Math fail


Until  my early 20s, I never knew that one could become good at math. In high school, I ended up failing 10th-grade math.

That’s Marc Bellemare discussing his struggles with learning mathematics in high school and undergrad. For those of you don’t know, Marc is now an economics professor and is comfortable enough with math to write theory-heavy journal articles. His story about grappling with the subject and eventually learning to master it is well worth a read, especially for those who believe they are inherently bad a math.

I didn’t struggle with mathematics for quite as long as Marc did, but was nearly dissuaded at a much earlier age by the tyranny of early math education: arithmetic.

I’ve never been particularly good at adding, subtracting, multiplying or dividing. How much should we leave for a tip? I’ll let my calculator decide. It’s no surprise then that I found math in elementary school so daunting: we were required to do randomised times tables,where we had to answer as many addition/multiplication questions as possible before an alarm clock went off. I found this immensely stressful and found it very difficult to remember what 7 x 13 was when I knew that any minute now a clock was going to go BZZZZZZZ (I sense there has been a generational improvement though: my father noted that his math classes at a Roman Catholic seminary involved the lecturer smacking students in the back of the head until they got the question right).

When I go back and look through my elementary report cards, I can see how poorly I did: Cs and Ds in basic math, with worried remarks by teachers. Clearly math wasn’t my thing.

Then I was introduced to algebra. You see, arithmetic was usually taught as an exercise lesson: you don’t think about what 7 x 13 means, you remember it. But once math becomes more abstract, it becomes more conceptual and substantially less about memory. I loved algebra. In fact, I loved algebra, trig, and calculus so much that I went on to major in math in university, where I eventually semi-defected to the economics department.

Readers of this blog will probably be past the point where they make significant choices about their math education, but something to keep in mind when you have kids: it’s incredibly easy to be discouraged by math, especially in the early days when it is more about memorization. Others struggle with the more abstract stuff, but as Marc points out, this is a better reason to double down, rather than abandon it for good.*


*Obviously this should only be done to a point – everyone has comparative advantages.

Too cool for school

"Perhaps it's time to re-examine the notion that kids really love going to school."

“Perhaps it’s time to re-examine the notion that kids really love going to school.”

Despite, as Lee pointed out, having a bloody good time at the Cowley Road Carnival yesterday, I rolled out of bed in time today to get to the Young Lives conference on inequalities in child outcomes. I’ll share some thoughts on the other plenaries later on, but I was particularly entertained by the final talk of the day by Lant Pritchett on why kids in developing countries might not always want to spend all of their time in school.

Pritchett’s point was fairly simple: in many settings school can be a pretty awful place to be, especially if the curriculum is moving faster than you can keep up with it. Eventually, all but a select few are left behind, leading to a “flattening out” of the learning curve. At this point, you can’t really learn anything when you are this far behind, so why stick around? At one point – and without warning – Pritchett presented an entire slide in Spanish, to give the audience a sense of how this must feel.

His argument was backed up by some fairly disconcerting evidence – Karthik Muralidharan had presented results showing that learning trajectories were nearly flat in many Indian schools, the result of a system which adheres too strictly to a curriculum designed to weed out the best at the expense of other children (which Pritchett referred to as the Russian gymnastics theory of education).

This all reminded me of my time spent running a survey in Dar es Salaam – for simplicity and safety I would meet with my enumerators within a primary school compound. Often, when the school’s security guards opened the front gate for me, they’d physically strike at children with a switch to prevent them from slipping out and running off. Not exactly the picture painted by most of those working on education in developing countries.

While Pritchett laid most of the blame on overambitious curriculum, there were some complains about teachers themselves, especially from the audience, who pointed out that dismal learning outcomes were equally a result of teacher discrimination and absenteeism.

This is a popular line to take nowadays – and has led to a focus on interventions which directly change incentives for teachers, such as improving local accountability, performance pay, or using cameras to make sure they show up. Of course, these interventions feel increasingly marginal when the entire system is broken.

We also tend to forget that schools can also be miserable places for teachers. You might have to live in places you really don’t want to live in. Teaching dozens of children whose learning outcomes are all over the place. Not everyone can be Edward James Olmos. When I lived in Malawi, I briefly volunteered at a local orphanage – attempting to teach math to a group of kids aged 8-15, whose understanding was all over the place. I lasted one day.

Perhaps the most successful interventions are those which are complementary – incentivising both teachers and students to show up and make things happen.

PS – there should be a video of Pritchett’s talk up sometime soon – watch this space. Dude is so famous he doesn’t even bother wearing a name tag.

Sentences deserving skepticism

Unfortunately, attendance is not education's most reliable metric

Despite the inevitable concerns about standards, there are still millions of children attending school who otherwise wouldn’t have been, which means they are learning.

That’s Ugandan thinktanker Lawrence Bategeka, quoted in Jonathan Glennie’s recent article on the results of Uganda’s shift to universal primary education.

The tricky ethics of education information, J-Pal edition

The Roving Bandit discovered this graph produced by J-Pal on cost-effective interventions for education.

That red bar is a result from a RCT in Madagascar which provided families with information on the “returns to education,” resulting in a reasonable increase in attendance (3.5%).

What’s the catch? The study wasn’t actually giving people an accurate measure of the returns to education in Madagascar, it was giving people the average correlation between education and income, job availability.

Why the distinction? Most economists believe that education attainment is highly endogenous – this means that brighter people and those from my advantaged backgrounds are more likely to attend and do well in school. This muddies the waters, as high-ability people are also more likely to earn higher wages.

There have been many, many attempts to control for the sort of characteristics that might bias the effect of education on earnings, but the study cited by J-PAL doesn’t really do this. This means they aren’t presenting people with an accurate estimate of their own gains from further education, but instead giving them a picture of the sort of lives educated people live.

Shouldn’t we be luring people into school anyway, though? Isn’t more education, in general, a good thing? J-Pal’s cost-effectiveness chart assumes this (notice that it assumes education is an end in itself, even though the intervention uses education as a means to further income).

Possibly, but I am dubious about the ethics of boosting people’s underlying demand for education. Providing accurate information on returns would allow them to make informed decisions (i.e. does this really make sense given my situation?), but instead providing them with a rosy picture may be leading them to make decisions that aren’t actually in their own best interest.

Supply-side interventions that lower the cost of attending schooling – pretty much everything to the right of the red bar – are more likely improve outcomes without the implicit deception.

One laptop per C-student

Come on, you know you want to

An article on Slate about the growing backlash against laptops in the classroom:

The trend of laptop-banning seems strongest at law schools, where discussions and understanding the material are vital to getting past the dreaded first year. Georgetown University Law Center professor David Cole bans laptops, as does University of Memphis Law School professor June Entman. George Mason Law professor Michael Krauss has been banning laptops for five or six years now.

The way his first-year law-school classes are taught, Krauss said, is by asking questions for the students to answer in discussion. Distractions and the Internet aren’t Krauss’ concern in banning laptops; the reason for the ban is that laptops have “become a substitute for thinking.” The material in a law class requires a lot of thought to help understand concepts, and students who type verbatim what is said in class into their notes aren’t giving themselves any time to absorb and analyze.

I was still an undergraduate at Clemson University,  when the idea of laptop-enabled classrooms was being introduced. I could never quite understand how they could really help with the material – they were being pushed first in math and engineering programmes, where usually a pencil is more friendly than a keyboard. I got the required laptop, but graduated before the university got around to enabling wi-fi access in most of its classrooms.

Today, laptops are an everyday accessory in American lectures. Some students use them for typing notes, some for fact-checking their professors (my father, who teaches political science, now has his assertions constantly tested by Google), but many use them as an excuse to goof off during class. These distractions might be reducing performance:

At the University of Colorado-Boulder, Professor Diane Sieber also knew her students weren’t all paying attention in class. She carried out a very unscientific study simply by comparing the grades of students who used laptops in class with those of the students who didn’t. According to the Chronicle of Higher Education, Sieber privately informed the students after their first exam that they scored lower by 11 percent than their counterparts without laptops.

Of course, there are selection problems here – students that decide to bring laptops to class are probably different types of people than those who choose to constrain themselves with pen and paper – but they are interesting nonetheless. A related (but not equivalent) study in Romania found that computer recipients spent more time playing computer games, but not learning.

A child of the internet revolution, I’m one of the first to embrace any advances in technology that brings me closer to living in a Gibson-esque dreamworld. I remember being excited at the prospect of upgrading my 14.4 kbs modem to a 28.8, or the creation of my first Geocities page, or signing up to Facebook back when it was being rolled out on a university-by-university only basis!

However, as I’ve gotten older I’ve begun realise just how massively debilitating the effects of  internet access are on one’s attention span. Facebook, twitter, wikipedia, e-mail and blogging creates a multiplicity of microincentives for the brain to constantly divide its attention (I’ve done a few dozen other things while writing this blog post).

Programmes like One Laptop Per Child tend to be run by technophiles (like me) who consider greater access to the web to be one step closer to nirvana. When we consider bringing such technology into the classrooms, especially in developing countries, we need need to carefully consider that the net effects on basic learning might be negative. Trying to keep up in honors advanced calculus with pencil and paper might have given me hand cramps, but at least I was paying attention.