Mailman 3 September 2006 - Edu-sig

Your dream Linear function class
by Kevin Driscoll Sept. 27, 2006

Sept. 27, 2006

Hi y'all, My Pre-Calc peoples are finishing up a refresher unit on Linear Functions. This week, they are working on a "mini-text" with definitions, examples, tips, and tricks. They'll be wiki-izing this work next week. Each unit will follow the same pattern as a way to build a "math portfolio" for the year. I am planning to take them into Pythonic PreCalc after each unit to add a new class to their growing library. These will be reproduced on the wiki and in their portfolios as well. So what would your ideal Linear Function class contain? Methods: - return slope - return x-int - return y-int - maybe one that takes another Line and returns the coords for their intersection? - return expression (e.g. mx + b) About a third of the students have studied Python with me before in CS so they can help bring the rest along. (We are my smallest class at 15 11th and 12th graders.) We aren't afraid of import. Is there an easy graphing solution? Getting psyched for Quadratics and Complex numbers in October! Kevin

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Functions & Generators (gnu math memo)
by kirby urner Sept. 26, 2006

Sept. 26, 2006

Logo -> Squeakland ->... Python: Functions and Generators (build directly off algebra, no need to harp on "variables", although most students will want a strong "types" discussion, as their earlier math was probably very weak in this area, especially around strings) Building on the potential of Squeakland Creatures (the warmer fuzzier objects of a younger day), we make a big deal of the "arguments mouth" (except you don't really need arguments), i.e. those curved parentheses are like lips (optional link to fish lips in FS Coupler segment (not the same as Vesica Pices, though related)).** Remember, DO NOT postpone Generators as an advanced topic. Every since lazy list comprehensions (another used of curvy parentheses), earlier really, we've had good reasons for harping on Generators. This will get students acclimated with the Namespace that is Python (or metapython): iterators, generators, callables, special names, type, class. Early Functions: ============ GCD Totatives Totient Triangular Numbers Tetrahedral Numbers Cuboctal/Icosahedral Numbers Curriculum context: Difference between Composite and Prime, concept of Relatively Prime (strangers). Leading to: Integers Modulo N groups, germutation groups, polyhedrally defined symmetry groups. Note that J has some primitives for generating cyclic notation, which you could use to motivate the need for a Python counterpart. Early Generators: ============= Triangular Numbers Tetrahedral Numbers Cuboctal/Icosahedral Numbers Fibonacci Numbers Mandelbrot Set decider (convergent or not?) Curriculum context: Growing sphere packings per my OSCON 2005 and London Knowledge Lab presentations, i.e. divergence represented with polyhedral numbers ala 'Book of Numbers' (cites Martin Gardner), with volume expanding as a 3rd power rate of linear growth (expressed in the scale method of our Polyhedron parent class). Of course list comprehension syntax is used from the get go, per the usual approach of using collection types to go over basic dot notation (per my EuroPython 2005 presentation). Followup (where to go from here): Once we're good at writing functions and generators, it'll be easy to define new classes, as methods are simply functions with a self argument (a basis for object instrospection). Remember the "two passes": First pass: treating the builtins as read-only givens (axiomatic) Second pass: rolling our own, coding up a namespace (interactively, with unit testing) Plus we might get back to the warm fuzzies by this route, now feeling more like puppetmasters or cartoon animators i.e. we *make* cartoons, don't just watch them (multi-track editing isn't just for others to do for us). I'm signing and returning my gnu math teaching contract today. If you don't have a gig yet, hang in there. Once our DVD libraries are easier to come by, you'll be ready, having trained hard while waiting. Maybe you'll do it with Ruby, if our Python seems "too noisey" a language for you. For more on Gnu Math (both Memos and Meanderings), search math-teach at the Math Forum, a principal outlet and recruiting ground for us. Or look for more private lists in your own local neighborhood (does your town have a Wanderers chapter?). Kirby Gnu Math Teacher Portland "open source capital" Oregon Also check "focal points" in my Bizmo Diaries around this time, if new to our curriculum and just trying to get some overview. And no, you don't have to be a snake charmer. I'm relying on the other Open Source language communities to spin their own distros. ** might be able to do something around teeth when treating of default and/or optional arguments, per Tow Mater example. Re Coupler "fish lips": http://groups.yahoo.com/group/synergeo/message/29178

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Re: [Edu-sig] creating an interface vs. using one
by Michel Paul Sept. 25, 2006

Sept. 25, 2006

Yes, thank you. I have been reflecting on this, and so far I haven't been able to pin down a site specific issue that Python would clearly address. I should point out that I haven't been stifled in pursuing Python - I have been tolerated. I did have a small group of kids at the beginning of this semester with whom I planned to explore this stuff, but to balance out enrollment numbers they had to close either that class or the AP. Unfortunate, but I do know the kids liked Python. I do keep seeing ways in which Python would be more elegant and more powerful than a clunky interface, and I do see how exploring Python would address a lot of the very issues people have raised in pretentious brain-storming sessions about how we will use our new math/sci/tech building. The biggest issue that I keep finding myself drawn to is not site specific. I keep seeing the need for students to develop more number sense. The emphasis on statistics and the typical use of calculators, I believe, has created a general tendency among both students and teachers to regard numbers as "data". The statistical theme is important, but I think it's time to balance it out with a computational number-theoretic theme. I'm saying that numbers are not just data, they are data STRUCTURES. I think there should be more number theory in the math curriculum, and we could provide that beautifully with something like Python. But I will remain alert to site-specific issues that the use of Python could address. - Michel -----Original Message----- From: Radenski, Atanas [mailto:radenski@chapman.edu] Sent: Sat 09/23/06 08:10 AM To: Michel Paul; edu-sig(a)python.org Subject: RE: [Edu-sig] creating an interface vs. using one From: edu-sig-bounces(a)python.org on behalf of Michel Paul > Also - our school is building a new math/science/technology center. I see Python as an excellent kind of thing to get > people to explore. I attended the SciPy conference at CalTech in August, just to see what kind of things were going on, > and it was amazing. But no one at school seems to care. It's weird. I feel like I've found this treasure, and I keep saying to > people, "Hey! I've found this treasure!" But no one cares. It's so weird. Michel, I do not think it is weird that your school does not care about Python. It is natural. People normally do *not* care about answers to questions that they never asked. Simply offering something that you believe is cool (Python in this case) is not going to work with adults/administrators. I would suggest that you think of a concrete problem that your department chair is facing. She certainly has some problems to solve as a chair and she certainly would be open to possible solution. Is retention a problem? Is diminishing student interest a problem? You have to identify her problems and then try to convince her how and why Python can be the solution to those problems. Just believing that Python is cool, beautiful, and useful may not do it. But addressing some real concrete needs of your school can do it. They may get quite interested. Show them how Python is a solution to their problem(s). Atanas

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Re: [Edu-sig] creating an interface vs. using one (Michel Paul)
by Arthur Sept. 25, 2006

Sept. 25, 2006

Andy Judkis wrote: > In my humble opinion, there would have to be a "Math teacher" > distribution of Python that has this stuff built in before most > teachers would even consider trying it. Is there such a thing already? If I had a leadership role in the Python community I would be attempting to direct energies toward overcoming the(very real) issues related to making something very much like VPython part of the standard distribution. Its utility is general enough, its footprint small enough, and its spirit as a visual extension to Python on point enough - that the effort would IMO be well worth it. I know Dethe has made some discouraging efforts. And perhaps more radical surgery than Dethe has tried to undertake is necessary to make it adequately crossplatform. But in the scheme of levels of difficulty, and with the resources available to the community, I can't believe this is not doable - were some sense of importance attached to it. Consider - even Kirby begins to understand its potential.. ;) Art

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KwangJu, Korea -> Linux City -> Linux University
by Jason Cunliffe Sept. 25, 2006

Sept. 25, 2006

<quote> The Korean government plans to pick Kwangju this month as the nation's first ``Linux City,'' where open-source software will become the mainstream programs. ... it will be required to install open-source software as a main operating system of their infrastructures, a job which the ministry will support with funds and technologies. In the long run, Kwangju will have to migrate most of its public desktop and notebook computers away from the Windows program of Microsoft, the world's foremost producer of software. ``The test city will prompt other regions to follow suit via demonstrating that Linux can be the go-to operating system without any technological glitches or security woes,'' Lee said. To that end, the ministry seeks to invest 1 billion won ($1 million), although the amount may change depending on the situation. Together with Linux City, the government will also choose a ``Linux University,'' another test bed for the emerging software that is an alternative to the proprietary Microsoft Windows. </quote> source: http://times.hankooki.com/lpage/tech/200603/kt2006032117045611780.htm

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Blender reminder
by Jason Cunliffe Sept. 25, 2006

Sept. 25, 2006

...while you're disagreeing to agree about VPython, thought I'd remind you about Blender API http://www.blender3d.org/documentation/242PythonDoc/index.html SCRIPTS http://www.blender.org/cms/Python_Scripts.3.0.html GAME ENGINE LOGIC http://www.blender.org/documentation/pydoc_gameengine/PyDoc-Gameengine-2.34… Python programming Index http://jmsoler.free.fr/didacticiel/blender/tutor/index_prog_python_en.htm Intro http://jmsoler.free.fr/didacticiel/blender/tutor/python_script00_en.htm Show this next page to your students and I imagine they'll be quite motivated to learn Wireshadows http://jmsoler.free.fr/didacticiel/blender/tutor/python_wireshadows_en.htm Where to find Python scrtipts for Blender http://jmsoler.free.fr/didacticiel/blender/tutor/cpl_localiserpythonscript.… French site for Blender and Python scripting http://www.zoo-logique.org/3D.Blender/ Forum http://www.zoo-logique.org/3D.Blender/newsportal/thread.php?group=3D.Blender links to other French Blender sites http://www.zoo-logique.org/3D.Blender/index.php3?zoo=lie wow there must be a lot of Python 3D knowhow developing most if it self-taught / community-taught I think Holland and Gemany also are big fans of it ------ Jason

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Re: [Edu-sig] creating an interface vs. using one
by Michel Paul Sept. 24, 2006

Sept. 24, 2006

Oh yeah - another idea that's been forming - I think an argument can be made for computational modeling to become part of the math/science curriculum. I keep reading articles about how science, particularly biology, is pushing math in new directions, and it seems to me that it's only a matter of time before the concept of creating computational models becomes part of what students learn to do in high school. I've put this idea out to the math and science depts. So far there simply has been no response. But I'm NOT going to shut up. : ) - Michel -----Original Message----- From: edu-sig-bounces(a)python.org on behalf of Michel Paul Sent: Sun 09/24/06 09:47 AM To: Radenski, Atanas; edu-sig(a)python.org Subject: Re: [Edu-sig] creating an interface vs. using one Yes, thank you. I have been reflecting on this, and so far I haven't been able to pin down a site specific issue that Python would clearly address. I should point out that I haven't been stifled in pursuing Python - I have been tolerated. I did have a small group of kids at the beginning of this semester with whom I planned to explore this stuff, but to balance out enrollment numbers they had to close either that class or the AP. Unfortunate, but I do know the kids liked Python. I do keep seeing ways in which Python would be more elegant and more powerful than a clunky interface, and I do see how exploring Python would address a lot of the very issues people have raised in pretentious brain-storming sessions about how we will use our new math/sci/tech building. The biggest issue that I keep finding myself drawn to is not site specific. I keep seeing the need for students to develop more number sense. The emphasis on statistics and the typical use of calculators, I believe, has created a general tendency among both students and teachers to regard numbers as "data". The statistical theme is important, but I think it's time to balance it out with a computational number-theoretic theme. I'm saying that numbers are not just data, they are data STRUCTURES. I think there should be more number theory in the math curriculum, and we could provide that beautifully with something like Python. But I will remain alert to site-specific issues that the use of Python could address. - Michel -----Original Message----- From: Radenski, Atanas [mailto:radenski@chapman.edu] Sent: Sat 09/23/06 08:10 AM To: Michel Paul; edu-sig(a)python.org Subject: RE: [Edu-sig] creating an interface vs. using one From: edu-sig-bounces(a)python.org on behalf of Michel Paul > Also - our school is building a new math/science/technology center. I see Python as an excellent kind of thing to get > people to explore. I attended the SciPy conference at CalTech in August, just to see what kind of things were going on, > and it was amazing. But no one at school seems to care. It's weird. I feel like I've found this treasure, and I keep saying to > people, "Hey! I've found this treasure!" But no one cares. It's so weird. Michel, I do not think it is weird that your school does not care about Python. It is natural. People normally do *not* care about answers to questions that they never asked. Simply offering something that you believe is cool (Python in this case) is not going to work with adults/administrators. I would suggest that you think of a concrete problem that your department chair is facing. She certainly has some problems to solve as a chair and she certainly would be open to possible solution. Is retention a problem? Is diminishing student interest a problem? You have to identify her problems and then try to convince her how and why Python can be the solution to those problems. Just believing that Python is cool, beautiful, and useful may not do it. But addressing some real concrete needs of your school can do it. They may get quite interested. Show them how Python is a solution to their problem(s). Atanas _______________________________________________ Edu-sig mailing list Edu-sig(a)python.org http://mail.python.org/mailman/listinfo/edu-sig

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Re: [Edu-sig] creating an interface vs. using one
by Michel Paul Sept. 24, 2006

Sept. 24, 2006

>2+3 > >What I see from a mathematical point of view is two things, >and an operator that acts upon those things. What I see is a partition of the number 5. We commonly say that 2 + 3 "makes" 5, but I prefer to say that the number 5 has the property that it can be partitioned into a group of 2 and a group of 3. That it can be partitioned in this way is what we mean when we say that 2 + 3 == 5. Mathematically, 2 and 3 do not necessarily "turn into" 5, rather, a group of 5 already contains a group of 2 and a group of 3. The concept of an operator acting upon operands is something we develop later. It is also a fact that a group of 5 can be partitioned into a group of 2 and a group of 3 in 10 different ways. It would seem odd to say that these 10 different partitions into 2 and 3 each act to produce a different five, and it would also seem odd to say that these different partitions each act to produce the SAME 5. Rather, the one group of 5 can be partitioned in various ways. In a computational context it is true that 2 .__add__(3) creates a new object, 5, and this is sort of an interesting contrast: computation occurs in time and produces new data from old data, but many kinds of mathematical relations already exist as facts - they do not have to "happen". >The OO point of view is *nothing like* the mathematical point >of view. Numbers already are objects that have properties. They are abstract objects, sure, so you can't analyze them in physical or chemical terms - those aren't the kind of properties they have. A set of N things has geometric properties that are different from a set of N + 1 things. Object-oriented thinking doesn't always have to mean object-oriented PROGRAMMING. Object-oriented thinking already has a deep and rich history in mathematics. For Pythagoras and Plato, numbers were things in themselves, not just wisps in our mind, and I don't think Heisenberg was wrong to say things like QM vindicated Pythagoras. Thematically speaking, of course. What we have accomplished with our technology is to give object-oriented thinking computational power. We no longer have to perform computations - objects themselves can. >In math, operators and numbers are two different things and the >former don't "belong" to later. I see arithmetic statements composed of operators and operands as our descriptions of the ways in which numbers can be partitioned. A sum is the fact of a particular partition. A difference is a complementary partition. Products and quotients involve partitions containing equally sized parts. Our syntax of operators and operands arises later. Or, that's just how I'm able to make sense of things for myself. - Michel -----Original Message----- From: edu-sig-bounces(a)python.org on behalf of Daniel Ajoy Sent: Sat 09/23/06 12:50 PM To: edu-sig(a)python.org Subject: Spam: Re: [Edu-sig] creating an interface vs. using one On 23 Sep 2006 at 12:00, edu-sig-request(a)python.org wrote: > You CANNOT articulate OO on a TI. You can?t create a class. Most people > don?t care, right now, because they don?t even know what that means, but I > can guarantee you that there?s a bunch of scientists at places like > CalTech who DO care! Mathematics is already object-oriented, and the > curriculum of the future will need to make students conscious of that > fact. OO is not something just for CS majors! Seriously. I don't believe this to be true. 2+3 What I see about from a mathematical point of view is two things, and an operator that acts upon those things. The OO point of view is that 2 is an object and that the plus sign is a method of this object and that 3 is the argument of this method. The OO point of view is *nothing like* the mathematical point of view. In math, operators and numbers are two different things and the former don't "belong" to later. Daniel _______________________________________________ Edu-sig mailing list Edu-sig(a)python.org http://mail.python.org/mailman/listinfo/edu-sig

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creating an interface vs. using one
by Michel Paul Sept. 24, 2006

Sept. 24, 2006

A couple of days ago I attempted to describe to my math dept chair the elegant way you can zip two lists in Python to create a set of ordered pairs. Her response was dismissive, saying you can do the same thing on a TI using lists. Her point was that we were each doing the same thing in a different way. My response was uhhh ... no, there's a huge difference. My point was, and always has been, that thinking in a language is not the same thing as, is deeper than, using a gadget. What follows is the body of an email I sent her. I'd welcome any feedback to help develop my argument. Also - our school is building a new math/science/technology center. I see Python as an excellent kind of thing to get people to explore. I attended the SciPy conference at CalTech in August, just to see what kind of things were going on, and it was amazing. But no one at school seems to care. It's weird. I feel like I've found this treasure, and I keep saying to people, "Hey! I've found this treasure!" But no one cares. It's so weird. A big problem that I see is the focus on the glamour of tech toys. Our district is willing to spend money on SmartBoards, and these are really cool things, but there's so much else they just aren't paying attention to. The focus is on getting gadgets. But my point is that education should be more about language and the articulation of ideas. So here is what I sent my dept chair. Thank you for any suggestions to help get across to my dept what kinds of things COULD be done - I'm still finding out about Python myself. - Michel ============================================================ Here are some points I think are important: Using calculators vs. thinking in a language are NOT two different ways of doing the same thing. What is the thing? True, if youre creating a list of ordered pairs from two lists, you can do it on a TI or in a Python shell, but the difference in the two approaches is immense. On a TI you have to learn where the buttons are. In a Python shell, all you need to learn is Algebra: >>> x = [0, 2, 4, 6, 8, 10] >>> y = [9, 7, 5, 3, 1, -1] >>> myListOfPoints = zip(x, y) So far, the only syntax issue beyond Algebra is zip. >>> myListOfPoints [(0, 9), (2, 7), (4, 5), (6, 3), (8, 1), (10, -1)] What Im showing here is precisely what you would get INTERACTIVELY in a Python shell session. What you type at the >>> prompt simply gets evaluated. Its SO easy! Theres a tremendous unity here not a bunch of different buttons. If a student can articulate their thoughts in Algebra, then they can articulate their thoughts in Python. You dont need yet ANOTHER piece of software to record and display the history of button presses. The symbols hang together NATURALLY because of MEANING. That is important! It really is. Look how simple this is: >>> def f(x): return 2.0*x + 3.0 >>> def g(x): return (x - 3.0) / 2.0 >>> f(5) 13.0 >>> g(13) 5.0 >>> f(g(7)) 7.0 >>> g(f(7)) 7.0 Again, WYSIWYG! Thats it! Ive defined a function and its inverse, and Ive shown their composition. The only syntax required other than Algebra is def and return. Sure, you could do it on a TI as well, but it would be kind of clunky. What you see above, you can do on the fly. The argument that not every kid can have access to a computer is, first, false, and second, irrelevant. Its like using a SmartBoard the kids dont have to have SmartBoards at their seats. That isnt the point. The teacher uses the SmartBoard as a canvas on which to create artworks of ideas. A record can be kept of what was created. Same with Python. It blends in perfectly with this SmartBoard kind of world. With a language that looks like Algebra, the kids dont have to learn how to use a piece of software or a gadget. They can take the concepts home with them and download Python for free. You can put Python code on the school web page, and they can download it and use it directly. No special hookups needed. No gadgets. Nothing to buy other than the computer, but these days, computers are as common as TV sets. You CANNOT articulate OO on a TI. You cant create a class. Most people dont care, right now, because they dont even know what that means, but I can guarantee you that theres a bunch of scientists at places like CalTech who DO care! Mathematics is already object-oriented, and the curriculum of the future will need to make students conscious of that fact. OO is not something just for CS majors! Seriously. Language transcends device, because a language can create a device. Devices dont create language. What a language is is deeper than what a gadget is. With just a slight bit of tweaking, the language of Algebra can become a computational language! Thats really cool. I just dont get why more people dont care about that, at least at a high school level. Because, again, I can guarantee you that there are a lot of scientists at CalTech, and JPL out there who DO care and who agree with me that THAT is what 21st century math should be about! Not USING interfaces articulating them!

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Harmonographs + curves
by Jason Cunliffe Sept. 23, 2006

Sept. 23, 2006

see http://local.wasp.uwa.edu.au/~pbourke/curves/harmonograph/ and http://local.wasp.uwa.edu.au/~pbourke/curves/

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