What mathematics should any well-educated person know? It’s rather rare that people have a chance not just to think about this question, but do something about it. But it’s happening now.
There’s a new college called Yale-NUS College starting up this fall in Singapore, jointly run by Yale College and the National University of Singapore. The buildings aren’t finished yet: the above picture shows how a bit of it should look when they are. Faculty are busily setting up the courses and indeed the whole administrative structure of the university, and I’ve had the privilege of watching some of this and even helping out a bit.
It’s interesting because you usually meet an institution when it’s already formed—and you encounter and learn about only those aspects that matter to you. But in this case, the whole institution is being created, and every aspect discussed. And this is especially interesting because Yale-NUS College is designed to be a ‘liberal arts college for Asia for the 21st century’.
As far as I can tell, there are no liberal arts colleges in Asia. Creating a good one requires rethinking the generally Eurocentric attitudes toward history, philosophy, literature, classics and so on that are built into the traditional idea of the liberal arts. Plus, the whole idea of a liberal arts education needs to be rethought for the 21st century. What should a well-educated person know, and be able to do? Luckily, the faculty of Yale-NUS College are taking a fresh look at this question, and coming up with some new answers.
I’m really excited about the Quantitative Reasoning course that all students will take in the second semester of their first year. It will cover topics like this:
• innumeracy, use of numbers in the media.
• visualizing quantitative data.
• cognitive biases, operationalization.
• qualitative heuristics, cognitive biases, formal logic and mathematical proof.
• formal logic, mathematical proofs.
• probability, conditional probability (Bayes’ rule), gambling and odds.
• decision trees, expected utility, optimal decisions and prospect theory.
• sampling, uncertainty.
• quantifying uncertainty, hypothesis testing, p-values and their limitations.
• statistical power and significance levels, evaluating evidence.
• correlation and causation, regression analysis.
The idea is not to go into vast detail and not to bombard the students with sophisticated mathematical methods, but to help students:
• learn how to criticize and question claims in an informed way;
• learn to think clearly, to understand logical and intuitive reasoning, and to consider appropriate standards of proof in different contexts;
• develop a facility and comfort with a variety of representations of quantitative data, and practical experience in gathering data;
• understand the sources of bias and error in seemingly objective numerical data;
• become familiar with the basic concepts of probability and statistics, with particular emphasis on recognizing when these techniques provide reliable results and when they threaten to mislead us.
They’ll do some easy calculations using R, a programming language optimized for statistics.
Most exciting of all to me is how the course will be taught. There will be about 9 teachers. It will be ‘team-based learning’, where students are divided into (carefully chosen) groups of six. A typical class will start with a multiple choice question designed to test the students understanding of the material they’ve just studied. Then the team will discuss their answers, while professors walk around and help out; then they’ll take the quiz again; then one professor will talk about that topic.
This idea is called ‘peer instruction’. Some studies have shown this approach works better than the traditional lecture style. I’ve never seen it in action, though my friend Christopher Lee uses it in now in his bioinformatics class, and he says it’s great. You can read about its use in physics here:
• Eric Mazur, Physics Education.
I’ll be interested to see it in action starting in August, and later I hope to teach part-time at Yale-NUS College and see how it works for myself!
At the very least, it’s exciting to see people try new things.