short calculus - review request, and the challenges of learning mathematics online

[Joe Corneli]

The Short Calculus course seems to have been essentially silent, but
Math for Game Designers has at least a fairly steady trickle of
comments.

I've asked for a "general" review of Short Calculus in the course
design orientation -

http://p2pu.org/general/node/11464/forums/25663#comment-10612

I thought I'd ask again here; perhaps those of you with both math and
teaching backgrounds could give me some reflections about why this
course didn't take off.

The comment linked to above also brings up some more general concerns
about "doing mathematics online". Do you think that we are *always*
going to run into problems with people being shy? The Internet seems
like it could really feed someone's math phobia...!

Is there a problem even with the idea of "courses"? Is learning
online easier in a (larger) "learning community"? - These are some of
the questions on my mind at present.

Joe

[Maria Droujkova]

Joe,

I think people need to see a sample of a task and a response before they will do the task. In the case of short calculus, I submitted a problem (that was a task) and then - ? So I was not sure if I needed to submit more problems, or do something else with this one, or what.

This is just one task. And I had a task like this for Math-Rich course, which I amended (basically, responded to a few people, since the response task did not take off) and it helped somewhat.

Cheers,
Maria Droujkova

Make math your own, to make your own math.

[Carol Cross]

Hi, Joe--

The whole introversion may be one factor.  In my Psychology of Math Learning class, people were supposed to take a Myers Briggs personality test and post their results so we could see if there are any correlations between personality styles and math experience (good at/enjoy math vs. not good at/didn't enjoy math).  Well, there are supposed to be 24 people in the class, but only 10 posted their results.  And of the 10 who posted their results, only 1 was an Introvert!  LOL-- I'm pretty sure that more than 10% of the entire class is Introverted....

But another thing our class was talking about last night is how most of us haven't been taught math as a social activity; for most of us, it has been an isolated, individual activity.  Thus, it may feel strange and intimidating for people to do math in this way and "expose" their math problem (and possibly incorrect solution) in a group.   On the other hand, game development is much more commonly done in a group setting, so perhaps those students are more accustomed to working on these things in a group setting.  Also, game development has much more of a problem-solving, "this is better/faster/cooler than that" mindset, rather than the black and white perspective of "right versus wrong" of most traditional math (in MBTI terms, more P than J).

So I would spend some time modeling how to do calculus "socially" or collaboratively.   I never took calculus--I'm one of those math anxiety type people--so I can't give you an example.  But maybe if you asked people to solve a problem together, or posed a problem they analyze together or something, that might ease them into being willing to post their problems to the group.  Or I don't know if this is applicable to calculus, but maybe post a problem where the goal is for the group to generate as many different answers as possible, even if they are intentionally "wrong." If there is no stigma attached, discussing "wrong" solutions can be valuable, and if people see that even if they get it "wrong," they are not judged and are appreciated for contributing to the educational discussions and learning, maybe they will be more willing to post.

Carol

____________________________________

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[Joe Corneli]

Good comment. This is one reason why I think an archive of solved
problems, a way to submit solutions, and a way to ask for help would
be a nice alternative recipe for successful learning.

I had hoped with this course to find people who wanted to work on
"bootstrapping" that process. Apparently it needs still more "basic"
bootstrapping (i.e. I could find a bunch of public domain calculus
problems, perhaps with solutions, and post them somewhere).

Joe

[Joe Corneli]

Hi Carol:

Nice story about the psychology of math learning class, best example
of self-selection bias I've ever heard.

> But another thing our class was talking about last night is how most of us
> haven't been taught math as a social activity; for most of us, it has been
> an isolated, individual activity.

Quite so. I didn't get into doing math socially until I was a fairly
advanced undergraduate. That said, my youngest sister (who is still
in high school) seems to approach most subjects in a "social" way.
I'm just saying, there are very different academic cultures. While
P2PU courses don't have to cater to *all* of them, whoever we are
going to get "on board" needs to know what's going on in the "P2PU
culture".

> So I would spend some time modeling how to do calculus "socially" or
> collaboratively.   I never took calculus--I'm one of those math anxiety type
> people--so I can't give you an example.

Hm...

My perception is that the best learning activities enhance what people
were going to do "anyway". In other words, in this particular case,
if we find people who are already eager to learn calculus, that would
be a step in the right direction. For example, Maria put me in touch
with the parent of a high school student who it seems is doing some
sort of self-study. This quarter, I felt a bit like a carnival
barker, trying to draw people in.

Now, I'm not saying that people shouldn't learn calculus - but a
rather critical step is for them to *want* to learn it.

Much more generally: I think a lot of "math anxiety" would go away if
people were in the habit of learning about what they want to learn
about rather than learning what they "have to" or are "supposed to"
learn about! (Check out the "doodling in math class" videos on
YouTube if you haven't seen them!)

> But maybe if you asked people to
> solve a problem together, or posed a problem they analyze together or
> something, that might ease them into being willing to post their problems to
> the group.

Kind of like with the suggestions about tools to use: I think there
are some more basic issues to solve before I could get people on board
with specific learning activities like that one. Somewhat more
"fundamental" things. I'm not saying that P2PU is a bad place to work
on those issues -- but I do think it would be advantageous to better
prototype the kind of learning environment I have in mind for
PlanetMath and *then* ask people to try it out.

The current courses are really just organised into "discussion forums"
-- where I have essentially asked people to do as you indicated.
However, there isn't a whole lot of "momentum". I think seeing other
people (besides just me) solving problems in a larger context might
help...

> post a problem where the goal is for the group to generate as many different
> answers as possible, even if they are intentionally "wrong."

That's definitely an interesting exercise to try!!

Joe