Why doesn't Monopoly have a calculator piece?
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@Gąska said in Why doesn't Monopoly have a calculator piece?:
@Bulb said in Why doesn't Monopoly have a calculator piece?:
and the task needs to be designed so that you can't find ready made solution anywhere and have to show some skill and understanding whatever you use
Step 1: block WolframAlpha.
Step 2: block all proxies that allow access to WolframAlpha.
Step 3: block all WolframAlpha ripoffs.
Step 4: block everything that allows non-HTTP connection that would make it possible to bypass your block on WolframAlpha.
Step 5: block all methods of removing the 4 blocks mentioned above.
Because if you don't block WolframAlpha, you might as well not bother with the test and give A+ to everyone.Three words:
Show your work
WolframAlpha, like Mathematica back when I was in uni, excels at giving you the answers but doesn't generally tell you how it arrived at them.
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@Gąska I suppose there are people who would pay to be able to cheat. I don't know what it outputs, so I don't know if it would fool the teacher - if it completes the square manually rather than applying the standard formula, that would make most teachers suspicious.
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@PleegWat said in Why doesn't Monopoly have a calculator piece?:
@Gąska I suppose there are people who would pay to be able to cheat.
It's not that expensive, either. Especially compared with private lessons.
I don't know what it outputs, so I don't know if it would fool the teacher - if it completes the square manually rather than applying the standard formula, that would make most teachers suspicious.
It does apply standard formulas.
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3x² + 17x - 8 = 0 x = (-17 ± √(17²-4*3*-8))/(2*3) = (-17 ± √(289+96))/6 = (-17 ± √385)/6or
3x² + 17x - 8 = 0 x² + (17/3)x = 8/3 (x + 17/6)² = 8/3 + 289/36 = (96 + 289)/36 = 385/36 x + 17/6 = ± √(385/36) x = -17/6 ± √385/6
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@PleegWat That took me longer than it should have. But then, I don't think in school they ever gave me one where the root didn't work out.
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@PleegWat said in [Why doesn't Monopoly have a calculator piece?]
I don't think in school they ever gave me one where the root didn't work out.
I wonder why that is …
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@Bulb The best solution is word problems. If you don't understand the material, you won't know what to put into Wolfram Alpha in the first place.
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@pie_flavor As in: “If a car travels at 50 km/h, how long does it take to go from town A to town B if these are 50 km apart?”?
That kind of questions have come under criticism in this country in recent years because (IIRC) the opinion is that they’re being over-used, and therefore overly obstruct kids who could do the maths if it’s presented as a maths problem, but are not good at reading comprehension.
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@Gąska said in Why doesn't Monopoly have a calculator piece?:
@Bulb it can solve any integral, polynomial, and differential equation you want, and it's very permissive in how you write the query. It even prints out all the steps required.
There are many cases where WolframAlpha is basically useless (for educational purposes). I can't remember how exactly right now, but it is trivial to design exercises so that WolframAlpha misses the point of the exercise.
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@PleegWat said in Why doesn't Monopoly have a calculator piece?:
@Gąska I suppose there are people who would pay to be able to cheat. I don't know what it outputs, so I don't know if it would fool the teacher - if it completes the square manually rather than applying the standard formula, that would make most teachers suspicious.
In my experience (ie. using WolframAlpha as an aid to help me work out what I did wrong) there are loads of instances where WolframAlpha provides a step by step solution that reeks of "computer algorithm" from miles away. Of course it requires teachers to actually put in the effort to design non-WolframAlpha-solvable exercises
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@admiral_p As I suggested above, I've never actually tried WA for that since it's a paid feature. In my university days it wasn't around yet, but I do recall how mathematica would only give you the answer, and usually not in anything like the formulation you'd get if you worked it out yourself.
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@PleegWat I tried the premium version a few years ago when they provided a free trial. Not worth the money really. And anyway. High school or even university calculus, at least for engineers, is basically solved through patterns. Multiply divide, factorise, add and subtract, etc. and with practice you learn to recognise what you have to do straight away.
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@Gurth said in Why doesn't Monopoly have a calculator piece?:
@pie_flavor As in: “If a car travels at 50 km/h, how long does it take to go from town A to town B if these are 50 km apart?”?
That kind of questions have come under criticism in this country in recent years because (IIRC) the opinion is that they’re being over-used, and therefore overly obstruct kids who could do the maths if it’s presented as a maths problem, but are not good at reading comprehension.
I don't see the problem.
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@Gurth said in Why doesn't Monopoly have a calculator piece?:
@pie_flavor As in: “If a car travels at 50 km/h, how long does it take to go from town A to town B if these are 50 km apart?”?
That kind of questions have come under criticism in this country in recent years because (IIRC) the opinion is that they’re being over-used, and therefore overly obstruct kids who could do the maths if it’s presented as a maths problem, but are not good at reading comprehension.
And I would walk 500 miles, and I would walk 500 more:
@error_bot !wa "500 miles / (walking speed * 8 hours a day)"
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Wolfram|Alpha said:
Input interpretation
Result
Unit conversions
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@admiral_p said in Why doesn't Monopoly have a calculator piece?:
Of course it requires teachers to actually put in the effort to design non-WolframAlpha-solvable exercises
The problem with that approach is also that, for teaching purposes, you sometimes need to give the students problems that are easily solvable by a calculator (or WA), because this is how they're going to learn the basic rules.
I mean, if you go back to maths in primary schools, if children could use a calculator instead of learning how to do a simple sum, they would fail at so many things afterwards. So even though asking students to compute "42 + 24" is more than trivial with a calculator or similar, at one point you have to go through that kind of problem by hand to make sure they learn. Which doesn't mean that they'll keep doing the sums manually, after a few years (when they've learnt how to do it well enough to be able to build on that) it's OK to use a calculator, but not initially.
That one was a trivial example, but it's easy to find more at all levels. Working with fractions, solving a quadratic polynomial, deriving or integrating a simple function... They're all used in more advanced maths/physics/science so even though once learnt they are obvious to do with a machine, at one point in the learning process you need to ensure that pupils know how to do it themselves.
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@remi ...which is why even calculators are often banned outright (at least in my experience). When they aren't, it's because it doesn't matter any more or because some things are supposed to be done with a calculator. And anyway, if a student writes 0.707... instead of √2/2, you all know what that means. (Apart from also being wrong, because there is no other way of writing √2/2 just like there is no other way of writing π). Now this is an easy example, but in many instances WolframAlpha provides calculations instead of exact forms.
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By the way, I don't know how things are done abroad, but here in Italy, we have at least three oral tests ("interrogations") and three written tests per term. Students are expected to solve problems at the blackboard, as well as proving theorems and stuff. It would be trivial for a teacher to select a student he or she suspects of having cheated and ask him to do something similar to what was in the test there and then. You could easily count that as an oral test (when to test students is up to the teacher's discretion, you are expected to be always ready to take one). Or, with sufficient doubt, discard his written test and ask the student to take it again.
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@admiral_p said in Why doesn't Monopoly have a calculator piece?:
@remi ...which is why even calculators are often banned outright (at least in my experience). When they aren't, it's because it doesn't matter any more or because some things are supposed to be done with a calculator.
... aaaaaand we're circling back to the reason why WA was first mentioned in this thread. Sometimes you're working with intermediate concepts that are still easy for WA to solve for you, but that are also made easier by allowing calculators for some of the steps, because some of them are not ultra-basic (I don't know, for example if you're doing some combinatorics, without a calculator that can do
n!that becomes tedious very quickly, unless you stick to tiny numbers that may make problems too simplistic).So sometimes it better for teaching to allow calculators (so that you can test the concept of the day, not whether pupils are good at doing arithmetic on paper), but you don't want to allow them access to something like WA that will solve the whole problem for them. Hence TIs/Casios as discussed upthread.
just like there is no other way of writing π
<
>
You could use a formula whose value is π, like (first one I found on wiki):
But then you could argue that this isn't π, just a formula that yields it, but then what else is π if not some abstract symbol that stands for the actual number, and how different is that from a formula?
</ >(I'm not really interested in that discussion though, I just said that in passing because
)
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@Gurth said in Why doesn't Monopoly have a calculator piece?:
@pie_flavor As in: “If a car travels at 50 km/h, how long does it take to go from town A to town B if these are 50 km apart?”?
That kind of questions have come under criticism in this country in recent years because (IIRC) the opinion is that they’re being over-used, and therefore overly obstruct kids who could do the maths if it’s presented as a maths problem, but are not good at reading comprehension.
Doing the math without being able to do the formalization is pointless anyway. Math is not an end unto itself, it is a tool for analyzing things and those things will invariably be described either by rather vague words, a picture, or demonstrated. So you have to learn to find the math in the description and use it to learn something about the situation.
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@Bulb Many pure mathematicians would disagree. They tend to look down on any form of application of math to non-math purposes, and need no justification further than "that's a neat formalism".
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@dkf computer scientists seem so down to earth in comparison. Even if you remember they've invented Haskell.
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@Bulb said in Why doesn't Monopoly have a calculator piece?:
@Gurth said in Why doesn't Monopoly have a calculator piece?:
@pie_flavor As in: “If a car travels at 50 km/h, how long does it take to go from town A to town B if these are 50 km apart?”?
That kind of questions have come under criticism in this country in recent years because (IIRC) the opinion is that they’re being over-used, and therefore overly obstruct kids who could do the maths if it’s presented as a maths problem, but are not good at reading comprehension.
Doing the math without being able to do the formalization is pointless anyway. Math is not an end unto itself, it is a tool for analyzing things and those things will invariably be described either by rather vague words, a picture, or demonstrated. So you have to learn to find the math in the description and use it to learn something about the situation.
And then the pupils go on to complain that they'll never need math in life, anyway. Well, they would, if they hadn't flunked the word problems and realized when the math actually applies to their problems at hand.
Seen this often enough in adults.@dkf said in Why doesn't Monopoly have a calculator piece?:
@Bulb Many pure mathematicians would disagree. They tend to look down on any form of application of math to non-math purposes, and need no justification further than "that's a neat formalism".
Looking down on anybody who's below you in the ivory tower is fine until you run out of oxygen.
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@topspin said in Why doesn't Monopoly have a calculator piece?:
@dkf said in Why doesn't Monopoly have a calculator piece?:
Many pure mathematicians would disagree. They tend to look down on any form of application of math to non-math purposes, and need no justification further than "that's a neat formalism".
Looking down on anybody who's below you in the ivory tower is fine until you run out of oxygen.
I see that you have met some pure mathematicians!
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@Gąska said in Why doesn't Monopoly have a calculator piece?:
Even if you remember they've invented Haskell.
But Haskell was meant to be used. Otherwise they'd have just stopped at lambda calculus and called it a day.
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@remi said in Why doesn't Monopoly have a calculator piece?:
I might be missing something, but this caught my eye already last week when it was first posted.
Isn't that integral for the area of half the unit circle? In which case it's off by a factor 2.
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@topspin yeah, that's my point. We laugh at those egg heads in academia with zero real life programming experience, but unlike their colleagues in math faculty, they actually made something.
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@PleegWat said in Why doesn't Monopoly have a calculator piece?:
I might be missing something
Likely the "1/". The radicand is in the denominator.
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Not sure what that integral is based on then.
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@Bulb said in Why doesn't Monopoly have a calculator piece?:
@Gurth said in Why doesn't Monopoly have a calculator piece?:
@pie_flavor As in: “If a car travels at 50 km/h, how long does it take to go from town A to town B if these are 50 km apart?”?
That kind of questions have come under criticism in this country in recent years because (IIRC) the opinion is that they’re being over-used, and therefore overly obstruct kids who could do the maths if it’s presented as a maths problem, but are not good at reading comprehension.
Doing the math without being able to do the formalization is pointless anyway.
The criticism isn’t that there should be no problems where everything is wrapped up in a story, but that that method is being overused. There were arguments for a better balance between doing/showing the actual mathematics and putting them into more words.
@dkf said in Why doesn't Monopoly have a calculator piece?:
@Bulb Many pure mathematicians would disagree. They tend to look down on any form of application of math to non-math purposes, and need no justification further than "that's a neat formalism".
How do these people work out if their shopping bill is correct, or when to leave to get somewhere on time?
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For example, one may directly compute the arc length of the top half of the unit circle, given in Cartesian coordinates by the equation x2 + y2 = 1, as the integral:[11]
I didn't check the maths, I assumed Wikipedia has enough money for someone else to do it.
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@dkf said in Why doesn't Monopoly have a calculator piece?:
@Bulb Many pure mathematicians would disagree. They tend to look down on any form of application of math to non-math purposes
A mathematician friend told me the story of a tenured cohomologist who reflected contentedly that he had chosen a field which was of no use to anyone. Then he was watching an interview with someone who had worked on the Apollo project and said, "We just couldn't have done it without cohomology." The cohomologist then abandoned math and took up the violin.
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@jinpa said in Why doesn't Monopoly have a calculator piece?:
cohomology
Como (no) … cohomo (have I got that right? yes) … cohomology …?
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homology. Some versions of cohomology arise by dualizing the construction of homology. In other words, cochains are functions on the group of chains in homology theory.
I can now certainly see why the cohomologist abandoned maths and took up the violin.
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@dkf said in Why doesn't Monopoly have a calculator piece?:
@Bulb Many pure mathematicians would disagree. They tend to look down on any form of application of math to non-math purposes, and need no justification further than "that's a neat formalism".
How do these people work out if their shopping bill is correct, or when to leave to get somewhere on time?
They don't. That is what cashiers, self-checkout registers and Google Maps are for. (lol)
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@Gurth said in Why doesn't Monopoly have a calculator piece?:
@jinpa said in Why doesn't Monopoly have a calculator piece?:
cohomology
Como (no) … cohomo (have I got that right? yes) … cohomology …?
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homology. Some versions of cohomology arise by dualizing the construction of homology. In other words, cochains are functions on the group of chains in homology theory.
Cricket thread is
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@Gurth said in Why doesn't Monopoly have a calculator piece?:
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homology. Some versions of cohomology arise by dualizing the construction of homology. In other words, cochains are functions on the group of chains in homology theory.
Would someone please explain cricket to me? While speaking Punjabi? I'll probably understand more of that explanation than this one.
Edit:
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@Bulb said in Why doesn't Monopoly have a calculator piece?:
but it's true that when I looked for something on Android some time ago, the choice was pretty bad.
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@Tsaukpaetra I was looking for something that can understand equations like
sqrt(1000 ft * gee) / 2 to knots. qalculate can (sqrt((1000 * foot) * gee) / 2 = approx. 53.137283 knots). It has a console and Qt UI, but unfortunately Linux only:
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@Bulb said in Why doesn't Monopoly have a calculator piece?:
It has a console and Qt UI, but unfortunately Linux only
There's a windows binary on the page you linked, though!?
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@HardwareGeek said in Why doesn't Monopoly have a calculator piece?:
@Gurth said in Why doesn't Monopoly have a calculator piece?:
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homology. Some versions of cohomology arise by dualizing the construction of homology. In other words, cochains are functions on the group of chains in homology theory.
Would someone please explain cricket to me? While speaking Punjabi? I'll probably understand more of that explanation than this one.
Yeah, I gave up on the rest of the article (I got it from Wikipedia) after I couldn’t make heads or tails of the introduction either. TBH it reminded me of the bridge column I used to read every week in a magazine about twenty years ago: I knew the meaning of every word in it (which is more than I can say of the text above), yet comprehended nothing whatsoever of the things being explained. I kept reading it for the amusement value of that experience.
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@Bulb said in Why doesn't Monopoly have a calculator piece?:
@Tsaukpaetra I was looking for something that can understand equations like
sqrt(1000 ft * gee) / 2 to knots.Interesting, I decided to see if macOS Spotlight can, given that it has a built-in calculator. It refuses to do much of anything with the formula above, but just “1000 ft” produces:
Making it more complicated, though, such as by just adding “* 2” after the above, confuses it and results only in files, email messages etc. that contain “1000”, “ft” or similar.
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@topspin said in Why doesn't Monopoly have a calculator piece?:
There's a windows binary on the page you linked, though!?
Well, I use Linux even at work now and last time I wanted it on Windows it wasn't there yet. Good to know.
Also it looks like they made some progress lately even to the point that
Qalculate! version 3.6.0
[…]
A binary snap package, with all dependencies included, is available at snapcraft.io/qalculate for those using a slow moving GNU/Linux distribution$ qalculate --version 2.8.2I guess it's my case even though I've updated to Ermine about a month ago.
