[sage-edu] Re: *Independently* doing Sage notebooks doesn't seem to work in high school...
> > 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. > > This is certainly pedagogical, not really computer or math per se. 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 -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-...@googlegroups.com. To unsubscribe from this group, send email to sage-edu+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
[sage-edu] Re: *Independently* doing Sage notebooks doesn't seem to work in high school...
> 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://day.scratch.mit.edu/ In 2009, "there were 120 events in 44 different countries". Wow! - kcrisman -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-...@googlegroups.com. To unsubscribe from this group, send email to sage-edu+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
[sage-edu] Restricting the field used when solving equations.
I am a high school teacher in Turtleford, SK Canada and am thinking about using sage in some of my teaching. The one problem I have right now is all of the complex roots found when solving an equation. Is there a way to restrict the returned solutions to the Reals? -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-...@googlegroups.com. To unsubscribe from this group, send email to sage-edu+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
Re: [sage-edu] Restricting the field used when solving equations.
jason.t.stein wrote:
> I am a high school teacher in Turtleford, SK Canada and am thinking
> about using sage in some of my teaching. The one problem I have right
> now is all of the complex roots found when solving an equation. Is
> there a way to restrict the returned solutions to the Reals?
>
You can take all of the returned solutions and test them to see if they
are real. Then you can just return the real ones.
sage: all_roots=solve((x^2+1)*(x-1)==0,x,solution_dict=True)
sage: all_roots
[{x: -I}, {x: I}, {x: 1}]
sage: real_roots=[root[x] for root in all_roots if imag(root[x])==0]
sage: real_roots
[1]
Jason
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Re: [sage-edu] Re: *Independently* doing Sage notebooks doesn't seem to work in high school...
On Thu, Dec 10, 2009 at 7:11 AM, kcrisman wrote: > >> >> 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. >> >> > > This is certainly pedagogical, not really computer or math per se. > 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 These are particularly good because the students who *want* to can 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 -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-...@googlegroups.com. To unsubscribe from this group, send email to sage-edu+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
Re: [sage-edu] *Independently* doing Sage notebooks doesn't seem to work in high school...
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. 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 -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-...@googlegroups.com. To unsubscribe from this group, send email to sage-edu+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
Re: [sage-edu] *Independently* doing Sage notebooks doesn't seem to work in high school...
On Thu, Dec 10, 2009 at 11:59 AM, Robert Bradshaw wrote: > 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. > > 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. Another thing that I find helpful is to imagine being tossed into a 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 -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-...@googlegroups.com. To unsubscribe from this group, send email to sage-edu+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
[sage-edu] Re: Restricting the field used when solving equations.
I prefer Polynomials than symbolic expression :
sage: R. = PolynomialRing(QQ, 'x')
sage: P = (x^2 + 1) * (x^2 - x - 1)
sage: P.roots() # no root in QQ
[]
sage: P.roots(RR) # two roots in RR
[(-0.618033988749895, 1), (1.61803398874989, 1)]
sage: P.roots(CC) # four roots in CC
[(-0.618033988749895, 1), (1.61803398874989, 1),
(-8.79016911342623e-17 - 1.00*I, 1),
(-8.79016911342623e-17 + 1.00*I, 1)]
But it can also be done with symbolics
sage: x = var('x')
sage: P = (x^2 + 1) * (x^2 - x - 1)
sage: P.roots(x, ring=QQ)
[]
sage: P.roots(x, ring=RR) # two roots in RR
[(-0.618033988749895, 1), (1.61803398874989, 1)]
sage: P.roots(x, ring=CC) # four roots in CC
[(-0.618033988749895, 1), (1.61803398874989, 1),
(-8.79016911342623e-17 - 1.00*I, 1),
(-8.79016911342623e-17 + 1.00*I, 1)]
sage: P.roots(x, ring=SR) # the symbolic ring
[(-1/2*sqrt(5) + 1/2, 1), (1/2*sqrt(5) + 1/2, 1), (-I, 1), (I, 1)]
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[sage-edu] Re: *Independently* doing Sage notebooks doesn't seem to work in high school...
On Dec 9, 2:23 pm, William Stein wrote: > Do you have a list of things those students do like? I don't have any specific things about Sage I've heard yet. cs -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-...@googlegroups.com. To unsubscribe from this group, send email to sage-edu+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
[sage-edu] Re: *Independently* doing Sage notebooks doesn't seem to work in high school...
On Dec 10, 9:11 am, kcrisman 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, I think this is sage advice (pun intended). Starting with @interacts avoids all the gotchas of typingand I've noticed a lot of issues with that. cs -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-...@googlegroups.com. To unsubscribe from this group, send email to sage-edu+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
