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Thursday, March 15. 2012
At City Journal, The Math of Khan - Not just a YouTube phenomenon, but a model for educational transformation.
I know somebody whose son relies on this in High School. Inspiring and enthusiastic math teachers are rare. In fact, everybody seems to like Khan Academy except Profs of Education. That tells you something.
Here's The Beauty of Algebra
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We homeschool and have found Khan to be very helpful. Most of the clips are so short that the kids don't have time to get bored. Short, sweet and to the point.
OT: Something very funny
I've been taking online courses, including mathematics. More tools in the shed I suppose, but I'm becoming more aware of the advantages of having a good teacher. (Never having finished school, this is a revelation). The fellow in the video held my attention and conveyed his own passion well, (subsequently bringing life to the subject).
ADD? Yesterday I wrote a post on my blog, which was obliquely related to my learning style. It's as close to a self-diagnosis of ADHD as I suppose I could come, though I have little regard for any such diagnosis; I refuse to accept my learning style as symptomatic of a deficit.
The Farmers' zeal for a lifelong commitment to education is appreciated. It's a good work to bring attention to the work of The Khan Academy.
Well, at least he doesn't teach "reform" math, it appears. But also not fixed procedural math either.
Here is an article on the problem with the "reform" math now taught. Seems a lot those kids kicked into special ed for having problems do very well with the old way of teaching algorithms. I'm all for teaching concepts and not just formula but this from the "Reform" math wikipedia scares me:
Reformers do not oppose correct answers, but prefer to focus students' attention on the process leading to the answer, rather than the answer itself. The presence of occasional errors is deemed less important than the overall thought process.
As a holder of a BS in Physics who started out in engineering, I'm glad they aren't opposed to correct answers. Understanding concepts is great, essential for academics, but out in the working world, the correct answer is far more important.
An obvious yet important reminder:
Mathematics exists only within the human brain.
It was initially induced via human senses, and is now deduced based on the scientific method.
Still, no humans = no mathematics.
Son #5 survived on it in Algebra 1. He has used it less in Geometry, which he understands intuitively a bit better.
I wish we had had it for Son #4.
The presence of occasional errors is deemed less important than the overall thought process.
I've seen this come by before. The end result is kids who can't do math, or physics, or whatever the 'hard' subject is. I'm convinced these scams are invented by folks who can't do math and are more for the teachers, who also can't do math, than for the students. It's a cop out all around, since being able to evaluate and teach 'concepts' requires a lot more talent than needed to teach a skill. And I'd say a lot more talent than the average teacher is likely to possess.
Most mathematicians probably tend towards Platonism, that is, math consists of eternal truths discovered by the human mind in contrast to being a peculiar arrangement of neural connections that only exist in the human mind. It is perhaps closer to religion than to mechanics ;)
I've seen this come by before: Egad! I made a fortune as an eighth grader tutoring my brother's 5th grade friends in the New Math. Since then, THIS has come by...again...and again...and again. I josh a friend who is in sales for a major text book firm that his company does this so it is assured of huge sales every few years. He blames it on Texas (Bush) (sarc).
Khan Academy and other on-line education sites are a boon to education. My grandkids move every two years as their dad is in the military, but many children of corporate managers have an equally challenging educational experience. The Internet allows parents and student to confirm one's ability to grasp a subject without the torment of outside evalution. I've also seen it help all ages to become self-starters and life-long learners -- not a bad idea when technology changes every nano second.
BD's often referenced Teaching Company, though not free, is another excellent source, especially for the humanities. Many universities (maybe thanks to Khan) are opening on-line classes for free or a small materials charge. I love it!
I saw Khan on 60 Minutes. My sons have used it in the past. It's a terrific tool.
My older son struggled with math, and for this very reason. The reform version of math, after it was explained to me, drove me nuts. I'd have failed, and I was always excellent with numbers.
There is a similar problem with spelling and grammar taking place. Neither of my boys or their friends are particularly strong at spelling, and their teachers have never seemed to care.
Just because we need our brains to explain it doesn't mean it doesn't exist.
Phi is a fairly useful tool in nature, don't you think? The fact someone was capable of figuring it out doesn't mean math didn't exist.
Math is about concepts (brain driven) and application (appearance/explanation in nature).
I made a fortune as an eighth grader tutoring my brother's 5th grade friends in the New Math.
In high school I took "Illinois Math," the creation of Max Beberman. I loved it, as it had a lot of proofs. Before Illinois Math, I was indifferent to math. As a result of Illinois Math, I love math. Unfortunately, many less able students couldn't hack the proof writing that Illinois Math required. It isn't for everyone.
There were a lot of problems in taking Illinois Math/New Math down to the lower grades. A lot of elementary school teachers thought that Illinois Math/New Math meant that basic arithmetic skills-addition, subtraction, multiplication, and division - should be downgraded.
Years later I took a math course with a professor who knew Max Beberman. In a conversation after class, the professor said that Max told him that he had never intended that Illinois Math resulted in shunting basic arithmetic skills to the wayside. Why did so many elementary and junior high teachers think this was the case? Where did this misinterpretation come from?
IMHO, it came from the fact that a very high proportion of elementary school teachers are not very good at math. When Illinois Math/New Math was thrown at them, concepts which required not less math but more math, the elementary school teachers were overwhelmed, and did less math. Which meant the downgrading of basis arithmetic skills.
The presence of occasional errors is deemed less important than the overall thought process.
I tend to agree with that. You apparently do not. I have seen high school physics students write out just the numeric answer, and not the equation. This is the default result of having calculators. It is MUCH more important to write out the equation, do the process thingy, even if there is an arithmetic error, than to write down only the "correct number."
You do the process thingy, write out the equations, you will understand it a lot more in the long run. This is especially important when students have calculators, and punch in numbers, without always thinking where the numbers came from.
At the same time, I am not of the opinion that one can do well in high school math and beyond if one does not have a good grasp of basic multiplication and division.
The NEW MATH courses I had in high school back in the 60's, where I had to do a lot of work in proving various mathematical principles such as the distributive principle, were of later assistance in estimating, which is a very useful skill in later life. Due to work in the distributive principle et al, I was able to see that 370X39 is ~400X40 less 10%. But one cannot estimate well if one doesn't have a basic grasp of multiplication and division.
With Khan Academy, one can bypass one's own bad teacher and learn from a good teacher- in this case an online teacher. My 9th grade math teacher, in spite of being a Phi Beta Kappa math graduate, was a horrible teacher. I ignored her, and taught myself from the Illinois Math textbook, which was a very good text. In a sense, the textbook was my equivalent of Khan Academy, decades earlier.
Concepts do not exist outside the human brain. Thank you for proving my point.
In fact, you could never prove that anything at all exists outside of the human brain in general, and your brain in particular.
Ever seen the movie entitle The Matrix?
The process is very important early on, perhaps more important than the correct answer. The student hasn't finished, though, until he can get the right answer. It would be nice to see students given projects to do where the failure to come up with the right answer will cost them something concrete and immediate -- like the inconvenience of having to run out and buy more of a critical component, because they couldn't correctly calculate the amount up front.
I'm not a big proponent of coddling or "relevancy," but I do believe we all learn better when the rational task also strikes an emotional chord. And just speaking for myself, I can't learn the "what" for beans unless I can grasp the "how" or "why."
Does whatever point "The Matrix" makes exist outside your brain? If not, why should the rest of us care?
Part of the "right answer versus "process" argument is on what level you are at. At the elementary level, doing basic addition, multiplication, subtraction, and division, I see getting the right answer as very important. It indicates that you have internalized the computational process the teacher has outlined. Or you have made your own process.
Before leaving elementary school a student really does need to have an automatic understanding that 8X7=56. Among other things. By whatever method.
At the same time, teachers at the elementary level should be open to students finding answers by their own methods. As the saying goes, there is more than one way to skin a cat.
One problem with math education is that educators have tried to introduce snippets of interesting mathematical information at the lower levels, such as tiling, when it is more important for more basic skills to be addressed, such as competence in fractions and decimals.
The process is more important higher up the ladder. There is a reason why science and engineering professors will take off only 10-15% if the equation is all written out, and there is a multiplication error. [Orders of magnitude errors should be taken more seriously.]
Re relevance. I have read that there are children in Brazil who work as/with small vendors who have developed excellent computational skills in their head- a necessary skill as a small vendor. When in school, they have problems. Go figure.
Another point about relevance. Word problems are an attempt to make math relevant, and many students have a big problem with them.
No simple answer.