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"Hence the knowledge that is enacted in curriculum and pedagogy becomes a
byproduct of the political incentives that operate on teachers-discrete bits of information, emphasis on coverage rather than depth, diffuse and hard-to-understand expectations for student learning, little convergence between the hard day-to-day decisions about what to teach and the largely content-free tests used to assess student performance, and a view of pedagogy as a function of the personal tastes and aptitudes of teachers rather than as a function of external professional norms. Students who do well in such a system recognize that they are being judged largely on their command of the rules of the game, which reward aptitude rather than sustained effort in the pursuit of clear expectations. All systems have a code; the job of the student is to break it. Some do, some don't."
Richard Elmore
The Politics of Education Reform
57 comments:
How do you keep finding his stuff???
You're amazing.
I wonder if he'd do an interview for ktm?
I'm going to get his PowerPoint on nominally high-performing schools posted asap (your other brilliant find).
Richard Elmore has explained the world to me.
The question that has come to me recently is whether there actually are rules of the game that a student could divine.
My sister and I both think things have changed in that respect, too.
My sister said, "The rules keep changing."
When you have very young teachers who believe they are assessing "inferential thinking," and who have free run of a bank of Canned Comments about the quality of a student's "thought," I think it's tougher to figure out the "game," or to know whether there is a game in the sense of a situation with a stable & consistent set of implicit rules.
I love this line:
Most statements of content and performance standards coming from professionals and policymakers take no account whatsoever of such basic facts as the amount of time teachers and students have in which to cover content. They are merely complex wish lists.
I like this one too:
In the absence of explicit external standards for content and student performance, teachers give great weight to the way content is portrayed in textbooks, which is the "default mode" for instructional guidance. Commercial publishers have little or no incentive to focus content; their incentives are to produce materials that are marketable to the broadest possible cross-section of customers and to gear content to the largely content-free nature of existing standardized tests.
Have you read this one?
What (So-Called) Low-Performing Schools Can Teach (So-Called) High-Performing Schools
I've only read the abstract:
In this article, the author examines successful schools with high concentrations of poor and minority children--those in which students were doing as well as or better than those in affluent schools on statewide standardized tests--to see what they were doing to improve the level of instruction in their classrooms. These high-performing, high-poverty schools were not just different in degree from other schools, they were different in kind. School leaders had clearly articulated expectations for student learning, coupled with a sense of urgency about improvement; they adopted challenging curricula and invested heavily in professional development. Teachers in these schools internalized responsibility for student learning; they examined their practices critically, and if they weren't working, they abandoned them and tried something else. Although these schools may be stigmatized as "low-performing" or "in need of improvement," they are working hard to learn about their practice and beginning to focus on the individual and organizational conditions that create more powerful learning for adults and children.
It's sounds like a fascinating read.
I was sold on teachers abandoning practices that weren't working in favor of something else that does. Seems simple enough, but I'm not seeing that in my school.
Teachers don't abandon practices that aren't working in high performing schools because someone once told them that the practice in question was "best practices" therefore it works. So then alternative reasons are generated to explain the poor performance -- blame the student, blame the parent.
I'm going to see if I can find that article.
Ed just brought up his student-body swap experiment. We need to switch the Irvington student body with a rural white student body and see what happens.
We both think the rural kids' achievement would drop -- definitely in the middle school.
Schools in general, and high-performing schools in particular, produce a large part of their performance with social capital, not with instruction. Families and communities bear a large part of the role of educating young people—often directly, such as in the purchase of tutoring services to compensate for the shortcomings of instructional practice in schools; often indirectly, such as creating pressure for attainment and performance in the lives of children independently of what the school does. For this reason, it is wise to treat the population of high performing schools with some skepticism as a source for “successful” practices, or “high quality” instruction. My experience—however limited—working with high performing schools is that it is an extremely bi-modal population. Some high-performing schools actually do contribute significantly to students’ learning and performance through instructional practice. Many high-performing schools are
stunningly mediocre in their practice, and produce most of what they do with social capital.
Leadership as the Practice of Improvement
Richard Elmore
* parents hiring tutors
* parents reteaching at home
* parents pressuring their kids for achievement
All true here.
The point he's failing to make is that none of this works particularly well.
Yes, it puts kids in these schools at or close to the top of the heap for U.S. public schools.
Students coming out of good private schools wipe them out and they're not even in spitting distance of kids in good schools in Europe & Asia.
Ed said this morning, "I dread getting the scores."
The ISEE scores, that is.
The ISEE is taken by 100,000 kids -- all of them attending or planning to attend private schools.
Now that is a rude awakening.
We spent 3 weekends frantically trying to teach C. how to write so he wouldn't completely bomb the essay section.
I read a great line the other day: "the downward spiral of remediation."
That's what I see.
Remediation is a terrible, terrible way to go about educating kids -- and remediation is what we parents are constantly doing.
Not all of us, I realize - a lot of folks here are doing enrichment and acceleration. I've been doing remediation for the past 2 years and it's not education.
It's First Aid at best.
I feel the same way about tutoring -- and I'm pretty sure I'm right.
I have to make an exception in the case of the family we know who hired a college professor years ago to "tutor" and manage their kids' education here. They call her a "tutor," but she's really.....a private teacher?? I don't have a term for her. She teaches the kids, yes, but she's also managing their education in this district. Two of the kids are doing spectacularly well; they are academic stars. The mom is worried about the 3rd child, who is doing quite well but not as well as they'd like.
I don't know what to think about the difference there. My guess is that the 3rd child, who is the firstborn, received less "tutoring/managing" because that child was the first.
The mom's learning curve happened with the firstborn.
Setting that family aside, I don't see tutoring as especially successful. This is a terrific problem in terms of dealing with the district because our administration sees tutoring as superior to classroom instruction. They look at the one-to-one teaching ratio and conclude that parents are using their ample resources to purchase the ultimate reduction in class size.
That's not what's happening.
A tutor does not a tutorial make.
Improving High-Performing Schools (on sidebar)
I'm trying to figure out how to order a copy of this issue.
coupled with a sense of urgency about improvement
this is a constant around here: zero sense of urgency
Last year I went to a couple of board meetings. The atmosphere was relaxed, happy, and self-congratulatory. The superintendent praised the board; the board praised the superintendent; then the superintendent praised the other superintendents & the other superintendents modestly acknowledged the praise, and on and on it went.
One school board member described the tour she'd been given of the K-3 school.
I was sitting there with my Saxon Algebra 1 book doing Mixed Practice so I could teach math to my middle school child while the district was having a tea party.
urgency = motivation
Many high-performing schools are
stunningly mediocre in their practice, and produce most of what they do with social capital.
Precisely.
Stunningly mediocre.
I've been to those tea parties myself.
They just can't wait to talk about the standardized test scores and how well our students do despite the fact that we spend at least 1K less than the state average per pupil.
It couldn't possibly be because parents remediate, re-teach, and enrich at home. Parents provide everything from scotch tape, art supplies, musical instruments, books and disinfecting wipes to the school. In addition, they volunteer countless hours for lunch duty, cutting stuff out, or working on printing projects.
Yes, Elmore is right. Parents provide the "social capital" that makes high performing schools appear successful. Schools then take all the credit for the fantastic results. Accolades and pats on the back become the order of the day.
When things don't turn out well, however, it's the parent's fault.
[Schools in general, and high-performing schools in particular, produce a large part of their performance with social capital, not with instruction.]
I agree with that. I believe that high-SES kids succeed not because of progressive ed mumbo-jumbo (self-servingly called "best practices") but despite of it. Many educationists then make the mistake of foisting this mumbo-jumbo on the disadvantaged to make them the "beneficiaries" of a rich kid's education.
This is also the premise of the Gates folks. The schools they create and support (at least here in Chicago) are all steeped in progressive (constructivist) ed ideology.
The following excerpt is from Education Next and discusses the roots of the creed governing Gates giving:
A Foundation Goes to School
By Paul T. Hill
Bill and Melinda Gates shift from computers in libraries to reform in high schools
Though the high-school reform message came from all sides, including education traditionalists, Vander Ark initially leaned toward ideas associated with progressive education. He liked the notion of low-income public-school students’ getting the same kind of instruction as rich kids in private schools. Small size, in fact, became a proxy for other desirable features missing from the modern high school: intimacy, coherence, transparency, and equity. Vander Ark was deeply impressed by Deborah Meier’s vision of a small school as a personalized environment where adults do whatever is necessary to ensure that students learn. He was also strongly influenced by Harvard researcher Tony Wagner, himself a disciple of Meier and Sizer. With Wagner’s help, Vander Ark sought out educators who wanted to help small schools adopt teacher-developed curriculum and project-based learning.
Over the break, I've had more time to reflect.
Here's one chunk of thought:
Talking about k-12 education as a whole is a distractor. Why? While I am not a wholesale Piagetian, it is possible that what suits the preK-to-2nd grade learner is inappropriate for the 2nd-to-4th grade learner, and so on.
Here's another chunk of thought:
Because my daughter has dyslexia, I am particularly interested in methods of teaching reading. I gather that in the Scandinavian countries, children don't start formal literacy instruction until the 2nd or 3rd year of school (when they are about 7). Yet there's plenty of language learning in the classroom: oral learning of rhymes, poetry & classic tales, oral recitation of learning, listening to stories, and so on. Would this be a better model for US classrooms? I don't know. Stand by for details.
Liz stated
"I gather that in the Scandinavian countries, children don't start formal literacy instruction until the 2nd or 3rd year of school (when they are about 7). Yet there's plenty of language learning in the classroom: oral learning of rhymes, poetry & classic tales, oral recitation of learning, listening to stories, and so on. Would this be a better model for US classrooms? I don't know. Stand by for details."
I'm not sure about delaying reading instruction, as I homeschool and I start reading instruction around age 5. However, I agree with and have provided "language learning" as you've described it. I always encourage parents to expose their children to literature well above their reading level. Whether one chooses to read aloud or play books on CD. EXPOSE you young child to vocabulary and ideas ("Background Knowledge") - do not wait until they can read on their own. My own children have fantastic reading comprehension skills and a wide vocabulary due mainly to all the oral learning opportunities that we provided them at a young age. We did and continue to do a lot of memorization and recitation (mainly grammar and poetry). Sadly, I would think that teacher's not find enough "hands on" or "engaging activities" in these methods to find them acceptable.
My view is that many over-think education. It's not that difficult. Just dive right in and get to work. Select a good curriculum and ensure mastery of content and skills. If a child has trouble, try to figure out the problem.
As soon as my son was old enough to understand, we started on the alphabet and phonics. (He loved Mrs. Phipps and Snoothy. I can still sing their alphabet song.) Of course we didn't shove it down his throat. He loved to watch the video over and over and over. He was and is a sponge for knowledge. Most kids are. I think you waste too many opportunities if you wait too long. My son was reading at 4 and could phonetically sound out words like volunteer. Waiting to learn how to read would have been a disaster for him.
My nephew had reading issues that his school interpreted as more severe learning issues. My sister and her husband had to do it themselves. The school gave them all sorts of ed school talk (and low expectations), but they didn't care. They dove right in and solved the problem. He now has a degree in computer science.
Too often I see low expectations hidden behind flowery pseudo-scientific talk in the lower grades. The model I would like to see for US classrooms is choice.
I agree with that. I believe that high-SES kids succeed not because of progressive ed mumbo-jumbo (self-servingly called "best practices") but despite of it. Many educationists then make the mistake of foisting this mumbo-jumbo on the disadvantaged to make them the "beneficiaries" of a rich kid's education.
I'm glad you said that -- I want to know what teachers think of this claim.
I believe it absolutely myself.
I took a look at one of Howard Gardner's books the other day...."The Educated Mind" -- something like that?
The book struck me as being probably one of the best books for a person like me, who has had it with constructivism and all the rest of the fol de rol, to read.
He is a progressive ed person, and he says bluntly that the only kids who can learn well in a progressive ed environment are high-SES kids with strong family support.
I think it's entirely possible that there are terrific progressive ed schools for high-SES schools with strong family support....but I just don't know much about it.
Would kids in these schools do better with direct instruction and precision teaching?
I believe the answer is yes.
My view is that many over-think education. It's not that difficult. Just dive right in and get to work. Select a good curriculum and ensure mastery of content and skills. If a child has trouble, try to figure out the problem.
I dunno.
I think that teaching reading & math may fall into the rocket science category.
I'm constantly amazed at the gaps in my comprehension of math, and I'm a "serious" math student -- serious meaning motivated, reasonably intelligent, and reasonably diligent.
It's not easy.
The school gave them all sorts of ed school talk (and low expectations), but they didn't care. They dove right in and solved the problem. He now has a degree in computer science.
Too often I see low expectations hidden behind flowery pseudo-scientific talk in the lower grades. The model I would like to see for US classrooms is choice.
Absolutely.
No question there are all kinds of kids out there whose learning "problems" are being essentialized as learning disabilities.
I want to see choice within schools as well as between schools. If I have to read one more debate amongst the experts as to whether kids should or should not be taught long division I will scream.
Ultimately it's really none of these people's business whether my kid does or does not learn long division.
That call should be up to me.
I want him to learn long division, I'm paying phenomenally high school taxes, ergo I should be able to choose the math teacher & math class that includes long division.
Parents who don't want long division can choose the class & teacher without.
>>I'm glad you said that -- I want to know what teachers think of this claim.<<
I believe a whole lot of students - not just high performing - succeed in spite of schools and progressive ed.
>>Teachers don't abandon practices that aren't working in high performing schools because someone once told them that the practice in question was "best practices" therefore it works.<<
Two other reasons, for many schools, not just high-performing:
1) Teachers don't abandon practices that aren't working because they do not work collaboratively enough with other teachers or admin to develop data which concretely illustrates what's working and what isn't. The only real indicator of student "success" right now is either the state test, generally a lowest-common denominator situation, or grades, which are set by the teacher who has made the lesson plan and decided what will be graded and how. Add to that a "progressive ed" determination of what skills the student should master, and you've got some pretty wishy-washy, weakly supported or thought out learning goals. I can't tell you how many times I talk to a teacher who will half-seriously, half-jokingly, tell me they're wondering what they will teach the next class day. If there's no vision of even the next class day, what vision can there be of what student input should be assessed and why?
2) Teachers don't abandon practices that aren't working because someone once told them that their autonomy in the classroom was not a privilege but a right, and that it should be so jealously guarded that teachers often fiercely protect the solitude of teaching - wary of or downright refusing to cooperate in collaboration for fear their autonomy will be stripped away.
But this has all been said before...
Actually, these things haven't been said all that often to me -- at least, not by someone in a position to know.
I'm actually surprised by teachers telling you they don't know what they're teaching the next day.
I can see that for a first year teacher, but it seems strange for someone who's been working for awhile --- ???
Richard Elmore makes my heart go pitter-pat.
I found this (I will try embedding links)
Elmore sagacity
A good discussion here:
more good stuff
This observation is SO true:
Professor Richard Elmore claims that “education is a profession without a practice”.
Some good comments:
He justifies his assertion through reference to an absence of a clear body of knowledge and a clear body of practice.
For Elmore the weakness of the profession is the mistaken notion that:
autonomy = professionalism
Yet such a relationship is essentially anti-professional - “Within a true profession an individual does not have autonomy over it’s body of knowledge and it’s practice” - which would appear to be the case for education. Yet other professions such as medicine, law, dentistry or accountancy have a body of practice and knowledge, which must be learned, mastered and implemented within agreed and non-negotiable norms
Elmore asks,
"Consider what would happen if you were on an airplane and the pilot came on the intercom as you were starting your descent and said, 'I've always wanted to try this without the flaps.' Or if your surgeon said to you in your pre-surgical conference, 'You know, I'd really like to do this the way I originally learned how to do it in 1978.' Would you be a willing participant in this?
"People get sued for doing that in the 'real' professions, where the absence of a strong technical core of knowledge and discourse about what effective practice is carries a very high price. Instructionally, we know what works in many content areas. But the distribution of knowledge is uneven, and we resist the idea of calibrating our practice to external benchmarks."
See also Bonnie Grossen's excellent article on why teaching is not a research-based profession:
Grossen article
There's a great book, "How Doctors Think" by Jerome Koopman that talks about the cognitive processes that lead to medical mistakes, and what great diagnosticians do that makes them different from their average peers. It has some real parallels to education. The "art" and "heart" are clearly evident but BASED ON SOLID AND EVER-GROWING DOMAIN KNOWLEDGE as well as an attitude of enquiry, openness to new learning and constantly questioning preconceptions. Check it out.
How Doctors Think
>>For Elmore the weakness of the profession is the mistaken notion that: autonomy = professionalism
<<
Oh, look at that. I could speak at Harvard. :) I'm kidding, I'm kidding!
But seriously, I'm growing sick of the notion of autonomy when it stands in the way of change, or useful collaboration. Autonomy is such a pale excuse for expertise and ability.
"Would kids in these schools do better with direct instruction and precision teaching?
I believe the answer is yes."
It's because "strong family support" means doing what the school should be doing. Direct teaching.
"I think that teaching reading & math may fall into the rocket science category."
Perhaps for a few students, but for most, I wouldn't agree. It also depends on what level you are talking about. At the level of where the schools (and standardized tests) are, it isn't rocket science. Just look at the questions and the results. What are they doing for those 6+ hours?
"I'm constantly amazed at the gaps in my comprehension of math, and I'm a "serious" math student "
I was a serious math student, but I didn't master algebra until I was a junior in high school. Some things take time, but that doesn't mean that it's rocket science. It's hard work and practice.
The problem I have with this issue is that schools want us to believe that it is rocket science. They talk all about developmentally appropriate and how the brain works, but the majority of kids on a 4th grade NAEP test can't say how many fourths are in a whole. If schools can focus the conversation on vague concepts of learning, then we won't see that they are screwing up the basics.
I don't want to talk about brain function. I want to talk about competence. If our school started to use Singapore Math, they would still allow kids to get to sixth grade without knowing their times table.
High-SES families do a whole lot more than read to their kids and take them to museums. They do what schools should be doing. I don't know a darn thing about how to teach writing. That doesn't stop me from working with my son, and I don't worry (too much) about finding just the right book or technique.
There are two levels to the debate about education. Schools like to engage us parents on the "rocket science" level, but the real problems are way below that.
"Two other reasons, for many schools, not just high-performing: "
I don't even like the term "high-performing" when I disagree with how the schools and state define that term. "Best practices" doesn't mean much to me because I disagree with many of their basic assumptions on content and mastery. Is there a "best practice" for using crayons for making 100 3X5 pictures of scientific terms in sixth grade?
Lower schools set low expectations and allow kids to move along at their own pace. Developmentally appropriate allows them to avoid accountability.
In middle school, they expect a lot more, but the onus is on the students, and there are consequences. There is no accountability for the schools because students have to take responsibility for their own learning. It's the students fault.
In high school it's too late.
I was looking at the guidance section (an ASCA National Model) on our high school's web site. They were talking about preparing for college. They say that the clock is ticking and that you should start thinking about the path to college in 7th grade. They talk about taking courses like algebra in 8th grade. We don't hear a word about this in the middle school. They don't stand up at open houses and tell parents that they need to make sure that their kids get to algebra in 8th grade. It was only this year that the school got rid of CMP in the middle school and offered the same algebra course that's taught in high school. This is incredible! Lower schools are in their own world with very little accountability, and they complain about the low expectations imposed by the state.
Schools want parents to think that this is a complex process. That way, kids will think that they just don't like math or are not math brains, not that the schools screwed up year after year.
"Meanwhile, the usual remediation strategies we employ when kids fail to meet the statewide testing requirements are to give them the same unbelievably bad instruction they got in the first place, only in much larger quantities with much greater intensity. This is what we call the louder and slower approach."
--hey, it's my life story!
thanks for the link, palisadesk!
this guy's real good on
the politics of education,
pointing at a lot of true things
that seem never to be discussed.
seems to believe that the revolution
will be led by ed-school profs, though.
there is room for doubt.
vlorbik
SteveH-- it gets worse.
Nobody seems to be able to spell any more. My previous principal used to load me down with report cards to proofread (full of spelling and grammar errors) before they would go home. The Kindergarten reports really got my attention, and not for the spelling. Many contained the darkly foreboding observation, "X urgently needs to take responsibility for his own learning." These kids (some of them anyway) were four years old (need to turn 5 by Dec 31 for K)!!
If schools won't agree to take responsibility for 4-year-olds, can we anticipate they will be responsible for anyone?
And vlorbik, doing more of what didn't work the first (or second, or third, or fourth..) time -- that seems to be de rigeur. If I had a $ for every time I read in some student's cumulative record: Gr 1 -- J. has not yet learned the 50 "Dolch words"..Gr 2.... 3......4.....5... 'J is still working on the 50 "Dolch words"'.. Aaaaaaaak! [Bleep] the Dolch words! Try something else already!
I've come to see educational terms as Newspeak, a la Orwell's 1984 ("Freedom is Slavery") . "Best Practices" usually means, "Worst Practices". "Professional Development" usually means, "Inducing Brain Death." "Differentiated Instruction" means, "Pointless Time-Wasting for All." "Unmotivated Student" means "Never Been Taught." After all, it's the student's responsibility to "take responsibility for his own learning." Don't look at me, they pay me the big bucks to show up and spout bafflegab. Oh, and "facilitate."
Feeling sardonic today;-)
Palisadesk,
Thank you for your insightful comments regarding motivation. While volunteering in my son's first grade classroom today, I was tasked with getting the children in my group to put a sequencing puzzle together and write about the puzzle. The goal was to get the kids to write what happened first, next and last.
While the children had no problem putting the short puzzles together (the puzzle was for 3+ age group), it was a challenge to get them to focus on writing sequentially. One little boy said he hated writing and preferred to just put the puzzles together. I thought this made perfect sense.
Surely there is a better way to get six-year-olds motivated to write than to have them do puzzle pieces designed for three year olds? By the way, my son took one look at the box and said it was for babies.
These kids seem to be on their own. Center time seems so vague and random. Pick a center and do it. No direction whatsoever.
Meanwhile, the usual remediation strategies we employ when kids fail to meet the statewide testing requirements are to give them the same unbelievably bad instruction they got in the first place, only in much larger quantities with much greater intensity. This is what we call the louder and slower approach.
oh my god!
who said that!
I've been forcing myself NOT to have a fight with the district over Extra Help.
C. is now supposed to "come in for extra help" with Earth Science of all things.
Our entire curriculum & pedagogy are predicated on Extra Help.
As the math chair said to us, "If he hasn't come in for extra help there's nothing I can do for him."
That was a pretty great moment, because she made this statement not knowing that we had faithfully shlepped C. into school for Extra Help every single week for 5 months straight and it hadn't helped.
Not only that, but the teacher kept telling him "not to come in if he didn't need it" and we took him anyway.
The problem is, I am the only person in the entire town, apart from the person to whom I am married, who does not believe in Extra Help.
Extra Help is pretty much on par with Small Class Size where parent opinion re: quality education is concerned.
The mantra of "Extra Help" effectively stifles critical thinking about more substantive issues which are screaming to be addressed. Questions like (in no special order):
-- is this curriculum well-designed? Does it have an appropriate mix of challenge, massed and distributed practice, mastery of foundation skills, opportunities for individualization (curriculum compaction or supplementary work as required)?
-- are the expectations, requirements, objectives et alia clearly communicated to the students (and parents), so that they know what they have to do, by what criteria they will be evaluated, and what the timelines and parameters are for various assignments, projects or presentations?
-- is daily work, both classroom participation and assignment completion, regularly monitored (NOT necessary to grade everything, but monitoring and feedback are essential), and both formal and informal feedback given?
-- is this student appropriately placed in this class/program/course? Does s/he have the needed prerequisite skills or knowledge? If not, is a plan in place to address those gaps or significant needs?
-- is there a regular channel of communication (via student planner, communication book, telephone, e-mail, website or other) whereby teacher, parent or student can bring up a concern or problem and get needed information or response in a timely manner?
-- is the student (and/or parent as appropriate) aware, from regular ongoing feedback, of how successful s/he is in meeting course objectives?
-- is an appropriate area available where students may work on assignments during free periods or after school (library, study hall, homework club, whatever)?
I could go on and on.
The point is, "extra help" may be an entirely inappropriate response to the problem. At best, it is one step in a multifarious approach to ensuring student success. It's no panacea. At worst, it's a diversionary tactic that delays resolution of more fundamental issues.
One of the truest and most thought-provoking observations I have ever heard is this one (I may not have the exact words): " The problem that presents itself is not necessarily the problem to solve."
I have observed the veracity of this astute insight in numerous situations. I believe it comes from an article about generative instruction by Drs. Kent Johnson and T.V. Joe Layng.
" The problem that presents itself is not necessarily the problem to solve."
Programmers know all about defining problems and fixing them, and it doesn't involve guess and check. Most people see a problem, don't try to really understand it, and then just guess at a solution. It would take you forever to debug a program this way. Problems can seemingly go away, but they are still there, doing damage.
You first have to really understand the problem. Is there a number that isn't good? For education, this usually means test results of one sort or another. You then have to ask where that bad number came from and how it was calculated. You have to work backwards. I've tried to do this with our state tests and it can't be done. Absolute data (% correct) from the tests get manipulated with statistical methods to get relative results using an unknown merit function (I can't find it) to produce something like a proficiency index. Often, the proficiency index is in the 90's, but the raw percent correct on the tests are in the 50's. In this case, bad numbers are changed into good numbers and you never know that there is a problem. They do this on purpose.
Then there are cases where errors happen, but the source of the problem is not where the error occurs. For some computer errors of this type, you can't even trace backwards to find where the error comes from. I've had stack overflow errors that cause unrepeatable and seemingly random errors. This is generally not what is happening in education.
For education, the most common mistake (of this class) is to look at the high school test numbers and think that the problem is in high school. At our high school, their solution to bad math grades is to provide an algebra course with a math lab. Everyone thinks it's a great succcess. Did they ever consider that if the lower schools did their job, this course would not be necessary? (Actually, I think that there is a curriculum and philosophy wall between 8th and 9th grades that prevents this.)
Problem solving in education seems to be focused completely on relative, not absolute, and they are always looking for "the" solution. How many times have we heard that all we need is one thing ... like better teacher training? Of course, they think that traditional math curricula were the problem, not teacher training.
Complex systems can have many different problems or errors that interact. The problems could be "miles" away from the location of the error(s). You have to search for these problems and track them down methodically.
My favorite approach to programming is to use a prototype method, where you start with a simple stub of a program that you can easily test. New functions are added and tested along the way. This minimizes the amount of new testing that has to be done and minimizes the potential of errors interacting.
Education is like getting someone else's unknown program to debug. Nothing could be worse, and guess and check won't get the job done. You have to dig into the code, line by line, and understand everything. You can't wait for errors to appear just by running the program. You have to go looking for them.
Unfortunately, the problems of education are being solved by guess and check. That's why I don't like statistical analysis applied to education. You have to break down education, line by line, and see exactly what is going on. You have to examine exactly why some kids do well and some don't. Our state sends home a questionaire that asks whether we parents feel comfortable with helping our kids with their math homework rather than asking how much time we spend teaching our kids or sending them to tutors.
They talk about critical thinking, but they don't have the content and skills to even begin.
The two comments immediately preceding (posted by Palisadesk and SteveH) need to go into Greatest Hits!
"You have to search for these problems and track them down methodically."
Having worked on ESGNs (electrostatically supported gyro navigators) aboard trident submarines for 20 years, my husband can tell you the importance of tracking problems down methodically.
I cannot imagine the U.S. Navy taking a laid back approach to solving problems that if not fixed could render the entire strategic weapon systems useless. As a matter of fact, Boeing was a awarded a $25.2 million contract to provide maintenance, support, and troubleshooting for the ESGN euqipment for the U.S. and United Kingdom navies.
I find it ironic that schools talk about problem solving so much, but they seem to have no idea of the whole field of systems analysis or how complex systems are designed and tested. They talk about skills needed for the 21st century, but they have no understanding about what these skills are. They don't even know enough content to look it up.
They do "play" problem solving, like guess and check, draw a picture, act it out, or some sort of generic "work backwards". If they knew more about systems analysis, then they would be able to translate real (any century) skills to ones students can understand.
An example of this is "divide and conquer". This technique appears in so many forms and variations. A classic one is the binary search of a list. Students can try this out by searching for a word in the dictionary. I mentioned on another thread that if you bracket the solution in a search for the root of an equation, you can then apply a binary search to find the solution to any desired accuracy.
Their talk of problem solving and understanding is only a cover for low expectations.
At worst, it's a diversionary tactic that delays resolution of more fundamental issues.
One of the truest and most thought-provoking observations I have ever heard is this one (I may not have the exact words): " The problem that presents itself is not necessarily the problem to solve."
wow
amazing
It's getting to be a full-time job just corralling all these fantastic comments and putting them some place we can find them.
I find it ironic that schools talk about problem solving so much, but they seem to have no idea of the whole field of systems analysis or how complex systems are designed and tested.
yup
I find it ironic that schools talk about problem solving so much, but they seem to have no idea of the whole field of systems analysis or how complex systems are designed and tested.
yup
"The problem that presents itself is not necessarily the problem to solve."
My head is spinning.
Part 2 of this idea is the question of making some kind of assessment as to whether the real problem, assuming you have an idea what the real problem is, can be solved.
At the moment, I feel that dealing with a high performing school district has been a more complex challenge than dealing with an autistic child.
And autism is phenomenally complex. (Autism may turn out not to be complex once we know more about it. But for a parent, teacher, friend etc., given what little we do know, it is utterly bewildering and many-sided.)
What is a "merit function"?
I assume I'm following Steve's comment, but I'm not sure.
Teaching reading well isn't rocket science, I agree, but the science of teaching reading well is.
Basing one's teaching in the science and doing it well isn't a simple undertaking. Obviously people can learn to do it and do it well with practice.
But I wouldn't call it simple.
I once watched Ivar Lovaas work with Jimmy.
Pretty amazing.
Technically he was doing standard-issue "ABA."
But wow.
He was a master.
As for math, I may have to stick with the rocket science metaphor!
I constantly have the experience of discovering I don't understand some element of math -- and we're talking about arithmetic and algebra here -- that I thought I did understand....and I'm working with a decent curriculum....
When I see the kinds of problems I'm having I don't see how anyone can teach math well to groups of students all showing up with different levels of preparation, comprehension, etc.
Leaving that aside, I'm amazed at the idea that math could be taught well even to groups of students who are well-prepared and on the same level. It's so complex....
otoh, this is a case where I probably should not be generalizing from my own experience. I'm teaching myself a subject I don't know. For quite some time now I've been teaching myself concepts & procedures I've never seen before in my life, things I'd never even heard of in some cases. (Polar coordinates?)
It's a bit of a strange undertaking when you think about it. It's quite different from all the self-teaching I do to write a book.
I'm probably going to set a new "rule" that the various bumps and gaps I encounter are useful for thinking about bumps and gaps an individual student might have due to his individual history, not for thinking about math teaching in general.
Saxon, by the way, explicitly stated that his books were not to be used as self-teaching textbooks.
I think his position was that the teacher would make the connections amongst the various topics for the student.
I'm constantly discovering connections amongst topics and being stunned when I finally figure them out....and I don't think that would be happening IF I HAD A MATH CLASS & A MATH TEACHER.
It's really getting to be time.
They talk all about developmentally appropriate and how the brain works, but the majority of kids on a 4th grade NAEP test can't say how many fourths are in a whole. If schools can focus the conversation on vague concepts of learning, then we won't see that they are screwing up the basics.
I think I mentioned that the 5th grade was given the "find a number larger than 7/8 and smaller than 1" problem the other night.
C. overheard us talking about it and I said, "Find a number larger than 7/8 and smaller than 1."
He did it easily, thank God. (He may have said 8/9; can't remember.)
"What is a 'merit function'?"
A merit (or objective) function is a way to reduce a bunch of data (usually via a formula) down into one number that can tell you whether a complex system is doing well (merit). (I could spend a long time on whether this is a good or bad thing to do, but it's a common tool in engineering.)
A simple example is grading for a course. The teacher says that tests are worth 40 percent of the grade, quizzes are worth 25 percent, homework is worth 25 percent, and class participation is worth 10 percent. The merit function would require taking the average of the test scores (0 - 100) and multiplying it by .4, the average of the quizzes by .25, the averages of the homework by .25 and the class participation mark (0 - 100) by .1, and then adding up the results. The result is a number between 0 and 100.
This sort of thing is done with the raw (% correct) scores of our state testing, but the merit function changes the raw data into a number (proficiency index) which reflects only how many kids get over some (obscure) proficiency level. In making this change the numbers go from ugly (and easily understood) numbers like an average of 65% correct, to a vague (but nice sounding) proficiency index number, like 95%, that reflects how well the school is meeting expectations. Any sense of what meeting expectations means is lost in the process.
I've also noticed that these functions are nonlinear, just like the rubrics used at our school. Grades from 0 - 100 get translated into rubric grades from 1 - 5, where almost everyone gets a 3 or 4.
Like statistics, merit functions (rubrics, proficiency indices) can be used for good or evil.
Check it out.
C. said this morning that math is now his favorite class.
That's just amazing.
Amazing, amazing, amazing.
This is the kind of thing that's going to make me believe in maternal instinct. Ed was never on board for everything I've been doing -- not until recently, that is, and "recently" would have been too late.
Everyone, universally, has said, "C's strength is in history, in verbal fields; he's not a math type;" etc.
This has been universal.
I've just never, EVER, been willing to go with what everyone's perception of C's "strengths" and "interests" are.
I don't know why.
I think some of it is that I'm hooked on math myself...so I know that there's really no way to say whether you're "interested" in math when you know very little about it.
I believe that there are mathematically gifted kids who can know they're interested in math even when their instruction has been poor, although I'd be willing to bet there are mathematically gifted folks out there who don't know math is what they're supposed to be doing.
I know what I'm thinking!
I think math is an acquired taste.
I don't think there's any way to know whether a child who hasn't been consistently taught well is interested in math or not.
"I think I mentioned that the 5th grade was given the 'find a number larger than 7/8 and smaller than 1' problem the other night."
7.5/8
or
.999999999999999
Of course, he hasn't actually said he likes math.
He likes math class.
But I'll take it. He wouldn't have been in this class without all the work I've done for the past 3 years.
.999999999999999
Hey!
That's a good one!
Many contained the darkly foreboding observation, "X urgently needs to take responsibility for his own learning." These kids (some of them anyway) were four years old (need to turn 5 by Dec 31 for K)!!
Were these canned comments from the Comment Bank?
".999999999999999
"Hey!
"That's a good one!"
Not .9999 repeating, though, since that's equal to 1.
8-)
Eureka!
I found it. My quote was not exact (and I generalized the applicability of the insight to many other domains), but the article by Johnson and Layng from which the statement is taken is this one:
American Psychologist 1992 article
The discussion is in the first column of the second page, on generative instruction and fluency.
My experience is that it applies in many areas, especially when you're troubleshooting academic performance problems.
And did I mention Jerome Groopman's How Doctors Think? From a different field, many vivid examples illustrate the same principle at work.
On another topic:
I'd be willing to bet there are mathematically gifted folks out there who don't know math is what they're supposed to be doing.
I think I might be one of them. I had a keen interest from early childhood in numbers (words, too) and in science -- chemistry, geology, herpetology, etc. Got steered into traditional female subjects (English, history, languages) in which I excelled without effort. Math took work, and I had some awful teachers, which did not foster intrinsic motivation. Didn't realize I must have aptitude until I took the GRE and got something like a 740 without having taken any math as an undergraduate.
You're right to keep C.'s options open. We are "naturally" drawn to fields in which we are successful and feel competent. 12 is too early to be making life choices. At 12 I wanted to be a medieval herpetologist/cryptanalyst -- an arcane occupation with few openings;-)
As an adult I studied a lot of math topics on my own; I have a small library of math books, some serious, others recreational.
In my next life I will be a scientist, combining both theoretical and applied aspects. Or perhaps, a la Hawking and the "many-worlds" hypothesis, I'm already doing it in a parallel universe:-)
I think math is an acquired taste.
I don't think there's any way to know whether a child who hasn't been consistently taught well is interested in math or not.
That was John Mighton's experience. Anyone who is not familiar with his work, check these out:
Mighton bio
Wikipedia entry
I have both his books and highly recommend them. He has (independently it seems) grasped some key ideas central to PT: the importance of component skill fluency, the non-linear aspects of learning, the motivational power of challenge and competence.
That is fascinting!
That's Carolyn's story.
(I'll link later...)
She was an art major in college; I think she flunked algebra in high school?? Something like that.
She decided she wouldn't be able to get a good job as an art major so she told her advisor she'd decided to switch her major to math.
Her advisor said, "I advise you not to do that."
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