James Tanton on the Math Common Core Standards

James Tanton is an experienced math teacher and educator of other teachers whom I respect a lot. Part of his take on math is that it should relate to the real world and it should be a joyful activity, because math is all around us if we care to look; if we do, it makes our lives better.  (My paraphrase of his general ideas, not a literal quote at all; but the way I expressed it, expresses my own personal thoughts on the topic. If you want to see examples of his work, I suggest you look at his site, . Again, I think he does excellent work, and I wish I could be one-fifth as original in my own teaching as he is.

In this video, Tanton gives his take on why the Common Core State Standards in math are actually a very good thing, not a bad thing at all, IF they are implemented correctly.

That “if” is a big one. Let us assume Tanton is right, that the CCSS in math (don’t know about any other subject) was written in a very thoughtful way and will promote these eight general concepts and practices in students towards math:

math practice standards

 

I’ll retype those for clarity:

 

  • Make sense of problems and persevere in solving them.
  • Reason abstractly and quantitatively.
  • Construct viable arguments and critique the reasoning of others.
  • Model with mathematics
  • Use appropriate tools strategically.
  • Attend to precision.
  • Look for and make use of structure.
  • Look for and express regularity in repeated reasoning

Those are, in fact, excellent ideals.

And those ‘Mathematical Practice’ goals you see above are, in fact, expressed better there than I recall having seen before in all my years of teaching math.

But — remember that “IF” clause? “If they are implemented correctly?”

As far as I can see, judging by what I see in mathematics classrooms in both charter and public schools in DC, it looks to me as if the worksheets and practice tests were written either by low-paid, low-skilled temps who have almost no experience in teaching math, or else were written by very clever and evil people who want to seriously dumb down the education of urban youth.

And, what’s more, those inequities are being primarily visited upon our poorest kids, especially [but not limited to] those of color.

Let me give examples, judging again by my own personal visits to schools in DC and what math teachers in DC tell me and what students of my acquaintance know tell me and show me (some of whom I have known for years).

What I see is that in the expensive private schools in DC, where there is no test-accountability on the part of the USDoEd, they are continuing to give a pretty good education, sometimes joyful and interesting, sometimes not, mostly depending on the individual math department members and the incoming ability levels and work ethics of the students they teach. Some of the departments use some pretty old textbooks because they prefer them to anything in print at this moment.

At the magnet high schools in DC, there is some pressure from the NCLB and RTTT testing mania, but since nearly all the students are already at or above grade level by any reasonable measurement, they can continue to teach.

However, at the regular, comprehensive high schools and at the middle and elementary school levels, I see that the curriculum is rigidly prescribed and regimented from above, in such a way that NONE of those eight laudable goals can possibly get implemented.

Instead

(1) Unbelievable number of typos and sloppy and incorrect problems (some of which I’ve been documenting on this blog) on centrally-produced tests and worksheets;

(2) Problems that are self-contradictory and involve huge amounts of difficult and confusing text;

(3) Large numbers of multiple-choice test items, which, in my considered professional opinion, can do almost nothing to promote any of those wonderful thought processes; nor do they give useful information to eachers about what the student does or does not understand;

(4) Requiring schools to spend an enormous fraction of their time on testing and test prep, thus preventing them from doing any open-ended investigations into math;

(5) Reliance on electronic on-line worksheets that are at times just as buggy as the worksheets;

(6) Loading teachers with so much time-consumiing but useless busy-work regarding data collection and entry and analysis that they have no time to actually read what the students wrote and drew — and believe it or not, it’s just as important in math as it is in any other class!

(7) Deep understanding is prevented because instead of going at a breakneck speed through umpteen standards a mile wide and an inch deep, it’s now 1.6 kilometers wide but only a couple of millimeters deep! (Get the joke?)

(8) And from what I see over time (30 years in DCPS and 5.5 years retired now), while I thought math instruction in some ways had improved from 1978 to the mid-2000s, it seems to have taken a real turn for the worse since Michelle Rhee and the then-head of the Washington Teachers’ Union, George Parker, along with AFT head Randy Weingarten and the heads of several large foundations (Walton family, an ENRON family, the Broads and one more), along with then-mayor Adrian Fenty and the blessing of Congress and the White House, were able to impose a weird settlement upon teachers which required them to teach to the many, many tests I’ve been complaining about for some time, in exchange for mythical bonuses amd high salaries that almost no teacher will be able to earn because they will be fired or burn out first.

My conclusions:

In mathematical logic, the word “if” is a really big deal.

And it looks to me as if the authorities in DC (both public and charter, with some exceptions as noted above) are NOT implementing the Common Core Standards correctly at all, because everything I see tells me that everything being done in the charter schools and in the public schools that serve poor or working-class kids in DC is in fact thwarting those laudable goals.

Remember what Tanton said, which I granted to him as being valid: If they implement the Math CCS standards correctly, then the results will be excellent.

Logicians say that when you have a sentence of the form  “If A. then B”, then it’s only false in the case where the “A” section is true and the “B” section is false. There are three other cases and they all have overall values of “true”. In particular, if the “A” part is false, it doesn’t matter whether B is true or not: the entire “if A then B” statement is true.

I maintain that the “A” part is false. So in one sense, whether the CCSStandards in math are as clearly- and as well-written as many math teachers think, it remains the case that even by their own standards, the idiots running the USDoE and the other billionaire education ‘reformers’ who think they know all the answers, are implementing it in a way as to subvert every single one of the laudable goals that are promoted by the CCSS themselves.

And that’s quite a trick.

It’s kind of like some of the absurdities in 1984 or recent world history: many regimes upholding the universal brotherhood of all working people while imprisoning, torturing, murdering or enslaving millions of said working people. I know it’s not nearly as bad, but this current situation sure is perverse.

So, what do you think? Believe it or not, there is a ‘comments’ button below this text, but it’s really tiny and you have to search for it.

Again, the link to Tanton’s video.

 

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7 CommentsLeave a comment

  1. I could not agree more with what you have posted–with one caveat. I cannot get over the fact that almost all blogs discussing math fail to ever mention the devastating effect of students not knowing the times tables. For five years I taght middel school math and with each new class I waited anxiously to see how many of “Mr. Mack’s” student I would get. Anxiously, because I knew that those kids not having Mr. Mack would not know the tables. Moreover, most of them believed that they never would. These students had a rough time-almost as rough as I had tryi ng to bring them up to snuff. Mr. Mack’s former students breezed through. He taught them the tables. I always mention this to educators introducing Common Core Math. Their eyes glaze over. Do I have a point?

    Walter McMann

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    • Yes, you do have a point. Actually, knowing the times table is merely an adventure in pattern-recognition, which is something that humans are really, really good at, and which we all enjoy, a lot. For example: What do all of the multiples of 5 have in common, and how do they differ? Ditto for multiples of 9, and so on. Look at the symmetries in the entire table. What about the patterns in that main diagonal?

      And after discov ering those patterns, what few ‘facts’ remain that are a bit hard for you? Not many, right? Well, if you can memorize all the words to a song, you can certainly memorize a handful of math facts…

      If other teachers are imparting the idea that they can never learn those facts or find those patterns, then that’s definitely counter to the concepts in the stanards, it seems to me.

      On Fri, Jan 9, 2015 at 2:28 PM, GFBrandenburg's Blog wrote:

      >

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      • I have tried the pattern application and still hold that nothing short of sitting down with flash cards will remove this impediment to mastering math. Show me a student that can reduce 35/63 and I will show you a kid that knows his times tables while perhaps not quite a master of those beautiful patterns. wsm

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  2. My takeaway from the article has less to do with math than with myths of economics. It would seem that the much vaunted private sector has all but completely failed to respond to competitive pressures and produce high quality instructional materials. Instead, we have a profit driven system of mediocrity where he who is first to the public trough wins no matter how abysmal the quality of his product.

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    • Not sure what your comment has to do with anything. Can you elaborate?

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  3. It wasn’t until I had to teach struggling students math that math became fun for me. (I was a special education teacher.) I never taught beyond Algebra 1 (and that not very well), but at a more basic level, I had to take apart concepts to figure out how to reach my students. Guess what? It was fun! It was very difficult to get past their requests to just teach them the formula, but it was so satisfying to watch them “get it” and be able to use their skills with confidence. I see the same problems that you see with the curriculum. Too many districts are using rigid prescriptive programs. I even subbed in a classroom where I had to read from a script, and I couldn’t see what the students were doing! The teacher’s manual was totally isolated from the student workbook. I went to school during a time when no one asked out loud why we were doing something and no one ever volunteered a reason. I just knew I liked some subjects better than others. As I got older, math only made sense to me when it was applied to other areas of study: measurement in chemistry, statistics in psychology,… As a teacher I finally fell in love with the patterns in numbers that I found much easier to see in language. I really worked hard/struggled with what I was trying to teach and how to teach it. I will always be a better problem solver with words, but at least now I can admire the world as described by numbers.

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  4. James (and really all the teachers on this post),

    We are doing a project looking for that IF where is the CC being implemented with success and where does it need more attention Given your expertise as a teacher and experience with the Common Core, I’d love for you to share your knowledge with our network of teachers. Here is a link to a live conversation that teachers are having around the Common Core. The goal is to collect opinions in one location in order to increase the visibility of teachers voices. http://vivacommoncore.mysocialsphere.com

    Thanks,

    Jamie

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