This is the P2PU Archive. If you want the current site, go to www.p2pu.org!
Short Calculus
My recent threads
You haven't posted any discussions yet.
Recently updated threads
- Constructivist Calculus Sun, 2011-03-06 13:21
- week 3: post mortem Thu, 2011-02-24 17:47
- week 2: what's up Wed, 2011-02-02 18:54
- Week 1: resources Mon, 2011-01-31 21:20
- Meeting times - and initial introductions Mon, 2011-01-31 21:09
Constructivist Calculus
Go back to: General discussion
Dove-tailing off the Week 3 discussion I am wondering what everybody thinks about the following questions:
- How can we make learning Calculus tangible (i.e. physical and kinesthetic)?
- How can we find personally, and collectively, relevant situations to explore the concepts and techniques of Calculus?
- How can we encourage dialogue around our personal experiences with and understanding of Calculus?
Please feel free to add any additional questions to the discussion as my perspective is natually limited :-)
How can we make what we do accessible to noobs? An example of such efforts: "Calculus for seven year olds" project http://www.mathman.biz/html/map.html
I guess there are 3 (5 really) learning modalities.
Visual
Auditory
Kinesthetic
Is most math content conveyed in visual and auditory dimensions?
If we're talking about school, then I think the answer is "yes". (Despite a few examples like cuisenaire rods.)
If we're talking about life, then I think kinesthetic stuff actually conveys LOTS of mathematical meaning. "Geometry", for example, means "measuring the earth". So, I do "embodied geometry" when I figure out how long it takes me to get from X to Y on my bicycle.
One of my dreams would be a course on the "physics of bicycles"... I'm pretty sure it would be possible to deal with most of the topics in first year physics course that way, and probably a few others besides. First year physics can also be taught in a way that is more or less "mathematically synonymous" with first year calculus...
Curious to know what the 2 "extra" learning modalities are that you didn't list!
There is a good book "Where mathematics comes from" explaining that ALL math is based on embodied metaphors. So, theoretically, every piece of math has kinesthetic representations. However, humans being symbolic creatures, there is no need to literally enact (or even be aware) of this metaphoric connections to the body. Our brain can provide some of the connections.
This is where grief happens in mathematics education. Because movement is hard to manage in small rooms with many kids, embodied activities become exceedingly rare in schools - and in curricula overall, which is still largely driven by schools. This deprives kids of the ability to make enough connections to abstract math, and eventually, from operating at the formal level.
There do exist resources for kinesthetic mathematics, as Joe mentioned. For an interesting example,look at math through dance program: http://www.mathinyourfeet.com/ The general term for hand-held math learning objects, or their virtual counterparts, are "manipulatives". With tools like Kinect, the distinction is blurring.