This seems interesting because it addresses the issue of "show your work." Many years ago, I spent a semester teaching the freshman algebra course at the nearby Big 10 university. This is the course that you take if you don't get into calculus. My students were bright kids -- they were all admitted to the state flagship school -- but not mathematicians.<p>There was huge variation in the preparation that kids brought with them from high school. In particular, very few of them understood what "show your work" means. They were told "show your work," but nobody told them what it really entails. Is it just to provide evidence that you did some work, to deter cheating, or is it something else? Many of my students were taught "test taking skills" such as the guess-and-try method. So on one exam, a question was:<p>x^3 = 27<p>One student's work:<p>1^3 = 1<p>2^3 = 8<p>3^3 = 27<p>Answer = 3<p>I asked the professors to tell me what "show your work" means. None of them had a good answer! These were the top mathematicians in the world. I wanted to talk with my students about it, but I'm not even sure that my own answer was very good.<p>But if we did well in math, then we just know what it means. It's not just evidence that you did the work. It doesn't mean "turn in all of your chicken scratch along with the answers." It means something along the lines of supplying a step-by-step argument, identifying the premises and connecting them with the conclusion, in a language that is "accepted," i.e., that mimics the language of the textbook / teacher. In fact, the reason to read the textbook and attend lectures, is to learn that language. (It's not so different in the humanities courses).<p>At least, that's my take on it, as just one teacher with one semester's worth of experience.<p>In my view, a problem solving tool that actually addresses the process of building the <i>argument</i> and not just determining the answer, would be beneficial to students.
Has anyone done a study to see if this kind of aided solving actually helps students learn? I'm worried that "Eh, I'll just write this solution down today, I'm sure I'll learn it tomorrow" is what's happens.<p>Awesome software though.
Some years ago I tried to do something a bit more complex: <a href="http://telauges.appspot.com/mathsolver/" rel="nofollow">http://telauges.appspot.com/mathsolver/</a><p>My idea was to use planning and A* search to solve any type of math problem, even create probes for things like the quadratic equation <a href="https://en.wikipedia.org/wiki/Quadratic_equation" rel="nofollow">https://en.wikipedia.org/wiki/Quadratic_equation</a> . I gave up after learnt the search space was so big for it that it was impossible to solve. If I had to do it today I will explore deep learning as heuristic, but I think it probably wont work.<p>I always like to see this type of projects, I hope they succeed where I failed.
It's a nice program and I can see it being both helpful and harmful. From my perspective, as a teacher of mathematics at a community college, students are unwilling to engage in thought about a problem. If they can't see the solution in a few minutes then they want to look at a complete solution. Mostly they are not willing to struggle through a problem.<p>I vacillate on whether, with the advent of computer algebra systems, it is necessary for students to master algebraic manipulations. I started to think that conceptual questions are better.<p>For instance, give me an example of an equation with no solution. Explain how a baseball player can have the highest batting average the first half of a season and in the second half of a season but not have the highest overall average. Draw the graph of a function defined on [0, 1] but has not maximum or minimum.<p>Students can't do those types of problems either. They are very frustrating problems for students because it requires you to really think about what the words mean and to think of extreme situations. So I've reverted back to the traditional style of teaching math. Manipulation of symbols.
Worked on something like this as a hobby project a while ago, but to avoid the complexities associated with solving arbitrary exercises, instead I had it set up as an algebra exercise generator: you start with the solution, which you then (algorithmically) obfuscate by splitting terms and recombining things for a couple of rounds. Never got around to finishing it, but the neat thing is that you've already generated one possible way to solve the problem, it's just how you generated the exercise in reverse.<p>Another thing that's quite easy to do is to check intermediate steps in a solution for equivalence. You don't even really need CAS, just brute force the problem by probing the equations: set all variables to randomly chosen values, n times and if the sets of results are the same for both equations, you're good.<p>Anyhow, Socratic looks great and a great deal more advanced and useful than what I came up with, so kudos!
I'm jealous of kids these days... homework would've been so much easier with this.<p>You could always use a calculator but the whole 'show your own working' catch meant you had to do it all manually. Not any more!
My academic math journey stopped at pre-calc, and I had been a C student for quite a long time. HS Algebra II would never have happened for me if I hadn't discovered XMaxima, an emacs-based CAS. Fortunately I took a Discrete Math course before dropping out of college, and it gave me a new admiration for math.<p>In spite of my weak math background, this has been the most enjoyable comments section on HN I've read so far.
People here keep saying this will change learning and be good for the students, but the only real difference is it's open-source. You can already get step-by-step solutions for more types of problems from Wolfram Alpha, and you can already get API access if you're a 3rd-party developer who needs it:<p><a href="http://www.wolframalpha.com/input/?i=2*y+-+x+%3D+(8+*+x+%2B+2)" rel="nofollow">http://www.wolframalpha.com/input/?i=2*y+-+x+%3D+(8+*+x+%2B+...</a><p>I don't think it will have any real effect.
Very interesting work, and well-explained in the post.<p>Like many others here, I suppose that in it's basic form this would mostly be used for cheating on homework; although it would certainly be useful for those (few?) students who are truly motivated to self-learn the material, rather than just pass the tests.<p>One thing which springs to mind is "Benny's Conception of Rules and Answers in IPI Mathematics" ( <a href="https://msu.edu/course/cep/953/readings/erlwanger.pdf" rel="nofollow">https://msu.edu/course/cep/953/readings/erlwanger.pdf</a> ), which shows the problem of only focusing on answers, and on "general purpose" problem sets. Namely that incorrect rules or concepts might be learned, if they're reenforced by occasionally giving the right answer.<p>I think it would be interesting to have a system capable of some back-and-forth interactivity: the default mode would be the usual, going through some examples, have the student attempt some simple problems, then trickier ones, and so on.<p>At the same time, the system would be trying to guess what rules/strategies the student is following: looking for patterns, e.g. via something like inductive logic programming. We would treat the student as a "black box", which we can learn about by posing carefully crafted questions.<p>Each question can be treated as an experiment, where we want to learn the most information about the student's thinking: if strategies A and B could both lead to the answers given by the student, we construct a question which leads to different answers depending on whether A or B were used to solve it; that gives us information about which strategy is more likely to be used by the student, or maybe the answer we get is poorly explained by A and B, and we have to guess some other strategies they might be using.<p>Rather than viewing marking as a comparison between answer and a key, we can instead infer a model of the domain from those answers and compare <i>that</i> to an accurate model of the domain.<p>We can also use this approach the other way around, treating the <i>domain</i> as a black box (which it is, from the student's perspective) and choosing examples which give the student most information about it.
Now... the only thing remaining is to translate this to common core :).<p>I say that in jest, but doing so would make common core much easier for parents AND teachers to grasp. There's an enormous divide between those who get it and those who hate it, and providing parents/teachers with something that would help them understand the benefits of common core concepts would be a gigantic win.
That's so cool.<p>Reminds me of how different the learning experience is now. When we were at school (80s/90s), there was nowhere to turn if you didn't have the answer. My parents had an Encyclopedia Britannica set, so at least there was a paragraph to go on. It's amazing how good you became at fleshing out that paragraph into an essay :-)
Now that this exists I think it's worth creating an opensource version of the TI-Nspire for engineers & mathamaticians. Something based on cheap hardware, runs linux, and can implement this + a theorum prover to basically make the most handy lab calculator.
that feels like a nice application of AI in a way. we often use a computer that can help in making a plan (e.g. a kind of map or "steps" as here). this might be nice to help understand problem solving in general. also, nice to see the project is in javascript, that means quite a few non-professional programmers could learn from it.