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Tuesday, April 9, 2013


Educators seem to be a mixed bag of afraid of vs. jazzed about the CCSSM Standards for Mathematical Practice. At first read-through, they seem very sensible, and like things math students should be doing as a matter of course.

But if you think you really get them, try a little experiment: ask a small group of math teachers what they think "Attend to Precision" means. What does it look like if a classroom task requires it? What does it look like when a teacher is facilitating it? What does it look like when students are doing it? Here are some responses you might hear:

  1. Rounding correctly according to the directions
  2. Rounding sensibly based on the problem's context
  3. Being careful when plotting points
  4. Labeling axes and diagrams correctly
  5. Drawing sketches and diagrams to scale
  6. Using an appropriate number of sig figs based on the precision of the measuring device
  7. Using precise mathematical terms in written and verbal communication
  8. Defining variables and symbols
I've spoken to teachers who express their understanding with numbers 2, 6, and 7, but I've talked to teachers whose understanding hews closest to numbers 1 and 3. Which is not to pass judgment, but is to say: it might be wise to be aware that you and your colleagues could have different, and potentially incorrect, assumptions about the SMPs. 

And "Attend to Precision" seems like one of the more concrete ones. See what your colleagues have to say about "Look for and express regularity in repeated reasoning," and I bet the answers will be even more all over the place.

Another observation: it can be really hard to evaluate which SMPs are highlighted or emphasized in a classroom task. When I try, I tend to go "uummmm...all of them...?"

So what kind of task lends itself to "Modeling with Mathematics"? What does it look and sound like when teachers and kids "Look for and Make Use of Structure"? 

I'd like to point you to a recently published resource: A Rubric for Implementing Standards for Mathematical Practice. It was written in July of 2011 by Danielle Maletta, Mimi Yang, and Mariam Youssef as part of the Visualizing Functions working group at PCMI. It gives an observer specific items to look for in a task, as well as specific teacher behaviors, to help evaluate how faithfully a standard is being met in a particular lesson. The accompanying Resources document will also give you a deeper understanding of each standard.

Also, heads up that Illustrative Mathematics, in addition to the Herculean undertaking of trying to illustrate every K-12 content standard, has put a significant amount of effort into illustrating the Standards for Mathematical Practice using both sample videos and classroom tasks. 

Check them out. Share widely.

Monday, April 8, 2013

Pop Quiz

Was this published in 2001, or this morning?
New York State United Teachers, the state's largest teachers union, is urging members and parents to call on the state Education Department to stop implementation of this year's tests, which will be more challenging, because schools have not received all of the necessary curriculum. 
"If we want our children to be ready for college and meaningful careers, we need higher standards — and a way to measure whether those standards are being met — and we need them now," Education Department spokesman Dennis Tompkins said.
Give up?

Saturday, April 6, 2013

The Tests Matter

Here is what is going on right now, in the time before the Common Core Standards have really hit high schools, and before a common assessment has been inflicted on any live children. The non-teachers in education are going: "Just start teaching the right way. Pay no attention to the tests. If you teach right, you don't have to worry about the tests. The tests will take care of themselves." The teachers are saying: "The way I teach is basically fine, anyway, so I'll make whatever adjustments I need to make once I see what they want kids to do on these new tests." I know there are probably some teachers changing their practice, and some non-teachers with half an eye on assessment. I'm painting with a broad brush. Go with it.

This is what I am afraid of: the thing that happened in New York State, starting in 1999. That's when NY changed from Course1/2/3: a decontextualized, integrated curriculum with very predictable though rigorous exams that were none of them a graduation requirement... to Math A/B, standards with more focus on applications and much less predictable tests -- also, kids had to pass the Math A exam to graduate. (This was a huge deal. Regents exams had traditionally been taken by your college-bound academically-oriented students, and suddenly everybody had to take one of them.) The new requirements were supposed to make things tougher, with all the rhetoric that comes with such changes. June 1998:
Yesterday, officials at New York City public schools welcomed the tougher tests, while some education advocates worried about the lack of resources to train teachers to teach for the higher standards.
If it sounds familiar, that's because it's straight from whatever school-reform-article-generating-machine the news has been using for thirty years. Moving on.

Some shit started hitting some fans. October 2000:

Mr. Mills said middle schools ''need to rethink what they are doing'' and quickly figure out how to teach students the skills they need to meet the new standards. He said he had no intention of backing down on the standards, which as of last June required every high school student to pass an English Regents exam to graduate, and by next June will require every high school student to pass a Regents math exam as well.
People started freaking out when they realized that requiring a passing score on an algebra test was going to be a graduation-rate debacle:
Students in the next class, which entered in fall 1997, will have to pass both the English and Math Regents to get their high school diplomas. If the results hold steady, about a quarter of this year's seniors will not be allowed to graduate.
There were protests (May 2001). There were districts trying to opt out (Nov 2001). 

I don't know what happened to all the kids in the early 2000's who were denied a diploma because they couldn't pass the Math A Exam. A bunch of heartbreaking shit, I'm sure. 

In June 2003, there was TESTMAGEDDON. The Math A Regents exam was the straw that broke New York's resolve
Though many districts have not finished tabulating their scores, superintendents, principals and math department heads are reporting preliminary results that some described yesterday as ''abysmal,'' ''disastrous'' and ''outrageous.''
It was not a good test. Post-Course 1/2/3 exams were not good tests, generally: problems that didn't make sense, weird, contrived contexts, a fetishization of goofy vocabulary and notation. Too much content was a huge problem. A test that didn't know whether it was an algebra or geometry test was a huge problem. A test that didn't know what it was measuring -- readiness for higher mathematics courses? Basic skills that should be expected of every graduate? -- was a huge problem. In the end, the test measured nothing but whether or not a kid had passed that test. The accountability movement compelled schools with lower scores to make their math courses all about passing the test. Math A became a de facto curriculum, and a horrible one. 

NY tried to raise the bar. Then, a whole mess of kids ran head-first into the bar and fell on their asses. Then, instead of re-evaluating any of their faulty premises, NY responded by lowering the bar.

On the June 2003 exam, they relented and lowered the cut score

Then, they eased up on subsequent tests

New York State's education commissioner, Richard P. Mills, said Wednesday that the state would loosen the demanding testing requirements it has imposed for high school graduation in recent years, including the standards used to judge math proficiency.
They made the tests easier. Lots easier. Also, the thing happened that took all the respectability out of the historically respected  regents exams: for the tests required for graduation, the score you needed to pass got dramatically lower. They said it was a 65, but after June 2003, you only needed a raw score of around 42% to pass the Math A with a scaled score of 65. (The raw scores in the linked table are not percentages -- they are out of 84 points.)

I wasn't around when this all happened. I didn't start teaching until 2005. And I don't think we're getting exactly a repeat with the Common Core. For one, there does seem to be a coordinated, genuine effort to support teachers in changing their practice, independent of testing. For two, there's a coherence and focus in the CCSS that New York was sorely lacking. But also, there's the whole added wrinkle that tests are trying to fulfill still another purpose: teacher evaluation. The disaster story might not be "so many kids can't graduate", it might be "so many teachers are being rated poorly, even good ones that kids, parents, colleagues respect."

But I still think it serves as a cautionary tale, and I'm still curious about how this is going to play out once the new tests hit a computer lab near you. If they really measure the stated goals of the new standards, they're going to be very different. Because of that, they're going to be perceived as too hard. How the test-writing consortia, DoE, states, districts, etc react to that is going to be really interesting.