3 ms·

The author writes, in the interesting blog post submitted here, "We should wonder why Khan Academy emphasizes this particular work. I have no inside knowledge o

The author writes, in the interesting blog post submitted here, "We should wonder why Khan Academy emphasizes this particular work. I have no inside knowledge of Khan Academy’s operations or vision." Actually, here on Hacker News we have had public discussions blessed with direct participation by Khan Academy developers, so I think I have some sense of what Khan Academy intends to do as it continues to develop online lessons. I've even had some off-site email interaction with Khan Academy developers after threads here in which I have "met" them while we discuss our common interest in mathematics education. I certainly hope that Khan Academy staff will join the discussion of this post. The author also writes, "I find it more likely that Khan Academy’s exercise set draws an accurate map of the strengths and weaknesses of education technology in 2014. Khan Academy asks students to solve and calculate so frequently, not because those are the mathematical actions mathematicians and math teachers value most, but because those problems are easy to assign with a computer in 2014." I think this statement is correct. The Khan Academy developers have devoted a lot of thought to how to computerize problems rather than exercises, and they are still working on building new problem types for the mathematics lessons. I'm actually quite impressed with some of the problem types that show up in more advanced mathematics lessons on Khan Academy that go beyond the eighth grade level implied by current United States curriculum standards. But the author's point is well taken that the Common Core, and good mathematics curricula around the world, expect reasoning and explanation from pupils in mathematics lessons already at elementary school age. That currently is indeed difficult to automate. The author's comments on development of Smarter Balanced Assessment (SBC) as a new platform of online mathematics instruction is of course especially interesting. I will be curious to see how this program continues to develop, and I would be glad to hear from developers of that program in this thread too. (Disclosure: I am a teacher of voluntary-participation prealgebra mathematics classes to advanced pupils of third-, fourth-, and fifth-grade age, using the Art of Problem Solving prealgebra textbook by Rusczyk, Patrick, and Boppana as a core text with many supplementary materials from around the world. I do not view Khan Academy as a competitor to my classes, but rather as a helpful supplement for many mathematics learners around the world. My daughter, who is of a younger age than eighth-grade age, is currently doing many of the same Khan Academy lessons as those just reviewed by the blog post author. I recommend Khan Academy to my friends, and it will probably stay in the mix for the mathematics studies of my three minor children for quite a few years yet.)

spicyj 12y ago
(I work at Khan Academy.) > The Khan Academy developers have devoted a lot of thought to hope to computerize problems rather than exercises, and they are still working on building new problem types for the mathematics lessons. I'm actually quite impressed with some of the problem types that show up in more advanced mathematics lessons on Khan Academy that go beyond the eighth grade level implied by current United States curriculum standards. Thank you. > Common Core, and good mathematics curricular around the world, expect reasoning and explanation from pupils in mathematics lessons already at elementary school age. That currently is indeed difficult to automate. This is definitely true. By no means is Khan Academy a complete solution for mathematics instruction, nor is it likely to become one in the next few years. Our site should ideally be used alongside other materials that test reasoning and explanation in a non-automated way, as well as projects that allow students to apply their knowledge. We have early experiments that take a much more interactive approach to teaching certain concepts and encourage more experimentation, but we're probably years away from developing them into a shipping product. > The author's comments on development of Smarter Balanced Assessment (SBC) as a new platform of online mathematics instruction is of course especially interesting. I will be curious to see how this program continues to develop, and I would be glad to hear from developers of that program in this thread too. If I'm not mistaken, many of the SBAC problems (especially free-response ones) are hand-graded, which can work if you charge for each test taken, but can't work for us when we have millions of problems done every day, all graded automatically. That said, we're exploring strategies like peer grading in other subject areas (particularly our programming curriculum) and would be excited to bring them to math as well.
- zanny 12y ago
  > that test reasoning and explanation in a non-automated way > early experiments that take a much more interactive approach > we're exploring strategies like peer grading Are you guys working on any genetic / learning algorithm implementations of AI sufficient enough to evaluate responses to arbitrary prompts? It sounds both like something that should be feasible with modern tech, especially when time to response can be large (a student can wait hours for an answer to a complex essay response) and the scale can be arbitrary (as many server clusters as "its worth" yet also feasible (we can see similar scale literary processing in other spaces). I can imagine such an algorithmic implementation where you take some common query given to students across hundreds of schools, with all the teacher graded responses, and maybe after a few years it can get within an accuracy confidence threshold to start grading the prompt, and after another few years providing critique on that grade. That would be the most revolutionary educational tech since the Internet itself, even if it were pigeonholed in several years studying the same single problem for now. Sounds awesome either way. You can even use that peer grading tech to build up a library of problem / solutions to build your causal relations table from. I just hope you guys have someone in a back room working on this, because to me it seems as real world usable computational linguistics happen more often, there arise a ton of useful applications even in the minimum case.

spicyj 12y ago

(I work at Khan Academy.) > The Khan Academy developers have devoted a lot of thought to hope to computerize problems rather than exercises, and they are still working on building new problem types for the mathematics lessons. I'm actually quite impressed with some of the problem types that show up in more advanced mathematics lessons on Khan Academy that go beyond the eighth grade level implied by current United States curriculum standards. Thank you. > Common Core, and good mathematics curricular around the world, expect reasoning and explanation from pupils in mathematics lessons already at elementary school age. That currently is indeed difficult to automate. This is definitely true. By no means is Khan Academy a complete solution for mathematics instruction, nor is it likely to become one in the next few years. Our site should ideally be used alongside other materials that test reasoning and explanation in a non-automated way, as well as projects that allow students to apply their knowledge. We have early experiments that take a much more interactive approach to teaching certain concepts and encourage more experimentation, but we're probably years away from developing them into a shipping product. > The author's comments on development of Smarter Balanced Assessment (SBC) as a new platform of online mathematics instruction is of course especially interesting. I will be curious to see how this program continues to develop, and I would be glad to hear from developers of that program in this thread too. If I'm not mistaken, many of the SBAC problems (especially free-response ones) are hand-graded, which can work if you charge for each test taken, but can't work for us when we have millions of problems done every day, all graded automatically. That said, we're exploring strategies like peer grading in other subject areas (particularly our programming curriculum) and would be excited to bring them to math as well.

zanny 12y ago
> that test reasoning and explanation in a non-automated way > early experiments that take a much more interactive approach > we're exploring strategies like peer grading Are you guys working on any genetic / learning algorithm implementations of AI sufficient enough to evaluate responses to arbitrary prompts? It sounds both like something that should be feasible with modern tech, especially when time to response can be large (a student can wait hours for an answer to a complex essay response) and the scale can be arbitrary (as many server clusters as "its worth" yet also feasible (we can see similar scale literary processing in other spaces). I can imagine such an algorithmic implementation where you take some common query given to students across hundreds of schools, with all the teacher graded responses, and maybe after a few years it can get within an accuracy confidence threshold to start grading the prompt, and after another few years providing critique on that grade. That would be the most revolutionary educational tech since the Internet itself, even if it were pigeonholed in several years studying the same single problem for now. Sounds awesome either way. You can even use that peer grading tech to build up a library of problem / solutions to build your causal relations table from. I just hope you guys have someone in a back room working on this, because to me it seems as real world usable computational linguistics happen more often, there arise a ton of useful applications even in the minimum case.