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Seamstress
Trad climber
Yacolt, WA
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Jul 24, 2014 - 01:08pm PT
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The key to any learning is desire. How do you make it real and how do you make it possible?
Teachers who really understand the subject and really understand their students learning and social skills can readily prepare the vast majority of kids tfor real life math applications. Two trains travleing towards each other - no one cares. However, a real life lesson like here are your credit balances, interest rates, and minimum amount due, how should you prioritize your payments and how long will it take to be out of debt - those are far more real life problems that kids need to solve. My former A student in Math needed Mom to show her that she could dig out of debt with a better prioritization, and bankruptcy was not necessary.
I would not be a fan of the group grope for understanding. I was a shy and awkward kid who would have HATED math if it was a group guided discovery. I was also not a fan of memorization, though I will admit that it was terribly efficient not to be actively computing 12x12 every time.. In my mind, nothing replaces true understanding. That needs to start with the teacher.
Always hated the gross generalizations - Why Americans stink at math......I am American, and I am great at math. That is inaccurate characterization of an array. Much better stated as "Why many Anericans stink at math", "Why the mean mathemeatical literacy of Americans is lower than other countries".......
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Ed Hartouni
Trad climber
Livermore, CA
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Jul 24, 2014 - 01:39pm PT
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...can readily prepare the vast majority of kids tfor real life math applications.
what is "real life math applications"? those examples you provided are interesting, but not the end of "real life" applications. In fact, "application" is a very interesting word, it implies that something is being applied, in this case, mathematics, which by the same implication is not "applied" but "pure."
So without learning mathematics, you don't have anything to apply.
You could just teach those specific lessons, and have the students use those lessons by rote, to the specific "real life applications" but you can't anticipate all the different application.
However, teaching students how to apply the same mathematics to different applications would seem to be a goal. If you can't see debt rates and trains as applications of constant rate coupled equations to be solved algebraically, then you've missed the point.
It is easy to disparage word problems, but the idea of the word problem is to learn how to analyze the problem and set it up to be solved. Once you learn how to do that, you can apply it to trains, and to debt, or any other such problem, or the issues related to the national budget and the assumptions going into the arguments over default...
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kev
climber
A pile of dirt.
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Jul 24, 2014 - 01:48pm PT
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Teachers who really understand the subject and really understand their students learning and social skills can readily prepare the vast majority of kids tfor real life math applications. Two trains travleing towards each other - no one cares.
College freshman relate much better to a (albiet fictitious) drinking/exponential decay/DUI word problem than the traditional half life problem.
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Ed Hartouni
Trad climber
Livermore, CA
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Jul 24, 2014 - 02:01pm PT
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another problem: we generalize our own education.
Why is this a problem? because we don't actually understand how we were educated. Somehow, everyone thinks their an expert, and that their own experience is some self evident truth. Following this logic, it is not too difficult to see why teachers aren't respected and that learning about education is considered a waste of time.
If everyone is an expert, it should be no problem to teach our children. It is even easier to do that by telling the children that the teacher doesn't know how to teach and that the particular assignment is stupid and irrelevant and that the parent can testify that surviving in the "real world" doesn't require mastery of the subject.
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TGT
Social climber
So Cal
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Jul 24, 2014 - 02:06pm PT
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It's not just math it's the entire teaching paradigm that needs to change.
The greatest impediment are the university education departments.
There's a national database with about every Masters and PHD thesis on education collected in it for the last 20 years or so called ERIC.
The standards on what gets accepted and published would get you laughed out of any other department including the soft ones if submitted.
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Ed Hartouni
Trad climber
Livermore, CA
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Jul 24, 2014 - 02:06pm PT
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is it a grammar mistake or a typo?
you're saying I don't understand the difference between: there, their and they're? or that I typed it incorrectly...
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Ed Hartouni
Trad climber
Livermore, CA
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Jul 24, 2014 - 02:11pm PT
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The standards on what gets accepted and published would get you laughed out of any other department including the soft ones if submitted.
interesting assertion, perhaps you can actually support it with some real cases, or are you just passing on what you heard somewhere else?
Not that that sort of logic would get you laughed out of the STForum, since that sort of logic is pervasive.
And then to generalize it to state that College/University Education Departments are the root cause of bad teaching, well, you might want to shore up that conclusion a bit too.
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Ed Hartouni
Trad climber
Livermore, CA
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Jul 24, 2014 - 02:12pm PT
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yes, good catch of a mistake in an ironic setting...
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klk
Trad climber
cali
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Jul 24, 2014 - 02:23pm PT
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It's not just math it's the entire teaching paradigm that needs to change. The greatest impediment are the university education departments. There's a national database with about every Masters and PHD thesis on education collected in it for the last 20 years or so called ERIC. The standards on what gets accepted and published would get you laughed out of any other department including the soft ones if submitted.
that's a bit colorful, but yes, the general rule is that professional schools generally--ed, med, law, and business--produce scholarship that on average is less rigorous than that in many of the disciplines. there are stacks of exceptions, obviously, but yes, that is the consensus.
until very recently, much research on education in k-12 was driven by a desire to produce quantifiable measurements of outcomes and efficiency. that came partly from dynamics internal to education (quantitative research looks more rigorous) but also in response to policy demands for cheaper public ed that could be measured in metrics so simple than even an average st poster could understand them.
one of the ironies of the standardized tests, is that in undergraduate education, education majors consistently rank in the lowest percentile of students by major. another irony is that business consitently ranks as another of the lowest performers.
put "business" and "education" together and you get NCLB and other horror shows.
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JEleazarian
Trad climber
Fresno CA
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Jul 24, 2014 - 02:24pm PT
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Pedagogy is an entire field of study itself. In other words, there is nothing "easy" or straighforward about teaching. I've taught sciences and math (statistics/probability mostly) at the high school and college levels. There are many different learning styles, and accomodating all of those styles in a teaching lesson is a big challenge. Some kids are visual/spatial learners, some are verbal, some conceptual, others relative/analagous.
El Cap for the win. My daughter and son-in-law both teach math and statistics at the high school level, and both get consistently excellent reviews. Math was one of my undergraduate majors, and always came easily and intuitively to me, so I can't offer any personal stories about overcoming difficulty. I have, however, taught law and economics for over 25 years, and always got superior reviews from my students, despite having no formal training in education. Well, there is one exception. One Summer School economics class I taught at Fresno City College had a one-student review in Ratemyprofessors.com that gave me a "C," but that's an outlier. ;-)
Anyway, I think the idea that anyone who "knows how to teach" can teach anything simply does not fit my experience. I find no substitute for thorough knowledge of the subject matter. Unfortunately for teaching, math is one of the few undergraduate majors that offers a lucrative field with just a bachelor's degree, namely being an actuary. I calcualte that it costs my daughter and son-in-law a combined $150,000+/year to teach math, rather than to be employed as actuaries.
In California, however, the courts have ruled that it is illegal to base a teacher's pay on the subject matter taught, even though the opportunity cost differs radically for different subjects. My other daughter has an advanced degree in music composition, but her opportunity cost of teaching is zero. Why should she be paid more than my other daughter, who has only a bachelor's degree, but in a field with a very high opportunity cost?
I realize many people don't understand, appreciate, or even believe in opportunity costs, but they are, in fact, the only real costs in life. Consequently, a teacher with a master's degree in education and an undergraduate minor in mathematics is often paid more than one with a bachelor's degree in math but "only" an education credential. Our California teacher compensation system says, in effect, it's more important to know how to be an educator than it is to know your subject matter.
Be careful bashing Common Core, though. My favorite math prof at Berkeley, Hung-Tsi Wu, co-wrote an Op-Ed piece for the Wall Street Journal endorsing Common Core standards for math. Dr. Wu didn't exactly choose the most friendly forum, but his arguments had a great deal of force. While I have issues trying to teach "relevance," I realize that when I teach a class, I normally incorporate -- either as problems or examples -- so many of my "war stories" that I show and teach the relevance as a matter of course.
All of this is a very long-winded way of saying that I think the article makes some good points, particularly in warning about relying on the "new, best, way to teach math" to the exclusion of every other option. Teaching remains an art, and art generally remains incompatible with "best practices."
John
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Spider Savage
Mountain climber
The shaggy fringe of Los Angeles
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Jul 24, 2014 - 02:29pm PT
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Okay, here is my math epiphany and rant:
All math was created by the human mind.
You have a human mind.
You are capable of creating all math.
If anyone has a problem with math you find them chanting this: "I'm bad at math." It's the biggest lie in the world.
Repeating a negative suggestion such as this over and over is a form of self-hypnosis and it will be true until you just get off it.
If you go back and revisit your education in math you will find you started to be bad at math at the point when the math teacher used a word you did not understand, like "arithmetic" or "algebra."
Math teachers fail because they fail to clearly define the terms of mathematics.
Also, there is is a fundamental missing from math instruction:
There is a form of math more fundamental than simple addition and subtraction. It is "counting."
The skill of counting goes back to the street markets of ancient Egypt or even counting the number of animals in heard or members of a tribe that need to be fed. Counting should be well drilled in young children and practiced regularly throughout education until a person can look at a pile of apples and in less than a second or two, state precisely how many apples are present.
Counting is done on Sesame Street and many kindergarten classes but is not emphasized enough. High standards need to be set and enforced.
Counting being done well, the rest of math, with terms understood, follows forward very quickly.
Our education system should be producing people who don't just know formulas, but are aware enough to invent formulas as needed to solve problems in life.
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TGT
Social climber
So Cal
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Jul 24, 2014 - 02:30pm PT
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I went back to school late in life and got my BS in my 40's I needed lower division units and since I was working for a school district at the time could take the classes to clear a Voc Ed credential for next to nothing so both the wife and I took the classes.
One of the requirements was to use ERIC as a research tool.
I was frankly astounded at the lack of rigor generally accepted in Masters and PHD work in Education departments. If I'd turned in work like that in any of my undergraduate Business Administration classes, I'd have flunked.
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klk
Trad climber
cali
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Jul 24, 2014 - 02:32pm PT
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one of the most ridiculous things about the constant chant that we need to teach kids only what they can use on the job, is that the people who say that have created a curriculum that is truly useless. look at what we have the kids actually do --
if an alien visited an american classroom to observe the results of that philosophy, he'd conclude that most americans get paid to fill in little circles with number 2 pencils all day long.
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kev
climber
A pile of dirt.
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Jul 24, 2014 - 02:33pm PT
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So to elaborate on my experience with topologists....
So I had taught Trig, Freshman Alg, 1st and 2nd semester enginnering calculus
and so I got "picked" for Dr x's pet project. Dr X (a topologist) had become so frustrated with the quality of the undergraduate students as well as the math ed department he felt he needed to do something. So he studied the problem. He went to the TIMMS studys (world wide math/science studies) and learned that the Singaporeans placed very very high year after year. Dr X then went out and got the ciriculioum they used. He then (much to the chagrin of the math ed dept) wrestled control over the course entitled "Mathematic for Elementary Education Majors". Basically the elementary ed required math ed calss - typically sophmore and juniors. His goal was to teach the future teachers how to think and understand the ciriculium of the Singaporeans - a noble idea. Sadly I got stuck teaching this class for a few semesters. The reason I say sadly goes as follows: Although about 1/4 of the class put forth a reasonable effort and perhaps 1/2 of that 1/4 might turn out to be good teachers, the other 3/4 had the attitude that "Well I don't need to know this I just want to teach kindergarden or 1st grade - I just need a D to pass this class." Unfortunatlely that's not how getting your first job out of college works and they all (the ones who graduated) are certified for K-6.
I don't think it's a leap to see how this creates very very unperpaired bad teachers.
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JEleazarian
Trad climber
Fresno CA
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Jul 24, 2014 - 02:43pm PT
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Good points, Kev. I have known a great many elementary school teachers that are functionally innumerate, and see no problem with that state of affairs.
To be more OT on something explicitly OT, I think that topology was my favorite branch of math, but Berkeley only taght it at the graduate level. We did have a "Measure and Integration" class, that could in theory be taken by sophomores, that was full of graduating seniors and grad students. The real analysis in that class got me hooked on real topology. I think it helped that John Kelley, who wrote the intro graduate topology text, taught that class as well. I think my enthusiasm rubbed off on my nephew, who got his Ph.D. in algebraic topolgy. Good stuff!
John
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blahblah
Gym climber
Boulder
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Jul 24, 2014 - 03:16pm PT
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that's a bit colorful, but yes, the general rule is that professional schools generally--ed, med, law, and business--produce scholarship that on average is less rigorous than that in many of the disciplines. there are stacks of exceptions, obviously, but yes, that is the consensus.
Hmm, that's an interesting way to look at it; legal "scholarship" is fair game for criticism I'm sure, but I've never heard anyone really compare it to whatever they hell do in education curriculum (or medicine or business schools for that matter, but education just stands out as an apples-to-oranges comparison). Rightly or wrongly, I can assure that you high-brow law professors would be pretty surprised to hear themselves being lumped in with D.Ed types.
About teacher pay: I'm sure teachers would like more money, wouldn't we all? But is there a shortage of teachers, at current salaries? I haven't heard that. On the contrary, I've heard that newly minted teachers have a hard time finding jobs. That suggests that teacher pay (which after all, is set by the government, heavily influenced by teachers unions in support of higher pay) is higher than it "should" be in something like a free market, not lower.
And I question the job market for all these math majors--if you want to pretend that everyone with a BS in math could get a high paying job as an actuary, fine, but how many actuaries do you know?
Computer programmers, sure, but that's not really math, especially these days.
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Ed Hartouni
Trad climber
Livermore, CA
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Jul 24, 2014 - 03:24pm PT
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Rising Above the Gathering Storm:
Energizing and Employing America for a Brighter Economic Future (2007)
http://www.nap.edu/catalog.php?record_id=11463
"Today there is such a shortage of highly qualified K–12 teachers that many of the nation’s 15,000 school districts4 have hired uncertified or underqualified teachers. Moreover, middle and high school mathematics and science teachers are more likely than not to teach outside their own fields of study (Table 5-1). A US high school student has a 70% likelihood of being taught English by a teacher with a degree in English but about a 40% chance of studying chemistry with a teacher who was a chemistry major.
These problems are compounded by chronic shortages in the teaching workforce. About two-thirds of the nation’s K–12 teachers are expected to retire or leave the profession over the coming decade, so the nation’s schools will need to fill between 1.7 million and 2.7 million positions5 during that period, about 200,000 of them in secondary science and mathematics classrooms.6
We need to recruit, educate, and retain excellent K–12 teachers who fundamentally understand biology, chemistry, physics, engineering, and mathematics. The critical lack of technically trained people in the United States can be traced directly to poor K–12 mathematics and science instruction. Few factors are more important than this if the United States is to compete successfully in the 21st century."
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TGT
Social climber
So Cal
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Jul 24, 2014 - 03:47pm PT
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The problem is that the "educators" at the university level have never had a real world job or any experience teaching at a primary or secondary level.
The worst thing that happened was the nationalization of education and the expansion of the Federal dept of Ed.
Administrative staffs and expense in local school districts exploded during the Clinton administration and never has slowed down since. Focus became getting grants and checking all the right boxes to keep the federal dollars rolling in.
The most desired job in many districts has come to be that of grant /program administrator. Lots of power, no accountability, and with a six figure salary.
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kev
climber
A pile of dirt.
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Jul 24, 2014 - 04:17pm PT
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A US high school student has a 70% likelihood of being taught English by a teacher with a degree in English but about a 40% chance of studying chemistry with a teacher who was a chemistry major.
Ouch
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