political debates and that we need to incorporate technology. We need to find enriching tasks that use technology in part.

The last concerns that Kepner expressed were for the high performing (gifted) and the low performing (special needs) kids. He is afraid that the high performing kids will get missed or lost. It’s not like you can just move them ahead a grade level in math and then expect them to test for their own grade. And as far as the struggling students, we have lost some of the time for development since CCSS does many things once.

Whew! That was a lot but I was glad I went to the sessions. It gave me a better perspective on how CCSS was developed and some of the issues that go along with it. I now also have a better appreciation of how CCSS ties in with what NCTM has done since 1989 (which has encompassed my entire teaching career). I am still not sure where I stand on the CCSS, but like it or not, I have to teach under it. I have to make it work as best I can. And when I get back to my school, I have to get the word out that we have to all make it work. That may be a challenge, especially at the high school end. We shall see.

This post originally appeared on An “Old Math Dog” Learning New Tricks.
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