What I’m learning – 8/5/14

Learning How to Learn (MOOC, Coursera) Week 1 contains a good collection of topics. I’m familiar with most of them: spaced repetition, the benefits of sleep and exercise, the pomodoro technique. An interesting framing that they use is focused versus diffuse modes of the brain. I love Coursera’s mobile app for watching videos: they can be downloaded and watched at 2x speed.

Real World Haskell (Online book) I recently did CIS194: Introduction to Haskell, which was excellent for learning Haskell concepts but left me still confused about how to structure programs. This book is already teaching me a lot of practical tips that CIS194 didn’t cover (to be fair, they give RWH readings for each lecture). The embedded comments are a great way to see a variety of solutions for the exercises in the book. It’d be nice to have top quality solutions available too, but sometimes it helps to see the thoughts of another newbie.

Probabilistic Models of Cognition (Online book) I’ve been hugely interested in modeling cognition for many years. I neglected this book because seemed it’d be like too much of a rabbit hole to tackle. However, it so far turns out to be a great review of probability and functional programming (it uses Church, which derives from Scheme) in addition to the interesting domain. I really enjoy being able to modify and run programs in-line. There’s an element of feedback that is nearly effortless because I usually have an expectation of what a program does right before pressing “Run”. Then I immediately see whether that expectation was correct or I need to think more about it. There are also more traditional exercises that push harder but with the convenience of being in the browser.

Why Do Americans Stink at Math? (Article, NY Times) There is a ringing endorsement among those who are good at math: “don’t just memorize a procedure, understand the concept.” Unfortunately, it rarely goes beyond that platitude, and it starts to break down on closer examination: if you have an understanding, isn’t the concept memorized as well? Most likely, unless you have to reconstruct it very slowly, you’ve memorized the procedure too. So which really came first: your self-proclaimed “understanding” or an explanation that you constructed for the procedure that you memorized? The big reveal is to try to get most of them to actually explain a concept they understand to you. “Argh, well, you just do this.”

And yet, when you read an article like this, there is something obviously and dreadfully wrong with something like “Draw a division house, put ‘242’ on the inside and ‘16’ on the outside, etc.” An interesting counterexample is where math was learned by the uneducated in a way that is procedural but also embodied. That is, math was learned or used in commerce or factory work–but clearly still requires a long path to learn symbolically and abstractly (see also The Real Story Behind Story Problems). Another fascinating possibility for teachers using a Japanese technique called lesson study. A lot to digest in this article. (I have some more writing from my grad school days on concepts.)