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Sunday, November 24. 2013
I see no reason to accept the author's assertion that math education in the US is broken:
What do readers think? What was Isaac Newton's math education like?
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The author's an idiot. What does "more equitable achievement" even mean?
What good does it do to explain your answer when the person you are explaining it to doesn't understand it.
Common core, the old method, both are ignorant. Math is a language. You have to learn the grammar before you can use it to demonstrate complex ideas. But as a language, it is cumulative. Teaching on the average isn't doing anyone any good.
The most significant development in teaching mathematics is the Khan Academy. Students can work at their own pace, racing ahead when comprehension comes easy, slowing to capture when they hit a trouble spot. If schools adopt the flipped classroom for math instruction, the results will be even greater.
We are no longer limited to retarding those who get the concept and abandoning those needing a bit more time to move the average along. We have the technology, what we need to dispose of are the "education" theorists.
And if kids need something real to apply it to, well, woodworking is probably the easiest. They'll use more math, fractions, trig, geometry, planing, cutting, fitting, wood in the designing and building of a stool than they'll ever get from some academics idea of a math problem.
Just enough truth to wash down the poison.
When a person uses the word "disprroved" the standards should be pretty high, especially when we are talking about math. Evidence that the brain can adapt - that under intense usage certain areas can grow - is nothing remotely like disproving that some people are math people.
He doesn't know enough statistics himself to know what is driving down math scores in some western countries but not others. I'm not seeing much about teaching statistics and how data can be looked at in different ways.
That said, there are good points about his methods, though not quite the ones he thinks. Expanding math instruction to focus on the reasoning, connecting, and explaining are good things. Those draw on mathematics and are useful in the practical application of math. But they are all somewhat related to verbal strategies, especially the latter. What he is doing is teaching students to make up for math deficits by relying on other strengths that they might have. That's a good thing, but it's not the same thing. I think that is a good way to teach math, as many more people will use math in that way as adults. But it's not the same thing as math. Not to people who will actually make their livings with those tools.
People hate the idea of innate mathematical ability, and will go to great lengths to show it's not true.
I have come to understand that on the whole one can expect it to be possible to threaten, bribe, bully ALMOST anyone into seeing things their way. This guy is just one more example of how very, very easy it is to get "teachers" to cave in to orders from above.
There is nothing about this guy that would make me want to spend 20 minutes over coffee with him. Just another male cow looking to suck his way up the escalator reserved for approved women only.
Got my best grade in math my senior year of high school. I was not some math genius. Took Trig my senior year. The reason I did well (got an A)? My Trig teacher was scary. He would select people whom he knew did not complete the homework to bring to the front of the classroom to do a problem. The teacher knew very well this kid would make a fool out of himself because he didn't do the homework.
That fear of not knowing the answers and being dragged in front of the rest of the class got me to work very hard on my homework and make sure I had it done!
Strict teachers don't fit this new idea of coddling children and making them feel good about themselves. Fear of humiliation works wonders!
In many ways this is how the Obama health care advocates used flawed statistics to support their agenda. There is no doubt that the U.S. is behind in math when compared to the rest of the world. BUT, the rest of the world does not inculde their poor students in the data. In a lot of European countries students headed for blue collar work are out of the school system by age 16 and working as apprentices so they are not counted. In most Asian countries only the best get to go to school and they are pushed and monitored so intensely that if they stumble and can't keep up they are out and working in the fields. So while the rest of the world "high grades" their students the U.S. Counts everyone includng people who snuck in here from another country and are stealing from our publiuc school fundng and resisting learning English (to satisfy another agenda). Another problem for American higher education is that it is beneficial for colleges to enroll foriegn students and since only the cream of the crop come to the U.S. from other countries they tend to bump Americans out of limited slots in some of the science and high tech programs.
The fix: Allow poor students to opt out of higher math in secondary schools. This would allow high schools to provide a better learning environment for students who can do well in math.
With fewer students in advanced math in high school make it a requirement that the teachers are qualified to teach math. Today it is not uncommon for science and math to be taught by the gym teacher or the social studies teacher etc.
Make some changes in the system to favor American students applying for college. We are cutting our own throat by excluding American students in favor of foriegn students.
We home-schooled our 4 children from k-12 and when they got college age, the first one scored a 1600 (perfect) on the SAT, and the second only missed one question on the SAT and the third got a 35 on the ACT.
Their teachers were surprised that they already knew calculus and easily tested out of Calc I.
I realize I have a limited knowledge of how to teach everyone's children, but know how to teach my children to succeed at Maths.
I find the teaching methods I used to be direct opposites of the program that this author promotes (common core), in fact I find the common core curriculum deficient in several ways, and my children would not prosper with that as their course of study.
I find it amusing to see "experts" decry other ways of teaching in favor of common core, when I find the opposite true. Can't really recommend this article as having any merit.
I had an employee not too long ago who had been graduated from the local high school and she could add but she couldn't subtract. She also had considerable difficulty putting files in alphabetic order.
Children need to learn to add, subtract, multiply and divide. They need to learn the alphabet. They need to learn how to read and write. These are skills that require practice, repetition to master; just as learning to play the piano requires practice, learning scales.
If that example of the right triangles and whether they're similar or congruent is truly how geometry is being taught, it's no wonder that no one under thirty knows geometry, or addition, or subtraction or the alphabet.
This was common core propaganda. What we need are enthusiastic math teachers. We do not need teachers who write letters to the editor complaining they have never used algebra in their lives. They use simple algebra all the time. they just don't recognize it.
And that is the answer to problem, teachers who enjoy their work and take pride in it, instead of viewing it as an alternative to stocking the local grocery store.
Sailer makes a pretty convincing argument that math scores in the U.S are just fine.
My guess is that we're going to see in a few years that Common Core is just another fad that won't have done anything to improve real educational outcomes.
...the speed- and test-driven classrooms of the last decade... There is no reason to think Common Core is going to change anything in the teaching to the test culture we have.
Also, even if Boaler is correct, and I do hope against experience that she is correct, it won't close the gap.
As a student my best teacher gave a quiz every Thursday on that weeks work and then ordered the seating for the following week accordingly, worst score in the front left seat and serpentine back to the best score in the rear right seat. Every day the kids in the front had to begin the class with displaying their solution to a couple of the homework problems on the board. Homework was turned in as you entered class, so those kids had to know all those problems by heart so that when they were told which problem to solve on the board they could do it.
Math education was mechanical and skill focused. We all finished the term with darn good grades and an excellent understanding of the subject.
My children, on the other hand, were educated in group discussions. As young kids they used the "Chicago method" which was ridiculous, it high school math was inane. Homework was never graded and only erved as a discussion starter. The kids had three graded tests typically, and those were there only grades of the term. They taught themselves math at home, in other words, or when they really needed it for something, like chemistry or physics. A terrible system for teaching math, and smart kids (who taught themselves) survived it while less capable kids learned very little.
Isaac Newton had unremarkable schooling until he was 23 years old, when Cambridge was shut down by the 1665 plague, which sent him home to study on his own. That's when he really flowered as an autodidact. He quickly ran through the classic texts and burst out on his own, creating the mathematics he needed to do the work that interested him.
In a case like Newton, the main job of an educational system was to stay out of his way.
This is why there is an emphasis on reading within elite UK institutions of learning.
Check out the reading lists for Balliol College at Oxford sometime -- to Americans they might seem shockingly large. (The last I recall, the German reading list alone has roughly three hundred works on it -- they cleverly add a certain piece by Rilke toward the end where it would have greater effect.)
These reading lists do not serve as a comprehensive list of works that students are expected to read. Instead, this is the starting point for what is effectively a dialogue with a professor acting as a mentor.
That's part of why Balliol College has produced some of the most noticed intellectuals in the UK -- Aldous Huxley immediately comes to mind as an example.
The university can exist as a means to support individual initiative. It simply appears that in the American context, it usually doesn't.
The main job of American educational institutions for the auto-didact may in fact be to stay well out of the way, providing only an extended reading list ...
Not to disagree but to add a point. I don't think the value of the reading list example is specifically the reason why the students excel. Rather I think the rigorous requirements puts off the inferior student and weeds out lesser students that weren't put off by the requirements leaving the best students who then rise to the level expected of them. This illustrates the real problem that U.S. schools have which is they try to bring everyone up to some arbitrary level of excellence and that attempt fails. Not only do the poorer students fail to achieve anything close to excellence but additionally with the resultant stretched too thin resources the better students are not given the opportunity to excel. Our current system was designed to meet conflictng agendas but not to produce great graduates.
It's too little too late.
This is the educational form of so-called "shock doctrine" -- if what you're doing isn't working, double down with something else that sounds like a curative even if it turns out it isn't one.
I would love to see the empirical studies that show that the "common core" produces anything but common results, as in its ability to produce well-educated free minds. So far I see bad faith masquerading as proof, and even more bad faith masquerading as the disproof of the alternatives.
I see the "common core" concept as a vestigial form of the mass industrial economy that the United States has lost to other more agile countries. A standardised, one-size-fits-all education seems to be precisely what isn't needed. A system that produces mass men for a mass industrial labour economy that no longer exists is precisely what isn't needed.
Now that the United States seems to wish for a "knowledge economy", it's doing all it can to ensure that it won't have the base for it. Instead, America as a mass society has chosen to default to a "service economy", in which we're meant to believe that Americans can remain an affluent society by performing the economic equivalent of scratching each other's backs.
Standardising mediocrity at any cost won't help anyone.
The only useful function for the "common core" standardised testing regime is that it tells the competent and capable that at a certain point, the system will no longer be able to provide for their advanced educational needs.
If you are a parent and your child comes home with a 99th percentile result on any American standardised test, it is time to realise that your child is at the end of the line with regards to the mass of children he or she is stuck with.
What's left is what less cynical people might call "individual initiative" -- I prefer to think of it as going to war with the herd for the sake of individual self-preservation.
There is a reason America has its elites and its second-tier near-elite support class.
Without them, America as a nation would barely function at all, except as a disorganised mass of labour in the Russian model, nails being driven by hammers ...
Dmitry Orlov has said enough about the "sovietisation" of the American state -- his ideas and concepts are worth mulling over, especially within the context of its education systems, most especially as applied to the "common core".
We need to change the way we teach math in the U.S.
Which has been said how many times over the last 50 years?I would estimate that there is a new math teaching fad/initiative every five years or so. Which is why I roll my eyes at "Common Core." Which is most likely the common response of anyone who has taught school.
As a schoolboy I started out with "Regular Math." In high school I was switched to "New Math/Illinois Math." I was indifferent to math before "New Math/Illinois Math." I was enchanted with all the proofs that "New Math/Illinois Math" pushed me to prove. However, I realize my enjoyment of "New Math/Illinois Math" came with at least three caveats.
1) "New Math/Illinois Math" was better fitted for the most capable students than for more run of the mill students.
2) Working in "New Math/Illinois Math" did not mean that one should throw out traditional addition,subtraction, multiplication, and division skills. Unfortunately, some teachers didn't realize this.
3) Less capable math teachers- and there are many elementary level teachers who are not good at math- made "New Math/Illinois Math" a disaster for students.
Years later I spent several years in a second career, teaching math. Some observations follow.
1) Too many primary and secondary level math textbooks, nearly always authored by someone teaching at the college level, are enchanted with adding a a smorgasbord of topics to the math curriculum. Why do middle school students need to learn about tesselation, for example when they can't even divide and multiply correctly? It would be better to learn fewer topics in depth instead of many topics not very well.
2) The emphasis in the last 20 years on exit tests has its points. We would not like to have students entering college who cannot deal with decimals and fractions- topics which should have mastered by 8th grade or even earlier. [ I knew someone whose college admission was held up by his not yet passing such a test- which he finally did.]
At the same time, mastering the skills required by such tests will not be done merely by practicing such tests. It takes a LOT of work to embed the mastering of such skills into the curriculum.
3) There is a wide variety of skill levels out there. I taught some 9th graders who were taking 11th grade algebra, and doing very well at it. Then there were the 8th graders I taught at a "poverty level" school. Let's just say not as capable. [Both examples had something in common- a teacher who, while he knew math well, was not ready for prime time when it came to teaching it.]
4) A lot of students have difficulty with word problems. It is one thing to be able to calculate or solve an algebraic equation, and another thing to apply this knowledge to the "real world." It would appear to me that the textbook writers need to get some feedback regarding constructing word problems that capture the interests of students.
"authored by someone teaching at the college level" ... Why are they trying to create mini-seminars rather than teaching what the students need to know?
I know the mini-seminars are cute, but that's just throwing stuff at the wall and hoping something will stick.
I always wanted to make the 5th graders walk their way through filling out a full sized Form 1040 with several schedules. They've already covered all the math (so they should have no problem with that part) and it is an interesting exercise in civics.
We've been through this too many times. The problem is at the Elementary level and the teachers aren't helping it a bit. Too many of the students in the "Colleges of Education" come from the lower 20%ile of the entering students. Typically they can't do math and are required to take remedial math classes to get their degree. Those remedial classes just revisit what they should have learned in 7th and 8th grade math.
The current approach to teaching math is to forget all about Newton's "standing on the shoulders of giants" and make the students derive the mechanism for the math operations from scratch.
The students are being made to recreate the past 1000 years of math development just to get started.
It is simpler to show them how the mechanism works using several different ways (visual, manipulative, whatever) and then get them to learn their times tables so that they know them cold.
If you don't know the times relationships, you can't factor. If you can't factor, you are never going to see the factors in the equations when you are trying to solve them.
Right now the teachers (who don't understand) are forcing the students to discover everything from scratch. As a result we come out with students that don't know what they are doing and don't have a good enough feeling for numbers to make change without the till telling them what to do.
With this whole "discovery" approach how can a student learn to do Trig? Do they make the students derive the Taylor series for each of the functions or what?
I have an honours math degree. I quit my master's program when I realized I could do it, and get a Ph. D., but that I had a second class mathematical mind. Or even third class.
I was good, but not great.
50% of us are below average. Probably, my guess, 80% of us simply cannot do even slightly advanced math. So what? There are lots of things neither Herr Einstein nor I could do.
People good at math will do good math even in the face of the complete ignorance of the education community, which is, of necessity, profound. Were it otherwise, they would be in the mathematical disciplines, which are profoundly addictive. I had four education students in my elementary algebra class, hoping to be math teachers. Math-wise, they were dumber'n a sack of hoe handles.
Perhaps, math students do better when they are taught by mathematical ignoramuses, for whom the gifted student can enjoy a great contempt.
Why should we all do math? Should we all be lawyers? No. Hire it when you need it, otherwise work hard at what you can do, enjoy it, learn the basics of math enough to know when your hireling is BSing you and enjoy what talents you have.
Obama, for example, knows nothing of math, but is the best confidence man I have ever seen. Surely he will never go hungry, and surely he has a great talent, and I write that as a compliment. I wish he would turn his talent for persuasion to better ends, but the talent is undeniable.
The author is confusing different things.
At the lowest level, I suspect that a lot of people would benefit from simple drilling in basics and simple algorithms. It is even possible to work up some algorithms for translating simple word problems into an equation: state the problem yourself, look for the magic words "each", "of" and "is" etc, look for building blocks ( like $/hour and hour/$ ), and see how the pieces fit together. Pick one method for dividing polynomials and stick to it--Algebra I gives equivalent methods (just varying the notation: synthetic division anyone?) that just confuse the student.
At a more skillful level, being able to analyze problems from a number of different approaches helps a lot--but that low-level foundation needs to be there. If you know Euclidean geometry and analytic geometry, is it faster to find X with triangles and proofs or by solving the equations? (maybe use symmetry arguments too?)
I've seen the difference between average and gifted, and the author is talking through his hat. Speed at mastering new ideas is one of the signs of giftedness.
Are you talking about genius, Fred Z? A competent second class mathematician still makes discoveries--just not as fast or as fundamental as the Erdos-level people.
A pet peeve of mine is when people lump everything together as "math" (often including arithmetic). I'm old enough to have had geometry as a proof-driven course in high school. Some kids found algebra painful and geometry easy; others the reverse. Different branches, different approaches, different interests, different skills.