Discussion Topic |
|
This thread has been locked |
Ed Hartouni
Trad climber
Livermore, CA
|
|
|
Jul 25, 2014 - 11:47am PT
|
"...I suspect that the implementation of the process did not take into account the entire educational system."
a suspicion you could easily verify by doing a little work with Google. It was relatively easy to find the basis for the standards, you might look first at the Wiki entry, then track down the references...
http://en.wikipedia.org/wiki/Common_Core#Mathematics_standards
|
|
rgold
Trad climber
Poughkeepsie, NY
|
|
|
Jul 25, 2014 - 12:10pm PT
|
This has me scratching my head.
Engineers have a "dysfunctional model for doing math?"
Engineering, by definition, is the application of math toward a beneficial purpose.
If engineers aren't doing functional math ... then who is?
Well, first of all, I said "a dysfunctional model for doing math" and you changed that to something completely different, "doing functional math." Second of all, I didn't mean to tar the entire engineering profession with the dysfunctional model brush, just my two friends. Thirdly, the engineers in question were using math but in strictly procedural ways, with an arguably tenuous grasp of underlying issues. This works as long as it works, maybe for a whole career depending on what the challenges are, but it put them in a position of only being able to explain procedures to their kids. If the kids, for some reason, were taught a different (but equivalent) procedure for the same underlying result, they couldn't adapt.
Perhaps we might make an analogy based on your own experience. A person who understands place-value can do addition and subtraction, almost immediately, in any base, as I'm sure you can. But a person who doesn't understand place-value and is perfectly competent in base 10 arithmetic will be utterly lost if they are presented with a base 5 arithmetic problem, nor will they ever notice the parallels between, say, polynomial evaluation and number representation, and they surely won't recognize problems that are naturally expressed in terms of other bases, such as the Cantor subset of the interval from 0 to 1.
The latter type of knowledge is strictly procedural and leads nowhere beyond its immediate application to adding and subtract ordinary numerals. If something about the procedure is forgotten, there are no mental props for recovering it. If some different procedure is proposed, there is again no mental infrastructure for deciding whether or not the proposal is equivalent to the known method and, if not, under what circumstances the proposed method is valid.
The former type of knowledge is far more general, allows for reasoning about the algorithms for addition, allows the framing of appropriate questions about them, allows for understanding what kinds of modifications will or will not be valid, and opens entirely new mental pathways for either using or recognizing the presence of representations in other bases. For an engineering example, it seems highly unlikely to me that anyone unfamiliar with different base representations would have thought to investigate ternary logic as more efficient model for computer chips.
Our education system, at all levels, often doesn't address the distinction between the merely procedural and something else that we call understanding. Some of the reasons for this are obvious; it is easy to teach and test procedures and hard to even define, much less test, understanding.
When it comes to elementary and perhaps also secondary education, there are very reasonable concerns about intellectual readiness for the kinds of thinking that might be involved. This might mean, as the Washington Post article suggests, that some of the features of understanding in the common core are inappropriate for the age levels that are supposed to be learning them, which leads to a very old claim that we should teach 'em how to do it and later they'll understand it. I'm guessing that's exactly how you arrived at your current state of expertise, but the counter argument is that this process doesn't work for a large number of people, including some engineers, who really do need it to work for them.
|
|
Ed Hartouni
Trad climber
Livermore, CA
|
|
|
Jul 25, 2014 - 12:16pm PT
|
just a thought, but, is it so bad that parents will have to learn math to help the kids in school?
it seems that that could be a great consequence of the new standards...
|
|
rgold
Trad climber
Poughkeepsie, NY
|
|
|
Jul 25, 2014 - 12:22pm PT
|
just a thought, but, is it so bad that parents will have to learn math to help the kids in school?
As if...
The kids of parents willing to do that probably have nothing to worry about for a host of reasons.
I suspect that the general attitude will be more like, "if English was good enough for Jesus, it's good enough for me."
|
|
JEleazarian
Trad climber
Fresno CA
|
|
|
Jul 25, 2014 - 01:03pm PT
|
I suspect that the general attitude will be more like, "if English was good enough for Jesus, it's good enough for me."
Good one, Richie!
I also have my personal foreign language analogy. When I was a grad student in economics at UCLA in the 1970's, we had a language requirement for a Ph.D. The doctoral candidate had to know French (for Walras, primarily), Russian (under the theory that Marxist theory would probably be most developed in the USSR) or math, because math is a foreign language to economists.
John
|
|
kev
climber
A pile of dirt.
|
|
|
Jul 25, 2014 - 01:57pm PT
|
Hmmm engineers and math...
My job title is "Senior Research Engineer" (i must be getting old),
and my education is in mathematics....
Guess what I just spent 3 hours doing at work - finding a slick way to solve an equation that had people stumped. Next step is to write it up as a proof.
|
|
blahblah
Gym climber
Boulder
|
|
|
Jul 25, 2014 - 02:10pm PT
|
Engineer is sort of a vague word (remember the good ol' sanitation engineer, f/k/a garbageman). Even assuming we're talking about ones who have legitimate engineering degrees, I'm sure there's lots of variation regarding how much math they use in their jobs, if any.
Still, as the holder of an engineering degree from a prestigious university, I'm surprised that anyone who calls himself an engineer is stumped by elementary-school math problems (I don't write this to insult anyone; it's just genuine surprise).
Can anyone post an example of a problem that has the engineers scratching their heads?
Maybe that will shed some light on whether the problem is with the engineers, the modern curriculum, both, or neither.
|
|
Festus
Social climber
Enron by the Sea
|
|
|
Jul 25, 2014 - 03:26pm PT
|
"In 23 years of teaching, I've met very few teachers that fit that description."
I have to agree completely with Wbw. I'm not a teacher but I've got two kids, one about to be a junior in high school and one entering his second year of middle school. That adds up to a lot of teachers I've come to know pretty well, and from kindergarten until now I've seen exactly three teachers in that whole bunch who probably put tenure above the the needs of their students. So, three bad teachers out of 45, and the majority of that remaining 42 were very good to excellent, truly dedicated teachers. Our community strongly supports its public schools and teachers (Mira Mesa, in San Diego Unified) to a great degree (and I'm not talking about $ here), something that isn't true for virtually every school in this large district that has problems. You're either part of the solution or...
|
|
blahblah
Gym climber
Boulder
|
|
|
Jul 25, 2014 - 04:50pm PT
|
Thanks, very interesting. I have to admit, at least on my cursory inspection, I have little if any idea of what the questions are getting at.
More straightforwardly, I imagine I would "flunk" the assignment.
I can sorta see how the Glenn Becks of the world see this sort of stuff as a vast liberal conspiracy, seems sort of intended to make sure that parents are "outsiders" to the curriculum. Even if that's not the intent, that's the clearly foreseeable result.
As someone posted above, at some not-super-high level, a good student is going to surpass what a typical parent knows about math and science.
But I think most of use would be surprised when this happens at second grade.
|
|
rgold
Trad climber
Poughkeepsie, NY
|
|
|
Jul 25, 2014 - 08:56pm PT
|
The Huffington post article is interesting. Of course, as I've suggested above, it suggests an implementation problem.
But frankly, I see something else. Someone with a BS in engineering---electrical engineering at that, the most mathematical of the engineering majors---who can't immediately grasp what method is being suggested and can't immediately see what went wrong, much less is incapable of puzzling it out, is a classic example of what I was speaking of when I said that the people who have been trained to replicate procedures may end up with very limited mathematical abilities.
We can argue all day about whether the process illustrated is a good way to conceptualize subtraction or, if it is, whether it is appropriate for the audience it is intended for. But when someone with a degree in electrical engineering can't grasp what is happening in that picture and can't explain it to someone else, eg a kid, then we are looking at an example, and I'm afraid not too uncommon an example, of a substantial failure of the the entire classical education edifice.
Whether this type of mathematical disability can be addressed by this or that new curriculum or set of standards is an open question, but as a symptom of the kinds of problems the current education system manages to produce, the example is stark.
|
|
blahblah
Gym climber
Boulder
|
|
|
Jul 25, 2014 - 09:39pm PT
|
OK after reading rgold's response, I have to change my response slightly and sort of agree with him. Part of my initial problem is that I ignored the handwritten numbers on the numberline (I found them hard to read). Feeling spurred on, challenged, and/or insulted by rgold, I took a closer look and agree that the subtraction method that Jack was supposed to use does seem to be relatively clearly suggested, and perhaps understanding that method does give a better "feel" for what subtraction means and what base 10 numbers mean than doing it the "standard" way that the parent wrote in his letter (which could be done, I suppose, mechanistically in such a way that the person performing the subtraction doesn't really have any idea what the process means).
But Jack's seeming errors are so random and nonsensical (how does he get from 127 to 107?) it seems silly to make that a standard math question instead of some sort of strange intelligence test (which apparently the parent and I did poorly on, at least the first time around).
|
|
Ed Hartouni
Trad climber
Livermore, CA
|
|
|
Jul 25, 2014 - 09:52pm PT
|
Jack forgot to subtract 10, first subtracting 3 100s then 6 ones, that's only 306
the handwritten numbers are the engineer father not figuring out what is going on... and playing around with it to try to get it to work out...
that's a pretty standard behavior among first year physics students if you know the answer (maybe it's in the back of the book) and you just play around with combinations until you get the answer. Of course you can't explain it... and you don't get any points for your solution.
here is a resource for teachers that helps them find resources to develop lesson plans
maybe it would be useful for interested parents.
https://www.kansasprojectsuccess.org/system/files/95/original/NCTM%20Document%20Making%20It%20Happen%20Common%20Core%20Standards.pdf?1309461005
|
|
Todd Eastman
climber
Bellingham, WA
|
|
|
Jul 25, 2014 - 10:02pm PT
|
... cause they expect God to do the heavy lifting when things get tough...
|
|
rgold
Trad climber
Poughkeepsie, NY
|
|
|
Jul 25, 2014 - 10:23pm PT
|
I didn't mean to insult anyone. We are speaking of educational failures, not personal ones.
The handwritten numbers in the example come from the confused engineer. Just look at the printed numbers.
Jack was supposed to subtract 316. That means he needed to "back off" by three 100's, then by one 10, and then by 6 ones. But Jack forgot to back off by the 10; the rest is ok.
All the engineer dad can do is to illustrate, with absolutely no explanation, how to get the right answer with the standard subtraction algorithm. He can't figure out what Jack was supposed to do, he can't see what Jack did right, and he can't tell Jack what he did wrong.
Let's take this out of the context of the engineer dad and suppose this guy was the class teacher. He's got a student Jack who, I would say, understands the problem fine but has just overlooked the operation with the ten. What Jack gets from the "teacher" is that his method is long, confusing and will get him terminated from his job when he grows up, and here is the right way to do with with no explanation and no connection to what Jack had in mind.
I think this nightmare scenario probably plays out in homes and classrooms across the country over and over again. Kids who have begun to make sense of arithmetic are told they are all wrong when they are not, and are asked to substitute meaningless (to them) manipulations for the beginnings of understanding they have begun to formulate. Then we're surprised when people say the most logical of subjects is obscure and confusing. We're surprised to hear about math anxiety after we attack children's valid attempts at sense-making and replace them with catechistic incantations with no intuitive content.
You'd have to know something about what went on in class to decide whether this question was appropriate for the audience it was addressed to, but I don't see anything the matter with it as a question at all. The fact that it is being bandied about as some sort of failure of the common core strikes me as powerful evidence for the failure of what came before.
EDIT
I guess I was typing this as the same time as that other ivory tower denizen Ed was posting. I'm so surprised to get this from Kos, who surely understands exactly what the Huffington post problem is driving at, and just how much of a problem it is for the education system that a guy with a BS in electrical engineering can't grasp what the question is about. I'm even more surprised that Kos pretends to divine base motivations for my opinions and brands me simultaneously arrogant and pathetic.
Ah well, but its the internet right? What was I thinking.
|
|
Todd Eastman
climber
Bellingham, WA
|
|
|
Jul 25, 2014 - 10:43pm PT
|
Could the fact that we don't negotiate when buying things at markets diminish our ability to utilize basic math on a daily basis have any impact on the original question?
Math as an element in everyday things like going to market does shape how the basics get re-enforced. Make no mistake, nimble thinking is essential in providing food in other nations.
|
|
Ed Hartouni
Trad climber
Livermore, CA
|
|
|
Jul 25, 2014 - 10:57pm PT
|
I wrote a long explanation but decided in the end that Dave Kos would just see it as supporting his contention that the "only objective of" my "posts is to demonstrate that you are smarter than everyone else. It's arrogant."
It reminds me of a story that involved my wife, Debbie, who had gone back to school and was taking undergraduate physics. She rarely asked me anything about her assignments (maybe she had me check her homework before she submitted it) but one time.
At breakfast I was reading the NYTimes, which is routine, and she was hovering around waiting for me to finish the front section. I folded the paper and "bam" she put her Physics text in front of me and said "how do you do problem 35?!"
I had a reputation, in my household, of trying to lecture on the subject of problems rather than "just doing it" from both Debbie and our daughter. Debbie wasn't in a pleasant mood, due to this particular problem, so I decided to "just do the problem."
On a clean piece of paper, I wrote down each step, sequentially, explaining briefly the logic of the solution for each step, inexorably arriving at the conclusion that matched the answer in the back of the book exactly.
She burst out in tears and wailed "it's so easy for you!" which was not the response I was trying to achieve...
I reminded her that I had been studying physics since I was 10, and that I taught at the University for 10 years, and was employed as one, and that it pretty much better be easy for me, at least compared to someone who had been doing it for less than 3 months. She never asked me again, I like to think she understood that she could figure it out, it wasn't impossible.
If the solution to the problem seems easy to me (and to rgold) and you believe that we are arrogant because we do it to demonstrate how smart we are, you've really lost control of yourself over this issue, STForum is not the place I come seeking professional affirmation. And not only that, you're letting your ego get in the way of a child's education.
That collective ego is that 2nd graders can't possibly understand math that their parents can't.
The tragedy is that the educational system in the country has produced multiple generations of parents whose math understanding is less than what the Core Curriculum expects from a 2nd grader.
If that ego can't deal with that, then yet another generation of students will be let down by their education. While there will still be students that will achieve an understanding and use that to their great advantage in the future workplace (actually it is the workplace of today) a great majority of students won't have the opportunity.
All because some dad couldn't do his kid's homework?
[remember a couple of generations ago most of the parents couldn't do their kid's homework...]
it would seem that it should be relatively easy for that dad to learn what is being taught and support the teacher and the lesson... what lesson do you think that poor kid learned?
|
|
Todd Eastman
climber
Bellingham, WA
|
|
|
Jul 25, 2014 - 11:30pm PT
|
Ed, you are never arrogant... ever.
|
|
Ken M
Mountain climber
Los Angeles, Ca
|
|
|
Jul 26, 2014 - 09:16am PT
|
So, three bad teachers out of 45, and the majority of that remaining 42 were very good to excellent, truly dedicated teachers.
This was apparently in a high-performing school. You might accept that in a lower-performing school, that ratio might be higher.
Here is another thought, since we are talking engineering. You have a car that has only 45 parts, but 3 don't work. How well does your car work?
Only one bad teacher can have a devastating effect if it comes at the wrong time.
But the converse it true: If you talk to most successful people, they can name the teacher(s) that were responsible for the person they became, and generally speaking, those teachers were few.
I do not understand the argument that a superb teacher is irrelevant and meaningless.
I imagine that there is a normal distribution of teaching skills. A few bad, a bunch average, and a few superb.
Why would we not want to have a system that tends to push the average towards the superb column? We seem to have a system that protects mediocre performance, and protects the terrible from termination in any rational timeframe.
|
|
Ed Hartouni
Trad climber
Livermore, CA
|
|
|
Jul 26, 2014 - 09:49am PT
|
How is having a central agency determine the standards a step up from having teacher unions handle it? Why can no one answer this question?
what is this question?
is it:
why shouldn't educational standards be determined at the local level?
If we presume that the educational systems being independent is a way to experiment with many different approaches, then we can benefit from looking at the outcomes from all the experiments and find new ways to educate our children.
But no single educational entity can afford to do that kind of analysis and synthesis. Who would pay for it?
Now that sounds like the role of some larger organization, perhaps the states, and then the federal government to do it across the states.
At some point we have synthesized the most effective lessons from all the various ways of educating students.
Further, while teacher groups, the private sector, etc., may have specific agendas, the larger government organizations can provide guidance on larger issues, important at the state and federal level. These governmental organizations can embark on research to determine what standards are required for future needs of the state and the country, and from those studies propose those standards.
Changing teaching methods costs money, so those organization can also offer support to the schools seeking to change their curriculum to achieve the goals of the new standards.
Right now, it seems that that has been left as a choice to the various states and local government and to some extent to the local school districts, maybe even to local schools and to individual teachers themselves.
I am shocked that California, having adopted the Common Core has not made available support for teacher training to implement those standards, the state is currently running surplus budgets and can afford some level of support. Shame on the legislative bodies!
Now perhaps we can get rid of any outside influence of local schools, letting them get on teaching the three R's, after all, that was good enough for the parents, wasn't it? Why do more?
We've found that there are better practices, discovered in the vastness of the diversity of schooling. That students who were lucky enough to be educated in those ways did better. Is it ethical not to share that? It is every bit like some local hospital finding a miracle cure and it not being shared, only the local people are allowed to benefit from that knowledge. It is not so outlandish to equate the "miracle cure" to a superior education, they both effect the lifetimes of individuals.
The California Governor's budget for 2014-2015 proposes 42.4% to K-12 education. There is funding available for Common Core teacher training (enabled by Proposition 98), but that isn't available now... The total budget is something like $77 billion. This reflects a shift in the way education had been funded, with the passage of proposition 13 in 1978 which limited the rate of local property tax increases.
That Proposition 13 was a response to the findings of Serrano v. Priest http://en.wikipedia.org/wiki/Serrano_v._Priest that California's local funding of schools was in violation of the equal protection clause of the US Constitution 14th Amendment is another move away from local control to state control (in this case). Generalizing that, the federal government has an interest in seeing those same protections afforded to citizens in all states.
This is a long way from how schools were funded in the times of Ichabod Crane, were the townspeople of Sleepy Hollow foraged up a way to support a teacher for their children, those that felt an education was important for their children. Ichabod Crane is not a very sympathetic character, and in the end he looses out to the town rowdy in his bid for the hand of the Katrina, the only daughter of the wealthiest man in Sleepy Hollow.
Somehow teachers don't get a very sympathetic hearing in the United States, and funding education seems to always have been contentious. But given the global competition for a well educated and competent workforce, doing anything less seems to be ceding the future. And worse, we are making these decisions for the children, decisions that have the important legacy of determining their future. It's not something that should be taken lightly.
|
|
Ken M
Mountain climber
Los Angeles, Ca
|
|
|
Jul 26, 2014 - 10:19am PT
|
Which is better, a car with 100 parts and three not working (and not really fixable), or a car with 3 parts and one not working (and not really fixable)? Considering a perfectly working car is not a real-world possibility, which of these options do you choose?
I reject your premise.
why are you deliberately choosing failing options? Rather than "commitment to excellence", you appear committed to the least that can get by. No wonder education is in trouble.
This was the EXACT same premise that got American industry in such trouble, and pushed the Japanese to the front.
the case study taught to me in business school had to do with tolerances in production. The American company knew that the part could only be manufactured to specs 95% of the time. So they contracted to pay for only 95% of the product received. The Japanese manufacturer was confused by this, and they enclosed a note with the shipment:
"we do not understand why you have contracted for 5% out of spec parts, nor what use you will make of them, but we have included them in a separate box, so that you will not accidentally mix them up."
That was when the lines crossed in American and Japanese manufacturing (thanks to Deming)
|
|
|
SuperTopo on the Web
|
Let us know!