*Independently* doing Sage notebooks doesn't seem to work in high school...
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Chris Seberino
Dec 9, 2009, 12:16:55 PM12/9/09
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I tried an experiment where new math topics are introduced by having
students independently work through Sage notebooks.
Rather than me pushing info to the students in a dialog, they were
supposed to ask me questions when they got stuck on something in the
Sage notebook.
It seems that high students aren't aggressive/assertive enough to ask
questions and independently do Sage notebooks themselves. Due to
their shyness, they seem to prefer the old style where a teacher
dominates the class time by leading a discussion on a new topic.
Some may say I should persevere until the students "snap out" of their
old passive way of doing things. If I was sure this was the silver
bullet of math teaching, I would be confident enough to fight this
battle. I'm not sure this is the holy grail yet.
Sound familiar to anyone?
Chris
students independently work through Sage notebooks.
Rather than me pushing info to the students in a dialog, they were
supposed to ask me questions when they got stuck on something in the
Sage notebook.
It seems that high students aren't aggressive/assertive enough to ask
questions and independently do Sage notebooks themselves. Due to
their shyness, they seem to prefer the old style where a teacher
dominates the class time by leading a discussion on a new topic.
Some may say I should persevere until the students "snap out" of their
old passive way of doing things. If I was sure this was the silver
bullet of math teaching, I would be confident enough to fight this
battle. I'm not sure this is the holy grail yet.
Sound familiar to anyone?
Chris
William Stein
Dec 9, 2009, 12:22:24 PM12/9/09
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the internet with chat?
My experience with (unusually bright, enthusiastic) high school
students is that they can be far less inhibited about asking questions
than college students. But my experience is in a computer lab
setting, not online.
Certainly teenagers are used to engaging in online interactive
experiences, since many play online multiplayer video games (or use
Myspace) a lot.
-- William
Chris Seberino
Dec 9, 2009, 1:14:33 PM12/9/09
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On Dec 9, 11:22 am, William Stein <wst...@gmail.com> wrote:
> Are you physically with the students or is this all being done over
> the internet with chat?
> My experience with (unusually bright, enthusiastic) high school
> students is that they can be far less inhibited about asking questions
> than college students. But my experience is in a computer lab
> setting, not online.
The puzzle is the less motivated less enthusiatic students online.
(Note this isn't a fault of Sage, rather it is a puzzle regarding
teaching.)
cs
William Stein
Dec 9, 2009, 3:23:30 PM12/9/09
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(I make no claim to have any solutions -- I'm just curious.)
William
michel paul
Dec 9, 2009, 3:44:13 PM12/9/09
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> Sound familiar to anyone?
Absolutely! Yeah, the average HS student just wants to be told what to do. So this has been very tricky - how to get the kids to use something like Sage/Python as a way to explore ideas on their own when all they really want is to be told exactly what steps to follow to guarantee an A.
But I can report that I was very pleased with my FST students today. I told them we were going to expand our idea of a function. Instead of the traditional schoolish notion that a function consumes a single number and spits out some other number, instead we were going to create functions that consumed lists and created new lists from them. So, for example, write a function that will return a list of the reciprocals of the values in list L. Now write a function, harmonic(n), that will return the nth harmonic number making use of the previous reciprocal function. Yeah, I had to ask just the right questions, and it was a lot of work, but wow, they were getting it! They could see the connections. There are some kids in there who have always hated math and thought they couldn't do it but who are starting to light up with this. So this was encouraging.
We didn't do this in a lab - just a classroom dialog with Sage as the blackboard, but tomorrow we have the lab.
--
"Computer science is the new mathematics."
-- Dr. Christos Papadimitriou
Absolutely! Yeah, the average HS student just wants to be told what to do. So this has been very tricky - how to get the kids to use something like Sage/Python as a way to explore ideas on their own when all they really want is to be told exactly what steps to follow to guarantee an A.
But I can report that I was very pleased with my FST students today. I told them we were going to expand our idea of a function. Instead of the traditional schoolish notion that a function consumes a single number and spits out some other number, instead we were going to create functions that consumed lists and created new lists from them. So, for example, write a function that will return a list of the reciprocals of the values in list L. Now write a function, harmonic(n), that will return the nth harmonic number making use of the previous reciprocal function. Yeah, I had to ask just the right questions, and it was a lot of work, but wow, they were getting it! They could see the connections. There are some kids in there who have always hated math and thought they couldn't do it but who are starting to light up with this. So this was encouraging.
We didn't do this in a lab - just a classroom dialog with Sage as the blackboard, but tomorrow we have the lab.
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-- Dr. Christos Papadimitriou
calc...@aol.com
Dec 9, 2009, 5:53:11 PM12/9/09
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>>
So, for example, write a function that will return a list of the
reciprocals of the values in list L. Now write a function,
harmonic(n), that will return the nth harmonic number making use of the
previous reciprocal function. Yeah, I had to ask just the right
questions, and it was a lot of work, but wow, they were getting it!
They could see the connections. There are some kids in there who have
always hated math and thought they couldn't do it but who are starting
to light up with this. So this was encouraging.
<<
Sounds like the MATLAB/Octave approach to manipulating data with
So, for example, write a function that will return a list of the
reciprocals of the values in list L. Now write a function,
harmonic(n), that will return the nth harmonic number making use of the
previous reciprocal function. Yeah, I had to ask just the right
questions, and it was a lot of work, but wow, they were getting it!
They could see the connections. There are some kids in there who have
always hated math and thought they couldn't do it but who are starting
to light up with this. So this was encouraging.
<<
functions. COuld you show some more details as to how you did this
with SAGE/python?
TIA,
A. Jorge Garcia
http://calcpage.tripod.com
Teacher & Professor
Applied Mathematics, Physics & Computer Science
Baldwin Senior High School & Nassau Community College
michel paul
Dec 9, 2009, 7:06:14 PM12/9/09
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Well, I started by having them construct very simple algebraic functions like f(x) = 2^x - 5, in both Python and Sage syntax, and then asking them to create lists of ordered pairs such as [(x, f(x)) for x in [-10..10]]. We did a bunch of these in the lab one day till they were comfortable creating things like this fluidly. I would simply throw out a function and a domain, and they had to implement it. I was a little surprised, but it was very good to see, how challenging just this little bit was for many of them. I found that they had to repeat over and over and over the same kind of constructs till it finally made sense.
So today I asked them to create functions like def reciprocals(L): return [1/x for x in L] on their own. Little details, for example - using 'for x in L' instead of 'for x in range(..)' or 'for x in [..]' required some discussion. This was the first time we had constructed a list from some other already existing list. Though it is essentially the same thing we had been doing earlier using range() or interval notation, little tiny differences like this will throw them.
Having written reciprocals I then asked them to create def harmonic(n): return sum(reciprocals([1..n])). I described to them what the harmonic numbers were, and once we got the function written they could appreciate how the code essentially read like the English phrase I kept repeating. That's something I really want them to see.
So again, this happened via class discussion. Getting them to be able to pursue this *independently* - wow, still a lot of work to do.
- Michel
So today I asked them to create functions like def reciprocals(L): return [1/x for x in L] on their own. Little details, for example - using 'for x in L' instead of 'for x in range(..)' or 'for x in [..]' required some discussion. This was the first time we had constructed a list from some other already existing list. Though it is essentially the same thing we had been doing earlier using range() or interval notation, little tiny differences like this will throw them.
Having written reciprocals I then asked them to create def harmonic(n): return sum(reciprocals([1..n])). I described to them what the harmonic numbers were, and once we got the function written they could appreciate how the code essentially read like the English phrase I kept repeating. That's something I really want them to see.
So again, this happened via class discussion. Getting them to be able to pursue this *independently* - wow, still a lot of work to do.
- Michel
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kcrisman
Dec 10, 2009, 10:11:43 AM12/10/09
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>
> Some may say I should persevere until the students "snap out" of their
> old passive way of doing things. If I was sure this was the silver
> bullet of math teaching, I would be confident enough to fight this
> battle. I'm not sure this is the holy grail yet.
>
>
But (at least in the US) nearly every math class is more or less
formula-driven, so it can extremely intimidating for a student to have
to do something like this - and then to add to it a non-click way of
interacting with computers, where one has to precisely word what one
wants the computer to do, adds an additional layer of difficulty.
That doesn't mean you shouldn't try it! But having students have to
learn both math and to program (understanding lists and defining
functions is definitely real programming to someone who has only used
GUIs, especially ones that mimic "natural" motion) at the same time
introduces a number of challenges, and certainly isn't a 'magic
bullet'. However, if you have the energy and support of
administrators and parents to continue getting students to really
interact and learn the material in this way, I think it could be quite
successful - especially if you are able to get the same students for a
couple years. It takes a long time to unlearn how to learn math, if
you know what I mean; even weak students are far more comfortable
doing it the 'traditional' way (which is not necessarily a 'bad' way),
because it's familiar, than trying something new which might help
those particular students internalize it better.
As a final suggestion, you might want to make the transition to the
typing a little more gradually - perhaps using Sage @interacts that
are completely click or drag, then ones where you have to type in
numbers, then ones where you have to type in functions or symbolic
expressions, then ones where depending on several controls different
things happen, then what you are doing. The Scratch project at MIT
(http://scratch.mit.edu/) is also an excellent way to think about
programming in a different way, though I don't know how usable it
would be for a math class.
Oh, and I missed the fact that this is online below. Yup, another
layer of pedagogical challenge, since you aren't 'right there' over
the shoulder. Sort of like the discussions on sage-support :)
Good luck!
- kcrisman
kcrisman
Dec 10, 2009, 10:14:18 AM12/10/09
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> The Scratch project at MIT
> (http://scratch.mit.edu/) is also an excellent way to think about
> programming in a different way, though I don't know how usable it
> would be for a math class.
Incidentally, as an idea for future Sage Ed Days concept... check out
> (http://scratch.mit.edu/) is also an excellent way to think about
> programming in a different way, though I don't know how usable it
> would be for a math class.
http://day.scratch.mit.edu/
In 2009, "there were 120 events in 44 different countries". Wow!
- kcrisman
William Stein
Dec 10, 2009, 1:56:57 PM12/10/09
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easily change the code for the interact, but the students for which
code looks like greek can just ignore the code and embrace the math
instead.
William
Robert Bradshaw
Dec 10, 2009, 2:59:56 PM12/10/09
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On Dec 9, 2009, at 12:44 PM, michel paul wrote:
> > Sound familiar to anyone?
>
> Absolutely! Yeah, the average HS student just wants to be told what
> to do. So this has been very tricky - how to get the kids to use
> something like Sage/Python as a way to explore ideas on their own
> when all they really want is to be told exactly what steps to follow
> to guarantee an A.
I'll second this. Unfortunately the same goes for many college freshmen.
> > Sound familiar to anyone?
>
> Absolutely! Yeah, the average HS student just wants to be told what
> to do. So this has been very tricky - how to get the kids to use
> something like Sage/Python as a way to explore ideas on their own
> when all they really want is to be told exactly what steps to follow
> to guarantee an A.
Another point that hasn't been brought up yet is that students don't
usually expect to have to ask questions. Since many expect to be told
everything, they often feel it's a sign of "stupidity" to not be able
to execute. When I'd give out worksheets and say "if you have any
questions, feel free to ask" I usually wouldn't get that much of a
response, but walking around the class as they worked asking them
about what they were doing would get them thinking and asking.
Another idea, since students just want to be told what to do (though
it's a bit silly), is making asking at least one question a requirement.
- Robert
William Stein
Dec 10, 2009, 3:07:53 PM12/10/09
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lab setting (or whatever) with some weird computer language I know
absolutely nothing of (e.g., COBOL? PL1?) and being asked to solve a
bunch of math problems with it and ask questions, etc., for the next
hour. That's how it feels for your students using Sage. This
thought experiment can help encourage one to be more gentle I think...
Anyway, it helps for me.
-- William
Chris Seberino
Dec 10, 2009, 7:53:28 PM12/10/09
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On Dec 9, 2:23 pm, William Stein <wst...@gmail.com> wrote:
> Do you have a list of things those students do like?
cs
Chris Seberino
Dec 10, 2009, 7:57:57 PM12/10/09
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On Dec 10, 9:11 am, kcrisman <kcris...@gmail.com> wrote:
> you might want to make the transition to the
> typing a little more gradually - perhaps using Sage @interacts that
> are completely click or drag, then ones where you have to type in
> numbers,
avoids all the gotchas of typing....and I've noticed a lot of issues
with that.
cs
kcrisman
Dec 11, 2009, 3:32:27 PM12/11/09
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>
> Another idea, since students just want to be told what to do (though
> it's a bit silly), is making asking at least one question a requirement.
This is not silly, it's actually a sound pedagogical strategy! You
> Another idea, since students just want to be told what to do (though
> it's a bit silly), is making asking at least one question a requirement.
just have to implement it in a sensitive way, which can be difficult.
Or, if you're one of my grad school profs, you implement it so rudely
that everyone thinks it's funny.
- kcrisman
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