Sonia Sotomayor

Sonia Sotomayor at Berkeley Unified Schools
Photo: Berkeley USD @ Flickr

Out of respect for Justice, I'll eschew my usual pun post titles.

I just finished My Beloved World, a memoir by Sotomayor of her life up to her first appointment as a judge. It is a well-written story, and she will impress you with her positive attitude, perseverance and grace. It makes me extremely glad to have her on the court.

By why blog about it here? Because there were a few bits about education to share. Her experiences in poor (low SES) schools, transitioning to Princeton, the importance of role models and mentors, the impact of service work, and addressing bias throughout her life are all worth reading. Her success in overcoming adversity (family alcoholism, diabetes, etc.) are inspiring.

This story made me think about the importance of genuine assessment, and the necessity of important objectives.

... Teachers, I was finally realizing, were not the enemy.

Not most of them, anyway. There was this geometry teacher nicknamed Rigor Mortis. Word had it that she'd been at Cardinal Spellman since before the invention of the triangle ... I was shocked when she called me into her office and accused me of cheating. The basis for her accusation was my perfect score on the Regents geometry exam. No one in all of her centuries of experience had ever scored a hundred on the Regents.

"So who did I cheat from?" I asked indignantly. "Who else got a hundred that I could have copied from?"

She looked flummoxed for a moment. "But you've never scored higher than eighties or low nineties on the practice tests. How could you get a hundred?"

The truth, as I explained, was that I'd never once got an answer wrong on the practice tests; points had been deducted only because I hadn't followed the steps she had prescribed. I had reasoned out my own steps, which made sense to me, and she had never explained what was wrong with them. On the Regents exam we only had to give the answer; no one was checking the steps.

What happened next truly amazed me. She dug out my old tests and reviewed them. Acknowledging the validity of my proofs, she changed my grades. Even Rigor Mortis, it turned out, wasn't quite as rigid as all that.  (Chapter 11)

One of her high school teachers expounded the value of critical thinking, but she had never learned to do it. Justice Sotomayor's first taste of argument came in a good forensics experience. (Itself a good story.) Then, at Princeton, freshman year:

Professor Weiss told a familiar tale: although my paper was chock-full of information and even interesting ideas, there was no argumentative structure, no thesis that my litany of facts had been marshaled to support. "That's what analysis is - the framework of cause and effect," she said. Her point was a variation of what Ms. Katz had been getting at, though now it was coming across more clearly and consequentially. Obviously, I was still regurgitating information. It was dawning on me that in all my classes I was so concerned with absorbing the facts in the reading that I wasn't marshaling them into a larger argument.  By now, several people had pointed out where I needed to go, but none could show me the way. I began to despair of ever learning how to succeed at my assignments when quite unexpectedly it occurred to me: I already knew how. (Chapter 15)

This is a call to me, again to emphasize what is important in mathematics, and to support students in achieving that. There's also a lot here for me about the importance of transfer, giving learners the oppportunity to apply math in their other work and to bring in their successes in other areas into the math classroom.

And she makes a nice plug for numeracy when discussing her diabetes, as well as a nice demonstration of questioning in problem solving.

I test my blood sugar and give myself shots five or six times a day now. When deciding what I'm going to eat, I calculate the carbohydrate, fat and protein contents. I ask myself a litany of questions: How much insulin do I need? When is it going to kick in? When was my last shot? Will I walk farther than usual or exert myself in a way that might accelerate the absorption rate? If I weren't good at math, this would be difficult. (Chapter 28)

There's also stories about K-8 teachers dissuading students from their dreams (Chapter 10), an interesting exchange about a teacher listening to her students about what a Spanish course should be (Chapter 11), a good interaction with a psychology prof at Princeton over a failed experiment (Chapter 15; rats!), how learning programming influenced her thinking (Chapter 15), the law as a way of thinking (Chapter 20) and more.

Of course, I'm interested in your thoughts, if you'd care to share them on Twitter or in the comments.

Math Memoirs

There's one of my favorite math teaching videos up in Keith Devlin's most recent blogpost.  (Thrilled that it's now on YouTube with several other of her interviews.) It's from the wonderful Marilyn Burns, who has really done more for math education than anyone in recent decades. Her stuff was good enough to get word of mouth sharing before there was an internet. (Dan Meyer is quite reminiscent of her in several ways.) Devlin uses the video to make the point that apparent understanding is not proof. A better assessment can uncover the truth, and Burns is excellent at questioning to get an accurate picture.




As a novice teacher I quickly found that the students giving an answer did not tell me whether they understood or not, and I moved to asking for how they got it. It took me years, however, to get to understand that how is better, but also does not get at understanding. It's their thinking that I want to hear. Then I should ask for it! Unfortunately, even spoiled university teachers don't have time to sit down and interview students over all of our major objectives. I can, however, ask questions to which I really

Dave Coffey found this excellent solution by Carl Barnard, a high school student, to the painted cube problem that crossed the line to be a memoir. We often introduce the idea of a memoir by having our students read it and comment on it. (Here's my most recent version of the workshop; Dave was almost certainly the original writer of it.) It's a start to learning how to communicate your thinking. While it's important and beneficial for any math student to do this, it is unbelievably crucial for math teachers, and a big part of pedagogical content knowledge to me.  Most students on end of term evaluations comment that this is an area where they grew significantly.

I wanted to experiment with what this looked like in elementary school, so I asked my daughter to give it a go. These are from the summer between her 4th and 5th grade. She was a bit precocious with her writing, but had had pretty traditional math instruction. (And not interested in talking with me about to a large extent.)

Just writing the method. A first attempt at memoir. I supported with a kind of questioning framework.




She was game enough to try twice more.






This is the sort of information that I want from an assessment. I get so much more an image of what ideas she has about number and operation. And it is far more interesting reading than traditional assignments where I'm looking for what I expect or not.