Thursday, November 12, 2009
Nate Silver, Math, and Quadrant D
The big mistakes we make with the rigor and relevance framework is that we assume higher-order thinking is "tougher" and that more relevant means a story problem from a 2nd-person perspective. And, neither are the case.
Math is a great example. If you were a math teacher, and you were asked to make your curriculum more rigorous, you would probably eliminate some of the easier skills and replace them with skills that are tougher. Or given that math often works sequentially, eliminate chapters 1-4 and replace them with chapter 21-24 in the textbook.
You'd definitely be upping the difficulty, but would that result in students having more rigorous thinking skills? Not if the replacement skills are taught the same way, it wouldn't be.
In that same vein, traditional math instruction is definitely analytical, I'd say more so than traditional language arts or social studies curriculum, and analysis is a higher-order skill. But is it critical thinking? How much do students actually critique what they are learning? Even the best math instructors struggle with that... it's hard to critique something as black and white as mathematical theorems.
One of the biggest names in math today is that of Nate Silver, the founder of the popular political statistics blog FiveThirtyEight.com as well as the inventor of the sabermetric statistical model for baseball PECOTA. Silver's use of statistics and mathematical logic, both in baseball as well as in politics, ranges from the simple to the extremely complex.
But above all, it's very accurate, as PECOTA was the gold standard in predicting player performances and team results for years (other mathematical models have now caught up to it), and 538 successfully predicted 49 out of 50 states from the 2008 election with an algorithm of polling data.
There are two ways teachers can use Silver's work as the basis for quadrant D math activities (and no, one of those is not to do a biographical report on him... the biographical report on the "famous mathematician" or "famous chemist" or whatever being one of the worst ways for a student to learn more about that subject). One is to look at how to mathematically determine an otherwise non-mathematical quality. Silver asked the question "How can we predict the success of a baseball team or a presidential candidate?" and then developed the mathematical model to do so. But that question could just as easily be to rate the "best" musical act of all time or the most influential president of all time.
Starting off with a theoretical question, and then looking at the math that could help you support the answer uses a higher order skill not often associated with math: creativity. It also is relevance... true relevance. Not just take my problem and make it a problem that involves money. But rather, actually look at how real mathematicians in the world would use the content and skills to solve a real-world, unpredictable problem.
The other way would be to look at the ethics behind math and statistics. As we mentioned earlier this week, Silver questioned the methodology of the polling company Strategic Vision, which has been producing some shaky polls used to advocate for certain political causes. The method he used is to look at the trailing digits used by the polling company, which shows a non-random pattern. Silver then concludes the company was fabricating the polls, quite the claim.
Not only has this episode been relevant in terms of its impact on the world we live in, but it also has unfolded before the viewers eyes through an ongoing blog (Silver does a fairly good job of explaining some very abstract patterns). Again, you have the task of working through some unpredictable situations (proving a statistical polling company is lying is not a predictable part of any curriculum). And oh by the way, Strategic Vision hasn't polled since Silver's inquiry.
Now, this comes from a non-math teacher's perspective, but this is what the Iowa Core is getting at. The counter argument to doing this quadrant D work would be 1) it's time consuming and 2) takes us away from the mastery of essential skills and concepts. But that's actually its strength. It does take a student away from the collector of formulas and theorems to becoming the critical thinker in an inquiry-based setting, and it gives the student an appreciation for how math is relevant in the world around them.
Arthur Benjamin talks about statistics (and how it is overlooked in American curricula) with this short TED talk.
An explanation of PECOTA
The methodology behind 538