"morals" in math
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kirby urner
Jan 4, 2013, 12:52:08 PM1/4/13
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On Fri, Dec 7, 2012 at 7:19 AM, Bradford Hansen-Smith <wholem...@gmail.com> wrote:
I put "morals" in quotes following Nietzsche, who wondered if "power" were more what at issue, say parental power to provide values for progeny.
Why don't we see K-12 or any commercial text books laced with savvy talk about cards and card play, decks of 52 + Jokers? Nor Tarot decks for that matter.
Lots of combinatorics, topics for mathematical treatment, an excuse to learn how rule-driven logic may result in puzzles with optimal solutions i.e. games of skill, not just chance, usually a mix of the two. Even an axiomatic system is somewhat a role of the dice, in terms of how interesting the math is, or, in the case of number crunching on formulas, how elaborate the visualizations. [1]
Of course it's because playing cards are charged with cultural voltages. They're simply "too hot to handle". A given teacher with trust and influence may talk about cards all she or he wants, here and there, but the text books are what I'm talking about. How many of those talk about "face cards" or "shuffling the deck".
When learning fractions, it would be logical and rhetorically useful to spend more time with the different measuring systems, those which divide up wholes into parts, such as quarts into cups into pints. How do teaspoons relate to table spoons? It's all somewhat complicated, mixed base, and highly relevant to one's cooking skills and comfort level around food prep. So why doesn't the culture routinely invite children down to the community kitchen in the course of a segment on fractions, adding them, dividing them. One quarter teaspoon: how many in a cup?
But then you would need real recipes, real heat, real risk of injury from using equipment. Real headaches in other words. We rather just have them imagine a kitchen. Do math in your head. Don't make problems for others. Parents should teach cooking skills, or at least we have home economics in some schools (some do, if property taxes are high). Entirely "not math" (home ec). The two faculties are so different. Population demographics, Diet for a Small planet, the economics of recycling (or not), the price of soy beans in Brazil... not talked about. Plenty mathy, at many levels (game theory, simulations...), but politically charged, geographically aware, and potentially redolent with "messages" -- or an at least an excuse to get kids thinking (e.g. about their diet).
We'll have none of that thank you. That's called "Rainforest Math", when you start looking at real ecosystems and talking about global equations, Gibbs Phase Rule, the mix of liquids, solids and gases as a function of pressure and temperature, rising CO2, the role of O2 in combustion and rust. That's chemistry. Word problems in mathematics texts are notoriously not about chemistry because that's the chemistry book's job. Mathematics texts are careful not to tread on any neighboring turf and not to venture into any "rain forests" e.g. don't get steeped in anything "too real".
Mathematics takes you *away* from the "real world" doesn't it? That's part of its job. You should read more 'Alice in Wonderland' and think about infinity, don't bother your little head with real world skills like cooking. Others will be cooking for you, most likely (the "classism" of "class rooms" is built right in, unquestioned, unstated, and often way obsolete -- we need to cook for ourselves more than these schools seem to realize). And you're to stay away from gambling. Computers? That's something else. No, we won't be talking about cryptography. No, no and no, to most of your proposals, sorry. Nope. Not in the cards.
I've cast this as an issue of parental control but of course we're talking state control, community standards, enculturization, whatever you want to call it. People are learning their roles. What comes through schools is put to the same test as what comes through the television: am I able to create an ambiance suitable for "my" children (my biological and/or legal dependents)? Schools should not send them home completely reshaped in a way I disapprove of or don't understand. Colleges do that more, but even there, colleges pick and choose their faculty to adhere to various slants and biases.
Of course many tribes, cultures, ethnicities, *do* experience the "school system" as an encroaching alien force, one that snatches up their children and returns them in an almost recognizable state. That's what people fear and don't want if they can help it. That's why schools bend over backwards to "not rock the boat" which means math must stay boring boring boring. That's what makes it safe, safe as a subject. Your brain is being made safer by this "discipline". Parents should pat little junior on the head and smile. Junior will come home more like the parent, more respectful, more steeped in similar ways of thinking. That's how it should be, right? Keep to the orthodoxy, have a better life that way.
What I'm interested in doing is producing more short clips for Youtube that question or, more specifically, stray outside of these boundaries. They may do so in an apparently unselfconscious take-it-for-granted manner, i.e. you'll see a teacher casually handing a deck of cards to each student. Is this a regular school? I see more world and regional maps than a math class should normally have (geography class?), plus it's darker in terms of illumination. It's more like an airplane at night with people either asleep, reading with personal chair lamps, or watching the movies. The background feels aerospace even if we're not really in an airplane. More screens.
I had a classroom more like this at a police station once, West Precinct near Intel in Hillsboro, Oregon. No windows, with computers in a U shape facing the wall, and chairs on wheels with a central table. Students could work at individual work stations, facing away from the center, or swivel around to attend a common focus, or scoot up to the table for a more meeting-looking environment. This is where I might pass out the decks of cards. Tarot? And what were we monitoring on these work stations, anyway? I've written it up elsewhere. This was with Saturday Academy again. Participation was voluntary. No students were there as prisoners.
Lastly (for now), the I Ching: so many useful stories and connections. There's a matrix of trigrams, 8 x 8, randomness, a rule-driven lookup procedure. The system is binary: broken vs not-broken horizontal lines, in combinations of 3, which is octal. A next bit would double to 16, which is our 0,1,2...9,A,B,C,D,E,F -- one of the most important number encoding systems of all time when you count all the ASCII and Unicode out there and how it's bitwise encoded. The I Ching as a topic could take us into that. But no, of course not. Not at the text book level, never. Too much "other stuff" going on (too like Tarot decks), too much danger of parents complaining about the socialization of their children.
See you on Youtube then, Vimeo etc. Even Hulu maybe.
Kirby
Yes, it is as important to be conscious of the effect common language has on math, and how math effects common language., Logic is relative to the frame, of which each is only partial truth.
Kirby, can you talk more about the morals in math, we need more discussion about this aspect of mathematics.
Isn't whistling in the dark a reaction to fear of something being there we don't know.
Brad
I put "morals" in quotes following Nietzsche, who wondered if "power" were more what at issue, say parental power to provide values for progeny.
Why don't we see K-12 or any commercial text books laced with savvy talk about cards and card play, decks of 52 + Jokers? Nor Tarot decks for that matter.
Lots of combinatorics, topics for mathematical treatment, an excuse to learn how rule-driven logic may result in puzzles with optimal solutions i.e. games of skill, not just chance, usually a mix of the two. Even an axiomatic system is somewhat a role of the dice, in terms of how interesting the math is, or, in the case of number crunching on formulas, how elaborate the visualizations. [1]
Of course it's because playing cards are charged with cultural voltages. They're simply "too hot to handle". A given teacher with trust and influence may talk about cards all she or he wants, here and there, but the text books are what I'm talking about. How many of those talk about "face cards" or "shuffling the deck".
When learning fractions, it would be logical and rhetorically useful to spend more time with the different measuring systems, those which divide up wholes into parts, such as quarts into cups into pints. How do teaspoons relate to table spoons? It's all somewhat complicated, mixed base, and highly relevant to one's cooking skills and comfort level around food prep. So why doesn't the culture routinely invite children down to the community kitchen in the course of a segment on fractions, adding them, dividing them. One quarter teaspoon: how many in a cup?
But then you would need real recipes, real heat, real risk of injury from using equipment. Real headaches in other words. We rather just have them imagine a kitchen. Do math in your head. Don't make problems for others. Parents should teach cooking skills, or at least we have home economics in some schools (some do, if property taxes are high). Entirely "not math" (home ec). The two faculties are so different. Population demographics, Diet for a Small planet, the economics of recycling (or not), the price of soy beans in Brazil... not talked about. Plenty mathy, at many levels (game theory, simulations...), but politically charged, geographically aware, and potentially redolent with "messages" -- or an at least an excuse to get kids thinking (e.g. about their diet).
We'll have none of that thank you. That's called "Rainforest Math", when you start looking at real ecosystems and talking about global equations, Gibbs Phase Rule, the mix of liquids, solids and gases as a function of pressure and temperature, rising CO2, the role of O2 in combustion and rust. That's chemistry. Word problems in mathematics texts are notoriously not about chemistry because that's the chemistry book's job. Mathematics texts are careful not to tread on any neighboring turf and not to venture into any "rain forests" e.g. don't get steeped in anything "too real".
Mathematics takes you *away* from the "real world" doesn't it? That's part of its job. You should read more 'Alice in Wonderland' and think about infinity, don't bother your little head with real world skills like cooking. Others will be cooking for you, most likely (the "classism" of "class rooms" is built right in, unquestioned, unstated, and often way obsolete -- we need to cook for ourselves more than these schools seem to realize). And you're to stay away from gambling. Computers? That's something else. No, we won't be talking about cryptography. No, no and no, to most of your proposals, sorry. Nope. Not in the cards.
I've cast this as an issue of parental control but of course we're talking state control, community standards, enculturization, whatever you want to call it. People are learning their roles. What comes through schools is put to the same test as what comes through the television: am I able to create an ambiance suitable for "my" children (my biological and/or legal dependents)? Schools should not send them home completely reshaped in a way I disapprove of or don't understand. Colleges do that more, but even there, colleges pick and choose their faculty to adhere to various slants and biases.
Of course many tribes, cultures, ethnicities, *do* experience the "school system" as an encroaching alien force, one that snatches up their children and returns them in an almost recognizable state. That's what people fear and don't want if they can help it. That's why schools bend over backwards to "not rock the boat" which means math must stay boring boring boring. That's what makes it safe, safe as a subject. Your brain is being made safer by this "discipline". Parents should pat little junior on the head and smile. Junior will come home more like the parent, more respectful, more steeped in similar ways of thinking. That's how it should be, right? Keep to the orthodoxy, have a better life that way.
What I'm interested in doing is producing more short clips for Youtube that question or, more specifically, stray outside of these boundaries. They may do so in an apparently unselfconscious take-it-for-granted manner, i.e. you'll see a teacher casually handing a deck of cards to each student. Is this a regular school? I see more world and regional maps than a math class should normally have (geography class?), plus it's darker in terms of illumination. It's more like an airplane at night with people either asleep, reading with personal chair lamps, or watching the movies. The background feels aerospace even if we're not really in an airplane. More screens.
I had a classroom more like this at a police station once, West Precinct near Intel in Hillsboro, Oregon. No windows, with computers in a U shape facing the wall, and chairs on wheels with a central table. Students could work at individual work stations, facing away from the center, or swivel around to attend a common focus, or scoot up to the table for a more meeting-looking environment. This is where I might pass out the decks of cards. Tarot? And what were we monitoring on these work stations, anyway? I've written it up elsewhere. This was with Saturday Academy again. Participation was voluntary. No students were there as prisoners.
Lastly (for now), the I Ching: so many useful stories and connections. There's a matrix of trigrams, 8 x 8, randomness, a rule-driven lookup procedure. The system is binary: broken vs not-broken horizontal lines, in combinations of 3, which is octal. A next bit would double to 16, which is our 0,1,2...9,A,B,C,D,E,F -- one of the most important number encoding systems of all time when you count all the ASCII and Unicode out there and how it's bitwise encoded. The I Ching as a topic could take us into that. But no, of course not. Not at the text book level, never. Too much "other stuff" going on (too like Tarot decks), too much danger of parents complaining about the socialization of their children.
See you on Youtube then, Vimeo etc. Even Hulu maybe.
Kirby
On Thu, Dec 6, 2012 at 11:38 PM, kirby urner <kirby...@gmail.com> wrote:
I think it's useful to stay conscious of the "not math meanings" of these words, like even and odd.
"Even" tends to mean "level" but also in the sense of "fair" as in "level playing field" and "even handed".
"Odd" tends to mean "peculiar" and/or "off" and/or "weird".
We're rediscovering on math-teach how we teach the number line and coordinate systems by relating "positive" to "right" and "up", "negative" to "left" and "down".
These are such relative terms though.
My right is your left when we're facing each other (theater: stage left vs. house left).
We think of "right" and "upright" as in "righteous" and/or "normal" -- "orthodox" and "orthogonal" go together (orthogonality is the prevailing orthodoxy).
Mathematics is riddled with moralisms, not just truisms. One may say they're just connotations, not denotations, so not "real".
That's whistling in the dark for sure. These ghost-meanings are everywhere.
Kirby
kirby urner
Jan 4, 2013, 1:21:27 PM1/4/13
to mathf...@googlegroups.com
Lots of combinatorics, topics for mathematical treatment, an excuse to learn how rule-driven logic may result in puzzles with optimal solutions i.e. games of skill, not just chance, usually a mix of the two. Even an axiomatic system is somewhat a role of the dice, in terms of how interesting the math is, or, in the case of number crunching on formulas, how elaborate the visualizations. [1]
I forgot to flesh out my footnote...
[1] After the huge success of the Mandelbrot Set, in making a splash as the hallmark "fractal" with the property of always yielding more interesting detail when zooming in, the search was on for some similar set in "3D" (i.e. one we could swim around in and look at from all angles). One of the most successful candidates is the Mandelbulb, which seems to be more a family than a singular solution set. Eighth powering is involved and it's all done with real numbers. The Youtubes have been amazing and were a source of fascination to my middle school aged students this past summer.
http://www.flickr.com/photos/kirbyurner/7720108440/in/set-72157630917499226
Jon Adie - Sky
Jan 4, 2013, 3:21:40 PM1/4/13
to mathf...@googlegroups.com
WHAT A REFRESHING ATTITUDE TO MATHS .. TO HARNESS (YOUNG) MINDS EMBRACING NUMBER SYSTEMS DRAWN FROM DIVERSE SOURCES .. THE I-CHING IS RICH IN SYMBOLISM, AND HAS BEEN USED BY MANY BRILLIANT MINDS, I BELIEVE ALAN TURIN WAS FASCINATED BY ALCHEMY, TERENCE MCKENNA FOUND CORRELATIONS BETWEEN ANCIENT MAYAN & CHINESE AND INDIAN NUMBER SYSTEMS .. NOT TO LOOK AT THESE SUBJECTS THAT ARE ALSO HISTORICAL RESOURCES (LIKE THE TAROT & KABBALA FOR THAT MATTER.. THERE SHOULD BE NO TABOO'S OR RESTRICTIONS, THESE SYSTEMS ARE IN THE PUBLIC DOMAIN AND SHOULD BE APPROACHED WITH AN OPEN MIND PURGED OF SUPERSTITION AND FEAR BY THE INTELLECT PENETRATING IT'S WORKINGS ... OR FIND USES FOR THE STRUCTURES AND SYSTEMS IN OTHER FIELDS. YOUR IDEAS ARE A REFRESHING CHANGE LETS MOVE FORWARD IN THIS NEW MILLENIUM .. I AM REMINDED THAT THE MIND IS LIKE A PARACHUTE AND WORKS BEST WHEN IT IS OPEN ! .....JON-A
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m...@ms.lt
Jan 4, 2013, 4:28:27 PM1/4/13
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Another example is the Law of Moses. Much of it exhibits deep
mathematical thinking. For example, if two neighbors each have an ox, and
one ox accidently gores and kills the other, then... they kill the
remaining ox and share it. (Averaging) But if the ox was known to be
dangerous, then they swap the oxen. (Transposition) If I remember
correctly.
I think that what's truly worth learning, of all things, is "right and
wrong". Math is worth learning as a study of models, of systems, of
simplifications, where they hold and where they break down, especially in
society. (For example, our current population growth rate is a great
exponential model in the short run, but it implies that Adam was created
some 1,000 years ago, 30 generations or so.) Reading and writing,
literature are worth learning because they help us empathize with all
kinds of people who we might never know personally, in situations we may
never experience.
Andrius
Andrius Kulikauskas, m...@ms.lt, http://www.selflearners.net
Andrius
mathematical thinking. For example, if two neighbors each have an ox, and
one ox accidently gores and kills the other, then... they kill the
remaining ox and share it. (Averaging) But if the ox was known to be
dangerous, then they swap the oxen. (Transposition) If I remember
correctly.
I think that what's truly worth learning, of all things, is "right and
wrong". Math is worth learning as a study of models, of systems, of
simplifications, where they hold and where they break down, especially in
society. (For example, our current population growth rate is a great
exponential model in the short run, but it implies that Adam was created
some 1,000 years ago, 30 generations or so.) Reading and writing,
literature are worth learning because they help us empathize with all
kinds of people who we might never know personally, in situations we may
never experience.
Andrius
Andrius Kulikauskas, m...@ms.lt, http://www.selflearners.net
Andrius
mok...@earthtreasury.org
Jan 4, 2013, 8:07:29 PM1/4/13
to mathf...@googlegroups.com
On Fri, January 4, 2013 12:52 pm, kirby urner wrote:
> On Fri, Dec 7, 2012 at 7:19 AM, Bradford Hansen-Smith <
> wholem...@gmail.com> wrote:
>
>> Yes, it is as important to be conscious of the effect common language
>> has
>> on math, and how math effects common language., Logic is relative to the
>> frame, of which each is only partial truth.
>> Kirby, can you talk more about the morals in math, we need more
>> discussion
>> about this aspect of mathematics.
The greatest impact of math on morals is in its dedication to truth over
> On Fri, Dec 7, 2012 at 7:19 AM, Bradford Hansen-Smith <
> wholem...@gmail.com> wrote:
>
>> Yes, it is as important to be conscious of the effect common language
>> has
>> on math, and how math effects common language., Logic is relative to the
>> frame, of which each is only partial truth.
>> Kirby, can you talk more about the morals in math, we need more
>> discussion
>> about this aspect of mathematics.
presupposition, except of course where that does not hold. Legend has it
that the Pythagorean who discovered "irrational" numbers was murdered for
his pains. I could catalog many other instances, none so vehement, of
rejection of new ideas in mathematics because of some non-mathematical
prejudice. I will only mention Catholic Church rejection of 0 as Muslim
blasphemy, a supposed denying of the Creator; Gauss's hesitation to
publish on non-Euclidean geometry due to his fear of "the howls of the
Boeotians; and the attacks on Georg Cantor's transfinite arithmetic.
But truth has so far won out each time, so these are not really
exceptions, even if they are warnings. As with the incursions of math into
Natural Philosophy, resulting in Physics, where some of the initial
objections were even more vehement than the Pythagoreans' visceral,
murderous rejection of irrationals. Giordano Bruno being burned at the
stake, for example, and Galileo getting the Second Degree from the
Inquisition. (First degree, threat; second degree, a tour of the torture
chamber with a viewing of the implements; third degree, actual torture.)
We would have to review the misuse of science, as in supposed Eugenics,
Soviet rejection of genetics under Trofim Lysenko, and so-called "Creation
Science" and "Flood Geology" to this day. Eugenics and Lysenkoism are
gone, and Young-Earth Creationism is in very slow but steady decline.
There is still a Flat Earth Society, but it has no political influence, so
the rest of us can ignore it. http://theflatearthsociety.org/cms/
The discovery that supposedly inferior peoples can actually do math and
science has been as important in human advancement as the discovery that
they can fight in wartime. (I saw yesterday on C-SPAN a class on Blacks in
the Union Army and Navy in the Civil War. The South refused to allow it,
some saying that if Blacks can fight, then our whole theory of slavery is
wrong.) The history of math and science in China, Arabia, Persia, Turkey,
India, Africa, South America, and elsewhere is a worthy study, an
excellent corrective to the White-supremacist historicism of recent
centuries.
>> Isn't whistling in the dark a reaction to fear of something being there
>> we don't know.
slaveowners' fears of slave uprisings. And worse again when you think you
know but you don't, as with Southern White fears of Reparations.
>> Brad
>>
>>
> I put "morals" in quotes following Nietzsche, who wondered if "power" were
> more what at issue, say parental power to provide values for progeny.
in the West, and not only in historical times. I am particularly
interested in the generation gap that is arising world-wide as the young
have taken to computers and the Internet much more than their elders, and
as we work to give up to a billion children at a time access. The Arab
Spring is just a small part of this.
> Why don't we see K-12 or any commercial text books laced with savvy talk
> about cards and card play, decks of 52 + Jokers? Nor Tarot decks for that
> matter.
Yes, there is an issue about using anything to do with gambling in
teaching probability. It might possibly be addressed by showing through
probability that gambling is stupid rather than sinful. We could certainly
use sports to create interest in probability and statistics.
> Lots of combinatorics, topics for mathematical treatment, an excuse to
> learn how rule-driven logic may result in puzzles with optimal solutions
> i.e. games of skill, not just chance, usually a mix of the two.
Dilemma, which is the basis of Robert Axelrod's theory in The Evolution of
Cooperation.
> Even an
> axiomatic system is somewhat a role of the dice, in terms of how
> interesting the math is, or, in the case of number crunching on formulas,
> how elaborate the visualizations. [1]
the systems that they generate, not out of the air. There is nothing
probabilistic about it. If it turns out that an axiom system doesn't work
as designed, it is amended (not-Euclidean geometry, for example) or
discarded (naive set theory). I can't make any sense at all of your number
crunching case.
> Of course it's because playing cards are charged with cultural voltages.
> They're simply "too hot to handle". A given teacher with trust and
> influence may talk about cards all she or he wants, here and there, but
> the
> text books are what I'm talking about. How many of those talk about "face
> cards" or "shuffling the deck".
>
> When learning fractions, it would be logical and rhetorically useful to
> spend more time with the different measuring systems, those which divide
> up
> wholes into parts, such as quarts into cups into pints. How do teaspoons
> relate to table spoons? It's all somewhat complicated, mixed base, and
> highly relevant to one's cooking skills and comfort level around food
> prep. So why doesn't the culture routinely invite children down to the
> community kitchen in the course of a segment on fractions, adding them,
> dividing them. One quarter teaspoon: how many in a cup?
monastery cook in Japan, and again in England during their changeover to
metric. It was a joke in The Very Last Goon Show of All, in which the
local council was disposing of its supply of pipe lagging (insulation)
because it was feet and inches lagging, and they'd gone metric.)
> But then you would need real recipes, real heat, real risk of injury from
> using equipment.
> Real headaches in other words. We rather just have them
> imagine a kitchen. Do math in your head. Don't make problems for others.
> Parents should teach cooking skills, or at least we have home economics in
> some schools (some do, if property taxes are high). Entirely "not math"
> (home ec). The two faculties are so different. Population demographics,
> Diet for a Small planet, the economics of recycling (or not), the price of
> soy beans in Brazil... not talked about. Plenty mathy, at many levels
> (game theory, simulations...), but politically charged, geographically
> aware, and potentially redolent with "messages" -- or an at least an
> excuse to get kids thinking (e.g. about their diet).
> --
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> "MathFuture" group.
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>
>
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(默雷/निशब्दगर्ज/نشبدگرج)
Cherlin
Silent Thunder is my name, and Children are my nation.
The Cosmos is my dwelling place, the Truth my destination.
http://wiki.sugarlabs.org/go/Replacing_Textbooks
kirby urner
Jan 5, 2013, 1:40:43 AM1/5/13
to mathf...@googlegroups.com
On Fri, Jan 4, 2013 at 5:07 PM, <mok...@earthtreasury.org> wrote:
>> Isn't whistling in the dark a reaction to fear of something being thereIt's much worse when you do know what is there, as with Southern
>> we don't know.
slaveowners' fears of slave uprisings. And worse again when you think you
know but you don't, as with Southern White fears of Reparations.
Yeah, slaveowners weren't about to arm their slaves and invite 'em to form some well organized militia based on their 2nd amendment rights. That wasn't the agenda in those days.
Some find South Park offensive, others gloriously so:
http://www.youtube.com/watch?v=ipujWRYUjS4
I am willing to leave out Tarot, because of its abuse in fortune-telling.
Yes, there is an issue about using anything to do with gambling in
teaching probability. It might possibly be addressed by showing through
probability that gambling is stupid rather than sinful. We could certainly
use sports to create interest in probability and statistics.
I want to follow the story of cards wherever it takes us. Through an Anthropology window I have plenty of patience to examine how people use combinatorics to tease themselves into thinking more profoundly and reflectively about their life situation.
Whether their new certainties about the future pan out is not ours to track as we're not on a war path to prove the should or should not do these things. They do, we start from observation of the species.
> Even an
> axiomatic system is somewhat a role of the dice, in terms of how
> interesting the math is, or, in the case of number crunching on formulas,
> how elaborate the visualizations. [1]
I don't understand what you mean. Mathematicians choose axioms based on
the systems that they generate, not out of the air. There is nothing
probabilistic about it. If it turns out that an axiom system doesn't work
as designed, it is amended (not-Euclidean geometry, for example) or
discarded (naive set theory). I can't make any sense at all of your number
crunching case.
I'm one of those who thinks you can axiomatize just about any game with suitable definitions and nomenclature. Chess, for example, may be presented with axiomatic rules upon which theorems may be based i.e. an optimal set of moves to a checkmate becomes the puzzling part and proofs arise. A mathematics develops, has developed.
Axiomatic systems in general are as multiplicitous and trivial as all the board games at your supermarket, each one axiomatizable. Some are more interesting than others.
A special few are grand and are imagined as great buildings with "foundations". Axioms start sounding more weighty and words like "self evident" gain in importance when you get close to these mental edifices.
Then I was thinking of the Mandelbrot / Mandelbulb algorithms and how some patterns are boringly repetitious whereas others are gloriously chaotic.
Not every game is equally a trade-off twixt dumb luck and pure skill.
Axiomatic systems, games in general, fit many a niche, and partially overlap within the whole of language (the greater game).
> When learning fractions, it would be logical and rhetorically useful to
> spend more time with the different measuring systems, those which divide
> up
> wholes into parts, such as quarts into cups into pints. How do teaspoons
> relate to table spoons? It's all somewhat complicated, mixed base, and
> highly relevant to one's cooking skills and comfort level around food
> prep. So why doesn't the culture routinely invite children down to the
> community kitchen in the course of a segment on fractions, adding them,
> dividing them. One quarter teaspoon: how many in a cup?
This only works in the US. The rest of the world cooks in metric. (I was a
monastery cook in Japan, and again in England during their changeover to
metric. It was a joke in The Very Last Goon Show of All, in which the
local council was disposing of its supply of pipe lagging (insulation)
because it was feet and inches lagging, and they'd gone metric.)
Well, lets remember wherever we may be geographically we have access to the world's recipes and need to decipher their units. If we're in Japan trying to read Joy of Cooking, we have to have our teaspoons.
Cosmopolitan kitchens tend to have the different measuring tools, just so they might be faithful to their sources. All the more reason to get practicing now and to develop that mental flexibility that allows changing units, currencies included.
Similar question:
How many mainstream arithmetic textbooks deal with currencies and exchange rates, including showing the symbols for different currencies? That's an empirical question. I don't know the answer, but I'm not remembering much of such in my own schooling, despite growing up amidst many currencies being used and needing to exchange them.
There's a definite attempt to not tread on others' turf in those math textbooks.
An arithmetic textbook would never talk in any depth or seriousness about banking would it? Little story problems are OK, involving interest. We want them to know about interest and credit cards so word problems about those.
http://www.amazon.com/Pigs-Will-Be-Math-Money/dp/0689812191
So how about a little simulation of a bank, a cartoon, showing how it stays in business? It's a number crunching operation, a kind of computer, based on rules. Surely an investigation of banking should be at the heart of many arithmetic books? Since the Italian Renaissance surely?
Fat chance. I don't think so.
Or check back on Youtube if you can't find one now. Khan Academy?
Is this lack of focus on how banks work (can't be that hard) all because "money is immoral?" No.
It's more that math should be "fun" but kind of "ditzy" (how do you say in English?).
We like to get more dreamy and imaginative in our math classes. More psychedelic some might say.
But that's not boring enough. It's a cross between clinical, dry, and vaguely fantasy-provoking. I'm talking about the aesthetics of mass-published math books and their content (I used to work at a big publisher).
Just doing some Anthropology here (along with some students).
"Why mass published textbooks will never feature the I Ching or playing cards" ties into this.
> But then you would need real recipes, real heat, real risk of injury fromThere are recipes requiring no cooking.
> using equipment.
Yes, many good ones. "Raw vegan magic" is said a lot around here (by one of the other cooks, that's not my specialty, but I partake).
Our faculty cooks in this house, including institutionally (at a nearby community kitchen). One of my co-residents serves by bicycle downtown on Tuesdays.
I consider this part of her math teaching requirement. Our mathematics is active, on duty, physically demanding. The idea that mathematics is primarily seat work is alien in our brand of Math (the brand I'm developing, with a little help from some vegans).
Kirby
http://wikieducator.org/Digital_Math
Bradford Hansen-Smith
Jan 5, 2013, 8:31:30 AM1/5/13
to mathf...@googlegroups.com
Kirby , you never disappoint with your responses. I see the negatives you have rightly mentioned have little to do with math or the pursuit of what is right and good. Maybe you are expanding on your statement about the power of parent to give the child values, and the schools power, or church power, or any other to do as they will, "for your own good." There is a tendency to talk about morals by the display of power in moral position. Fearing lack of power is covered over by whistling in the dark loudest without caring who we trip over. The math situations you described are the stew of the day, rationalizations used to demonstrate power over others. Morals have nothing to do with bad behavior that comes with fear of not having power or authority to control. It is easier to talk about bad things others do than to talk about personal relationship to our highest sense of duty to doing good. Moral behavior is consciousness seeking good, towards truth and higher order understanding. It is about love for others and choosing alignment with universal truths. It is not about denying these things. There are no bad morals. There is no bad math. We just do not teach students the duty and responsibilities that go with being carriers of knowledge. If education is the standard of cultural moral progress, then all schools have failed.
In terms of math, or any part of curriculum
there is nothing that speaks to the issue of ethics in any substantive way, to
say nothing about ideas of moral duty in choosing how we use the knowledge we are
taught. To say moral is choosing between good and bad is too simple, it puts it
on the abstract, we can think about it without having to actually make a choice
and do something. What is moral is the act of doing good, it is not a judgment
about what others do; it is knowing we have that choice. That well may be education at
its best.
Brad
kirby urner
Jan 5, 2013, 1:25:44 PM1/5/13
to mathf...@googlegroups.com
Hi Brad --
We hear a lot about STEM, and various writers, including me, have wanted to add an A, some for Art, me for Anthropology, but either way a door to what's not-STEM to make STEAM complete.
What pre-STEAM math was missing was much "lore" or "story". One had affiliated genres of fiction, such as 'Alice in Wonderland' (written by a logician) and a specific quirky sense of humor, but a math classroom was no place to learn much history. Thumbnail bios would go by (e.g. Galois), but not much sweep of civilization stuff. Roman numerals...
I'm not saying we didn't have a ton of trade books on these topics or that the history was unknown, just that math class was not self conscious about intellectual history and as a result did little to develop critical thinking around the content of the texts.
The inclusion or exclusion of topics was a political discussion taking place outside the classroom's purview. Students were told what they would need to know, and in what sequence, as a result of legislative bodies and advisory boards and so forth. There wasn't much inclusion of students in these debates. Math class was not a time to question the relevance of the content, as one always had the ready tautology: you need this to pass "the test" (whatever test).
With the advent of Youtube, one can make world viewable television for almost no money and it's easy to explore alternative interpretations of what STEM / STEAM might mean. For me, STEM means we get to bounce around in Science, Technology, Engineering, Math without apology i.e. there are no turf barriers we must respect among these subject areas. We go from the CCP's 1, 12, 42, 92... (see OEIS)[1] to the microarchitecture of the virus (follow link) with no thought of "changing subjects" (we're doing Geometry + Geography i.e. principles (timeless) + times & places (= events, sometimes fictions (e.g. in fictional geographies, like Middle Earth / New Zealand)).
In my ("my") Youtubes, we'll break the rules in various subtle (and obvious) ways, showing "classrooms" that don't match the usual mental pictures. This isn't a new idea. Science fiction like 'Serenity' have their classroom scenes.[2] Every kid had a tablet computer in that one. They might have a different style dress, hard to place. They might do target practice with crossbow next, with math tied in (principle of least action etc.).
Cooking is part of STEM. If you don't know how to cook, you're hardly a STEM teacher.
Weird. Is that Portland?[3] How does a culture get from there to here?
Given it's TV, we don't have to always answer those questions up front. Just present the results. Like magic. But of course, behind the scenes, wheels had to turn, meetings had to happen, funds had to be raised, etc., etc. That's a lot of boring back stage "making of" detail we don't need in the clips themselves necessarily (could be extra features for the DVDs).
We'll show kids other kids (their apparent peers) learning new things. Cooking with tetra-volumes even, with polyhedral mixing bowls, simple volume ratios. Weird. Kinda fun.
Kirby
[1] http://oeis.org/A005901 (Urner, K. in the links section)
[2] http://youtu.be/pRnIJM8NGok (movie trailer but no flashback to school with tablets)
[3] filmed in rural Oregon too, e.g. near Fossil, other places (storyboards galore)
http://www.flickr.com/photos/kirbyurner/8346677628/in/photostream/ (raw vegan magic -- kraut, in process)
We hear a lot about STEM, and various writers, including me, have wanted to add an A, some for Art, me for Anthropology, but either way a door to what's not-STEM to make STEAM complete.
What pre-STEAM math was missing was much "lore" or "story". One had affiliated genres of fiction, such as 'Alice in Wonderland' (written by a logician) and a specific quirky sense of humor, but a math classroom was no place to learn much history. Thumbnail bios would go by (e.g. Galois), but not much sweep of civilization stuff. Roman numerals...
I'm not saying we didn't have a ton of trade books on these topics or that the history was unknown, just that math class was not self conscious about intellectual history and as a result did little to develop critical thinking around the content of the texts.
The inclusion or exclusion of topics was a political discussion taking place outside the classroom's purview. Students were told what they would need to know, and in what sequence, as a result of legislative bodies and advisory boards and so forth. There wasn't much inclusion of students in these debates. Math class was not a time to question the relevance of the content, as one always had the ready tautology: you need this to pass "the test" (whatever test).
With the advent of Youtube, one can make world viewable television for almost no money and it's easy to explore alternative interpretations of what STEM / STEAM might mean. For me, STEM means we get to bounce around in Science, Technology, Engineering, Math without apology i.e. there are no turf barriers we must respect among these subject areas. We go from the CCP's 1, 12, 42, 92... (see OEIS)[1] to the microarchitecture of the virus (follow link) with no thought of "changing subjects" (we're doing Geometry + Geography i.e. principles (timeless) + times & places (= events, sometimes fictions (e.g. in fictional geographies, like Middle Earth / New Zealand)).
In my ("my") Youtubes, we'll break the rules in various subtle (and obvious) ways, showing "classrooms" that don't match the usual mental pictures. This isn't a new idea. Science fiction like 'Serenity' have their classroom scenes.[2] Every kid had a tablet computer in that one. They might have a different style dress, hard to place. They might do target practice with crossbow next, with math tied in (principle of least action etc.).
Cooking is part of STEM. If you don't know how to cook, you're hardly a STEM teacher.
Weird. Is that Portland?[3] How does a culture get from there to here?
Given it's TV, we don't have to always answer those questions up front. Just present the results. Like magic. But of course, behind the scenes, wheels had to turn, meetings had to happen, funds had to be raised, etc., etc. That's a lot of boring back stage "making of" detail we don't need in the clips themselves necessarily (could be extra features for the DVDs).
We'll show kids other kids (their apparent peers) learning new things. Cooking with tetra-volumes even, with polyhedral mixing bowls, simple volume ratios. Weird. Kinda fun.
Kirby
[1] http://oeis.org/A005901 (Urner, K. in the links section)
[2] http://youtu.be/pRnIJM8NGok (movie trailer but no flashback to school with tablets)
[3] filmed in rural Oregon too, e.g. near Fossil, other places (storyboards galore)
http://www.flickr.com/photos/kirbyurner/8346677628/in/photostream/ (raw vegan magic -- kraut, in process)
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