Wednesday, February 25, 2015

Prepping for the Test

            Four weeks ago I wrote about Pip and the letter he received about the accelerated program at his school. At the time I was feeling powerless with respect to a selection process that seemed heavily dependent on a single number generated by one unknown test given on one unknown day. I wanted to Pip to get into this program because he likes school and he likes learning and the accelerated curriculum would give him an opportunity to do more of both. While getting in isn’t the do-or-die situation that it is in some places (we use to live in a rust-belt city where you either got your kids into the accelerated programs or you took them to private schools – there was no in between) I felt like he deserved one of the small number of spots available. Not only has he consistently worked at the leading edge of the curriculum, he also treats others around him with genuine respect. The teachers trust him to take care of his business and do what has been asked of him. He contributes productively to the class and willingly helps others. Pip is the type of kid that these kinds of programs should be accepting.
None of these qualities though show up on the quantitative measurements that are used to determine who gets a place and who doesn’t. The test is the only thing that matters.
            A day or two after writing that post, I decided to get over my paralysis and embrace a moderate Amy Chua approach to taking on this thing. While I didn’t know exactly which test Pip would be taking, it didn’t take a big imagination to go to the internet and figure out which ones he might see. After reading through a couple of different possibilities, I went about putting together example questions that would cover the general scope of what he might see. Each day after dropping him off at school I’d come home and spend about thirty minutes drawing up a set of questions, some of which came from the internet and others of which I made up on my own. When Pip came home each day, we would work through the questions together. It took a couple of days for us to figure out how many he could reasonably do and how best to go through them, but we eventually fell a good rhythm. I even started splitting the questions into an easy practice group and a more complex group to give him some work both at getting used to the types of questions he would face and at working through problems that didn’t immediately make sense to him.
            The most valuable aspect of our work together over the ensuing weeks was what I came to think of as the post-completion review process. After Pip finished all the problems on a given page, I had him explain to me his thinking on each problem before I told him the answer. This process had two benefits. The first was that it forced him to slow down and articulate what he was thinking regardless of whether the answer was right or wrong. This was particularly important for the questions he got right as those he tended to know without really understanding why. The second benefit of this process was that it gave me insights into his routines of thinking that I could then pick at in subsequent days.
            Ultimately, we didn’t have long enough for Pip to really reconfigure his thinking processes to match those of the test or even develop a regular set of procedures for addressing various kinds of problems. However, he did get to see enough problems to demystify the test itself and for him to become aware of which approaches he favored in solving certain types of problems. For the time we had available this was a satisfactory result. As I told Ava the night before the test, I felt like we’d done well. He was prepared for the type of questions he would see. He would be able to spend his time figuring out answers and not having to figure out exactly what the questions were asking of him. This was the best position we could get to without having the test take over our lives.

            All of this work together had a couple of interesting side-effects that I had not anticipated. For one, it temporarily made me into a less friendly person. Usually I’m inclined to talk with other parents just before pick-up time to see what’s going on and to learn how they are feeling about various things taking place at school. It’s mostly an exercise in collaborative competition as people talk about what their kids are into, how they’re doing, things like that. There’s usually some soft bragging on all sides (mine as well) which is fine because it helps give each other a sense of what other kids are doing and what we might expect of our own. And for the most part, the kids are not competing with one another in these moments. It’s mostly just parental pride at stake.
But with respect to the accelerated program tests, I didn’t venture any questions. I decided I’d rather not talk about how Pip was preparing on the off-chance that I’d give someone else the idea to do the same. I preferred to preserve that (possibly imagined) edge for Pip. Of course, without talking about it, I had no idea what others were doing which may very well have prevented me from doing something else that was beneficial, but that was a gamble I decided to take. All of this made me edgy and less talkative than usual. When you’re thinking so much about not letting others know what you’re thinking, it becomes hard to actually speak like a normal human being. In the last couple of days before the test, I couldn’t help but think of Bill Belichick, the coach of the New England Patriots, and his gruff exercises in ambiguity and non-disclosure with the media. Standing around waiting for Pip and Polly to come out from school, I found myself doing much the same thing.
            On the flip side, now that the test is over, I’ve found that I am missing getting to spend extra time working with Pip. For the past couple of weeks, we’ve had a moment of comradeship each day when it was time to work through the questions I’d put together for him. Polly would come in and sit on my shoulders (literally) and look on while we talked through each of the problems. Pip would be proud when he got the hard ones right, frustrated when something didn’t fit his logic, and excited to do more the next day. The weekend before testing day he even asked for me to put together an extra set of questions for him. We both felt invested in the work and enjoyed having something to work on together in a focused and determined way. The day after the test was over and there was no more prepping to do, the afternoon felt kind of empty and directionless. It was missing the espirit de corps that had become part of our routine. Without that half-hour of intensely close work, I feel like I know him a tiny bit less at the end of the day and that makes me sad.

            So the test is done and now we wait. On the afternoon after the test, Pip said he felt comfortable with the questions and came up with reasonable answers to them all. The tricky thing with this whole test – and the reason it worried me so to begin with – is that the measurement is all relative. He could have done incredibly well and still not make it in to the program. Its all a matter of what everyone else does. Maybe this year was a good year. Maybe it was not. Maybe it won’t matter at all. We just have to wait and see.

Wednesday, February 11, 2015

Polly and Math

            Ten years ago, Larry Summers, a former Treasury Secretary and at the time president of Harvard University, gave a set of remarks to a conference on diversifying the science and engineering workforce in which he posed some hypotheses about why there were so few women in science and engineering fields. He ventured three hypotheses. The first was that the career pressures of such positions were not as attractive to married women as they were to married men. The second was that there were more men than women possessing the “aptitude” to work at the highest levels of mathematics. The third was that men and women were “inclined” for various reasons to go into other fields. While all three claims feel strangely ignorant for a person in Summers’ position to suggest, it was the second of his hypotheses that really struck a nerve with the public at large. While Summers’ defenders in the media brouhaha that followed pointed out that he wasn’t saying that all women are innately less mathematical than all men nor even that the average woman is less capable than the average man, when you parse his words and shift them from the language of academia to the language of everyday communication, he was basically saying he thought that as a matter of biological difference fewer women than men might be capable of doing math at the highest levels.
            Now, I’m ideologically suspicious of any biological claims made regarding the general superiority of one person or group over another. Usually, such claims are deployed – consciously or not – in a way that justifies a person or people’s position of power over others by claiming some inherent betterness in themselves. And if you look at Summers in this context - a white male economist moving in the upper echelons of academic, economic, and political power in America – such an alignment fits. He basically said within those remarks that women have neither the interest nor the capacity to handle the kind of work he does. He even made a spurious claim about how his twin daughters, despite not being given dolls, transformed other playthings into mothers and babies as a way of justifying his hypothesis on the differing inclinations of women and men. Hey Larry, did your children not go to preschool or have a nanny or play with other kids or watch TV? Where do you think ideas about gender roles come from? A child’s parents are only one out of a great many sources.
            Anyway, the whole Larry Summers episode was brought back to my mind recently when Polly told me about the math groups in her kindergarten class. Polly has a good feel for numbers and, for reasons I’ll discuss in a few moments, is way ahead of the average kindergartener in handling the basic functions of mathematical thinking. As such she is working in the most advanced math group in her class and, as it turns out, all the other members in her group are boys. Now, the highest level reading group in her class has an even mix of boys and girls. Why should the math group be any different? It’s an anecdotal result that would cheer Larry’s heart and one that makes me shake my head. I had hoped things would be better than this by now.


            In one chapter of his book Outliers, Malcolm Gladwell talks about hockey players and an interesting pattern that can be observed when one looks at which players ultimately make it into the highest levels of the sport. Interestingly, many have birthdays that come early in the year. Gladwell looked a bit more closely at this and found that Jan 1 corresponded with the cut-off date for kids joining youth hockey leagues in Canada. In other words, the kids who had birthdays early in the year – those who were at the oldest end of the league spectrum – tended to have a greater chance of developing the skills and talent necessary to play the sport at higher and higher levels. Gladwell attributes this correlation to the idea that the older kids were bigger, stronger, and more capable and thus garnered more developmental attention from coaches, got more playing time in games, and attained the kind of early success that keeps one interested in doing more. While Gladwell argued that one’s birthdate was no guarantee of success, it did create a slightly more favorable set of conditions and thus more of those players eventually made it into the professional ranks.
            I’ve been thinking about Gladwell and Summers together because it seems to me that much of Summers’ argument regarding the distributions of mathematical thinking at the highest levels could be explained by a Gladwell-type argument. While I don’t know why the distribution in Polly’s class is the way it is, I can see how it would propagate from there all the way up through the ranks into the highest levels of math and science. The kids in the advanced group are getting the same kind of feedback that Gladwell’s older hockey players are. They are getting the extra attention. They are encountering the success that makes one want to keep going and doing more. They are not all going to be great mathematicians, but the odds say good mathematical thinkers are more likely to come from one of these kids than from kids in any of the other groups. They essentially have a head start that can increase with time.


Before I had children I always thought of kindergarteners as little kids not that far removed from infanthood. They still have their entire school careers in front of them. They were, I thought, a blank slate waiting to absorb the world. However, that’s just not the case. By the time they turned 5 both Polly and Pip were well established as people. Their personalities were solidly in place. What they’re willing to do and not do were largely set. Their aptitudes and interests had a solid form. Their school years will certainly be a time of adding and molding, but the foundations regarding who they are and what they know about themselves are already poured.
This reality makes me think that all the effort put forth in later years to bring more women into math and science fields, while not a waste of time, is something of a rear-guard action. The real ground where much of these relationships is getting decided is in the zero to 5 age group. It turns out, I think, that if you really want to head off the cultural influences that shape girls’ relationships to mathematical thinking, you have to get to them really early. You have to get to them when they are learning to speak, when their brains are making the transition from basic stimuli response to conscious and considerate thought. From what I’ve seen with my kids, there is a sweet zone in the 2-4 range where so much of their basic thinking is worked out. If you can get to them then, you can shape a good deal of their capabilities later.
            And this is why Polly is in the highest math group in her class. I started doing simple math work at home with Pip when he was four and Polly was two (we used Singapore Math but I don’t think any particular program really makes that much difference). She looked over his shoulder for a full year then after he went to kindergarten the following year, I started her on the same program. By the time she entered kindergarten she’d had two full years of math already and was doing subtraction with three-digit numbers and substitutions. (She’s actually slipped a little since then because she hasn’t kept doing it). Polly is now good at math which makes all the stuff she’s doing in school easy. And because its easy, she does it well and she likes doing it. That momentum is going to carry her a long way. I don’t think she’ll be a math genius or necessarily pursue a career where math is central – right now she wants to be a veterinarian or zoologist or something else where she would work with animals – but, if we take the Gladwell effect seriously – and I do – she will be on the front end of her class in math from the rest of her academic career.
            I think this will probably be true for another reason as well. I’ve consciously made her aware of the ideas Summers was espousing, and this has given her a bit of a chip on her shoulder. It was Polly who brought to my attention to the fact that she was the only girl in the highest math group. And she took relish in telling me last week about how she was already done with her math sheet and the boys still had at least half the page to go. They weren’t serious enough about doing the work, she said with a touch of disdain.
            This chip is going to keep her working and that is something I don’t mind feeding. I even took advantage of her moment of triumph over the boys to start giving her one math problem a day when she comes home. We’re not going to do new material until the summer, but I’d like to get her back up to where she was this past fall. That way we can plow forward come summertime and Polly will be well situated for another year of math to come.


            I don’t know why the distribution of mathematical prowess in Polly’s class is the way it is. At this time, I don’t have the data to completely rule out Summers hypotheses regarding biological differentiation. However, I don’t think they’re right. Polly is not in the most advanced math group in her class by accident. She was not freakishly inclined towards mathematical thinking from the start. She was exposed to math principles early on and has been doing math work regularly ever since. This kind of socialization is more fundamental than any biological differences one may find.

Wednesday, February 4, 2015

What's good for one? What's good for all?

I grew up in a small town. There was one elementary school, one middle school, one high school. If you lived in that part of the county, these were the schools you went to. These were the schools your parents went to. These are the schools to which your grandchildren will go. The buildings may get updated or even built anew, but the link between the town and the schools will remain (seemingly forever) unchanged.
            This is not true of the city where we currently live. It has a population of around 250,000 and is served by a couple dozen elementary schools, ten to twelve middle schools, and four high schools. When the school district’s officials last rezoned the city over a decade ago, the neighborhood in which we live got a boost. While its elementary school remained the same, its middle school got shifted from one of the city’s worst to one of the city’s best. That shift was significant in that it made this low to middle income neighborhood a very attractive location for families with young kids. They could buy a small, reasonably priced house and still be able to send their kids to a decent elementary school, one of the state’s best middle schools, and a well regarded high school. Since that time, the quality of the elementary school has improved dramatically - a trend that probably has as much to do with changing demographics as it does with the admirable efforts of the school’s teachers and administration – making the neighborhood even more attractive. When more middle income families who care about education – and who have the time and monetary resources to devote to it - move in ( as we did this past April), your school’s performance goes up.  How much and in what ways may be personnel and location dependent, but the larger trend of improved test scores is often divorced from the specific actions of any given school.
            Unfortunately for us, given the city’s current and anticipated growth in population the school district decided this year that it is again time to make some adjustments in the school zone boundaries. After much whispering and gossip, the new proposed school zones were revealed this past week and while both their elementary and high school zones remain the same under the proposed plan, the kids in our neighborhood would be sent to a different middle school than the one they currently attend. This different school is about the same distance away as the present one, but its location is worlds apart. The present middle school is smack in the center of a set of rich, mostly white neighborhoods. The nearby businesses include a small-time hardware store, a French bakery, a local bookstore, and a home furnishings shop. The middle school our children would go to under the new plan is sited in a poorer and highly diverse neighborhood. To get to it, we have to drive past a low-end liquor store, a couple blocks of shotgun houses, and a church that used to be a restaurant. This school’s current test scores place it among the lowest third of all middle schools in the state. As someone who felt overjoyed at our good fortune in being able to buy a house in our neighborhood in part because of the schools to which we gained access, the proposed change in middle schools is a bit of a blow. I can’t help feeling like we got the rug pulled out from under us.
            However, I also am a bit conflicted about this reaction. Naturally, I’d rather my kids go to the ‘good’ school with the high test scores and the upwardly mobile environs. There is a comfortable certainty in sending them there, a certainty that whether they really thrive or not, they will at least be in an environment where most of the kids are doing well by conventional standards and so they probably will, too. But, the numbers don’t tell you what’s going on inside the school buildings, what kind of pressures exist or what the competition levels are like for participating in extracurricular activities. We can’t tell what the social and sartorial expectations are nor how the school’s dominant values align with the ways we want to live our lives. What’s good for one is not always good for another.
            Plus, what happens to this other middle school when the kids from our neighborhood elementary join it? Will the test scores go up? Probably. Will the school rise in the state rankings? Probably. Will we come to think differently about it? Possibly so. Will it become a ‘good’ school like our elementary school has over the last decade? It could. Should the district try to make that happen? Absolutely. So, should I complain when my children are the ones who get moved? Probably not. Why shouldn’t my children be the ones to move around? Why would I fight to send other kids to a school on principles of resource redistribution while maintaining a claim that my children should remain where they are? That would reflect a kind of ‘not-in-my-backyard’ hypocrisy that is the bane of so many worthwhile community ventures.

            All the same, this change worries me. Whereas the school gets a new crop of kids every year, I only get one chance at middle school with my children. If one year goes awry for a class or a school, the teachers and administrators get to try again next year. If one year goes awry for us, that is a year we’ve lost and will never get back. It makes one want to be hyper-conservative. It makes me want to fight for the most selfish and individual of outcomes. The tragedy of the commons has never felt more real.