- p5. Mathematics is the art of explanation.
- p6. Math is not about following directions, it is about making new ones.
- p7. It isn’t doing anyone any good having vague memories of formulas and clear memories of hating them.
- p11. Teaching is not about information. It’s about having an honest intellectual relationship with your students. Teaching means openness and honesty, an ability to share excitement, and a love of learning.
- p21. Mathematics is about removing obstacles to our intuition, and keeping things simple.
The University of Waterloo has switched first year students to Scheme.
There is a big difference between learning how to program and in learning a particular language. Scheme makes the former so much easier!
There is a joke among programmers: when the project manager asks how complete is the project, and you’ve finally reached the “%80 complete” mark, you tell him the good news because now you all know how long it will take to finish the 2nd %80 of the project! Sometimes this is just how efforts evolve; and it its not just limited to work efforts.
For the past month of so I’ve been practicing a beautiful song called “Over the Hills and Far away” (aka OTHAFA) by Led Zeppelin.
It has been a challenge for me. The practice-duration/song-duration ratio of OTHAFA’s has been a high. Learning it has almost been like work project: you get an idea of what needs to happen, start digging in, and eventually figure out what *really* needs to happen!
Ultimately, it took me about a month or so to learn all of the parts of the song (aka the first %80), and based on what I can see it will take another month to be able play it well enough to perform it (aka the second %80). Don’t get me the wrong, the first %80 means I play the parts correctly and it sounds nice. There are just all of the details that really take it from sounding “good” to “great”. It has been frustrating, though; as I started studying the 2nd %80 my progress slowed and it was a little bit disheartening. I soldiered on, but man…
Talking to my guitar teacher about it really helped me put things in perspective. He explained that the goal of learning the song was to learn all of the guitar playing techniques in OTHAFA that I would end up using in %80 of all of the other songs that I would end up learning. In other words, he had a clearly defined pedagogical approach to my course of study, mastering the 2nd %80 was more like a bonus, or an optional goal that I could pursue if I so desired. Wow, I had no idea; I felt a lot better after hearing that.
My take away from all of this is what when it comes to learning, it is really up to you to decide whether or not *now* is the right time to pursue that 2nd %80 of whatever you are learning. Perhaps even more important is using enough discretion to determine whether or not you are actually moving into that 2nd %80, or you are simply moving outside your comfort zone because *that* can feel even more difficult that the latter!
Whatever the case, keep on learning, whatever you can, and have fun doing it!
Email discussion lists and comp.lang.scheme are an excellent to start.
Another option is #scheme on IRC at Freenode; there is nothing like speaking to another human being about Scheme.
When you talk with folks; you learn faster and have a lot more fun. When you are really digging into a concept, the kind soul who answers your question at just the right moment can make the difference between learning the concept now, or in a few days. Not to say that learning is a race; it is just so much fun that I think everyone loves to learn the next thing!
An aside; I’ve found that my mastery of topics, and in particular the lack thereof, is revealed much more quickly to me when I open my mouth! I won’t miss a chance to do so!
The path born of wonder is endless, paved with knowledge, and unconditional. Walking it will change you, and the world. Follow it every chance you get.
Someone noticed that I’ve learned how to practice guitar. I asked what they meant by that, and they said that I “start slow, memorize the piece, and keep practicing, a little faster each time”. That is what works for me. When it comes to learning how to become a better programmer, I’m not sure that it is so simple (not to say guitar is simple of course!).
How do you practice programming?
I’ve got some ideas on how I do it, but it I’m going to take some time to think about it.
That post is over the hills and far away!