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So I guess if you are totally carried away by beautiful metaphors you can lose touch with reality. Measuring corn more often doesn't make it grow faster or taste sweeter but if you don't keep an eye on it you may end up with dried up, shriveled and stunted plants.The proof and the power of these metaphors expressed through the progressive empowerment frame is in the programs and activities that come from them. In The Framing of No Child Left Behind (NCLB), I described some general activities that come from thinking in the empowerment frame:
It makes more sense to assess learning holistically, using projects and real-life activities and through descriptions of progress (intellectual "growth"), as much as possible. Further, assessment is integrated into each student's learning activities, rather than being done as an external process, by and for others. What the teacher does or says is not expected to be absorbed directly by the students. Rather, like the air, soil, and water that a plant converts into its green structure, students construct their knowledge from the resources and experiences provided to them by the teacher and student understandings will look and be different than exactly what the teacher taught. Thus, the teacher and students must continuously assess and communicate about lesson goals and student progress.
In conservative production frame, knowledge is thought of as discrete objects that are delivered by the teacher and absorbed directly by the student. This is why standardized tests make sense in the factory metaphors of the conservative production frame, but not in the gardening metaphors of the progressive empowerment frame. Measuring corn more often doesn't make it grow faster or taste sweeter.
Tuesday, January 15, 2008
Photosynthesizing pupils
I shouldn't be posting late at night when I should be asleep and can't think straight. But reading this piece about education on a leftist site again raises a nagging question in my mind about the influence of political belief on curriculum and instruction. I like to believe that there is no intrinsic connection between political beliefs and forms of instruction (pedagogy). Things are probably much more complicated than that. I can see an entanglement of curriculum and instruction in this piece that makes pedagogy susceptable to political orientation. At least this writer sees a political angle:
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Their basic assumption is that there is either no argument over what education and learning should be (and they know that this isn't the case), or they feel that they need to be the ones who decide for everyone else. If they are not in a position of power, then they still feel that a certain model of education should be imposed on everyone.
What do they think about affluent parents who get to choose? Do they resent their choice, do they think that it's nice but too expensive, or do they just don't care? Do they think that poor families aren't smart enough to make that decision?
I could argue their points, but I don't have to. The onus is on them to justify their desire to force their opinions on others. They have to prove that it's anything more than opinion. Then again, that defines the public school system.
"At the Rockridge Institute, we believe progressives can begin to enact more effective laws in education (and other areas) once they add a cognitive dimension to their policymaking. That is, any policymaking process must have two goals: (1) the intended policy results themselves and (2) ensuring that the policy itself makes sense to people. To make sense, the policy must connect with and promote the right long-term values in the minds of citizens."
"cognitive dimension"? Blah, blah, woof, woof.
What if "long-term values in the minds of citizens" means an education that will give their kids good SAT scores?
They are using people to push their own agenda. They assume that those who don't have enough money to choose their own school want what they want. They are using education as a political tool. They could advocate choice to allow people to set up all sorts of progressive schools, but they don't. The arrogance and self-righteousness is palpable.
I couldn't read the whole thing. Even those who consider themselves progressive would think it's junk. If the Rockridge Institute is the best that progressives can do, then they're in deep trouble.
Instructivist,
You missed the point about measurement when you wrote "Measuring corn more often doesn't make it grow faster or taste sweeter but if you don't keep an eye on it you may end up with dried up, shriveled and stunted plants." Progressive educators measure learning constantly, not less so than conservatives using the factory model of education. I wrote that in this sentence here ("Thus, the teacher and students must continuously assess and communicate about lesson goals and student progress.")
The point is that you have to measure learning with assessments that accurately measure learning. Projects and real-life activities do that much better than the SAT, other standardized tests, or lots of worksheets and fill in the blank tests. And piling on more of these only makes it worse. More than 5 years of NCLB has shown us that.
Projects and real life activities are subjective....therefore, most colleges want to see your SAT and AP scores, then perhaps a portfolio of your projects and real-life activities. You aren't going to make the first cut without a decent SAT score....
FWIW, I want my doctor to pass state exams and my lawyer to pass the bar. I want a "certified" accountant. I want the guy driving next to me to have passed the multiple choice driving test. For what I pay to have my car fixed, I want an ACE certified mechanic. If my kids were in public school and I'm paying the bill, I'd want them to be able to pass the state test. Is that really asking for too much?
It's actually asking way too little. You better want your lawyer to have done better than pass the bar. And I could care less whether my mechanic is certified: I do not much stock in "certification" with respect to how well he can fix my car. As for passing the state education test, if that is the limit of what you expect your school to do, you are setting the bar too low.
"As for passing the state education test, if that is the limit of what you expect your school to do, you are setting the bar too low."
None of the regulars at KTM think that meeting state proficiency standards is anything more than a (pathetic) minimum, although our public schools think it's a big achievement. However (I sound like a broken record), what other knowledge and skills make it OK not to pass these trivial tests?
Good schools should laugh at standardized tests. It should take them a small portion of the school day to meet those requirements. We at KTM want so much more, but we don't want generalities and platitudes. We want to see concrete curricula and course syllabi. We want to see a detailed justification for selecting Everyday Math over Singapore or Saxon Math. We want details.
"Projects and real-life activities do that much better than the SAT, other standardized tests, or lots of worksheets and fill in the blank tests."
That's your opinion, and it all depends on the projects and real-life activities. But, if this is the case, then these kids should do quite well on the SAT test.
If you don't like the SAT test, tough luck. Go start your own school and experiment on those kids.
If passing a standardized test is only the pathetic minimum, why do you place so much importance on it? Of course, if the SAT is needed to get into college then we must ensure that our children do well on it. But that is a far cry from thinking the SAT has any much intrinsic value as a learning measure. And no one should base their curriculum or learning activities on it. I certainly wouldn't.
You want details on why the focus on isolated factoid factory learning is harmful, try this. I was a middle math and science teacher for 7 years. During that time, few of my incoming 8th grade students could answer this simple question (I taught in high SES schools):
Why is it that when you divide by a number bigger than 1 your answer is a smaller number (e.g., 8/4 = 2), but when you divide by a number smaller than 1 your answer is a bigger number (e.g., 8 divided by 1/2 = 16)? Nearly all of my students had had years of Saxon math, so they answered "invert and multiply." A truly logical non-answer if ever there was one. All these kids did really well on standardized math tests etc., but they had no idea what was really going on. That is the result of thinking that facts are solid objects to be dumped whole into the heads of kids. It doesn't produce complex understandings because it does a very poor job of helping the learner construct them, which is how learning occurs.
My "opinion" as you like to dismiss it, that the factory model of schooling is limiting at best and often destructive to critical thinking and sophisticated learning is based on years of teaching experience and supported by nearly 100 years of research on how the mind works and people learn.
It may be unsettling, but it's true.
If you are still unsure of this, check out "A Private Universe" (produced by Annenberg/CPB about 15 years or so ago) and the accompanying literature on scientific misconceptions perpetuated by schools using the factory method approach. It was originally on video but may now be available on DVD.
It follows a top tier high school student and her struggles to learn about how seasons work when she is being taught by an eager, experience and concerned teacher using a version of the fact delivery method for teaching.
Check it out and then come back to discuss "details" and "opinion."
Eric - the site's html currently appears to be screwed up, but this recent post will give you an idea of where we're coming from.
In short, none of us believes passing a standardized test by itself equals a good education, but not passing one generally is an indicator of a bad education. Outside of a learning disability or an ESL student, I can not think of a single way that a 4th grader could have mastered that material, yet not be able to answer those questions correctly, with or without a calculator. Likewise, getting a 700 on the SAT math doesn't mean you'll pass college calculus, but getting a 400 is a pretty good indicator that you won't.
Or, to use your own example, what would you make of the student who didn't even know that dividing by <1 yields a larger number in the first place? Being able to divide 12 by 3/4 is not the end of education, but it's pretty damned hard to move on without mastering that step first.
What is the "factory learning" method, or, more importantly, how does it differ from anything else you would do in an institutionalized environment (i.e. either public of private school). If that word means like it reads, then the only way to avoid "factory learning" would be through private tutelage or homeschooling. (Now, if you are just saying that homeschooling/private tutelage is better than institutionalized education, then I wouldn't disagree with you there. But, if you think that something else in such an environment isn't "factory learning", then I would really doubt the veracity of what you say.)
In terms of the reason why dividing by a number greater than 1 results in a smaller answer while dividing by a number less than one results in a larger answer, I think the real answer to that question is almost certainly not what you were expecting from your students. And, given that fact, then I wonder just what the right answer to expect to that question should be. The real answer relies on the axiomatic basis for ordering. It would go something like this...
Let P be a subset of the real numbers.
Definition: Let a and b be any two real numbers. Then, a>b iff a-b is an element of P, and conversely a<b iff b-a is an element of P.
Ordering Axiom I: If a is a real number, then one and only one of the following statements is true: a is 0; a is a member of the set P; -a is a member of the set P.
Ordreing Axiom II: If a and b are members of P, then a+b and a*b are members of P.
Suppose p>1. Then, p-1 is an element of P, by definition. Suppose n is an element of P, then by Axiom II, n(p-1) is an element of P. But, n(p-1)=np-n, so that np>n (by the distributive property and the above definition). That is, if p>1, then np>n.
Conversely, suppose p<1. Then, 1-p is an element of P, by definition. Suppose n is an element of P, then by Axiom II, n(1-p) is an element of P. But, n(1-p)=n-np, so that n>np (by the distributive property and the above definition). That is, if p<1, then np<n.
Oops, I forgot we were dividing rather than multiplying. Then, insert this theorem after Axiom II:
Theorem: If p is an element of P, then p>1 iff (1/p)<1.
Proof:
Suppose p>1 and (1/p)>1. Then, by definition, (p-1) is an element of P and (1/p-1) is an element of P. Then, by Axiom II, (p-1)(1/p-1) is an element of P. But, (p-1)(1/p-1)=p*(1/p)-p-(1/p)+1=-(p+1/p). But, since 1 is an element of P, 1-0 is an element of P, so that 1>0. Thus, (1/p-1)+(1-0) is an element of P by Axiom II. But, (1/p-1)+(1-0)=1/p so that 1/p is an element of P and, by hypothesis, p is an element of P so that p+1/p is an element of P. But, that contradicts the result that -(p+1/p) is an element of P. Thus, either p>1 and (1/p)<1 or p<1 and (1/p)>1 (or they are both 1).
And insert this statement at the end:
Therefore, by the theorem, then, if p>1, 1/p<1, so that n/p=n*(1/p)<n. And, if p<1, 1/p>1, so that n/p=n*(1/p)>n.
"If passing a standardized test is only the pathetic minimum, why do you place so much importance on it?"
If having a thousand dollars in your retirement account is only a pathetic minimum, why do you place so much importance on it? Because if you don't have a thousand dollars, you damn sure don't have a half-million dollars.
"The point is that you have to measure learning with assessments that accurately measure learning. Projects and real-life activities do that much better than the SAT, other standardized tests, or lots of worksheets and fill in the blank tests."
Argument by assertion deserves only the same in return: that statement is nonsense.
Is it possible to teach through projects and "real-life*" activities? Of course. Is it efficient? Of course not.
With even half-competent teaching, the material on any state test I've seen should be taught in no more than 10% of the school year. In addition, the material tested in these tests is a necessary precondition to basic competence. (It clearly does not, in itself demonstrate such basic competence.) Teaching this material is not a diversion from your job, it is the barest beginning of your job.
You may infer from this my opinion of teachers who decry these tests taking time out of the school day.
"My 'opinion" as you like to dismiss it, that the factory model of schooling is limiting at best and often destructive to critical thinking and sophisticated learning is based on years of teaching experience and supported by nearly 100 years of research on how the mind works and people learn."
Not just research, but "nearly 100 years of research". Somehow it's grown from your "opinion" to 100 years of research. Which is it, fact or opinion? And what, exactly is "critical thinking" and "sophisticated learning"? Is it anything like applying a "cognitive dimension"? This is a typical ploy. Argue with very vague generalities, but who gets to decide on the details. I could come up with a curriculum that stressed "critical thinking" and "sophisticated learning", but I bet you wouldn't like it.
By the way, I don't dismiss your opinion, but don't expect me to send my son to your school. Oh, that's the problem. You want to force all kids to follow your idea of education. Well, that's the real point, isn't it? You see education as a political tool. That was Instrucivist's real point.
"It doesn't produce complex understandings because it does a very poor job of helping the learner construct them, which is how learning occurs."
If you know of a more effective math curriculum than Singapore or Saxon Math, then please tell us. I would like to see what progressive education is all about. What specific math curriculum do you recommend? If you want to make your case, this is how you have to do it. Don't talk about "factory model". Talk about details.
eric says:
[If you are still unsure of this, check out "A Private Universe" (produced by Annenberg/CPB about 15 years or so ago) and the accompanying literature on scientific misconceptions perpetuated by schools using the factory method approach. It was originally on video but may now be available on DVD.]
I am familiar with "A Private Universe."
It teaches me that the reasons for phenomena like the seasons and phases of the moon are not easy to visualize and grasp (spheres can be nasty). Having a model is good. Furthermore it teaches me that misconceptions can be tenacious. The more personal attention and diagnosis of misconceptions coupled with heavy doses of interactive explicit instruction the better. Interactive means asking questions to check for understanding and stimulate thought processes.
To pull all of this off, you would have to teach a small number of students.
I am not sure what you mean by "factory model". Are you saying that anything over a handful of students becomes a factory? It would be great to teach to only a handful of students, but it sounds utopian.
Factory model is a strawman (just like saying that all we want is what we had when we were growing up) that one can use to push an educational agenda. Who doesn't want "critical thinking" and "sophisticated learning"? Who wants kids just to memorize facts? Nobody that I know. As I've said before, they argue with vague generalities, but they want to define the details. Critical thinking and sophisticated learning can happen via teacher-centered direct instruction. And direct instruction does include assessment integrated into each student's learning activities. Good schools laugh at state tests.
So what's the real issue? On one hand they dismiss standardized tests as if they contain questions that one does not need to be able to answer, and then they say that kids have to be prepared for the SAT. Which is it? I can't imagine anyone doesn't want the combination of good SAT scores and "sophisticated learning".
The best I can figure it is that progressives (like many in education) want to approach education top-down, in thematic or real-world ways. The (nasty) facts and mastery of skills will take care of themselves. This is how Everyday Math works. They spiral mastery (low expectations) and assume that if they give enough "Math Boxes" in later years, everything will be fine. It isn't fine. When they talk of critical thinking, it's on a superficial or conceptual (picture) basis, not an abstract or algebraic basis. I'll take the Saxon kid who knows about invert and multiply any day over one that can't. You can fix understandings, but you can't fix a lack of mastery of the basics. A top-down approach is very time-consuming and does not ensure mastery of the basics. That's why they don't like tests of basic skills. They have to claim that it's not that important or that it will somehow naturally happen.
But the progressive claim is much more than this. They claim that the factory model creates a two-tiered education system that does not provide the same opportunities to the urban poor.
"So, NCLB continues even though it goes against the overwhelming evidence of sound teaching practices from teachers in the classroom and education research. It continues even though it is creating a two-tiered educational system in the U.S.—a very un-American idea indeed—where students in under-funded urban schools get more and more drill and kill worksheet activities that temporarily bump up test scores, while students in better-funded suburban schools get computer and science labs where they do exploratory activities that promote the critical thinking skills used by managers, entrepreneurs and other professionals. We can do much better."
So, if you give urban schools all the money they want and remove all external test requirements, everything will be OK? Where is the critical thinking in this? If only 20% get the following problem correct, then this is not because of a lack of money or any type of lab. NCLB is the messenger, not the problem.
14. There will be 58 people at a breakfast and each person will eat 2 eggs. There are 12 eggs in each carton. How many cartons of eggs will be needed for the breakfast?
A) 9
B) 10
C) 72
D) 116
Did you use the calculator on this question?
20 percent correct.
"To re-frame education we begin with our values. These are empathy and responsibility, with the result that government has the twin purposes to protect and empower its citizens. Education is a clear aspect of empowerment. Substantive fixes to our public school systems are more likely when progressives include a cognitive dimension in their policymaking process."
This is a classic argument. I care and have no self-interest, so I must be correct. And the urban poor (and many others) still won't know how to invert and multiply.
There are a lot of connections like that, Sowell's "A Conflict of Visions" is a great explanation of that.
From reviewer Marc Cendalla on Amazon about Sowell's book:
"Sowell's main thesis is that contrasting visions of human capability, knowledge, perfection, and self-interest underlie two very different visions of humanity, and it is on these visions that political ideology, debate, and worldview rest. Sowell's two visions are named, rather unhelpfully, the constrained and the unconstrained vision. No gold star here for Sowell on Marketing. So instead, I'll use Pinker's terminology, as I was introduced to this book via Steven Pinker's Blank Slate.
The Tragic (constrained) vision of human nature views man as possessing foibles, incentives, and the desire to act in his own self-interest. The Tragic "sees the evils of the world as deriving from the limited and unhappy choices available, given the inherent moral and intellectual limitations of human beings." Thus, the perfection of governance in the Tragic Vision is the American Revolution with its checks and balances. Further, history should guide us, as the unknowable tradeoffs between different policies and procedures have been ironed out through unstated practice. The Utopians are to be scorned for their theoretical leanings that have little to do with the real world: "Hobbes regarded universities as places where fashionable but insignificant words flourished and added that `there is nothing so absurd, but may be found in the books of Philosophers."
The Utopian (unconstrained) vision holds that man has not yet achieved his full moral potential, and that that potential is essentially perfectible. It is "foolish and immoral choices explain the evils of the world - and that wiser or more moral and humane social policies are the solution." So while there are incentives that actually work in the here and now, this fact is somewhat irrelevant to the achievement of true justice. The Utopian holds that "potential is very different from the actual, and that means exist to improve human nature toward its potential, or that such means can be evolved or discovered, so that man will do the right thing for the right reason, rather than for ulterior psychic or economic rewards." So the Utopian "promotes pursuit of the highest ideals and the best solution" in the hopes of achieving this perfect man. And if the masses are slow in catching on, then it is the role of the intellectual vanguard to lead them there - even if in the short run, the masses are unhappy with the results because they have not yet achieved the ability to see the future. Their thought is that reason should guide us, but reason as determined by the best and brightest: professors, government workers, elected and unelected officials. In this regard, the French Revolution with its lofty ideals and disposal of the past is the perfection of governance."
What is 6 times 7 in the Utopian Plane?
OK.
What is it in the Tragic Plane?
"I wonder why?
I wonder why?
I wonder why I wonder?
I wonder why I wonder why
I wonder why I wonder?"
Richard Feynman
As a joke for a stupid non-science course at MIT. I think he got a good grade on it.
"This is REALITY, Greg."
When they talk of critical thinking, it's on a superficial or conceptual (picture) basis, not an abstract or algebraic basis.
I really hope that Eric comes back and explains what sort of answer he thinks that an eighth grader should be able give that explains why it is that dividing a number by a fraction results in a larger number, etc. It seems that anything less than the entire proof is not the correct answer.
Pictures and analogies are great pedogogical devices for demonstrating algorithms and concepts in math but they are not "the reason" why something works. The only basis for "critical thinking" in math is the formal mathematics (the proofs, the symbols, the algebra, the identification of the application of the distributive law in this step and reassociation in that step), etc. It's not the pictures.
Pictures and chicken scratch are not an alternative truth in math, not even superficially. Any K8 program that sacrifices basic math skills in order to teach "concepts" and "critical thinking" will end up with kids that have neither.
I seriously doubt those kids are any better at showing mathematically why any number multiplied by zero is zero than they are at churning out drill sheets.
[The Tragic (constrained) vision...
The Utopian (unconstrained) vision... ]
The tragedy is that the utopians who have given us voodoo education are failing to achieve even minimal proficiency.
"Any K8 program that sacrifices basic math skills in order to teach "concepts" and "critical thinking" will end up with kids that have neither."
Exactly.
Although they claim that they don't sacrifice basic skills, curricula like Everyday Math are based on not enforcing mastery at any particular time. That's why the sixth grade EM workbook is filled with remedial "Math Boxes". They don't think it's unimportant, exactly, but they leave it up to the kids and their parents to make sure it happens. That's why parents get notes from school telling them to practice the times table with their kids. Of course, this is least likely to happen with the people they would most like to help.
There are also different levels of understanding. Many topics and skills have to be covered with only a basic level of conceptual understanding at first. But higher levels of understanding are based on mastery of the skills. A deeper understanding of math derives from mastery of the skills, not the other way around.
I highly recommend watching "A Private Universe" (20 min). It could become the new Rashomon. Eric sees the ravages of the "factory model" in it (that concept needs further elaboration). I see the video as the perfect illustration of constructing one's own knowledge and as a slap in the face of constructivism.
If for no other reason, watch the video to see how Harvard graduates explain the reasons for the seasons.
http://www.learner.org/resources/series28.html?pop=yes&vodid=39449&pid=9
A Private Universe
Then click on the VoD icon.
Actually, it just occurred to me that I screwed up the proof of my theorem above. ..
(p-1)(1/p-1)=p*1/p-p-1/p+1=2-p-1/p
(not -p-1/p) which makes it even harder to prove. Now, we must show that (the larger) number 2-(p+1/p) still cannot be an element of P. And, to do so we must mess with a quadratic polynomial which makes it even less likely that eighth graders could possibly be expected to give this, the actual, answer.
Not that anyone cares, but 2-(p+1/p) = 2p/p - (p^2/p + 1/p) = -(p^2-2p+1)/p = -(p-1)^2/p. Since p is greater than 1, p-1 is an element of P, so that p-1 multiplied by itself is an element of P. And since (p-1)^2 and p are both elements of P, their quotient is, as well, which contradicts that the additive inverse of the quotient is a member of P by Axiom I. And, the rest of the proof carries on from there.
Given the subtle nature of this little calculation, I really would not expect an eighth grader to "get it" in any way, shape or form. Not only should they not get the intellectual aspects of rigor in the truly correct answer to the question, but I doubt they will even really appreciate how the reciprocal works around 1 like that just heuristically. The best they can do is examine a sequence of numbers increasing from a point less than one to a point greater than one and just leap to the conclusion (or perhaps graph 1/x and see how it goes through the point (1,1) which is still beyond most eighth graders).
"I really hope that Eric comes back and explains what sort of answer he thinks that an eighth grader should be able give that explains why it is that dividing a number by a fraction results in a larger number, etc. It seems that anything less than the entire proof is not the correct answer."
If the eighth grader or the eighth grade teacher is a critical thinker, he/she would realize that the fault lies with the question, not with the answer. Adrian provided a rather elegant proof that provided an explanation. Although the level of the proof is above the level of the eighth grader, it shouldn't be above the level of the eighth grade math teacher. Eighth grade math teachers are certified in mathematics and should follow that proof very easily.
Adrian's proof defines the set of numbers we are dealing with, the question presented to the students does not. Are the dividend and the divisor coming from the set of real numbers? or positive rationals, a subset of the reals? or do we just let the students make false assumptions.
Presented as a statement that eighth grade students can think about and test the validity, it becomes a good 'thinking' problem. Students can either agree with the statement and explain, or disagree and show a counterexample. They need not prove at that level. But providing a counterexample is an important pre-high school math tool.
Example: 8/2 is 4 (smaller than 8) while 8/(1/2) is 16 (larger than 8)
But eighth graders have dealt with negative numbers. So consider the counterexample: -8/2 is -4 (larger than -8) while -8/(1/2) is -16 (smaller than -8).
Example: 8/2 is 4 (smaller than 8) while 8/(1/2) is 16 (larger than 8)
But eighth graders have dealt with negative numbers. So consider the counterexample: -8/2 is -4 (larger than -8) while -8/(1/2) is -16 (smaller than -8).
So it sounds like a better question for eighth graders would have been, "Under what circumstances does dividing by a fraction result in a quotient that is less than the dividend?"
Yes, your question would be more valid. But I would like to allow them to think about question number two as well then, "Under what circumstances does dividing by a fraction result in a quotient that is greater than the dividend?"
Or better yet – Start with the statement :
When you divide by a number bigger than 1, your quotient is smaller than the dividend; but when you divide by a number smaller than 1, your quotient is greater than the dividend. Is this statement always true, sometimes true, or false? Explain by giving examples.
The key here is you are training the eighth grader to think of 'the dividend' as a variable. You want them to consider all possible values for that variable – positive, negative, and zero. -- I could probably have put a period after the word 'think' and the statement would be even more profound:)
We had quite a long tour of The Dalton School, which is progressive.
All I can say is: an elite 30K tuition progressive school in Manhattan bears no resemblance to anything coming out of the ed schools.
For instance: the Dalton mission statement mentions "the beauty of the disciplines."
You're not gonna hear Word One about the beauty of the disciplines in a public school.
This was the first time, ever that I saw why a person might want to attend a progressive school.
the words "highly structured" also appear prominently in school literature...
I just looked at the web site for The Dalton School and could find only happy talk. Under curriculum, they don't tell you what math texts or systems they use. The fact that they call it progressive is meaningless to me. I'm tired of happy talk and generalities. It's like crying wolf. I've heard it all before.
I oould teach math effectively using Everyday Math, but why would I when there is Saxon or Singapore Math. I could force kids to take charge of their own learning, but that could be good thing or a bad thing. I could apply all sorts of "sophisticated learning" techniques, but what are the details?
I don't want one example of dividing by some number greater or less than 1. I want to see what textbook or system that is used. I want to see if and how it's supplemented. I want to see syllabi, expectations of mastery, and sample tests. I want to see most kids taking a proper course in algebra by eighth grade.
This is not an argument over some vague ideas of progressivism. It's an argument over details, assumptions, and expectations.
[...30K tuition ...]
I got quite a chuckle out of Gadfly's comparison of recent wine-tasting results with the joys of high tuition. Something having to do with the medial orbital prefrontal cortex:
http://www.edexcellence.net/foundation/gadfly/index.cfm#3808
We learn from a study published Monday in the Proceedings of the National Academy of Sciences that cheap wine tastes better when its drinkers believe they're sipping a Grand Cru. One wonders: Are parents who enroll their children in tony schools perhaps guzzling Two Buck Chuck?
[...]
If schools are like wine, parents who can swing it (or get the requisite aid) surely derive pleasure from enrolling their offspring in a pricey institution. Their minds very likely correlate a school's educational quality with its lofty tuition. And wine is a useful analogy here, too, because it's as tough for most people to judge the worthiness of a glass of pinot as it is for them to judge the worthiness of a school. Thus, their perceptions of both are susceptible to tingeing by outside factors that have no intrinsic qualitative value, such as price.
Dalton offers a superb education - it's surreal. Another world. Ed and I felt like we were kids in a candy store.
Ed described Dalton as a liberal arts college for K-12, and it is.
Freshman year students read the Bible as literature, St. Thomas Aquinas, etc.
Their history department is so good that history professors at NYU say it's good. These are actual historians, content specialists, praising the history curriculum of a K-12 school.
That never happens with public schools.
Math is a tougher discipline to get information about, I find. No one ever knows what textbooks the school is using. I spotted a Glencoe pre-algebra text in the Dalton library.
Looking at teacher credentials in the elite private schools, you see more than a few ed school graduates in math -- and in math alone.
I grill the tour guide on math. So far it's obvious that all good private schools teach algebra in the 8th grade to everyone. This is assumed.
Of course, that means that 8th graders coming out of wealthy suburban schools like mine are far behind their peers in private schools. (And I mean WAY behind.)
Here are my Dalton figures, close to exact:
110 kids in 12th grade
100 taking calculus
20 taking statistics (AP statistics, I believe)
I'm pretty sure that the calculus course is the equivalent of advanced placement BC.
Another thing: Dalton dropped AP classes years ago but their students all take the AP tests and pass.
When I said, "You mean they get 3s, 4s, and 5s?" the director looked at me in surprise & said, "4s and 5s."
You don't get to 4s and 5s on the BC exam senior year teaching fuzzy math.
I've now spent time at 3 private schools. Across the board, they are teaching the liberal arts disciplines.
Yesterday the Director of Admissions at The Masters School said to me directly, "That is the difference between private and public schools." We hire teachers who are have been trained in a discipline, not in how to teach."
"That is the difference between private and public schools." We hire teachers who are have been trained in a discipline, not in how to teach."
It's not that simple. Some private schools are like wine that you buy at the 99 cent store, and our state requires that public school teachers in grades seven and above be trained (whatever that means) in the subjects they teach.
So, progressivism means whatever you want, but has little to say about the quality of education. And, it's not progressivism that gets most kids to algebra in eighth grade.
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