Compare and contrast: using computers to improve math education

Compare and contrast these two approaches:

1. Conrad Wolfram: Teaching kids real math with computers

2. Salman Khan: Let’s use video to reinvent education

Wolfram talks about how computers should be used to advance the understanding of math the way it’s really used in the real world.

Kalman talks about using computers to deliver traditional math instruction and gold stars.

Kalman reinforces the “teaching” paradigm; Wolfram blows it up and insists we look critically at what’s being taught.

Both these talks are about “improving education with technology” – but they couldn’t be further apart in world view.

But the TED audience applauds them both. This is why conversations about reforming education are difficult.

Sylvia

PS Wolfram makes a great point at the end of his talk about how, if we think that learning to calculate teaches procedural thinking, we have a much better way to do it by teaching programming.

You may also like...

21 Replies to “Compare and contrast: using computers to improve math education”

Great point. Two different approaches, each received enthusiastically. Salman’s point, though, is just about helping kids learn how to do the calculating – solving for x. The first skill to leave us when we distance ourselves from our math classes. I USED to know how to do some complex calculus problems. Not now, though.

I taught programming for many years. From Basic to PASCAL, COBOL, and C++. I agree completely that teaching programming is a great way to get kids to problem solve, plan, and work logically. I used to push for that idea – teach kids logo programming in elementary school, but as we know, if it doesn’t get tested it’s not going to get done.

Nice idea to put these two videos together.

BTW – good job introducing the folks at TEDxNYED. I watched from home that day.

As a math teacher, I’m enthusiastically applauding both. I’m so frustrated with the math paradigm that has caught hold, and so am encouraged by Wolfram’s thoughts (though, I’ll admit, I’m skeptical of some of his points). In particular, I love the idea of comprehension through programming. I’ve tried to do this with little success this year… will keep trying.

But Wolfram makes the point: this can’t change on a classroom-to-classroom basis, because of exams. If my (small, innovative, private) school taught applets instead of pencil-pushing, our kids could have awesome intuition but would likely fail their AP tests (and SATs).

In the meantime, Khan swoops in to save the day. He is streamlining the traditional model. That takes the pressure off the teacher and would truly revolutionize the classroom in terms of individual success and understanding.

The dichotomy here is false. In fact, if you want Wolfram, you need Khan. Khan’s model potentially collapses the time needed to learn the computational stuff. That frees up teachers to, as he puts it, tell how tall hills are based on their shadows. Wolfram would call this steps 1, 2, and 4. Once more classrooms do that more – freed by Khan’s model to at once satisfy traditional exams AND innovate – then there will be a foundation to jump the chasm to Wolfram’s model.

Things that have happened in the last two hours:

1) I received a note from a colleague saying that I MUST watch Khan on TED. 2) I think: I suspect I will not like this, but do not know how to respond. 3) I search ‘Khan Academy Sylvia Martinez’ because I knew you must have written something about this at some point. 4) I find this, which is basically perfect. So, thank you.

I was initially skeptical with what the Kahn Academy was trying to accomplish. However, from the talk I think they are heading in the right direction. The most important thing I heard was that Kahn considers this as a part of a bigger curriculum.

I saw the Wolfram talk a while ago, and I had several concerns with what he was saying. His problem is that he wants to use computers only in the classroom. I think that is only slightly less limiting than working entirely with pencil and paper. I wrote a critique of Wolfram’s talk on my blog.

I recently watched Salman Khan TED talk. My initial thoughts were what an excellent resource. Why couldn’t I have had this when I was doing high school mathematics! Within our current systems I can see Khan’s resources will be of value to students. The benefits are; his examples are clear and sequential. Students can set their own pace. It is relevant to current curriculum. I would applaud him for his efforts and particularly how he has made his resource open. Now contrasting the vision of Conrad Wolfram I would give this man a standing ovation! I agree 100% with what he is saying. Let’s put the emphasis on feeling the math. Spend more time on posing the right questions, then digging out the math and applying it to gain an answer. Bring it back to the real world question and validate the solution. Brilliant! But how does the average teacher achieve this in the classroom? Who will be brave enough to breakaway? I was at a conference last month called Learning@School in Rotorua. I attended one of Sylvia’s talks ”If Games are the Answer. What’s the Question?” and real enjoyed it. Thanks for that Sylvia. Why I mention the conference in regard to this post was that one of the products there caught my imagination and it fits in with conceptualising maths perfectly. 3D printing! I’m not a rep for the company however this technology impressed me with the possibilities it could bring. You can create a model in Google Sketch Up. Upload the model to their software and print the model in three dimensions. Next you can test and evaluate the model in real life. Cool! How could this change the way you teach maths? Take a look at the website if you are interested : http://3dprinting.co.nz/ . I teach children between the ages of 5-10 years. I’m not likely to persuade my school to purchase one of these printers. Well not this year! I would be interested in hearing from anyone who has been using 3D printing and how they have used it in their classrooms.

Hi Sylvia – Mathematics aside I think your post is a simple version of what is so desperately missing today … a thorough discussion about education where we look at what works, think and discuss why they work, how could things go together, what should we be trying (innovating) in education? And more. Instead we have a skewed discussion that mainly frustrates all involved. Here we have 2 views that are seemingly at one level opposed … but not really … and we can take the strengths and weaknesses of the approaches (as the commenters above have done) and see how we can try both and blend them and more to perhaps revolutionize education. Wouldn’t it be nice if media would help bring that discussion to the forefront so we could all be informed about the issues?

I believe there must be a good balance between the use of electronics calculations and calculations done by hand. There is no question that the advances in technology have made things that were not previously possible reality. I think though that to many times we rely on technology to solve problems for us instead of using our full mental capacity.

Programming doesn’t have to be hard. It is perceived as hard. One of the greatest free programming tools to come out of MIT has been Scratch (scratch.mit.edu). Very little structure is required to create a high level project.

But what keeps us from moving to a computational math system? The perceived cost. If a laptop was $100? Would computational math be as much an issue? Maybe. What if a laptop was $10? Would computational math still be an issue?

Khan’s approach does not use technology to transform pedagogy, but instead slaps a high tech solution to an early 20th century way of teaching. It also fits nicely into a world where NCLB and RttT is data driven and those gold stars really make it easy to measure.

There is a marvelous speech by Seymour Papert that Gary Stager just put online at the Daily Papert (http://dailypapert.com/?p=297) where he talks about the “someday vs. Monday” problem.

Is it somehow not fair to talk about how to reform education while children and teachers are showing up every day? We can’t just tell everyone to go home for a few years while we sort out the way schools should be run.

But you can’t also say that “both” or “balance” needs to happen in the same classroom, especially if the assessments only value one type of learning, and teachers are taught and rewarded for only one style of teaching. If we were talking about a “typical” classroom, I would wager that the Khan style instruction happens over 90% of the time.

Probably more like 99% of the time. I cannot think where the Khan method is more the norm (he just says his videos are better than your teaching which supports his videos).

I wouldn’t think the Khan method though would end up as a focus of an open house. What’s gets more oohs and ahhs from parents? The number of gold stars a kid has, or a project that pulls from so many different areas of math at once (i.e. a Scratch project)?

“But you can’t also say that “both” or “balance” needs to happen in the same classroom.”

I respectfully disagree. I’ve studied quite a bit of Russian history, and I see a parallel. Russia has enormous resources that are wasted because of a bad system. This is plainly seen, and so there is a massive revolution to completely change everything. Within a generation, the system fails. Later, rinse, repeat.

There *are* things that work with the system now. We may be short on scientists, but we have scientists, and brilliant ones at that, who were trained in the “Khan” paradigm. Could it be improved? Could improving require radical change? Certainly. But jumping from one to another is enormously dangerous. Particularly in America, where the system of education is so fragile, it won’t survive some miscalculated shock to teaching core subjects. Nicolas II was terrible, Stalin turned out also to be terrible. The Russians could do with a bit of healthy gradualism, and so could we as math teachers.

I view these more as complementory than conflicting.

Khan actually has a system that is working right now, and it is an improvement on the current system of teaching math. Khan has repeatedly said that his system will free up class time for alternative forms of learning. I do agree that programming (telling computers what to compute for us) would probably be a better use of time than just teaching math computation by hand). Khan even mentions at 10:40 that their system will be useful to teach programming and logic. I hope he does some programming tutorials in the near future.

The Wolfram talk was interesting, and I look foward to seeing a Wolfram Academy 🙂

I found Wolfram’s talk inspiring enough to blog about it last November: Maths not = calculating. I agree with James above that Wolfram’s most difficult challenge is that society still ‘values’ test results, if not testing itself as an assessment strategy. Also, there is the challenge of pedagogical shift even from the students/parents perspectives, i.e. if a teacher tries to be too different from the norm, he/she risks credibility or engagement – most kids want to be different but not too different as to be outcasts (sorry, struggling to be concise here).

Both are the same in their aim to improve maths instruction and desire to engage students – lofty and worthwhile goals. Both want to leverage technology in doing so.

The difference, I think, is deeper. Wolfram wants to clarify how we view maths instruction, shifting the focus from calculating to application – of which calculating is an integral part. For me, it’s a bigger picture and that is personally appealing.

I agree with David above in that the 2 approaches can be complementary. So you can do a Wolfram-style project, say, and if you get stuck with the calculations (e.g. needing year 12 maths while in year 10), the Khan academy may show you how.

My biggest issue with all things Wolfram is the skewed vision of how math is used in the real world… by most of the people going through our public school systems. I had some conversations with Wolfram folks a few years back when they were all kinds of stoked about how Mathematica helped students visualize math for better understanding and exploration. I explained that it was still much (MUCH) too abstract for most of my students. When I explained where my students were coming from, it was simply acknowledged that oh, yea, I was right. This wouldn’t help that. Wolfram’s approach will be great for people who already know some math. It won’t help the serious innumeracy problem.

I don’t have a problem with Wolfram making tools for high end mathematics. It would be nice if we gave younger students a chance to develop numeracy so that more people might make it to the higher levels.

Wolfram’s idea has merit but misses the concept of gradualism espoused by Tim. The chasm Wolfram shows is REALLY between conventional (even KA) mathematics and programming. Gradualism is handled however by a 30 year-old software paradigm: the spreadsheet. Integral to the spreadsheet, are most of the core ideas of programming: iteration, loops, recursion, 2D (even 3D) arrays, conditionals, logical/numeric variables/typing, etc. Procedural logical thinking, modularity…It’s all there…easily accessible…and on your computer right now. You get math and programming, together.

Many don’t see the costs of gear to handle Mathematica, and the extensive retraining of teachers as programmers as an obstacle. The spreadsheets will run on the $100 laptop that O’Hagan mentions. You can buy ten for the cost of Mathematica. Minimal training is needed; many students already know basic spreadsheet.

Great point. Two different approaches, each received enthusiastically. Salman’s point, though, is just about helping kids learn how to do the calculating – solving for x. The first skill to leave us when we distance ourselves from our math classes. I USED to know how to do some complex calculus problems. Not now, though.

I taught programming for many years. From Basic to PASCAL, COBOL, and C++. I agree completely that teaching programming is a great way to get kids to problem solve, plan, and work logically. I used to push for that idea – teach kids logo programming in elementary school, but as we know, if it doesn’t get tested it’s not going to get done.

Nice idea to put these two videos together.

BTW – good job introducing the folks at TEDxNYED. I watched from home that day.

As a math teacher, I’m enthusiastically applauding both. I’m so frustrated with the math paradigm that has caught hold, and so am encouraged by Wolfram’s thoughts (though, I’ll admit, I’m skeptical of some of his points). In particular, I love the idea of comprehension through programming. I’ve tried to do this with little success this year… will keep trying.

But Wolfram makes the point: this can’t change on a classroom-to-classroom basis, because of exams. If my (small, innovative, private) school taught applets instead of pencil-pushing, our kids could have awesome intuition but would likely fail their AP tests (and SATs).

In the meantime, Khan swoops in to save the day. He is streamlining the traditional model. That takes the pressure off the teacher and would truly revolutionize the classroom in terms of individual success and understanding.

The dichotomy here is false. In fact, if you want Wolfram, you need Khan. Khan’s model potentially collapses the time needed to learn the computational stuff. That frees up teachers to, as he puts it, tell how tall hills are based on their shadows. Wolfram would call this steps 1, 2, and 4. Once more classrooms do that more – freed by Khan’s model to at once satisfy traditional exams AND innovate – then there will be a foundation to jump the chasm to Wolfram’s model.

Things that have happened in the last two hours:

1) I received a note from a colleague saying that I MUST watch Khan on TED.

2) I think: I suspect I will not like this, but do not know how to respond.

3) I search ‘Khan Academy Sylvia Martinez’ because I knew you must have written something about this at some point.

4) I find this, which is basically perfect. So, thank you.

I was initially skeptical with what the Kahn Academy was trying to accomplish. However, from the talk I think they are heading in the right direction. The most important thing I heard was that Kahn considers this as a part of a bigger curriculum.

I saw the Wolfram talk a while ago, and I had several concerns with what he was saying. His problem is that he wants to use computers only in the classroom. I think that is only slightly less limiting than working entirely with pencil and paper. I wrote a critique of Wolfram’s talk on my blog.

I recently watched Salman Khan TED talk. My initial thoughts were what an excellent resource. Why couldn’t I have had this when I was doing high school mathematics! Within our current systems I can see Khan’s resources will be of value to students. The benefits are; his examples are clear and sequential. Students can set their own pace. It is relevant to current curriculum. I would applaud him for his efforts and particularly how he has made his resource open. Now contrasting the vision of Conrad Wolfram I would give this man a standing ovation! I agree 100% with what he is saying. Let’s put the emphasis on feeling the math. Spend more time on posing the right questions, then digging out the math and applying it to gain an answer. Bring it back to the real world question and validate the solution. Brilliant! But how does the average teacher achieve this in the classroom? Who will be brave enough to breakaway?

I was at a conference last month called Learning@School in Rotorua. I attended one of Sylvia’s talks ”If Games are the Answer. What’s the Question?” and real enjoyed it. Thanks for that Sylvia.

Why I mention the conference in regard to this post was that one of the products there caught my imagination and it fits in with conceptualising maths perfectly. 3D printing! I’m not a rep for the company however this technology impressed me with the possibilities it could bring. You can create a model in Google Sketch Up. Upload the model to their software and print the model in three dimensions. Next you can test and evaluate the model in real life. Cool! How could this change the way you teach maths? Take a look at the website if you are interested : http://3dprinting.co.nz/ . I teach children between the ages of 5-10 years. I’m not likely to persuade my school to purchase one of these printers. Well not this year! I would be interested in hearing from anyone who has been using 3D printing and how they have used it in their classrooms.

Hi Sylvia – Mathematics aside I think your post is a simple version of what is so desperately missing today … a thorough discussion about education where we look at what works, think and discuss why they work, how could things go together, what should we be trying (innovating) in education? And more. Instead we have a skewed discussion that mainly frustrates all involved. Here we have 2 views that are seemingly at one level opposed … but not really … and we can take the strengths and weaknesses of the approaches (as the commenters above have done) and see how we can try both and blend them and more to perhaps revolutionize education. Wouldn’t it be nice if media would help bring that discussion to the forefront so we could all be informed about the issues?

I believe there must be a good balance between the use of electronics calculations and calculations done by hand. There is no question that the advances in technology have made things that were not previously possible reality. I think though that to many times we rely on technology to solve problems for us instead of using our full mental capacity.

Programming doesn’t have to be hard. It is perceived as hard. One of the greatest free programming tools to come out of MIT has been Scratch (scratch.mit.edu). Very little structure is required to create a high level project.

But what keeps us from moving to a computational math system? The perceived cost. If a laptop was $100? Would computational math be as much an issue? Maybe. What if a laptop was $10? Would computational math still be an issue?

Khan’s approach does not use technology to transform pedagogy, but instead slaps a high tech solution to an early 20th century way of teaching. It also fits nicely into a world where NCLB and RttT is data driven and those gold stars really make it easy to measure.

What Wolfram is saying is we have to transform math and use the ubiquitous tools to reconnect us to what math really means and is. Damned be the tests. THAT is the hard part with what he is proposing. The real world does not allow this. Wolfram’s idea fly in the face, but also with, the writing of Jaron Lanier in the NYTimes (http://www.instapaper.com/text?u=http%3A%2F%2Fwww.nytimes.com%2F2010%2F09%2F19%2Fmagazine%2F19fob-essay-t.html%3F_r%3D3%26pagewanted%3D1) asking “Does the Digital Classroom Enfeeble the Mind?”

There is a marvelous speech by Seymour Papert that Gary Stager just put online at the Daily Papert (http://dailypapert.com/?p=297) where he talks about the “someday vs. Monday” problem.

Is it somehow not fair to talk about how to reform education while children and teachers are showing up every day? We can’t just tell everyone to go home for a few years while we sort out the way schools should be run.

But you can’t also say that “both” or “balance” needs to happen in the same classroom, especially if the assessments only value one type of learning, and teachers are taught and rewarded for only one style of teaching. If we were talking about a “typical” classroom, I would wager that the Khan style instruction happens over 90% of the time.

Probably more like 99% of the time. I cannot think where the Khan method is more the norm (he just says his videos are better than your teaching which supports his videos).

I wouldn’t think the Khan method though would end up as a focus of an open house. What’s gets more oohs and ahhs from parents? The number of gold stars a kid has, or a project that pulls from so many different areas of math at once (i.e. a Scratch project)?

“But you can’t also say that “both” or “balance” needs to happen in the same classroom.”

I respectfully disagree. I’ve studied quite a bit of Russian history, and I see a parallel. Russia has enormous resources that are wasted because of a bad system. This is plainly seen, and so there is a massive revolution to completely change everything. Within a generation, the system fails. Later, rinse, repeat.

There *are* things that work with the system now. We may be short on scientists, but we have scientists, and brilliant ones at that, who were trained in the “Khan” paradigm. Could it be improved? Could improving require radical change? Certainly. But jumping from one to another is enormously dangerous. Particularly in America, where the system of education is so fragile, it won’t survive some miscalculated shock to teaching core subjects. Nicolas II was terrible, Stalin turned out also to be terrible. The Russians could do with a bit of healthy gradualism, and so could we as math teachers.

I view these more as complementory than conflicting.

Khan actually has a system that is working right now, and it is an improvement on the current system of teaching math. Khan has repeatedly said that his system will free up class time for alternative forms of learning.

I do agree that programming (telling computers what to compute for us) would probably be a better use of time than just teaching math computation by hand). Khan even mentions at 10:40 that their system will be useful to teach programming and logic. I hope he does some programming tutorials in the near future.

The Wolfram talk was interesting, and I look foward to seeing a Wolfram Academy 🙂

I found Wolfram’s talk inspiring enough to blog about it last November: Maths not = calculating. I agree with James above that Wolfram’s most difficult challenge is that society still ‘values’ test results, if not testing itself as an assessment strategy. Also, there is the challenge of pedagogical shift even from the students/parents perspectives, i.e. if a teacher tries to be too different from the norm, he/she risks credibility or engagement – most kids want to be different but not too different as to be outcasts (sorry, struggling to be concise here).

Both are the same in their aim to improve maths instruction and desire to engage students – lofty and worthwhile goals. Both want to leverage technology in doing so.

The difference, I think, is deeper. Wolfram wants to clarify how we view maths instruction, shifting the focus from calculating to application – of which calculating is an integral part. For me, it’s a bigger picture and that is personally appealing.

I agree with David above in that the 2 approaches can be complementary. So you can do a Wolfram-style project, say, and if you get stuck with the calculations (e.g. needing year 12 maths while in year 10), the Khan academy may show you how.

My biggest issue with all things Wolfram is the skewed vision of how math is used in the real world… by most of the people going through our public school systems.

I had some conversations with Wolfram folks a few years back when they were all kinds of stoked about how Mathematica helped students visualize math for better understanding and exploration. I explained that it was still much (MUCH) too abstract for most of my students. When I explained where my students were coming from, it was simply acknowledged that oh, yea, I was right. This wouldn’t help that.

Wolfram’s approach will be great for people who already know some math. It won’t help the serious innumeracy problem.

I don’t have a problem with Wolfram making tools for high end mathematics. It would be nice if we gave younger students a chance to develop numeracy so that more people might make it to the higher levels.

Wolfram’s idea has merit but misses the concept of gradualism espoused by Tim. The chasm Wolfram shows is REALLY between conventional (even KA) mathematics and programming. Gradualism is handled however by a 30 year-old software paradigm: the spreadsheet. Integral to the spreadsheet, are most of the core ideas of programming: iteration, loops, recursion, 2D (even 3D) arrays, conditionals, logical/numeric variables/typing, etc. Procedural logical thinking, modularity…It’s all there…easily accessible…and on your computer right now. You get math and programming, together.

Many don’t see the costs of gear to handle Mathematica, and the extensive retraining of teachers as programmers as an obstacle. The spreadsheets will run on the $100 laptop that O’Hagan mentions. You can buy ten for the cost of Mathematica. Minimal training is needed; many students already know basic spreadsheet.

The cute waves in Wolfram’s video…my students were making that on a spreadsheet 10 years ago. Here’s a screenshot:

http://www.algebraplusplus.com/hello2.html#Oobj9