On Tue, Mar 23, 2010 at 7:29 AM, Bill Punch <pu...@cse.msu.edu> wrote:
<< snip >> > If you have any comments, we'd love to hear them. > Hi Bill -- I enjoyed poking through some of these, reminiscent of some of the SuperQuest challenges for Oregon's annual software competition, high school students working in teams, with a language of their choice, to come up with a working solution in a time race. I like how you cover a lot of territory. Just looking at your page reassures a student that computer programs are ubiquitous i.e. in all walks a life (or a lot of 'em). Teachers should feel heartened as well, especially math teachers, seeking new relevance amidst real world topics, like strangers in a strange land (some of them). I'm wondering if you sometimes revisit the same problem suggesting different strategies for solution, perhaps after students have struggled and turned in some work. The same problem tackled multiple times may help boost student self-confidence, as they perceive how their powers are growing (like working out in a gym, lifting that same stack more easily). For example, the Caesar Code stuff is pretty interesting, as a generic introduction to permutations, wherein rotations might be "multiplied". You've got finite groups going here -- a topic I try to import from the college math world, much of which hides behind "calculus mountain", a killer peak most have to climb before they're even told "abstract algebra" exists. Yet so much fun could be had, so much cavorting, if we could just play with "math objects" that play in groups. http://www.4dsolutions.net/ocn/flash/group.html (annoying noise!) Another definition of a Caesar Code (Nero Code? Hadrian Code?) allows these codes to be completely random, though still one-to-one of course, and includes the space character as another one to encode, makes it all seem the more cryptic cuz of the wrecked word boundaries. So what if a student hasn't used dictionaries yet, or has only just discovered them, and sticks with indexed strings, as your hints suggest. Coming back to the same problem later, newly armed with a dictionary, list comprehensions, maybe the whole exercise seems easier and more concise? Don't wanna get *too* concise. Example IDLE 2.6.4 >>> from string import lowercase as lowers; from random import shuffle Get lowercase a-z plus space character >>> thechars = lowers[:26]+" " >>> def makekey(instring): thecopy = list(instring) shuffle(thecopy) return dict(zip(list(instring), thecopy)) Build the secret key with thechars, get back a dictionary: >>> coding = makekey(thechars) >>> coding {' ': 'g', 'a': 'x', 'c': 'w', 'b': 'c', 'e': 't', 'd': 'n', 'g': 'h', 'f': 'm', 'i': 'j', 'h': 'k', 'k': 'a', 'j': 'o', 'm': 's', 'l': 'u', 'o': 'p', 'n': 'l', 'q': 'y', 'p': 'z', 's': 'f', 'r': 'b', 'u': 'q', 't': 'i', 'w': 'e', 'v': ' ', 'y': 'r', 'x': 'd', 'z': 'v'} Define encoding and decoding functions, then test them. Pass through any letters not in the key: >>> def encode(phrase, secretkey): output = '' for char in phrase: output += secretkey.get(char, char) return output >>> def decode(phrase, secretkey): output = "" reverselookup = dict((value, key) for key,value in secretkey.items()) for char in phrase: output += reverselookup.get(char, char) return output >>> p = "Able was I ere I saw Elba" >>> e = encode(p, coding) >>> e 'AejlgfwtgIglclgIgtwfgEjew' >>> decode(e, coding) 'Able was I ere I say Elba' My propensity, coming from a math teaching perspective, is to look at a Python module as a "fish tank" with multiple mouths to feed, i.e. I like to publish a simple API and feed arguments to functions (other denizens) directly, sans raw_input prompts. This more directly corresponds to the idea of a grab bag of tools, a library, whereas a raw_input cycle more corresponds to polling in a GUI, staying alert for user inputs. Both modalities make a lot of sense, so I'm not saying I wouldn't go with raw_input sometimes -- I know students like being prompted, even by their own code. Sometimes I even use text menus with switching. :) http://www.4dsolutions.net/ocn/pymath.html (example at the end). Didn't see whether some of your challenges drop the raw_input to seem more like libraries, or whether you ask for a menu. Another thing is to ask for command line arguments and use sys.args -- so much fun, we might have, eh? Anyway, we're all aware of these possibilities -- just thought I'd remind myself of some of them. Again: reassuring to see the broad-based examples. Hitting the same challenge multiple times, but with new tools and/or concepts each time, is what many teachers call "spiraling" as you likely know. Pre-written code may be called "scaffolding" if you wanna sound like you know the shoptalk. In the high school math teaching world, John Saxon is often cited for making especially strategic use of "spiraling" although his detractors would consider this unmerited crediting of an interloper (something of a maverick that guy -- never met him). I mention all this by way of background, in that I cite him in my Notes for Teachers for Pycon 2009 re spiraling FYI: http://www.4dsolutions.net/presentations/py4t_notes.pdf On another note, thanks to Edward Cherlin (and Maria too) for jumping in on math-thinking-l this month. That's a functional programmers' hangout and any incursion of "imperative programmers" tends to generate some ire -- kinda like West Side Story? In the old days, we'd find some eligible prince or princess to marry into the Great Lambda tribe (as in lambda calculus). I've been bugging philosophers to devote some bandwidth to this feuding but they're busy with paper and pencil logic, can't be bothered with "CS" apparently. Maybe I'm being overly judgmental, and anyway it's not like there's anything much at stake. Or is there? -- math teachers like Maria get caught in the cross-fire, Gary too for that matter, though he seems to hold his own. Maybe the floodgates would open for more funding of discrete maths at the high school level, if only the engineers weren't seen to be fighting amongst themselves so much? Nothing scares away wannabe investor-sponsors so much as feuding and acrimony eh? Speaking of Gary (Litvin), he got the ball rolling by commenting on corestandards.org, a K-12 standards-building initiative purportedly with real state governors on board. He sees signs that discrete math topics are losing ground, not gaining it. But that's perhaps more testament to an unimaginative and uninformed bureaucracy that has yet to achieve a strangle-hold? One may fondly so hope I suppose. Over on math-teach, I mention that our Pauling Center has not been consulted, and we're at the epicenter (evidence that these bureaucrats have gone way out on a limb?). http://mathforum.org/kb/message.jspa?messageID=7013136&tstart=0 See math-thinking-l archives if wanting more substance behind these ramblings (wanderings). Bill, if you're still with me, I look forward to poking around in more of your exercises and may well have more to say, hope OK. Kirby _______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
