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Stop teaching calculating; Start teaching math

152 points by p4bl0 14y ago

deleted 14y ago
[deleted]
kzahel 14y ago
Enjoyed skimming your article. If only more geeks actually wanted to teach kids... unfortunately most of us will only be able to do that once we've retired!
- ZoFreX 14y ago
  If I went back into education for 2 more years, piled more student debt on top of myself, not to mention living like a student again, PLUS having to have a part-time job while studying (while the loan is bigger for a PGCE, the costs of living are much much higher), and then got a job as a teacher, worked my ass off for 10 years, I would, if I was lucky, be earning the same salary I am today, a couple of years after leaving university. Sounds like a great fucking deal to me.
  - alexqgb 14y ago
    This cannot be upvoted hard enough. Education would reform itself overnight if teachers were hired from the top third of high school classes, not the bottom two thirds, and paid salaries that started ~$70k and reached ~$100k in five years if they were good. Students struggle because you have to be a saint or an idiot to teach under the conditions currently imposed. We don't have nearly enough of the former, and way too many of the latter. I have a really hard time imagining that brain-dead curriculum boards and mediocre administrators would sustain their death grip on a profession suddenly flooded with really sharp, well paid, professionals.
    - aggronn 14y ago
      Imagine the change in classroom atmosphere if teachers had the same social credibility as professors did (or more aptly, if high school teachers had the same respect and admiration from students as kindergarten teachers)
uncoder0 14y ago
Added to the reading list. I've been saying this for quite a while. I think we were able to capture this in our 9th grade math games we have been working on.
angersock 14y ago
I'm a bit concerned, as the article doesn't seem to cleanly define--and this may be just poor reading on my part--whether the idea is to use computers to expand math education (say, for solving large and complex problems), or to supplant entirely the teaching of calculation. It would seem to me that being able to perform basic arithmetic and algebra, by hand, is sort of a simple skill I would expect everyone to do. Computers are amazing devices, but not being proficient in doing those operations yourself when a computer or calculator is unavailable is not so good.
drewrv 14y ago
It's sad how many people think that math is arithmetic, and that if we let kids use computers or calculators then they're not "doing math". Not just the general public but PTA leaders, school board members, and school administrators.
- ShabbyDoo 14y ago
  I live in a relatively wealthy school district in Ohio where the schools generally are well-regarded. Last year, I went to the schools "parents math night". I had expected to be exasperated by, you know, those idiots who will be teaching my children (my older son is entering first grade this fall). However, I ended up impressed with the teachers and disappointed by the parents in attendance. The school had chosen the "Connected Math" curricula (connectedmath.msu.edu) for its middle school math program, and some parents were outraged that Little Johnny wasn't learning long division (or whatever). Their arguments could be summed up as, "Well, that's not the way we learned it." I angered the other parents by playing a bit dumb and asking for a short description of the curriculum. Then, I stated loudly that it "sounded delightful." The teachers barely contain their smiles. I ordered a couple of the books in used form from Amazon to see for myself, and I think I would have found the exercises fun as a middle schooler. I really wanted to ask the parents doing the complaining, "Don't you love your children? You pay more for a house just because it's in this school district, and then you lobby to dumb-down the math curriculum?"
- weaksauce 14y ago
  The problem is that the textbooks are teaching calculation. So in this instance "doing math" is calculating some equation. Solve some equation is easier to write in a textbook than an unambiguous word problem that a grad student needs to solve and put the answers in the back of the book and in the teachers solution manual. Not to mention that the math teachers are not always the best.
slowpoke 14y ago
I think he argues from the wrong point. Yes, we need to teach math, not calculating. No, the argument is not "because we can do calculating with computers today". Lockhart got it right in his famous lament - the problem is that we face a system of self-sustaining bullshit that actually thinks it's teaching math. My guess is that Conrad Wolfram probably plans to conveniently also sell the accompanying software for this new education, which would make it natural for him to focus on this point. I actually agree that computers can help us educate people better, and that we need to create appropriate software for this. But my concern would then be that such software must be free/libre. No compromise. We cannot risk the education of future generations to be locked into $corporation's proprietary products.
- ljd 14y ago
  I recently had the experience of helping a young algebra student with her homework. She is very bright and is in an accelerated math program that teaches algebra in the 7th grade. However, it was so disappointing to see the curriculum. I was in the same accelerated program 15 years ago and the curriculum hadn't changed a bit. It was still vague and unhelpful. They sent her home for the summer with a large packet of problems to solve without any explanation how to solve them. I majored in math and I still had to guess at what the worksheets were asking the student to do. They used vague variables and were essentially just teaching rote memorization. It reminded me of my own confusion in mathematics when I was growing up, how one year a variable would mean one thing and the next year it would mean something else. "Solve and explain," means just as little to me now, using math on a daily basis, as it did to the 11 year old version of me. After so many years, it would have been nice to see the curriculum focus more on application of mathematics and less on how to memorize and calculate.
  - numeromancer 14y ago
    I've noticed the same thing in all the school curricula I've seen. The word problems are often vague, and all to often completely ambiguous. They require guessing what the question writer had in mind when she wrote the question, which are usually unstated assumptions that apply only to the way math is done in schools. This is not the way to teach the kind of precise thinking and careful definition of terms that one needs to understand why math is the way it is: the “study of precisely defined objects.” Teachers, if you want your pupils to understand how to create a mathematical problem from a description of a practical one, you must train them first to state the situation with absolute precision and without ambiguity. The best way to do that is, as in the teaching of all virtues, to fastidiously follow that habit yourself. That the questions in math textbooks fail to do that so often is another sign of the enormous institutionality of our education problems.
vph 14y ago
Of course, his main point is to advocate for using computers to teach and learn math; he's selling Mathematica/Wolfram Alpha. But this is dangerous and a little shallow. And here is why. Math is the language of science; just like a C -- or any other programming language -- is a language of computing; just like English is a language of humans. There are many ways to learn a language, but I think they all have something in common. You have to spend a lot of time learning, reading and writing. The writing is quite important. You have to write the language to be good at it. The thing about math is that currently to write as it is supposed to look like can only be done most conveniently on paper. Writing a math formula in Mathematica or Wolfram alpha requires a latex-like mini language, another thing to learn, and can be disrupting. This fact alone means that computers can only supplement; and they can be an excellent supplement. But it can not replace doing math by hands, on papers, particularly for those who are learning this new language.
- UK-AL 14y ago
  Err. This what he saying, you focus more on manipulating equations in the language of maths such as algebra, calculus, and less time on remembering what's the answer to 7 * 8.
  - anonymoushn 14y ago
    Is this really a win? For most small problems or subproblems, a person who has solved similar problems many times before can solve it mentally much more quickly than by consulting a computer.
    - UK-AL 14y ago
      But one produces engineers, the other produces shop assistants.
      - anonymoushn 14y ago
        Which is which? A person who works in either role will do so more quickly by virtue of not needing to constantly consult a machine over trivial problems.
p4bl0 14y ago
I remember reading an article about almost the same topic by Felleisen, maybe Flatt, maybe Culpepper and some others from the PLT group, it was about using DrRacket to teach maths, there was an example involving the take-off of a rocket iirc. Is anyone able to find it? I don't remember the title nor where it was published.
- abecedarius 14y ago
  Sounds like http://world.cs.brown.edu/ http://world.cs.brown.edu/
  - p4bl0 14y ago
    Thanks but no, it was an article not a book, I think it was in a PDF that I read on scribd or Google Docs Viewer. edit: I feel like the title was something a little disruptive.
- fscof 14y ago
  I really like the idea of teaching math in tandem with elementary programming. It demystifies writing code and can be very helpful in teaching important math concepts like functions, variables and graphing. At the very least, exposure to programming at an early age will get more kids interested in the subject. Does anyone know of good examples of schools that are already doing this with something like Dr Racket?
  - takikawa 14y ago
    I think you'd be interested in Bootstrap World, which is basically what you described: http://www.bootstrapworld.org/ http://www.bootstrapworld.org/
- p4bl0 14y ago
  FOUND IT! The article was called "Computer Science Doesn't Matter" (ya, a little disruptive, like I said) you can find it here: http://www.cs.brown.edu/~sk/Publications/Papers/Published/fk-why-cs-doesnt-matter/paper.pdf http://www.cs.brown.edu/~sk/Publications/Papers/Published/fk...
RyanMcGreal 14y ago
In high school physics about 22 years ago, we did an experiment to calculate the acceleration due to gravity by repeatedly dropping a weight with a ticker tape attached to it that fed through a hole punch tool and measuring the spacing of the holes in the tape over time. As part of the analysis and write-up, we had to calculate the standard deviation across our sample runs. That seemed really tedious to me, so I wrote a program in BASIC that took a data file, ran the calculations and saved the results. I recall a certain to-do as the school deliberated over whether this was an acceptable way to complete the assignment, and I was asked to include the source code for my program so the teacher could determine that I understood the concept well enough to program it.
- bostonvaulter2 14y ago
  I think it would be cool if calculators weren't allowed in school unless you programmed them yourself. Now trying to enforce that might be difficult but it is an interesting idea.
magice 14y ago
This is sad. Really sad. My personal opinion is that Americans just dislike academic matters so much that they are incapable of forming a coherent solution for their children's schooling. Let me tell you some personal anecdotes. I moved to Minnesota during my High school senior year from Vietnam. It sucked: I couldn't hold on to conversations, and people couldn't understand my pronunciation; so I was bored and very lonely. You know what I do during my lunch time? Trying to re-prove Fermat's Last Theorem. Is there any "real world" application of that? Well, there may be, but I don't care. It was fun. You know how people listen to (and rock to) puke music on buses? I rode bus a lot during my college years, and spent that time wreaking my brain to work on various NP complete problems (my favorite is the man-woman-dog matching :D). Do I know it is beyond my capacity? Yes. Do I care about any real world problem of it? No. Why did I do it then? It's fun. It killed time. I still do this from time to time during meetings at work. When you think about it, most of math, or most of the academia for that matter, is not readily applicable. True, people use calculus to build Hoover Dam, but the effect of that information on whether or not a student likes math is equivalent of a political speech to a person political orientation: either you already like it (math/Obama) and cheer for it, or you already hate it (math/Obama) and boo/ignore it. These things, by itself, can't change a person's opinion regarding the big picture. You know why I like doing math in my free time? Because I have done a whole load of it. Vietnamese High School graduates are required to learn around sophomore math level in American college (and I fully expect most other East Asian systems to be the same). This explains neatly why Asian students are "smart." They freaking know the things already. Furthermore, the learning of math there involved an absurd amount of drill (compared to American high schools). Oh, calculators are banned until high school, and graphing calculators are banned. Period. Now, should that not make me abhor math? I mean, slaving myself so much time over such stupid and abstract matter must bore me to death, right? Actually, the opposite happened. It's like taste bud. You rebuild your taste bud every so often, so if you have been eating a whole load of broccoli lately, you will start to like broccoli. Yeah, after the first few days, you can't even digest to crap. However, after a few months, you can't digest without broccoli. Humans are adaptable. Do a lot of math, and you will like it. This also speaks of the problem with calculators and computers. The problem is no so much that they dump down math. The problem is that they alienate the students from math. When you do math, all of it, the result is made of your sweat. It may be wrong, but it's yours. It may be stupid and winded and long and whatnots, but it's yours. It's personal. I remember once, during 5th grade (yes, elementary school), there was this problem that I just could not solve, and we were kicked out of class for lunch break. Walking out, I cling to the teacher and cried out of frustration. The same frustration that keeps me up at nights when some stupid bugs could not be fixed. Must be the same frustration that all artisans experience at challenges. It's the indication of the bond that I have with my work, MY math, and it necessitates the toil, the slaving, the mind-numbing work of calculation. I hope you see my point: there is no elevator to interest in math. Math lovers must have toiled and slaved over stupid calculation over and over, until a point that they could actually produce the trace of math working, just like the zone in programming or any other art. That trace, that focus, that absorption builds the love for math. Of course, this means that the students must fist cross the initial barrier of math, just like the first few days of broccoli eating. In Asian cultures, academia is a point of pride. Parents take enormous pride in their children's academia success. Schools take enormous pride in their students' academia achievements. Think about football in American high schools. It's something similar. Study well, perform well in competition, and a student will enjoy numerous privileges and honors that is just unattainable through any other mean. The whole culture rates academia above any other activities, and use that as the measure for potential success. Playing sport well will earn praise, but it is understood to be temporary, fast passing. Studying well, and people will talk about how you will got to such and such colleges, and will become such and such person in the future. It's just different. Back to problem of American math schooling. Here is my prescription: just make the damn students do it. Require them to work on math. Forget about the whole, um, personality and uniqueness and whatnots. You know where these things are from? The toil of work (for students, that's studying) builds personality, values, and one's importance and uniqueness. You know where self esteem is from? It's from holding a piece of paper on which a problem has been solved and solution has been neatly presented; it's from the overcoming of frustration and challenges that the problem presents. Artisans take pride and esteem in their works. Students take pride and esteem in their tests and homework (except when you tell them that the football players will get the praise, the money, and the sex, and only these 3 things matter). Stop worrying about overworking them. Actually, overwork them to the ground. Leave them no energy and time to experiment with drugs and sex and alcohol. It takes challenges and toil to make a person. Stop taking these things away from the youngsters!
hybridthesis 14y ago
I noticed a few of articles on Hacker News has been about math recently. According to Google Trends, math is also rising in popularity, especially in US. I think math is even more appealing to programmers. You are allowed to assume that certain things happen. You may define a set on the fly and all of a sudden, the set is populated without pressing a single key. Let me try, {prime numbers}. There, I got an infinitely large data structure. I hope HN doesn't crash after posting this comment. As programmers, we put abstract ideas into implementations. Math seems to forgo all of that. Everything just happens magically as long as your mind can wrap around it and you have a precise definition for it. No debugging. Isn't this a dream? So I am wondering if there's a community of programmers who have turned to devote their time to math. Like the video said, computer frees you from computation. Hence, it makes sense for math's popularity to rise, especially since we got more people interested in programming. Math seems like the natural next step. I don't have any hard data about this, just my intuition.
felipellrocha 14y ago
On one end you will hear people equate math to calculating, this is almost exclusively how math is taught in school today, and on the other, people like to talk about math ideas, and how we shouldn't really teach people how to calculate anymore since we got computers for that. Like in many aspects of life, learning math is about balance. In truth, people should learn from both areas simultaneously, since they are mutually connected. Calculating is a tool that makes you a better problem solver, and being a problem solver will allow you to find new tools to calculate faster. You can't separate either discipline from one another. In my view, I think students should take one calculation, and one deeper math class a year starting in high school. That wat they could delve deeper in learning how to calculate (learning different methods for multiplication that might come in handy when doing mental math, for example), and start dealing with real, thought-heavy math from an earlier grade (learning about combinatorics, graph, game, and probability theory early in high school, etc).
- wtetzner 14y ago
  I would say, stop concentrating on calculation, and teach math. However, calculation is often a useful way to ensure you understand something. So, calculation will likely still be a part of learning math, but it shouldn't be the focus.
scoith 14y ago
He's basically trying to sell Mathematica.
scoith 14y ago
His talk is fundamentally wrong. Turning real life problems into a mathematical form (in other words, modelling) is not a subject of mathematics.
- dinkumthinkum 14y ago
  To be fair, I disagree with his position, but he is willing to call it something else, but the end of the day it is to teach his proposal as opposed what we now teach.
  - scoith 14y ago
    Using computers. And with computers, he means Mathematica.
brr 14y ago
"And, of course, as we all know, with a computer you can take a simple problem like solve 5x2+2x+1=7 but you can make it harder, for example solve 5x4+2x+1=7. The principle of the problem is still the same." This is not, in fact, true for polynomial equations of order greater than four. From Wikipedia, "the Abel–Ruffini theorem states that there is no general algebraic solution... to polynomial equations of degree five or higher." This is often featured as one of the main results in an undergraduate abstract algebra course. I'm all for automating calculations, but the algorithms behind calculations and their proofs are important and often fascinating. Handing students an implementation of such algorithms, e.g. Mathematica, takes away their opportunity to code up the algorithms and understand them deeply. Edit: Wording
- csense 14y ago
  For that matter, asking students at the high school level to derive the quadratic formula will likely be quite challenging for even the best students in the class. Asking students to come up with the formulas for 3rd or 4th degree polynomials on their own is probably going to be beyond anyone below the very top tier of human capability. A teacher would be extremely lucky to see one or two students that can do this in their career. Then again, most people could easily solve these problems if they know what terms to Google :) Anyway, as I recall the third- and fourth-degree cases require clever substitutions (whereas the derivation of QF is just completing the square with general coefficients).
csense 14y ago
Mathematicians are basically just accountants, right? And the IRS has gazillions of accountants who only really work during tax season...so, if our math programs suck, let's move our tax due date to overlap with schools' summer break, fire all the math teachers and replace them with those IRS guys! It might be better than the existing system and it could hardly be worse. There's already been some work done on a curriculum (warning: PDF link): http://www.cs.amherst.edu/~djv/irs.pdf http://www.cs.amherst.edu/~djv/irs.pdf
dinkumthinkum 14y ago
I didn't really see much specific stuff here, to be honest. There was some program that you could use sliders to figure the best life insurance policy ... I mean, ok ... that's great ... What's the big deal again? What are some specific examples. There's all this "wah schools only teach calculation." Well, what specifically are they teaching that is bad and what specifically should they teach that is better? So, are we saying, no reason for a student to know how to take a derivative, they should know how to turn the knobs on some program to figure out the best fuel efficiency of some device in some really neat simulator? The example about limits ... ok yeah that's cool but if you aren't actually teach them how to "calculate" (is the word "calculate" used as a boogey man?), how is that you are not doing anything other than teaching "math appreciation?"
dspeyer 14y ago
These how-to-apply-math skills are valuable, but they aren't math itself. Math is about building more general abstractions, keeping strict rigor, being careful with axioms, and developing techniques that are really, really broad as a result. Granted, calculation isn't a very good way to get into this either.
ivan_ah 14y ago
So basically what he is saying is that drilling kids into memorizing math procedures like LONG DIVISION is not a good way to get people interested in math and analytical thinking in general. Ok. Sure. He is right that modelling is probably what "people who don't get math" struggle the most with. But saying that math is just "computational stuff, turn the crank, let the computer do it" kind of thing is ludicrous. You can use mathematics as a blackbox model to do cool demos and stuff, but at some point you //have// to open the box and see how it is done. It just happens that the standard math curriculum (numbers, functions, sin, cos, etc.) is a very good mix of conceptual complexity and computational complexity that can all be understood with pen and paper. You won't need to trust anyone, the proof is right there on the sheet. Anyone trying to take that understand in order to replace with with a SolveEquation[.] is not on the right side of intellectualism. Demos yes, but view source (is there view source for Mathematica functions?) and explain source are //sine qua non// for deep knowledge.
Shank 14y ago
Though it isn't worth much, I'd like to put my two cents in as a student currently going through high school. In the district in which I'm partaking in public education, there's a dead even split between contemporary and traditional math courses. Our school offers both the Core-Plus Mathematics Project (http://wmich.edu/cpmp/ http://wmich.edu/cpmp/) and some variation of what I'd consider traditional (Geometry 1, 2, Algebra 1, 2, etc.). The students more often than not will prefer the Core-Plus Mathematics Project over the traditional courses early on in their education - but once the math switches over to a primarily calculating class (take, for instance, Calculus), the opinions shift and favor the other one. What we honestly have in my district is a case of a system that's trying to split itself down the middle politically - as we're attempting to switch to a modern, context driven approach to mathematics, whilst maintaining the link to processes like Advanced Placement, which only judge on the traditional aspects (http://www.collegeboard.com/student/testing/ap/sub_calab.html http://www.collegeboard.com/student/testing/ap/sub_calab.htm...). While it might be a better route for the future, the present is demanding math to be calculation based for the near future. It'll only start switching into a better realm when colleges and pre-college programs like those offered by CollegeBoard make the switch to context-based systems, rather than calculation based ones. (I'm very well aware of how rambling that is, sorry!)
ajuc 14y ago
I remember to this day the lesson in primary school, when we first started solving word problems. It was sth like 3rd class. Teacher would ask simple question, like "how many apples we had to add to each chest, if there is 4 chests with 7 apples in each, and we need to have total of 32 apples". And kids had to "brainstorm" and translate that into mathemathic process and solve (not algebra, just "first we need to know how many apples we lack, so we substract, then we need to know how many apples per chest we lack, so we divide", we didn't knew algebra yet). If the question wasn't specific, the kid that pointed it out got praise for being observant, and teacher specified what he meant. Most kids liked that lesson, and there was fierce competition to be the first to guess. That was the moment I felt in love with math, before that I thought I'm more of a humanist (which meant it's OK I can't understand decimal fractions ;) ). I think teaching kids to translate problem into math is very important, not only for math, but also if they want to be economists, computer programmers, etc. I cringe when I read that kids "know math, but don't know which equation to use to solve the problem". My wife taught math in secondary school for a while (in Poland, not USA, but we've recently had reform modeling our schools on those in "the West"). Many kids she taught had no idea how to translate word problem into math problem. They just pattern-matched keywords to equations. It's very sad, and I understand why they hate math - it must be completely frustrating to play this "guess the equation" game. So - I think there should be more focus on teaching kids to understand the basic word problems, before they even know algebra. To be sure, that they understand when we need to substract x, and when we need to substract from x.
deleted 14y ago
[deleted]

152 points by p4bl0 14y ago

deleted 14y ago

[deleted]

Enjoyed skimming your article. If only more geeks actually wanted to teach kids... unfortunately most of us will only be able to do that once we've retired!

ZoFreX 14y ago
If I went back into education for 2 more years, piled more student debt on top of myself, not to mention living like a student again, PLUS having to have a part-time job while studying (while the loan is bigger for a PGCE, the costs of living are much much higher), and then got a job as a teacher, worked my ass off for 10 years, I would, if I was lucky, be earning the same salary I am today, a couple of years after leaving university. Sounds like a great fucking deal to me.
- alexqgb 14y ago
  This cannot be upvoted hard enough. Education would reform itself overnight if teachers were hired from the top third of high school classes, not the bottom two thirds, and paid salaries that started ~$70k and reached ~$100k in five years if they were good. Students struggle because you have to be a saint or an idiot to teach under the conditions currently imposed. We don't have nearly enough of the former, and way too many of the latter. I have a really hard time imagining that brain-dead curriculum boards and mediocre administrators would sustain their death grip on a profession suddenly flooded with really sharp, well paid, professionals.
  - aggronn 14y ago
    Imagine the change in classroom atmosphere if teachers had the same social credibility as professors did (or more aptly, if high school teachers had the same respect and admiration from students as kindergarten teachers)

uncoder0 14y ago

Added to the reading list. I've been saying this for quite a while. I think we were able to capture this in our 9th grade math games we have been working on.

angersock 14y ago

I'm a bit concerned, as the article doesn't seem to cleanly define--and this may be just poor reading on my part--whether the idea is to use computers to expand math education (say, for solving large and complex problems), or to supplant entirely the teaching of calculation. It would seem to me that being able to perform basic arithmetic and algebra, by hand, is sort of a simple skill I would expect everyone to do. Computers are amazing devices, but not being proficient in doing those operations yourself when a computer or calculator is unavailable is not so good.

drewrv 14y ago

It's sad how many people think that math is arithmetic, and that if we let kids use computers or calculators then they're not "doing math". Not just the general public but PTA leaders, school board members, and school administrators.

ShabbyDoo 14y ago
I live in a relatively wealthy school district in Ohio where the schools generally are well-regarded. Last year, I went to the schools "parents math night". I had expected to be exasperated by, you know, those idiots who will be teaching my children (my older son is entering first grade this fall). However, I ended up impressed with the teachers and disappointed by the parents in attendance. The school had chosen the "Connected Math" curricula (connectedmath.msu.edu) for its middle school math program, and some parents were outraged that Little Johnny wasn't learning long division (or whatever). Their arguments could be summed up as, "Well, that's not the way we learned it." I angered the other parents by playing a bit dumb and asking for a short description of the curriculum. Then, I stated loudly that it "sounded delightful." The teachers barely contain their smiles. I ordered a couple of the books in used form from Amazon to see for myself, and I think I would have found the exercises fun as a middle schooler. I really wanted to ask the parents doing the complaining, "Don't you love your children? You pay more for a house just because it's in this school district, and then you lobby to dumb-down the math curriculum?"
weaksauce 14y ago
The problem is that the textbooks are teaching calculation. So in this instance "doing math" is calculating some equation. Solve some equation is easier to write in a textbook than an unambiguous word problem that a grad student needs to solve and put the answers in the back of the book and in the teachers solution manual. Not to mention that the math teachers are not always the best.

slowpoke 14y ago

I think he argues from the wrong point. Yes, we need to teach math, not calculating. No, the argument is not "because we can do calculating with computers today". Lockhart got it right in his famous lament - the problem is that we face a system of self-sustaining bullshit that actually thinks it's teaching math. My guess is that Conrad Wolfram probably plans to conveniently also sell the accompanying software for this new education, which would make it natural for him to focus on this point. I actually agree that computers can help us educate people better, and that we need to create appropriate software for this. But my concern would then be that such software must be free/libre. No compromise. We cannot risk the education of future generations to be locked into $corporation's proprietary products.

ljd 14y ago
I recently had the experience of helping a young algebra student with her homework. She is very bright and is in an accelerated math program that teaches algebra in the 7th grade. However, it was so disappointing to see the curriculum. I was in the same accelerated program 15 years ago and the curriculum hadn't changed a bit. It was still vague and unhelpful. They sent her home for the summer with a large packet of problems to solve without any explanation how to solve them. I majored in math and I still had to guess at what the worksheets were asking the student to do. They used vague variables and were essentially just teaching rote memorization. It reminded me of my own confusion in mathematics when I was growing up, how one year a variable would mean one thing and the next year it would mean something else. "Solve and explain," means just as little to me now, using math on a daily basis, as it did to the 11 year old version of me. After so many years, it would have been nice to see the curriculum focus more on application of mathematics and less on how to memorize and calculate.
- numeromancer 14y ago
  I've noticed the same thing in all the school curricula I've seen. The word problems are often vague, and all to often completely ambiguous. They require guessing what the question writer had in mind when she wrote the question, which are usually unstated assumptions that apply only to the way math is done in schools. This is not the way to teach the kind of precise thinking and careful definition of terms that one needs to understand why math is the way it is: the “study of precisely defined objects.” Teachers, if you want your pupils to understand how to create a mathematical problem from a description of a practical one, you must train them first to state the situation with absolute precision and without ambiguity. The best way to do that is, as in the teaching of all virtues, to fastidiously follow that habit yourself. That the questions in math textbooks fail to do that so often is another sign of the enormous institutionality of our education problems.

vph 14y ago

Of course, his main point is to advocate for using computers to teach and learn math; he's selling Mathematica/Wolfram Alpha. But this is dangerous and a little shallow. And here is why. Math is the language of science; just like a C -- or any other programming language -- is a language of computing; just like English is a language of humans. There are many ways to learn a language, but I think they all have something in common. You have to spend a lot of time learning, reading and writing. The writing is quite important. You have to write the language to be good at it. The thing about math is that currently to write as it is supposed to look like can only be done most conveniently on paper. Writing a math formula in Mathematica or Wolfram alpha requires a latex-like mini language, another thing to learn, and can be disrupting. This fact alone means that computers can only supplement; and they can be an excellent supplement. But it can not replace doing math by hands, on papers, particularly for those who are learning this new language.

UK-AL 14y ago
Err. This what he saying, you focus more on manipulating equations in the language of maths such as algebra, calculus, and less time on remembering what's the answer to 7 * 8.
- anonymoushn 14y ago
  Is this really a win? For most small problems or subproblems, a person who has solved similar problems many times before can solve it mentally much more quickly than by consulting a computer.
  - UK-AL 14y ago
    But one produces engineers, the other produces shop assistants.
    - anonymoushn 14y ago
      Which is which? A person who works in either role will do so more quickly by virtue of not needing to constantly consult a machine over trivial problems.

p4bl0 14y ago

I remember reading an article about almost the same topic by Felleisen, maybe Flatt, maybe Culpepper and some others from the PLT group, it was about using DrRacket to teach maths, there was an example involving the take-off of a rocket iirc. Is anyone able to find it? I don't remember the title nor where it was published.

abecedarius 14y ago
Sounds like http://world.cs.brown.edu/ http://world.cs.brown.edu/
- p4bl0 14y ago
  Thanks but no, it was an article not a book, I think it was in a PDF that I read on scribd or Google Docs Viewer. edit: I feel like the title was something a little disruptive.
fscof 14y ago
I really like the idea of teaching math in tandem with elementary programming. It demystifies writing code and can be very helpful in teaching important math concepts like functions, variables and graphing. At the very least, exposure to programming at an early age will get more kids interested in the subject. Does anyone know of good examples of schools that are already doing this with something like Dr Racket?
- takikawa 14y ago
  I think you'd be interested in Bootstrap World, which is basically what you described: http://www.bootstrapworld.org/ http://www.bootstrapworld.org/
p4bl0 14y ago
FOUND IT! The article was called "Computer Science Doesn't Matter" (ya, a little disruptive, like I said) you can find it here: http://www.cs.brown.edu/~sk/Publications/Papers/Published/fk-why-cs-doesnt-matter/paper.pdf http://www.cs.brown.edu/~sk/Publications/Papers/Published/fk...

RyanMcGreal 14y ago

In high school physics about 22 years ago, we did an experiment to calculate the acceleration due to gravity by repeatedly dropping a weight with a ticker tape attached to it that fed through a hole punch tool and measuring the spacing of the holes in the tape over time. As part of the analysis and write-up, we had to calculate the standard deviation across our sample runs. That seemed really tedious to me, so I wrote a program in BASIC that took a data file, ran the calculations and saved the results. I recall a certain to-do as the school deliberated over whether this was an acceptable way to complete the assignment, and I was asked to include the source code for my program so the teacher could determine that I understood the concept well enough to program it.

bostonvaulter2 14y ago
I think it would be cool if calculators weren't allowed in school unless you programmed them yourself. Now trying to enforce that might be difficult but it is an interesting idea.

magice 14y ago

This is sad. Really sad. My personal opinion is that Americans just dislike academic matters so much that they are incapable of forming a coherent solution for their children's schooling. Let me tell you some personal anecdotes. I moved to Minnesota during my High school senior year from Vietnam. It sucked: I couldn't hold on to conversations, and people couldn't understand my pronunciation; so I was bored and very lonely. You know what I do during my lunch time? Trying to re-prove Fermat's Last Theorem. Is there any "real world" application of that? Well, there may be, but I don't care. It was fun. You know how people listen to (and rock to) puke music on buses? I rode bus a lot during my college years, and spent that time wreaking my brain to work on various NP complete problems (my favorite is the man-woman-dog matching :D). Do I know it is beyond my capacity? Yes. Do I care about any real world problem of it? No. Why did I do it then? It's fun. It killed time. I still do this from time to time during meetings at work. When you think about it, most of math, or most of the academia for that matter, is not readily applicable. True, people use calculus to build Hoover Dam, but the effect of that information on whether or not a student likes math is equivalent of a political speech to a person political orientation: either you already like it (math/Obama) and cheer for it, or you already hate it (math/Obama) and boo/ignore it. These things, by itself, can't change a person's opinion regarding the big picture. You know why I like doing math in my free time? Because I have done a whole load of it. Vietnamese High School graduates are required to learn around sophomore math level in American college (and I fully expect most other East Asian systems to be the same). This explains neatly why Asian students are "smart." They freaking know the things already. Furthermore, the learning of math there involved an absurd amount of drill (compared to American high schools). Oh, calculators are banned until high school, and graphing calculators are banned. Period. Now, should that not make me abhor math? I mean, slaving myself so much time over such stupid and abstract matter must bore me to death, right? Actually, the opposite happened. It's like taste bud. You rebuild your taste bud every so often, so if you have been eating a whole load of broccoli lately, you will start to like broccoli. Yeah, after the first few days, you can't even digest to crap. However, after a few months, you can't digest without broccoli. Humans are adaptable. Do a lot of math, and you will like it. This also speaks of the problem with calculators and computers. The problem is no so much that they dump down math. The problem is that they alienate the students from math. When you do math, all of it, the result is made of your sweat. It may be wrong, but it's yours. It may be stupid and winded and long and whatnots, but it's yours. It's personal. I remember once, during 5th grade (yes, elementary school), there was this problem that I just could not solve, and we were kicked out of class for lunch break. Walking out, I cling to the teacher and cried out of frustration. The same frustration that keeps me up at nights when some stupid bugs could not be fixed. Must be the same frustration that all artisans experience at challenges. It's the indication of the bond that I have with my work, MY math, and it necessitates the toil, the slaving, the mind-numbing work of calculation. I hope you see my point: there is no elevator to interest in math. Math lovers must have toiled and slaved over stupid calculation over and over, until a point that they could actually produce the trace of math working, just like the zone in programming or any other art. That trace, that focus, that absorption builds the love for math. Of course, this means that the students must fist cross the initial barrier of math, just like the first few days of broccoli eating. In Asian cultures, academia is a point of pride. Parents take enormous pride in their children's academia success. Schools take enormous pride in their students' academia achievements. Think about football in American high schools. It's something similar. Study well, perform well in competition, and a student will enjoy numerous privileges and honors that is just unattainable through any other mean. The whole culture rates academia above any other activities, and use that as the measure for potential success. Playing sport well will earn praise, but it is understood to be temporary, fast passing. Studying well, and people will talk about how you will got to such and such colleges, and will become such and such person in the future. It's just different. Back to problem of American math schooling. Here is my prescription: just make the damn students do it. Require them to work on math. Forget about the whole, um, personality and uniqueness and whatnots. You know where these things are from? The toil of work (for students, that's studying) builds personality, values, and one's importance and uniqueness. You know where self esteem is from? It's from holding a piece of paper on which a problem has been solved and solution has been neatly presented; it's from the overcoming of frustration and challenges that the problem presents. Artisans take pride and esteem in their works. Students take pride and esteem in their tests and homework (except when you tell them that the football players will get the praise, the money, and the sex, and only these 3 things matter). Stop worrying about overworking them. Actually, overwork them to the ground. Leave them no energy and time to experiment with drugs and sex and alcohol. It takes challenges and toil to make a person. Stop taking these things away from the youngsters!

hybridthesis 14y ago

I noticed a few of articles on Hacker News has been about math recently. According to Google Trends, math is also rising in popularity, especially in US. I think math is even more appealing to programmers. You are allowed to assume that certain things happen. You may define a set on the fly and all of a sudden, the set is populated without pressing a single key. Let me try, {prime numbers}. There, I got an infinitely large data structure. I hope HN doesn't crash after posting this comment. As programmers, we put abstract ideas into implementations. Math seems to forgo all of that. Everything just happens magically as long as your mind can wrap around it and you have a precise definition for it. No debugging. Isn't this a dream? So I am wondering if there's a community of programmers who have turned to devote their time to math. Like the video said, computer frees you from computation. Hence, it makes sense for math's popularity to rise, especially since we got more people interested in programming. Math seems like the natural next step. I don't have any hard data about this, just my intuition.

felipellrocha 14y ago

On one end you will hear people equate math to calculating, this is almost exclusively how math is taught in school today, and on the other, people like to talk about math ideas, and how we shouldn't really teach people how to calculate anymore since we got computers for that. Like in many aspects of life, learning math is about balance. In truth, people should learn from both areas simultaneously, since they are mutually connected. Calculating is a tool that makes you a better problem solver, and being a problem solver will allow you to find new tools to calculate faster. You can't separate either discipline from one another. In my view, I think students should take one calculation, and one deeper math class a year starting in high school. That wat they could delve deeper in learning how to calculate (learning different methods for multiplication that might come in handy when doing mental math, for example), and start dealing with real, thought-heavy math from an earlier grade (learning about combinatorics, graph, game, and probability theory early in high school, etc).

wtetzner 14y ago
I would say, stop concentrating on calculation, and teach math. However, calculation is often a useful way to ensure you understand something. So, calculation will likely still be a part of learning math, but it shouldn't be the focus.

scoith 14y ago

He's basically trying to sell Mathematica.

scoith 14y ago

His talk is fundamentally wrong. Turning real life problems into a mathematical form (in other words, modelling) is not a subject of mathematics.

dinkumthinkum 14y ago
To be fair, I disagree with his position, but he is willing to call it something else, but the end of the day it is to teach his proposal as opposed what we now teach.
- scoith 14y ago
  Using computers. And with computers, he means Mathematica.

brr 14y ago

"And, of course, as we all know, with a computer you can take a simple problem like solve 5x2+2x+1=7 but you can make it harder, for example solve 5x4+2x+1=7. The principle of the problem is still the same." This is not, in fact, true for polynomial equations of order greater than four. From Wikipedia, "the Abel–Ruffini theorem states that there is no general algebraic solution... to polynomial equations of degree five or higher." This is often featured as one of the main results in an undergraduate abstract algebra course. I'm all for automating calculations, but the algorithms behind calculations and their proofs are important and often fascinating. Handing students an implementation of such algorithms, e.g. Mathematica, takes away their opportunity to code up the algorithms and understand them deeply. Edit: Wording

csense 14y ago
For that matter, asking students at the high school level to derive the quadratic formula will likely be quite challenging for even the best students in the class. Asking students to come up with the formulas for 3rd or 4th degree polynomials on their own is probably going to be beyond anyone below the very top tier of human capability. A teacher would be extremely lucky to see one or two students that can do this in their career. Then again, most people could easily solve these problems if they know what terms to Google :) Anyway, as I recall the third- and fourth-degree cases require clever substitutions (whereas the derivation of QF is just completing the square with general coefficients).

csense 14y ago

Mathematicians are basically just accountants, right? And the IRS has gazillions of accountants who only really work during tax season...so, if our math programs suck, let's move our tax due date to overlap with schools' summer break, fire all the math teachers and replace them with those IRS guys! It might be better than the existing system and it could hardly be worse. There's already been some work done on a curriculum (warning: PDF link): http://www.cs.amherst.edu/~djv/irs.pdf http://www.cs.amherst.edu/~djv/irs.pdf

dinkumthinkum 14y ago

I didn't really see much specific stuff here, to be honest. There was some program that you could use sliders to figure the best life insurance policy ... I mean, ok ... that's great ... What's the big deal again? What are some specific examples. There's all this "wah schools only teach calculation." Well, what specifically are they teaching that is bad and what specifically should they teach that is better? So, are we saying, no reason for a student to know how to take a derivative, they should know how to turn the knobs on some program to figure out the best fuel efficiency of some device in some really neat simulator? The example about limits ... ok yeah that's cool but if you aren't actually teach them how to "calculate" (is the word "calculate" used as a boogey man?), how is that you are not doing anything other than teaching "math appreciation?"

dspeyer 14y ago

These how-to-apply-math skills are valuable, but they aren't math itself. Math is about building more general abstractions, keeping strict rigor, being careful with axioms, and developing techniques that are really, really broad as a result. Granted, calculation isn't a very good way to get into this either.

ivan_ah 14y ago

So basically what he is saying is that drilling kids into memorizing math procedures like LONG DIVISION is not a good way to get people interested in math and analytical thinking in general. Ok. Sure. He is right that modelling is probably what "people who don't get math" struggle the most with. But saying that math is just "computational stuff, turn the crank, let the computer do it" kind of thing is ludicrous. You can use mathematics as a blackbox model to do cool demos and stuff, but at some point you //have// to open the box and see how it is done. It just happens that the standard math curriculum (numbers, functions, sin, cos, etc.) is a very good mix of conceptual complexity and computational complexity that can all be understood with pen and paper. You won't need to trust anyone, the proof is right there on the sheet. Anyone trying to take that understand in order to replace with with a SolveEquation[.] is not on the right side of intellectualism. Demos yes, but view source (is there view source for Mathematica functions?) and explain source are //sine qua non// for deep knowledge.

Shank 14y ago

Though it isn't worth much, I'd like to put my two cents in as a student currently going through high school. In the district in which I'm partaking in public education, there's a dead even split between contemporary and traditional math courses. Our school offers both the Core-Plus Mathematics Project (http://wmich.edu/cpmp/ http://wmich.edu/cpmp/) and some variation of what I'd consider traditional (Geometry 1, 2, Algebra 1, 2, etc.). The students more often than not will prefer the Core-Plus Mathematics Project over the traditional courses early on in their education - but once the math switches over to a primarily calculating class (take, for instance, Calculus), the opinions shift and favor the other one. What we honestly have in my district is a case of a system that's trying to split itself down the middle politically - as we're attempting to switch to a modern, context driven approach to mathematics, whilst maintaining the link to processes like Advanced Placement, which only judge on the traditional aspects (http://www.collegeboard.com/student/testing/ap/sub_calab.html http://www.collegeboard.com/student/testing/ap/sub_calab.htm...). While it might be a better route for the future, the present is demanding math to be calculation based for the near future. It'll only start switching into a better realm when colleges and pre-college programs like those offered by CollegeBoard make the switch to context-based systems, rather than calculation based ones. (I'm very well aware of how rambling that is, sorry!)

ajuc 14y ago

I remember to this day the lesson in primary school, when we first started solving word problems. It was sth like 3rd class. Teacher would ask simple question, like "how many apples we had to add to each chest, if there is 4 chests with 7 apples in each, and we need to have total of 32 apples". And kids had to "brainstorm" and translate that into mathemathic process and solve (not algebra, just "first we need to know how many apples we lack, so we substract, then we need to know how many apples per chest we lack, so we divide", we didn't knew algebra yet). If the question wasn't specific, the kid that pointed it out got praise for being observant, and teacher specified what he meant. Most kids liked that lesson, and there was fierce competition to be the first to guess. That was the moment I felt in love with math, before that I thought I'm more of a humanist (which meant it's OK I can't understand decimal fractions ;) ). I think teaching kids to translate problem into math is very important, not only for math, but also if they want to be economists, computer programmers, etc. I cringe when I read that kids "know math, but don't know which equation to use to solve the problem". My wife taught math in secondary school for a while (in Poland, not USA, but we've recently had reform modeling our schools on those in "the West"). Many kids she taught had no idea how to translate word problem into math problem. They just pattern-matched keywords to equations. It's very sad, and I understand why they hate math - it must be completely frustrating to play this "guess the equation" game. So - I think there should be more focus on teaching kids to understand the basic word problems, before they even know algebra. To be sure, that they understand when we need to substract x, and when we need to substract from x.

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