Times are dark now, but I'm actually excited about what kind of education system we'll produce when we finally tear down the 19th century one we have now and build a 21st century one. Can you imagine what kind of 20-year-olds would come out of a system that successfully produced deliberative practice across a wide variety of disciplines by harnessing the power of computers melded with the strengths of human instruction to build custom curricula for everybody?
The country that cracks this and builds this system instead of incrementally tweaking our 19th century system will own the rest of this century and most of the next.
It won't be a country; it will be a large network of individuals.
I can't help but think that the future of education looks like the current home schooling community. The results with my own children are remarkable.
The resources available now online are vastly better than anything I had when I was in school, and far cheaper. At Khan Academy one excellent teacher can teach the world. That's a science-fiction level of awesome.
And you can tailor the education to the strengths and weaknesses of the child. I don't think a large organization could ever replicate this process or get these results. It's too difficult and expensive to do on a large scale.
We are already working on that in the education community - project based learning. It has its detractors but the fundamental tenets are: 1) learning is the product of the work of learners, 2) students learn by doing. Science classrooms taught this way typically produce students who go on to be very successful academically and professionally in the maths and sciences. The secret? Integrate multiple disciplines, let students explore facets of the subject which appeal to them, and have them work on something - with each other (!!) - which has a tangible result or artifact. We have cracked it, and we have peer-reviewed papers to prove it. Now we just have to get the troglodytes in charge of public education to adopt it.
[Edit]
Some citations:
Rivet, Krajcik:"Achieving Standards in Urban Systemic Reform: An Example of a Sixth Grade Project-Based Science Curriculum"
Hmelo-Silver et al. "
Scaffolding and Achievement in Problem-Based and Inquiry Learning: A Response to Kirschner, Sweller, and Clark (2006)"
A lot of the problem is that practicing something is not only not encouraged but actively discouraged. Getting a CS student to code, a chemist to experiment, a physicist to experiment and a builder to build isn't hard. Throw them the equipment and say "Here, check this out!" and they'll go at it oldschool. Usually that doesn't happen, instead A) all equipment is kept away except during mandated times and for mandated purposes and B) they're held in classes and lectures long after they've gone "Ok, cool. Let's play with this for a bit and we'll do more theory later" so that they're pretty much sick of all of it at the end of the day. This is the most discouraging thing about the current system. You have to have the option of pacing yourself and also have the space to grow. I'd play in the CS labs in the wee AM. I'd borrow the machine shop. The cafeteria usually left the rest of the coffee out, me and my friends would sit and do electronics problems or calculus all night, perhaps take a break to learn sign language or how to tap out a proper 4/4 beat. No one complained because that's excellent - you're learning! Exactly what a university is there for!
Think bigger - what kind of 12-year-olds will come out?
Consider 8-hour school days: 3 hours in lunch/PE/hallways leaves 5 hours of group lectures. If the teachers spent the whole time in tutoring individual students in their 30-person classrooms, that's 10 minutes for you each day.
What happens when you get hours of individualized learning alternated with deliberate practice? Years of school compressed into months. With half of every day left over for socializing, athletics and exploration.
Its not really hard to imagine a better system - almost anything would be better.
I am not sure custom curricula are a good idea. Education is more about how it's learnt and less about what is learnt.
Beware of technology's cognitive biases too, see how TV is transforming education into entertainment. Computers have their own biases, just see the difference between today's teenagers and teenagers from 15 years ago.
I think the problem is that it won't work for all people. The system actually seems to work well for the average person. However, a country like the USA, can benefit from attracting these kind of people (Investors, Infrastructure, Big companies, Networks...) and it seems like it's already doing so to some extent.
I am afraid that the system will never change it would not surprise me if schools still used the same teaching methods they use today, a couple of centuries from now.
Those problem-set hours total almost a whole other working week laid on top of the other academic tasks of attending lectures and reading notes. In college as in grade school, where is the time for deliberate practice?
I can't help but think that this is a case of not seeing the wood for the trees. In a good university problem-sets obey most of the requirements of deliberate practice: they are designed, there is repetition, they are mentally demanding, and they gradually get harder so that you are working at the edge of your abilities.
The remaining requirements of deliberate practice are to do with meta-cognition - i.e. thinking about what you are doing - and that is down to you.
It reminds me of stories my mum (who's a teacher) tells about pupils complaining that they had no time for revision because of the practice exams she set. I mean, what do they think revision is?
Sanjoy Mahajan, the author of this article, is the Associate Director at the Teaching and Learning Laboratory @ MIT. If you're interested in education, he has an excellent OCW course [1] where you can hear more about his techniques for teaching.
I find that programming courses tend to force deliberate practice. Think about first year CS course: you're taught about loops and if statements, then you're asked to write a program. There's no direct connection between the material and the assignments: you have to think and practice and fail.
This is one of the reasons perhaps for why so many people quit computer science after the first year. So many people in my family expressed their frustration at programming assignments (none of them took more than one or two courses).
I feel like I'm in the minority here but rote practice has a role, just like playing scales or dribbling a basketball does. It lets you ingrain into your muscle memory the foundation-level skills. Once you're able to multiply arbitrary two digit numbers in your head or dribble a ball without really thinking about it, it frees you for when you're thinking about higher level problems.
Is there any information about what constitutes deliberate practice in math?
Here is the FAQ (just revised for this reply) that I send to parents of children in the math classes I teach:
1) 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 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 an explicit property P(x), prove OR DISPROVE that P(x) is true for for all x [existing in] X. . . .
Level 4. Given an explicit set X and an explicit property P(x), find a NECESSARY AND SUFFICIENT CONDITION Q(x) that P(x) is true. . . .
Level 5. Given an explicit set X, find an INTERESTING PROPERTY P(x) of its elements. Now we're in the scary domain of pure research, where students might think that total chaos reigns. This is real mathematics. Authors of textbooks rarely dare to pose level 5 problems."
Graham, Ronald, Knuth, Donald, and Patashnik, Oren (1994). Concrete Mathematics Second Edition. Boston: Addison-Wesley, pages 72-73.
This digression becomes the subject of a, um, problem in Exercise 4 of Chapter 3: "The text describes problems at levels 1 through 5. What is a level 0 problem? (This, by the way, is NOT a level 0 problem.)"
"First, what is a PROBLEM? We distinguish between PROBLEMS and EXERCISES. An exercise is a question that you know how to resolve immediately. Whether you get it right or not depends on how expertly you apply specific techniques, but you don't need to puzzle out what techniques to use. In contrast, a problem demands much thought and resourcefulness before the right approach is found. . . .
"A good problem is mysterious and interesting. It is mysterious, because at first you don't know how to solve it. If it is not interesting, you won't think about it much. If it is interesting, though, you will want to put a lot of time and effort into understanding it."
Zeitz, Paul (1999). The Art and Craft of Problem Solving. New York: Wiley, pages 3 and 4.
". . . . As Paul Halmos said, 'Problems are the heart of mathematics,' so we should 'emphasize them more and more in the classroom, in seminars, and in the books and articles we write, to train our students to be better problem-posers and problem-solvers than we are.'
"The problems we have selected are definitely not exercises. Our definition of an exercise is that you look at it and know immediately how to complete it. It is just a question of doing the work, whereas by a problem, we mean a more intricate question for which at first one has probably no clue to how to approach it, but by perseverance and inspired effort one can transform it into a sequence of exercises."
"It is easier to advance in one topic by going ahead with the more elementary parts of another topic, where the first one is applied. The brain much prefers to work that way, rather than to concentrate on ugly technical formulas which are obviously unrelated to anything except artificial drilling. Of course, some rote drilling is necessary. The problem is how to strike a balance."
Lang, Serge (1988), Basic Mathematics. New York: Springer-Verlag, p. xi.
"Learn by Solving Problems
"We believe that the best way to learn mathematics is by solving problems. Lots and lots of problems. In fact, we believe the best way to learn mathematics is to try to solve problems that you don't know how to do. When you discover something on your own, you'll understand it much better than if someone just tells it to you.
. . . .
"If you find the problems are too easy, this means you should try harder problems. Nobody learns very much by solving problems that are too easy for them."
Rusczyk, Richard (2007). Introduction to Algebra. Alpine, CA: AoPS Incorporated, p. iii.
[+] [-] jerf|15 years ago|reply
The country that cracks this and builds this system instead of incrementally tweaking our 19th century system will own the rest of this century and most of the next.
[+] [-] drblast|15 years ago|reply
I can't help but think that the future of education looks like the current home schooling community. The results with my own children are remarkable.
The resources available now online are vastly better than anything I had when I was in school, and far cheaper. At Khan Academy one excellent teacher can teach the world. That's a science-fiction level of awesome.
And you can tailor the education to the strengths and weaknesses of the child. I don't think a large organization could ever replicate this process or get these results. It's too difficult and expensive to do on a large scale.
[+] [-] gatlin|15 years ago|reply
[Edit]
Some citations:
Rivet, Krajcik:"Achieving Standards in Urban Systemic Reform: An Example of a Sixth Grade Project-Based Science Curriculum"
Hmelo-Silver et al. " Scaffolding and Achievement in Problem-Based and Inquiry Learning: A Response to Kirschner, Sweller, and Clark (2006)"
[+] [-] LarrySDonald|15 years ago|reply
[+] [-] JoeAltmaier|15 years ago|reply
Consider 8-hour school days: 3 hours in lunch/PE/hallways leaves 5 hours of group lectures. If the teachers spent the whole time in tutoring individual students in their 30-person classrooms, that's 10 minutes for you each day.
What happens when you get hours of individualized learning alternated with deliberate practice? Years of school compressed into months. With half of every day left over for socializing, athletics and exploration.
Its not really hard to imagine a better system - almost anything would be better.
[+] [-] proemeth|15 years ago|reply
[+] [-] csomar|15 years ago|reply
[+] [-] tomjen3|15 years ago|reply
[+] [-] Tibbes|15 years ago|reply
Those problem-set hours total almost a whole other working week laid on top of the other academic tasks of attending lectures and reading notes. In college as in grade school, where is the time for deliberate practice?
I can't help but think that this is a case of not seeing the wood for the trees. In a good university problem-sets obey most of the requirements of deliberate practice: they are designed, there is repetition, they are mentally demanding, and they gradually get harder so that you are working at the edge of your abilities.
The remaining requirements of deliberate practice are to do with meta-cognition - i.e. thinking about what you are doing - and that is down to you.
It reminds me of stories my mum (who's a teacher) tells about pupils complaining that they had no time for revision because of the practice exams she set. I mean, what do they think revision is?
[+] [-] jochu|15 years ago|reply
[1] http://ocw.mit.edu/courses/chemistry/5-95j-teaching-college-...
[+] [-] huherto|15 years ago|reply
[+] [-] hasenj|15 years ago|reply
This is one of the reasons perhaps for why so many people quit computer science after the first year. So many people in my family expressed their frustration at programming assignments (none of them took more than one or two courses).
[+] [-] MaxGabriel|15 years ago|reply
[+] [-] michael_michael|15 years ago|reply
[+] [-] Splines|15 years ago|reply
[+] [-] tokenadult|15 years ago|reply
Here is the FAQ (just revised for this reply) that I send to parents of children in the math classes I teach:
1) 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 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 an explicit property P(x), prove OR DISPROVE that P(x) is true for for all x [existing in] X. . . .
Level 4. Given an explicit set X and an explicit property P(x), find a NECESSARY AND SUFFICIENT CONDITION Q(x) that P(x) is true. . . .
Level 5. Given an explicit set X, find an INTERESTING PROPERTY P(x) of its elements. Now we're in the scary domain of pure research, where students might think that total chaos reigns. This is real mathematics. Authors of textbooks rarely dare to pose level 5 problems."
Graham, Ronald, Knuth, Donald, and Patashnik, Oren (1994). Concrete Mathematics Second Edition. Boston: Addison-Wesley, pages 72-73.
This digression becomes the subject of a, um, problem in Exercise 4 of Chapter 3: "The text describes problems at levels 1 through 5. What is a level 0 problem? (This, by the way, is NOT a level 0 problem.)"
"First, what is a PROBLEM? We distinguish between PROBLEMS and EXERCISES. An exercise is a question that you know how to resolve immediately. Whether you get it right or not depends on how expertly you apply specific techniques, but you don't need to puzzle out what techniques to use. In contrast, a problem demands much thought and resourcefulness before the right approach is found. . . .
"A good problem is mysterious and interesting. It is mysterious, because at first you don't know how to solve it. If it is not interesting, you won't think about it much. If it is interesting, though, you will want to put a lot of time and effort into understanding it."
Zeitz, Paul (1999). The Art and Craft of Problem Solving. New York: Wiley, pages 3 and 4.
". . . . As Paul Halmos said, 'Problems are the heart of mathematics,' so we should 'emphasize them more and more in the classroom, in seminars, and in the books and articles we write, to train our students to be better problem-posers and problem-solvers than we are.'
"The problems we have selected are definitely not exercises. Our definition of an exercise is that you look at it and know immediately how to complete it. It is just a question of doing the work, whereas by a problem, we mean a more intricate question for which at first one has probably no clue to how to approach it, but by perseverance and inspired effort one can transform it into a sequence of exercises."
Andreescu, Titu & Gelca, Razvan (2000), Mathematical Olympiad Challenges. Boston: Birkhäuser, page xiii.
"It is easier to advance in one topic by going ahead with the more elementary parts of another topic, where the first one is applied. The brain much prefers to work that way, rather than to concentrate on ugly technical formulas which are obviously unrelated to anything except artificial drilling. Of course, some rote drilling is necessary. The problem is how to strike a balance."
Lang, Serge (1988), Basic Mathematics. New York: Springer-Verlag, p. xi.
"Learn by Solving Problems
"We believe that the best way to learn mathematics is by solving problems. Lots and lots of problems. In fact, we believe the best way to learn mathematics is to try to solve problems that you don't know how to do. When you discover something on your own, you'll understand it much better than if someone just tells it to you.
. . . .
"If you find the problems are too easy, this means you should try harder problems. Nobody learns very much by solving problems that are too easy for them."
Rusczyk, Richard (2007). Introduction to Algebra. Alpine, CA: AoPS Incorporated, p. iii.
[+] [-] wnoise|15 years ago|reply
[+] [-] wnoise|15 years ago|reply