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- Concern over my learning style Fri, 2010-10-08 15:53
Concern over my learning style
I think that I've most struggled with math because of the way I learn. If I can use it and play around with it I can learn it for life. I'm not very good at just memorizing stuff and using it later. Which is why I find programming so easy for me, you give me the problem and I can do some research and then build it myself with every tool known at my disposal. I think that is what sets it apart from arithmetic is that there's little fog of war, no curtain blocking half of the building blocks I could use to reach an answer. Most of my experience in learning math has been being told to just memorize it and don't worry about it till later. That doesn't work for me, I need to know why I'm learning this and how it's working the way it is.
With learning math it seems teachers are intentionally holding back a lot of it to teach us in baby steps. In some programming courses I've taken they've been like this too, but with programming I have a wide amount of resources open to me that removes the curtain. Because of this 80% of what I know about programming I've taught myself. I can't find resources like this easily for math.
My concern is that math may not work like that. Will I always just have to memorize equations and not know why they're working? Will I ever have everything open to me?
Thanks
I totally agree. My problem with math has always been that I've always been taught it from a perspective of, you just have to assume this is true, don't worry about why, but I tend not to understand things unless I have access to the full picture. It is just how my brain works I am good at tackling large often abstract subjects, even the relationships between apparently separate things, but only if I can get access to a broad or full understanding of the subject, instead of being told to just remember something and work on it from there.
I just bought Concrete Mathematics: A foundation for computer science, by Graham Kunth and Patashnik, at the recommendation of Joe, and like the way it is set up and seems to explain things from the ground up, but it assumes an amount of background knowledge about math (it seems to almost be an attempt at reteaching math in a new way to people who have had a strong traditional education in it), that I am not necessarily comfortable with, but I think with a little help this book might be the right style of math education for me.
The other thing that help rekindle my interest in math was taking a Math Language course (it was dual listed under linguistics and philosophy) that explained set theory symbolic logic, and other foundational elements of math, which helped me get my head around what math "really is."
Hope my commiseration helps answer your questions to some degree Isaiah, although I'm more interested in hearing what other people have to say, I thought I'd just throw my own two cents in.
LOL kinda funny. I just realized I had to post on google groups so I moved it over there. And then I made a similar reply to yours there while you were replying here.
Hi guys: more in the google group soon, but for the record: I think your learning styles are AWESOME and I'm sorry that you've faced so much discouragement in traditional mathematics learning settings. The kind of learning that you're talking about is what I'm most interested in trying to build support for in my research work. (Math should be more like programming -- pretty straightforward, right?)
Regarding the background assumptions made by Concrete Mathematics: I think this is an excellent place to start asking questions. The difficult stuff gives you a whole lot of learning goals, which, as we've discussed, are helpful to have around. Now we can break it down into smaller pieces for understanding. (Oh, and the Math Language course sounds like a really good foundation, it would be great to have a tutorial version of that around... hm...)
I found this resource last night, after digging around for more help on discrete math, http://www.freetechbooks.com/discrete-mathematics-f65.html, it has 8 books on discrete math that include some more foundational stuff than concrete mathematics. I also have a big pdf file of the textbook I used for my math language class, its mostly set theory, pragmatics, and RTN's, but I'm not sure what the IP rights are for it, it was a work in progress at the time by one of the math profs at the school.
For the people who are having trouble memorizing - check out some of Theoni Pappas' work-- including math poetry for two voices, the mathematics calendar, and mathematical scandals.
For those trying to teach younger kids, check out almost anything by Marilyn Burns. My dad just bought me her 1982 book Math for Smarty Pants after I donated my copy of the Greedy Triangle to the elementary school classroom (4th/5th combo) that I work in. @James