I thought that looked really interesting, but then I did a double take. Is this app an interactive exercise app that's tied to the Khan Academy videos on the related topic, or is it just a portal directly to said videos? What exactly can the student do with the app?
From his description, I see 'interactive transcripts', but I'm not sure exactly what that means...
I think there's a big difference between showing a student how to do things, and giving the student the ability to clearly demonstrate an understanding of the things you're trying to teach. I don't know what the ultimate goal of this app is, but I hope at some point there will be student interactivity such that exercises can be attempted and directed, specific feedback can be generated...
edit: oh look, it says exercises are coming in the next release. I'm not sure how I missed that! I'm looking forward to seeing what they come up with!
In my opinion, the most impressive part of the Khan Academy approach is the emphasis they have put on demonstrating a student's understanding of the concepts - as demonstrated in that Ted Talk. The fact that the entry-point is "videos on the web" is a simplification of their overall mission.
Thanks for the video link! I'll check it out. I admit to hearing a lot about Khan Academy but not having had much time to actually investigate what they offer...
Khan Academy has had exercises for a while now. It's probably one of the best open source projects to work on, in terms of impact and how easy it is to contribute. You only need to know HTML and a little JavaScript. The exercises are modular, so you don't need to understand the whole codebase in order to work on it. Plus, saying "I've contributed to Khan Academy" is a pretty cool thing to put on a resume.
For all the upvotes Khan Academy gets, though, there really aren't that many contributors. I'd encourage everyone reading this with an afternoon to spare to try writing an exercise for KA.
Just for friendly advice to the Khan Academy exercise developers, I'll repost my FAQ about the distinction between "exercises" and "problems" in mathematics education. It would be great to see more problems on the Khan Academy site.
FAQ begins here:
PROBLEMS VERSUS EXERCISES
I frequently encounter discussions among parents about repetitive school math lessons, so a few years ago I prepared this Frequently Asked Question (FAQ) document about the distinction between math exercises (good in sufficient but not excessive amount) and math problems (always good in any amount).
Most books about mathematics have what are called "exercises" in them, questions that prompt a learner to practice the concepts discussed in the mathematics book. By reading one mathematics book, and then several more, I learned that some mathematicians draw a distinction between "exercises" and "problems" (which is the terminology generally used by the mathematicians who draw this distinction). I think this distinction is useful for teachers and learners to consider while selecting materials for studying mathematics, so I'll share the quotations from which I learned this distinction here. I first read about the distinction between exercises and problems in a Taiwan reprint of a book by Howard Eves.
"It is perhaps pertinent to make a comment or two here about the problems of the text. There is a distinction between what may be called a PROBLEM and what may be considered an EXERCISE. The latter serves to drill a student in some technique or procedure, and requires little, if any, original thought. Thus, after a student beginning algebra has encountered the quadratic formula, he should undoubtedly be given a set of exercises in the form of specific quadratic equations to be solved by the newly acquired tool. The working of these exercises will help clinch his grasp of the formula and will assure his ability to use the formula. An exercise, then, can always be done with reasonable dispatch and with a minimum of creative thinking. In contrast to an exercise, a problem, if it is a good one for its level, should require thought on the part of the student. The student must devise strategic attacks, some of which may fail, others of which may partially or completely carry him through. He may need to look up some procedure or some associated material in texts, so that he can push his plan through. Having successfully solved a problem, the student should consider it to see if he can devise a different and perhaps better solution. He should look for further deductions, generalizations, applications, and allied results. In short, he should live with the thing for a time, and examine it carefully in all lights. To be suitable, a problem must be such that the student cannot solve it immediately. One does not complain about a problem being too difficult, but rather too easy.
"It is impossible to overstate the importance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps. Every research article, every doctoral thesis, every new discovery in mathematics, results from an attempt to solve some problem. The posing of appropriate problems, then, appears to be a very suitable way to introduce the student to mathematical research. And it is worth noting, the more problems one plays with, the more problems one may be able to pose on one's own. The ability to propose significant problems is one requirement to be a creative mathematician."
Eves, Howard (1963). A Survey of Geometry volume 1. Boston: Allyn and Bacon, page ix.
I have since read about this distinction in several other books.
"Before going any further, let's digress a minute to discuss different levels of problems that might appear in a book about mathematics:
Level 1. Given an explicit object x and an explicit property P(x), prove that P(x) is true. . . .
Level 2. Given an explicit set X and an explicit property P(x), prove that P(x) is true for FOR ALL x [existing in] X. . . .
I've seen you paste this a few times now and find myself disagreeing with parts of your framing.
First, I don't know any mathematician personally who makes such a clear linguistic distinction between 'exercise' and 'problem'. Once you get to university-level mathematics, many exercises are problems in your sense but they still tend to be called exercises or something similar. If you insist on this terminological divide, I doubt most people will understand you.
Secondly, there is the matter of an exercise's pedagogical purpose. Is it to sharpen general problem solving skills or to enlighten the student on a conceptual level? This goes beyond difficulty. It's a false dichotomy when stated so simply, but there is still something there. Many IMO-style problems are conceptually barren but still very tricky to solve. Conversely, some of my most enlightening learning experiences were solving guided sequences of exercises in a mathematical form of Socratic learning where none of the steps were individually too hard but still involving enough that they forced me to think and thus develop some insight on my own. (This approach can also fail. Silverman's otherwise excellent book Rational Points on Elliptic Curves has a guided proof of Bezout's theorem in the appendix that is just too atomized to engender much understanding.)
Those are well-framed responses. Thanks. Khan Academy elicits my response because SO FAR, among the online exercises I have tried there, the "enlighten the student on a conceptual level" hasn't happened as much as just the habit-clinching drill. As Lang wrote (as quoted in the grandparent post), "Of course, some rote drilling is necessary. The problem is how to strike a balance."
The "mathematical form of Socratic learning where none of the steps were individually too hard but still involving enough that they forced me to think and thus develop some insight on my own" is what I attempt to provide in my live, face-to-face mathematics classes. I'm not worried about Khan Academy reducing the market for those classes (and in fact encourage current and prospective students to try out Khan Academy) because providing that sort of instruction is very hard to automate. As your example of Silverman's book points out, it is more of an art than a settled science to decide just how many steps to show with Socratic guidance, not to mention that different learners need different steps drawn out for them.
I thought that Apple had requirements that any applications be written in native code, doesn't this break that if it's written in html5? Looking at the github, the entire source is html/js...
There's no such requirement. At one point, they required everything to be in native Objective-C code or HTML/JS (both were allowed) but they have lifted even that restriction.
Off hand, browsing the source, it looks like a web app (index.html, CSS, JS). "With offline support" makes more sense in that context too, as you would expect a native iOS app to be mostly 'offline' anyway (sans perhaps streaming video).
I think this means it's a website designed for iOS and using the new HTML5 offline storage stuff for local operation.
Yep - we recently built a mobile app that utilizes local storage for offline support, with sync functionality for when users are connected again. HTML5 really opens the door for some awesome stuff.
Note that you combine the two approaches. In a native app you can embed a webkit window and show HTML/Javascript. Since the Khan exercises are written in Javascript this could be the plan (but I don't know).
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[ 2.8 ms ] story [ 71.0 ms ] threadFrom his description, I see 'interactive transcripts', but I'm not sure exactly what that means...
I think there's a big difference between showing a student how to do things, and giving the student the ability to clearly demonstrate an understanding of the things you're trying to teach. I don't know what the ultimate goal of this app is, but I hope at some point there will be student interactivity such that exercises can be attempted and directed, specific feedback can be generated...
edit: oh look, it says exercises are coming in the next release. I'm not sure how I missed that! I'm looking forward to seeing what they come up with!
Looks like this first release is a viewer+, but impressive iterations will not be far behind.
The breadth of Khan Academy's granularity for interpreting a student's understanding is staggering. The second half of Salman's Ted Talk shows how granular it gets: http://www.ted.com/talks/salman_khan_let_s_use_video_to_rein...
In my opinion, the most impressive part of the Khan Academy approach is the emphasis they have put on demonstrating a student's understanding of the concepts - as demonstrated in that Ted Talk. The fact that the entry-point is "videos on the web" is a simplification of their overall mission.
For all the upvotes Khan Academy gets, though, there really aren't that many contributors. I'd encourage everyone reading this with an afternoon to spare to try writing an exercise for KA.
https://github.com/Khan/khan-exercises
FAQ begins here:
PROBLEMS VERSUS EXERCISES
I frequently encounter discussions among parents about repetitive school math lessons, so a few years ago I prepared this Frequently Asked Question (FAQ) document about the distinction between math exercises (good in sufficient but not excessive amount) and math problems (always good in any amount).
Most books about mathematics have what are called "exercises" in them, questions that prompt a learner to practice the concepts discussed in the mathematics book. By reading one mathematics book, and then several more, I learned that some mathematicians draw a distinction between "exercises" and "problems" (which is the terminology generally used by the mathematicians who draw this distinction). I think this distinction is useful for teachers and learners to consider while selecting materials for studying mathematics, so I'll share the quotations from which I learned this distinction here. I first read about the distinction between exercises and problems in a Taiwan reprint of a book by Howard Eves.
"It is perhaps pertinent to make a comment or two here about the problems of the text. There is a distinction between what may be called a PROBLEM and what may be considered an EXERCISE. The latter serves to drill a student in some technique or procedure, and requires little, if any, original thought. Thus, after a student beginning algebra has encountered the quadratic formula, he should undoubtedly be given a set of exercises in the form of specific quadratic equations to be solved by the newly acquired tool. The working of these exercises will help clinch his grasp of the formula and will assure his ability to use the formula. An exercise, then, can always be done with reasonable dispatch and with a minimum of creative thinking. In contrast to an exercise, a problem, if it is a good one for its level, should require thought on the part of the student. The student must devise strategic attacks, some of which may fail, others of which may partially or completely carry him through. He may need to look up some procedure or some associated material in texts, so that he can push his plan through. Having successfully solved a problem, the student should consider it to see if he can devise a different and perhaps better solution. He should look for further deductions, generalizations, applications, and allied results. In short, he should live with the thing for a time, and examine it carefully in all lights. To be suitable, a problem must be such that the student cannot solve it immediately. One does not complain about a problem being too difficult, but rather too easy.
"It is impossible to overstate the importance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps. Every research article, every doctoral thesis, every new discovery in mathematics, results from an attempt to solve some problem. The posing of appropriate problems, then, appears to be a very suitable way to introduce the student to mathematical research. And it is worth noting, the more problems one plays with, the more problems one may be able to pose on one's own. The ability to propose significant problems is one requirement to be a creative mathematician."
Eves, Howard (1963). A Survey of Geometry volume 1. Boston: Allyn and Bacon, page ix.
I have since read about this distinction in several other books.
"Before going any further, let's digress a minute to discuss different levels of problems that might appear in a book about mathematics:
Level 1. Given an explicit object x and an explicit property P(x), prove that P(x) is true. . . .
Level 2. Given an explicit set X and an explicit property P(x), prove that P(x) is true for FOR ALL x [existing in] X. . . .
Level 3. Given an explicit set X and ...
First, I don't know any mathematician personally who makes such a clear linguistic distinction between 'exercise' and 'problem'. Once you get to university-level mathematics, many exercises are problems in your sense but they still tend to be called exercises or something similar. If you insist on this terminological divide, I doubt most people will understand you.
Secondly, there is the matter of an exercise's pedagogical purpose. Is it to sharpen general problem solving skills or to enlighten the student on a conceptual level? This goes beyond difficulty. It's a false dichotomy when stated so simply, but there is still something there. Many IMO-style problems are conceptually barren but still very tricky to solve. Conversely, some of my most enlightening learning experiences were solving guided sequences of exercises in a mathematical form of Socratic learning where none of the steps were individually too hard but still involving enough that they forced me to think and thus develop some insight on my own. (This approach can also fail. Silverman's otherwise excellent book Rational Points on Elliptic Curves has a guided proof of Bezout's theorem in the appendix that is just too atomized to engender much understanding.)
The "mathematical form of Socratic learning where none of the steps were individually too hard but still involving enough that they forced me to think and thus develop some insight on my own" is what I attempt to provide in my live, face-to-face mathematics classes. I'm not worried about Khan Academy reducing the market for those classes (and in fact encourage current and prospective students to try out Khan Academy) because providing that sort of instruction is very hard to automate. As your example of Silverman's book points out, it is more of an art than a settled science to decide just how many steps to show with Socratic guidance, not to mention that different learners need different steps drawn out for them.
I think this means it's a website designed for iOS and using the new HTML5 offline storage stuff for local operation.
That would be more up John Resig's alley as well.
That's pretty cool!