On a recent snowy day, I took a stroll through the park at lunchtime. This lovely round stone caught my eye.
The snow here has accumulated as a spherical cap. I also like how the area under the stone, untouched by snow, is some kind of projection of the sphere. I wonder what we can say about the direction of the snowfall, based on this snowless projection?
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Through Math for America, I am part of an ongoing collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here
Test Yourself — Math, February 26, 2014
This problem is about how differences in minimum wages can effect those living near state borders. How much more per year can someone earn in Oregon than in Idaho?
Here is another installment in my series reviewing the NY State Regents exams in mathematics.
The January, 2014 Geometry exam included something I had not seen on a Regents exam: a fill-in-the-blank proof.
While I see some value in these kinds of problems in the teaching of two-column proofs, they shouldn’t be used on the final exam for a Geometry course. The goal of teaching proof is for students to develop the skills necessary to construct their own proofs from scratch. This problem reduces “proof” to a series of recall tasks.
So why not just ask the student to construct the proof from scratch? The rubric suggests the answer to that question.
While grading an open-ended proof is hard, checking off a list of six reasons is easy! Or so you would think.
Reports from colleagues who were grading this problem in a distributed grading center were disheartening. In particular, there was a lot of disagreement about what constituted appropriate justification in moving from
to
Apparently, teachers in the room wanted to accept “cross multiplying” as a legitimate reason, but would not accept “multiplication property of equality”. The site supervisor agreed, despite my colleagues’ objections.
Problems like this highlight the tendency to test what is easily tested and graded, not necessarily what’s important. And grading room stories like this should give pause to those who like to believe that these tests represent objective measures of learning or knowledge.
The way the snow collected on the fence reminded me of a histogram, though you might have to rotate your head 225 degrees to see it for yourself! As I took this in, I wondered why some chains of snow were longer than others. I also wondered what this representation of data said about the direction of snowfall.
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