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beandelphikiOver in a teaching community last night (yes, I lurk and read education-related communities, shush), a tutor and education student(?), who seems to be very cool, posted her disagreement with Michigan requiring all of its students to take Algebra II.
Not being a teacher, or familiar with the education system in Michigan, I'm not qualified to say anything about the requirements in Michigan specifically, and I wasn't too interested in saying anything at all until she and another member of the comm (in Michigan) got into it.
Michigan teach (responding to someone else saying that they wished the state would bring back Consumer Math, which would teach students to budget, balance a checkbook, avoid being scammed by a mortgage company, etc.):
[...] So, my question is, if students take basic consumer math, how will they necessarily get those higher level problem solving skills that they won't get unless they have more difficult problems thrown at them as they do in algebra and algebra II?
Tutor/ed. student OP:
I think you're kidding yourself if you believe many students pick up "higher-level problem solving skills" from high school math classes. Most of them temporarily memorize rote procedures so they can succeed on exams and then have absolutely no underlying comprehension of mathematics. [...]
Michigan teach:
*flips out* OMG, I'm so mad! How can you not think that high school math teaches HIGHER-LEVEL PROBLEM-SOLVIN' SKILLZ! That's so horrible!
And she apologized, and they had this nice little thread where they made up and managed to agree on something or other, and blah. Whatever, I was still boggling that there's a high school math teacher out there so utterly delusional that ze thinks the sorry excuse for a math curriculum most people in North America go through prepares people in any way to be able to critically attack higher-level math.
Me (being polite):
Okay, my response here will probably just make you angry again. But I have to agree with the OP - I sincerely doubt most high schools students grasp much of the concepts learned in high school math unless they have significant innate math talent.
I explained my position (Canadian, notateacher, etc.), explained that I was an above-average math student, and proceeded to describe my experience in the high school math classroom. I said that I never really got the concepts behind what we learned (with the exception of areas in which I was interested), and said that I got through high school math mostly by rote (as the OP said). I said that I didn't think high school math prepared anyone for what I'd understand to be "higher-level" problem-solving.
I said that I didn't believe teacher instruction went much beyond what is required of standardized testing (and I don't). I said I was surprised anyone would think that it does. I concluded by saying:
It's not the teachers' fault, but I don't believe we have a system that is set up to do any better.
Probably, I'll avoid getting scammed by a mortgage company by asking my family how to avoid getting scammed, and enlisting their help.
I mean, what IS higher-level problem solving, anyway? Surely "higher-level" indicates something above the average, something that is more than what is expected of everyone! Surely "higher-level" indicates the ability to actually understand the formulas being used, to apply them critically, rather than by rote. Right?
...Right?
Apparently not.
Ze replied:
I don't think you really understood what I was referring to when I referred to the concepts learned. I'm not talking about the quadratic formula, or how to graph a circle. I'm talking about experiences such as shopping for a mortgage, how do you know which is a better offer (not a better company that won't scam you).
Ze went on to describe various situation in which math matters in Real Life. Budgeting, party planning, and so forth. Er?
Okay, my issue here is: HOW IS THAT HIGHER-LEVEL PROBLEM-SOLVING? Believe me, my dyscalculic mother can do those things, and she BARELY passed high school math. (Not really her fault that no one knew much about math learning disabilities at the time.) She has no faith in her math ability whatsoever, after having it take so many years of beating, but sheesh, she can budget!
Ze went on about how algebra courses teach the skills needed to do these things, that it is skills learned "behind the math." Okaaay, but...if that's It, if that's your big, ambitious goal - to teach people to budget - then why does ze have an issue with Consumer Math?
(Having poked around hir journal, I can say that the answer to this is that ze apparently doesn't think Consumer Math - which teaches these skills directly - does as good a job as a course which teaches those skills INDIRECTLY! Okay! If people actually GOT those things out of algebra courses, that would be true, I guess.)
Ze finished off by saying:
Also, on a personal note, I do NOT want members of the business world, of the factory world, of the engineering world, and so forth, to not possess these skills. all the poo-pooing of these standards is just enabling more people skate by without taking responsibility for what they need to know, evidenced by your response to the mortgage question.
Whoa! Was that making it personal, now? I think so. Evidently, earning myself a solid run of Honor's marks in mathematics makes me someone who hasn't "taken responsibility for what [I] need to know," if I'm still unclear on how to handle adult finance.
It's times like these, you wish you could reach through the screen and slap some goddamn fools smart.
I said that I did not consider budgeting to be "higher-level" math, and that taking responsibility for learning how to avoid a mortgage scam is precisely why I would ask my family to help me. (These are educators I ACTUALLY TRUST. These are people with personal stake in seeing me succeed, not people who consider me a number in a system.) I said:
I find it really rude of you to tell me that it's my responsibility to obtain specific knowledge from a high school math course that doesn't TEACH it. Frankly, it's arrogant to think that high school math is teaching such fantastic problem-solving skills that any student walking out the door will be able to navigate the world of adult finance with no outside help.
And that was pretty much the end of our conversation. Ze told me I was clearly a troll, since I apparently don't "think education is useful," and that my last response was "stupid." Okay!
Meanwhile, the OP commented to me saying that it's true that high school math does not teach essential problem-solving skills. She used an example from a book she has of students who were given a graphing problem that can be easily solved using the Pythagorean theorem; a problem that two-thirds of students taking the particular math exam in the book missed. Perfect example of how rote learning does not translate to problems-solving skills. (And an example that matches with my personal history, too, as I said over there, because students taking the graduating Diploma Exams in my province have missed problems like that too, despite being taught all the component skills to solve it.)
The Michigan teacher defended this by saying:
And how many of those students had had a graphing class? How many of them took, even, a class in which the pythagorean theorem was even taught?
Now, I am clearly not well-versed in what is taught in American math classroom, but can this be for real? Do student in the U.S. graduate without ever having graphed two points? More: do students in the U.S. actually graduate 9th/10th grade without being taught the Pythagorean theorem? HOW CAN THIS BE. MY BRANE. MY BRANE.
But yeah, look at that - a high school math teacher, defending a failure of education with the idea that the concepts may not have been taught. Weak.
Over in the Michigan teacher's journal after all this, there's more flipping out. Ze seems to be under the impression that both I and the OP were arguing the uselessness of teaching math. (Er?) And rants about people not wanting to do any work to graduate.
Sometimes, it simply amazes me what people take away from any given discussion. I mean, ze says:
One of them said that
People who go through high school math can generally budget to some degree
to which I completely disagree. If you haven't learned how to look at a situation critically, you won't know where to begin.
Which is kinda what I was saying - the last part, anyway. (If my mom can budget, I think most people can, but there's muddling through, and there's doing it well.) Unless, of course, you're either taught that skill directly, or you're taught the critical thinking skills to tackle this. And in many high school math courses, you aren't given either.
But most hilariously, ze finishes this thought with (bolds mine):
No, math is definitely not the only one in which you learn these skills, but math and science (and technology, too!) are problem solving/critical thinking throughout, overloaded more than in other classes. Yes, you think critically in English. Depending on the history class, also there, but mine were mainly "memorize these facts and talk about the stuff that happened".
"Whoosh!" as my dad would say. Don't you LOVE when the person you've argued with makes your own points FOR you?
Yeah, critical thinking skills SHOULD be used in a history class. They often aren't, though, just as they often aren't in math classes. What this person apparently fails to realize is that most people experience math the way ze experienced history - "we memorized stuff."
It would be funnier if I wasn't over here beating my head on the desk.
I don't know how anyone can seriously look at America (or Canada, for that matter) and think to themselves, "Boy, there's some critical thinking skills in action!"
Gah.
Not being a teacher, or familiar with the education system in Michigan, I'm not qualified to say anything about the requirements in Michigan specifically, and I wasn't too interested in saying anything at all until she and another member of the comm (in Michigan) got into it.
Michigan teach (responding to someone else saying that they wished the state would bring back Consumer Math, which would teach students to budget, balance a checkbook, avoid being scammed by a mortgage company, etc.):
[...] So, my question is, if students take basic consumer math, how will they necessarily get those higher level problem solving skills that they won't get unless they have more difficult problems thrown at them as they do in algebra and algebra II?
Tutor/ed. student OP:
I think you're kidding yourself if you believe many students pick up "higher-level problem solving skills" from high school math classes. Most of them temporarily memorize rote procedures so they can succeed on exams and then have absolutely no underlying comprehension of mathematics. [...]
Michigan teach:
*flips out* OMG, I'm so mad! How can you not think that high school math teaches HIGHER-LEVEL PROBLEM-SOLVIN' SKILLZ! That's so horrible!
And she apologized, and they had this nice little thread where they made up and managed to agree on something or other, and blah. Whatever, I was still boggling that there's a high school math teacher out there so utterly delusional that ze thinks the sorry excuse for a math curriculum most people in North America go through prepares people in any way to be able to critically attack higher-level math.
Me (being polite):
Okay, my response here will probably just make you angry again. But I have to agree with the OP - I sincerely doubt most high schools students grasp much of the concepts learned in high school math unless they have significant innate math talent.
I explained my position (Canadian, notateacher, etc.), explained that I was an above-average math student, and proceeded to describe my experience in the high school math classroom. I said that I never really got the concepts behind what we learned (with the exception of areas in which I was interested), and said that I got through high school math mostly by rote (as the OP said). I said that I didn't think high school math prepared anyone for what I'd understand to be "higher-level" problem-solving.
I said that I didn't believe teacher instruction went much beyond what is required of standardized testing (and I don't). I said I was surprised anyone would think that it does. I concluded by saying:
It's not the teachers' fault, but I don't believe we have a system that is set up to do any better.
Probably, I'll avoid getting scammed by a mortgage company by asking my family how to avoid getting scammed, and enlisting their help.
I mean, what IS higher-level problem solving, anyway? Surely "higher-level" indicates something above the average, something that is more than what is expected of everyone! Surely "higher-level" indicates the ability to actually understand the formulas being used, to apply them critically, rather than by rote. Right?
...Right?
Apparently not.
Ze replied:
I don't think you really understood what I was referring to when I referred to the concepts learned. I'm not talking about the quadratic formula, or how to graph a circle. I'm talking about experiences such as shopping for a mortgage, how do you know which is a better offer (not a better company that won't scam you).
Ze went on to describe various situation in which math matters in Real Life. Budgeting, party planning, and so forth. Er?
Okay, my issue here is: HOW IS THAT HIGHER-LEVEL PROBLEM-SOLVING? Believe me, my dyscalculic mother can do those things, and she BARELY passed high school math. (Not really her fault that no one knew much about math learning disabilities at the time.) She has no faith in her math ability whatsoever, after having it take so many years of beating, but sheesh, she can budget!
Ze went on about how algebra courses teach the skills needed to do these things, that it is skills learned "behind the math." Okaaay, but...if that's It, if that's your big, ambitious goal - to teach people to budget - then why does ze have an issue with Consumer Math?
(Having poked around hir journal, I can say that the answer to this is that ze apparently doesn't think Consumer Math - which teaches these skills directly - does as good a job as a course which teaches those skills INDIRECTLY! Okay! If people actually GOT those things out of algebra courses, that would be true, I guess.)
Ze finished off by saying:
Also, on a personal note, I do NOT want members of the business world, of the factory world, of the engineering world, and so forth, to not possess these skills. all the poo-pooing of these standards is just enabling more people skate by without taking responsibility for what they need to know, evidenced by your response to the mortgage question.
Whoa! Was that making it personal, now? I think so. Evidently, earning myself a solid run of Honor's marks in mathematics makes me someone who hasn't "taken responsibility for what [I] need to know," if I'm still unclear on how to handle adult finance.
It's times like these, you wish you could reach through the screen and slap some goddamn fools smart.
I said that I did not consider budgeting to be "higher-level" math, and that taking responsibility for learning how to avoid a mortgage scam is precisely why I would ask my family to help me. (These are educators I ACTUALLY TRUST. These are people with personal stake in seeing me succeed, not people who consider me a number in a system.) I said:
I find it really rude of you to tell me that it's my responsibility to obtain specific knowledge from a high school math course that doesn't TEACH it. Frankly, it's arrogant to think that high school math is teaching such fantastic problem-solving skills that any student walking out the door will be able to navigate the world of adult finance with no outside help.
And that was pretty much the end of our conversation. Ze told me I was clearly a troll, since I apparently don't "think education is useful," and that my last response was "stupid." Okay!
Meanwhile, the OP commented to me saying that it's true that high school math does not teach essential problem-solving skills. She used an example from a book she has of students who were given a graphing problem that can be easily solved using the Pythagorean theorem; a problem that two-thirds of students taking the particular math exam in the book missed. Perfect example of how rote learning does not translate to problems-solving skills. (And an example that matches with my personal history, too, as I said over there, because students taking the graduating Diploma Exams in my province have missed problems like that too, despite being taught all the component skills to solve it.)
The Michigan teacher defended this by saying:
And how many of those students had had a graphing class? How many of them took, even, a class in which the pythagorean theorem was even taught?
Now, I am clearly not well-versed in what is taught in American math classroom, but can this be for real? Do student in the U.S. graduate without ever having graphed two points? More: do students in the U.S. actually graduate 9th/10th grade without being taught the Pythagorean theorem? HOW CAN THIS BE. MY BRANE. MY BRANE.
But yeah, look at that - a high school math teacher, defending a failure of education with the idea that the concepts may not have been taught. Weak.
Over in the Michigan teacher's journal after all this, there's more flipping out. Ze seems to be under the impression that both I and the OP were arguing the uselessness of teaching math. (Er?) And rants about people not wanting to do any work to graduate.
Sometimes, it simply amazes me what people take away from any given discussion. I mean, ze says:
One of them said that
People who go through high school math can generally budget to some degree
to which I completely disagree. If you haven't learned how to look at a situation critically, you won't know where to begin.
Which is kinda what I was saying - the last part, anyway. (If my mom can budget, I think most people can, but there's muddling through, and there's doing it well.) Unless, of course, you're either taught that skill directly, or you're taught the critical thinking skills to tackle this. And in many high school math courses, you aren't given either.
But most hilariously, ze finishes this thought with (bolds mine):
No, math is definitely not the only one in which you learn these skills, but math and science (and technology, too!) are problem solving/critical thinking throughout, overloaded more than in other classes. Yes, you think critically in English. Depending on the history class, also there, but mine were mainly "memorize these facts and talk about the stuff that happened".
"Whoosh!" as my dad would say. Don't you LOVE when the person you've argued with makes your own points FOR you?
Yeah, critical thinking skills SHOULD be used in a history class. They often aren't, though, just as they often aren't in math classes. What this person apparently fails to realize is that most people experience math the way ze experienced history - "we memorized stuff."
It would be funnier if I wasn't over here beating my head on the desk.
I don't know how anyone can seriously look at America (or Canada, for that matter) and think to themselves, "Boy, there's some critical thinking skills in action!"
Gah.
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(no subject)
Date: 2006-04-06 02:22 am (UTC)We have college students who struggle with literacy, children who are taught to use the calculator as young as seven years old, and lementary teachers who no longer even insist upon the multiplication tables being memorized. So, the answer to your question is a definite yes.
More: do students in the U.S. actually graduate 9th/10th grade without being taught the Pythagorean theorem?
All the time.
(Found you via mutual friends, we've got three in common!)
(no subject)
Date: 2006-04-06 02:46 am (UTC)However, I myself don't know my times tables, and my computation skills are very weak. Without a calculator, there's no way I could have gotten through the math that I did (in later grades) - I need to subtract two-digit numbers on paper without a calculator.
My teachers did attempt to get me to memorize those things. I'm not sure it was time well-spent when I never did. I DID learn computational skills, but I cannot compute swiftly AND accurately. (One or the other.) I just can't, and never could. I don't remember things like what seven plus eight is, or what six times nine is, which would speed me up. My teachers even enlisted my parents in drilling me in addition/subtraction/multiplication/division facts in the summertimes. It just didn't help. My math grades throughout elementary were barely passing.
My grades shot up from "barely passing" to "honors," the moment I got into a math course that was more conceptual, and could use a calculator instead of slogging through all the basic computation I did so slowly. I'd spent a good six years before that being told, essentially, that I was a total math dunce.
It's not that I'd advocate replacing learning skills with calculators (wow, scary thought - I don't think 7-year-olds should be given calculators, either), or that memorizing the tables can't seriously increase speed and accuracy for those who can learn it. At a certain point though, it's just not worth making that what a complete education "is." Everybody should be able to add, subtract, multiply and divide, but I don't believe everyone HAS to be able to remember tables of these things.
And hello! We have good friends in common. :)
(no subject)
Date: 2006-04-06 12:34 pm (UTC)Oh, that's completely understandable, some people do struggle with math in that way, and it isn't your fault in any way.
My teachers did attempt to get me to memorize those things. I'm not sure it was time well-spent when I never did
I think it's a reasonable first step, for teachers to attempt. But once it's clear that it isn't working, I suspect the teachers should have stopped. Sounds like you were put the wringer, and that's not good for the student or the teacher. I agree that it wouldn't be time well-spent.
My teachers even enlisted my parents in drilling me in addition/subtraction/multiplication/division facts in the summertimes. It just didn't help. My math grades throughout elementary were barely passing.
Ugh. Sounds like a really bad experience.
My grades shot up from "barely passing" to "honors," the moment I got into a math course that was more conceptual, and could use a calculator instead of slogging through all the basic computation I did so slowly.
Wow. That's awesome.
It's not that I'd advocate replacing learning skills with calculators (wow, scary thought - I don't think 7-year-olds should be given calculators, either)
Yeah, it's pretty common now.
Or that memorizing the tables can't seriously increase speed and accuracy for those who can learn it.
We literally have teachers who take pride in the fact that their kids count on the fingers, the teachers really don't even try to teach the tables anymore. It's called "constructive math". It doesn't teach math in a way that challenged students can learn subjects either. It's more of a "Write an essay about how feel about the number 12". (Yes that's a real essay, for math class, not for creative writing).
And hello! We have good friends in common. :)
Don't we? *joins you in admiring the friends*
But why aren't you and I on each other's friends list? :) Maybe we should be!
(no subject)
Date: 2006-04-08 11:43 pm (UTC)I think it's a reasonable first step, for teachers to attempt. But once it's clear that it isn't working, I suspect the teachers should have stopped.
Pretty much my thoughts. The tried-and-true methods are generally best to start with, and are to be adjusted as necessary. It's funny, because there's been so many attempts to "update" education, only to turn around and find that the older methods really do work.
So. *shrug* I think learning should be as fun as possible, but I'm kind of a traditionalist in that I think phonics and drill aren't necessarily evil. It's just ironic that those methods (with maybe the exception of phonics) mostly failed with me. I'm weird, though!
We literally have teachers who take pride in the fact that their kids count on the fingers, the teachers really don't even try to teach the tables anymore. It's called "constructive math". [etc.]
My lord. I'm going to have to go look that up, because that just sounds like pure crazy.
...Although it reminds me of the time I walked into my younger sister's elementary class during a "reading period." There were first-grade kids "reading" a book on CD-ROM. Except it actually consisted of playing with the animated parts of the illustrations, and having the story electronically read TO them. I thought, Damn, this is supposed to be an IMPROVEMENT on Dick and Jane?
Yeah.
But why aren't you and I on each other's friends list? :) Maybe we should be!
Sounds like a good idea to me! I gotta warn you though, I have a friends page that needs trimming, and until school lets out I may not be the best commenter. But sure, I'm always happy to add people so level-headed as you sound.
Would it sound like sucking up at this point to say you have pretty icons? I just peeked. :P I like how the flowers are all so different, but each beautiful.
(no subject)
Date: 2006-04-09 02:02 am (UTC)LOL, so true! They keep reforming education, and yet addition is done pretty much the same way that addition was always done. Vowels/consonants haven't changed any, and yet they keep looking for new ways to teaching reading.
I'm kind of a traditionalist in that I think phonics and drill aren't necessarily evil.
I agree completely.
My lord. I'm going to have to go look that up, because that just sounds like pure crazy.
Constructivist math is really crazy. I have no idea why it's so popular. You wouldn't believe it. Because in a couple of places they've used it, the teachers are noticing the math scores going down (not a surprise to me), and yet, they still advocate for it.
My head explodes with thier faulty logic.
...Although it reminds me of the time I walked into my younger sister's elementary class during a "reading period." There were first-grade kids "reading" a book on CD-ROM. Except it actually consisted of playing with the animated parts of the illustrations, and having the story electronically read TO them. I thought, Damn, this is supposed to be an IMPROVEMENT on Dick and Jane?
Oh yes, it's call Language Arts instead of English. "Sustained silent individual reading" is not popular anymore. (My locale calls that SSIR. You and I probably called it "reading". But reading is now listening to audio. I don't know why).
Sounds like a good idea to me! I gotta warn you though, I have a friends page that needs trimming, and until school lets out I may not be the best commenter. But sure, I'm always happy to add people so level-headed as you sound.
YAY, ::rushes to add you to my friends list:: Don't worry about commenting. I know school's important. :)
Would it sound like sucking up at this point to say you have pretty icons? I just peeked. :P I like how the flowers are all so different, but each beautiful.
Oooo, thank you! I love flower icons, and the icons are all credited, so feel free to use at your leisure!
(no subject)
Date: 2006-04-09 01:46 pm (UTC)Ha! That's a great way to put it. Vowels/consonants haven't changed... They're not going to suddenly get more exciting, either. But really, being able to read stories to yourself was enough of a reward for most students (at least non-LD ones; for the LD kids, I'm happy we're progressing on methods of instruction) in the past, why is it not enough now?
Kind of boggles my mind, honestly. I said above that I would like learning to be fun, but I always think the "fun" should stem mostly from natural curiosity and such, and not from artificial incentives. (Like animated illustrations that talk to you if you finish a page.)
Constructivist math is really crazy. I have no idea why it's so popular. You wouldn't believe it. Because in a couple of places they've used it, the teachers are noticing the math scores going down (not a surprise to me), and yet, they still advocate for it.
My head explodes with thier faulty logic.
Oh my lord, it's the Whole Language debacle, but in math! I suppose we'd prefer a populace that can't read, write, or add...easier to control.
I'm mentally comparing the descriptions on some sites to my own experience though, and I'm pretty sure I got some contructivist math at one point, as it was starting to be implemented through schools.
I don't think it's entirely bad - I get the sense from the descriptions that the idea is to get children to figure out math from first principles. Not entirely bad, in theory. The problem I see is that I seriously doubt kids are developmentally ready to do all math from scratch. So either they struggle with stuff that is over their heads (and give up because it's too difficult), or have to have it so dumbed-down to manage it that they learn nothing.
I can see it working best if it's a small, challenging part of the curriculum, but not the whole thing. Which is mostly what it was like in my math classes in fourth grade. It was great, for a challenge, to devise our own methods to solve problems. We thought we could do anything for a while there. But at a certain point, there WAS too much of it. It got too strictly individual (I think learning to problem-solve from the ground up is best as group work that emerges organically) and there was less and less help available. It eventually was frustrating and disheartening.
I DID end up essentially writing my own algebraic formula for one problem, having never seen algebra in my life. It took me about 3 hours of hard noodling in my bedroom, and not much else, but I did it. A woman in
So, I did accomplish solving a tough problem (for a 4th grader) on my own. But that one took me HOURS, and it was the only one I solved in a few weeks of that type of math in the classroom. Not worth it, IMO. Thankfully, our teachers scrapped that soon after.
I see that sort of thing as a potentially valuable curriculum spice, done properly. But not much more.
Oh yes, it's call Language Arts instead of English.
Up here, English is called Language Arts up until high school. But it's really English, honestly. I don't know why they call it Language Arts when it's English. Essays, novel studies, Shakespeare, etc. Seems like we have funny names for things sometimes.
You and I probably called it "reading".
...Yeah. O.o I suppose I can see making a distinction between silent reading and reading out loud at a young age to specify you want them to read internally. But the idea that reading isn't popular anymore? What the heck. I can see it, too (I witnessed my sister's classroom, after all), but I don't get why it would be happening.
YAY, ::rushes to add you to my friends list:: Don't worry about commenting. I know school's important. :)
You're a sweetheart! Welcome aboard.
(no subject)
Date: 2006-04-06 02:25 am (UTC)That's all I have to say. Well, that and I'm glad my kids won't be learning critical thinking skills from that teacher.
(no subject)
Date: 2006-04-06 02:47 am (UTC)