Forced March: PTA Meeting Reveals Math Trail of Tears << The "More" Child
Is An Accelerated Math Course Appropriate For Your Gifted and Talented Student?
Wayside Parents Raise Concerns about Accelerated Math
Accelerated Math Classes Leave Some Students Playing Catch-Up
DC Urban Moms Forum: MCPS is Ending Math Acceleration?
Accelerated Math Challenge, For a Kid and Her Mom
Jay Mathews ... Live! << The "More" Child
More on Accelerated Math from Mathews << The "More" Child
"Montgomery's Math Miscalculation" -- Read It. << The "More" Child
Montgomery Back to Basics in Math Classes
Sunday, November 7, 2010
Decelerated Math
Faithful readers of StopHomework will remember that accelerated math was a big factor in our decision to take our older daughter out of public school. Now there's word that Montgomery County, Maryland has come to the conclusion that they've been pushing accelerated math too hard. Good.
I hope this is the beginning of much-needed change in our affluent school districts, including the one I live in. In my experience these districts are all about achievement at the expense of learning, and at the expense of our children's health. The result is kids with killer college applications who wind up needing remedial classes in their elite college, or have a nervous breakdown in their first semester.
It is astonishing how much schoolwork a child can do, and how many honors she can rack up, without actually learning anything.
I hope this is the beginning of much-needed change in our affluent school districts, including the one I live in. In my experience these districts are all about achievement at the expense of learning, and at the expense of our children's health. The result is kids with killer college applications who wind up needing remedial classes in their elite college, or have a nervous breakdown in their first semester.
It is astonishing how much schoolwork a child can do, and how many honors she can rack up, without actually learning anything.
Friday, November 5, 2010
Eye Contact?
Some years ago there was a Teletubbies episode that featured a young boy having a drumming lesson. He and his teacher each had a set of bongos; his teacher would drum out a riff, and then the boy would respond on his own drums, often repeating what the teacher did, and sometimes adding a little riff of his own.
When my husband saw the video he remarked that at first he thought the boy wasn't really paying attention, because he didn't look at the teacher while he was drumming. But it was clear to me that the boy was listening intently to everything the teacher did, while looking at the floor.
I'm the same way myself. I find it difficult to look at someone and simultaneously listen closely to what they're saying, especially if it's complicated. I need to look at something neutral, or even close my eyes.
So how would someone like me, or the boy in the video, function in a classroom that insists that the students look at the teacher every moment (e.g., KIPP)?
When my husband saw the video he remarked that at first he thought the boy wasn't really paying attention, because he didn't look at the teacher while he was drumming. But it was clear to me that the boy was listening intently to everything the teacher did, while looking at the floor.
I'm the same way myself. I find it difficult to look at someone and simultaneously listen closely to what they're saying, especially if it's complicated. I need to look at something neutral, or even close my eyes.
So how would someone like me, or the boy in the video, function in a classroom that insists that the students look at the teacher every moment (e.g., KIPP)?
Wednesday, November 3, 2010
EARMARKS?
I interrupt my regularly scheduled blog with a few political remarks.
I'm listening to President Obama's press conference after the Republicans took back the House in yesterday's midterm election. He claims that Americans are frustrated because his administration was in such a hurry to get things done that they didn't clean up how things are done in Washington. He promised to take another look at earmarks (the process by which Congressmen add little sweeteners to legislation.)
Wrong, wrong, wrong! People like me are frustrated because Obama didn't do enough in that magical 2-year window when he had a governing majority. Does anyone outside Washington spend their time worrying about earmarks? I doubt it.
He promises to work harder for consensus, a lost cause if there ever was one. The Republicans have no interest in reaching consensus, and Obama just looks like a weakling for attempting it.
Neither Obama nor any of the press mentioned what I believe to be the central problem of our time: the concentration of our country's wealth in the hands of a very few Americans. No search for consensus or yapping about preparing our children for the future can ameliorate our regressive tax structure and government policies that funnel even more money into the accounts of the filthy rich.
And now, back to our blog ---
I'm listening to President Obama's press conference after the Republicans took back the House in yesterday's midterm election. He claims that Americans are frustrated because his administration was in such a hurry to get things done that they didn't clean up how things are done in Washington. He promised to take another look at earmarks (the process by which Congressmen add little sweeteners to legislation.)
Wrong, wrong, wrong! People like me are frustrated because Obama didn't do enough in that magical 2-year window when he had a governing majority. Does anyone outside Washington spend their time worrying about earmarks? I doubt it.
He promises to work harder for consensus, a lost cause if there ever was one. The Republicans have no interest in reaching consensus, and Obama just looks like a weakling for attempting it.
Neither Obama nor any of the press mentioned what I believe to be the central problem of our time: the concentration of our country's wealth in the hands of a very few Americans. No search for consensus or yapping about preparing our children for the future can ameliorate our regressive tax structure and government policies that funnel even more money into the accounts of the filthy rich.
And now, back to our blog ---
Tuesday, November 2, 2010
The Overt Curriculum
We've all heard of the "hidden curriculum", the stuff that schools genuinely care about teaching: conformity, unquestioning obedience, the surrender of family life to the demands of the institution . I believe it is no longer accurate to call this curriculum "hidden". We should call it the "overt curriculum", or, in some schools, the "only curriculum". We should let kids major in the important subjects like "Sleep Deprivation", "Busywork Completion", "Erasure of Personal Life", and "Random Factoid Upchuck".
I've noticed that teachers increasingly make no distinction between learning actual subjects and learning how to do school. Getting Mom's signature has the same importance as working actual math problems. Classroom rules are included on the science (!) test. You know you're in trouble when the teacher claims to teach "responsibility" and "time management".
What would school look like if the goal was to teach actual subjects in the most efficient, streamlined way possible? I'd like to find out.
I've noticed that teachers increasingly make no distinction between learning actual subjects and learning how to do school. Getting Mom's signature has the same importance as working actual math problems. Classroom rules are included on the science (!) test. You know you're in trouble when the teacher claims to teach "responsibility" and "time management".
What would school look like if the goal was to teach actual subjects in the most efficient, streamlined way possible? I'd like to find out.
Monday, November 1, 2010
conversation with an advisor
So I had a conversation this morning with DD's advisor, Mr. A. I explained that my big concern is that I don't want DD to get depressed again, and I don't want her to be overworked and stressed out.
Mr. A: Well, we meet every week as a team, and we do try to coordinate the work. For instance, we try to have each subject have their own test day, so you don't have to study for a lot of tests at once.
Me: she's supposed to study for tests?
(I have never seen DD study for a test.)
We talked a bit about the science assignment of writing an outline of a paper they've read, which as I tried to explain has put the emphasis on the writing of an outline rather than understanding the paper, and got the time-worn response:
Mr. A.: Well, sometimes in life we all have to do things that don't make sense.
Me: That's not what school should be about. School should be better than that.
On the whole, though, I'm encouraged by the conversation we had. For one thing, he said one of the assistant principals actually got out to see Race to Nowhere and was impressed.
Mostly, I hung up the phone thinking that they clearly want to keep DD at the school, and they want to work with me enough to make that happen. I think it's a surprise to them to hear from a parent of a high-achieving kid, whose number one priority is said kid's mental health. I hope they'll be hearing from many more of us in the future.
Mr. A: Well, we meet every week as a team, and we do try to coordinate the work. For instance, we try to have each subject have their own test day, so you don't have to study for a lot of tests at once.
Me: she's supposed to study for tests?
(I have never seen DD study for a test.)
We talked a bit about the science assignment of writing an outline of a paper they've read, which as I tried to explain has put the emphasis on the writing of an outline rather than understanding the paper, and got the time-worn response:
Mr. A.: Well, sometimes in life we all have to do things that don't make sense.
Me: That's not what school should be about. School should be better than that.
On the whole, though, I'm encouraged by the conversation we had. For one thing, he said one of the assistant principals actually got out to see Race to Nowhere and was impressed.
Mostly, I hung up the phone thinking that they clearly want to keep DD at the school, and they want to work with me enough to make that happen. I think it's a surprise to them to hear from a parent of a high-achieving kid, whose number one priority is said kid's mental health. I hope they'll be hearing from many more of us in the future.
Sunday, October 31, 2010
This Math Depresses Me
From Parenting is Political, by NorthTOMom:
The other day, my 11-year-old daughter left a note on the scratch paper she was using to do her math homework. It read (caps hers):
Before I go any further, let me state a few facts about myself. Yes, I dislike reform math or "fuzzy" math or constructivist math, or whatever you want to call it. But . . . I am not an educational conservative, a back to basics advocate, or a nostalgic drill-and-kill enthusiast. On the contrary, I am a firm believer in progressive, child-friendly public schooling for all. I feel I have to say this because the "math wars" have been so politicized, both in the US and here in Canada (where in true Canadian style, the "war" was more of a minor skirmish followed by complete capitulation), that anyone who opposes the current math curriculum is branded as educationally retrograde. I think in order for an intellectually honest and productive discussion of math education to occur, this politicization and presumptive name-calling has to stop.
So why do I object to constructivist math? One reason is that it is, by-design, non-incremental or "spiral": its textbooks jump around from topic to topic, never staying on a subject long enough to allow for deep understanding or competence. I also dislike reform math because it frowns upon direct instruction. Since constructivist math teachers believe children can "construct" or "discover" mathematical truths and come up with their own algorithms to solve problems, they offer students minimal guidance, and are not averse to putting the cart before the horse: e.g., assigning algebra-type problems before teaching the tools of algebra, or asking kids to divide or multiply by decimals or fractions without having first taught them how decimals and fractions work.
All of this—the bouncing around from topic to topic, the "challenging" problems, the lack of direct teaching—constructivists defend in the name of what they call "conceptual" learning, which they oppose to both abstract instruction and their favourite straw man, "drill-and-kill" work. But there are two problems with this normative use of the term "conceptual." First of all, "conceptual" and "abstract" constitute a false binary opposition: a concept can be abstract, and an abstraction is not necessarily unconceptual. Take the standard algorithm for long division. Because this method of performing division—like all mathematical algorithms—can be separated from concrete or specific division problems, it is deemed to be abstract. Proponents of constructivist math argue that presenting it upfront would be tantamount to teaching division in a manner that does not allow kids to understand the concept behind it or why and how it works. But a mathematician (and it's interesting to me that most of the authors of constructivist math textbooks are not mathematicians) might counter that the algorithm embodies the concept—otherwise it would not work. So, let's say a teacher were to demonstrate the standard algorithm for long division at the outset of a lesson; he or she could, conceivably, set aside class time for practice and mastery, and then—with student participation—pick apart the algorithm to find out how and why it works. Would this be less conceptual than making kids stumble through division problems on their own, hoping they will discover an efficient algorithm, which most of them will never do?
Secondly, even if the terms conceptual and abstract were in fact polar opposites, why would we favour one over the other? There are some kids who love working in groups or with concrete materials (methods favoured by constructivists) but there are others, like both my daughters, who simply enjoy playing with symbols on a page, and who find all the illustrations, and colourful doodads in their current textbook patronizing and distracting. Why do we assume that math instruction must be a one size-fits-all proposition?
But my real opposition to the privileging of the conceptual in constructivist math is that it is misleading and even hypocritical: in my experience, constructivist textbooks do not encourage conceptual understanding at all. Indeed, my main problem with reform math is that it does not promote mathematical understanding, full stop.
The note from my daughter with which I started this post, in which she expresses her ongoing frustration with math, was sparked by a revealing instance of the true non-conceptual nature her constructivist math text. The problems my daughters were working on for their homework that night involved perimeter and area. In certain questions, they had to compare perimeters given in different metric units. To do that, they had to convert, for instance, metres to centimetres or vice versa in order to figure out which of two given perimeters was bigger. My daughters had no problem with this, but then they were confronted with a problem in which they had to compare the areas of two rectangles—one measuring 8400 centimetres squared and the other measuring .84 metres squared—and, again, indicate which was bigger. Their first instinct was simply to multiply .84 by 100 in order to carry out the comparison. This was my first instinct as well, but something (a residual spark of mathematical reasoning?) told me that in the case of area, it didn't quite work this way. Confused, I flipped back a page or two to see if any explanation of this type of problem had been given. I found no explanation, but I did find, in a coloured bubble in the margin of the previous page, these instructions:
My point here is neither to ridicule my daughters' math textbook nor to blame the school for choosing it; it is, after all, one of a handful of textbooks approved and financially supported by the provincial government. My purpose, rather, is to demonstrate that this so-called constructivist, "conceptual" textbook is neither. It's just poorly-presented, pedagogically dubious, bad math. Which is why I concur with my daughter: THIS MATH DEPRESSES ME.
The other day, my 11-year-old daughter left a note on the scratch paper she was using to do her math homework. It read (caps hers):
I HATE THE MATH IN THIS UNIT! IT MAKES ME CRY, AND IT DEPRESSES ME. THIS MATH TORTORES [sic] ME. — JThis note depressed me. But quite frankly, it did not surprise me. The math program in our public school—a Canadianized version of the reform math so reviled in the US—continually frustrates and confuses my twin daughters, both of whom are A students in math. Both of them have declared, on many, many occasions during the past three or four years of struggling through this program, that they hate math. This really depresses me, because my husband and I have gone to great lengths to instill in our girls a love of math, a sense that it can be interesting and fun and challenging, and that, contrary to the message they may be receiving from the culture in general, it is something about which girls and boys should be equally enthusiastic.
Before I go any further, let me state a few facts about myself. Yes, I dislike reform math or "fuzzy" math or constructivist math, or whatever you want to call it. But . . . I am not an educational conservative, a back to basics advocate, or a nostalgic drill-and-kill enthusiast. On the contrary, I am a firm believer in progressive, child-friendly public schooling for all. I feel I have to say this because the "math wars" have been so politicized, both in the US and here in Canada (where in true Canadian style, the "war" was more of a minor skirmish followed by complete capitulation), that anyone who opposes the current math curriculum is branded as educationally retrograde. I think in order for an intellectually honest and productive discussion of math education to occur, this politicization and presumptive name-calling has to stop.
So why do I object to constructivist math? One reason is that it is, by-design, non-incremental or "spiral": its textbooks jump around from topic to topic, never staying on a subject long enough to allow for deep understanding or competence. I also dislike reform math because it frowns upon direct instruction. Since constructivist math teachers believe children can "construct" or "discover" mathematical truths and come up with their own algorithms to solve problems, they offer students minimal guidance, and are not averse to putting the cart before the horse: e.g., assigning algebra-type problems before teaching the tools of algebra, or asking kids to divide or multiply by decimals or fractions without having first taught them how decimals and fractions work.
All of this—the bouncing around from topic to topic, the "challenging" problems, the lack of direct teaching—constructivists defend in the name of what they call "conceptual" learning, which they oppose to both abstract instruction and their favourite straw man, "drill-and-kill" work. But there are two problems with this normative use of the term "conceptual." First of all, "conceptual" and "abstract" constitute a false binary opposition: a concept can be abstract, and an abstraction is not necessarily unconceptual. Take the standard algorithm for long division. Because this method of performing division—like all mathematical algorithms—can be separated from concrete or specific division problems, it is deemed to be abstract. Proponents of constructivist math argue that presenting it upfront would be tantamount to teaching division in a manner that does not allow kids to understand the concept behind it or why and how it works. But a mathematician (and it's interesting to me that most of the authors of constructivist math textbooks are not mathematicians) might counter that the algorithm embodies the concept—otherwise it would not work. So, let's say a teacher were to demonstrate the standard algorithm for long division at the outset of a lesson; he or she could, conceivably, set aside class time for practice and mastery, and then—with student participation—pick apart the algorithm to find out how and why it works. Would this be less conceptual than making kids stumble through division problems on their own, hoping they will discover an efficient algorithm, which most of them will never do?
Secondly, even if the terms conceptual and abstract were in fact polar opposites, why would we favour one over the other? There are some kids who love working in groups or with concrete materials (methods favoured by constructivists) but there are others, like both my daughters, who simply enjoy playing with symbols on a page, and who find all the illustrations, and colourful doodads in their current textbook patronizing and distracting. Why do we assume that math instruction must be a one size-fits-all proposition?
But my real opposition to the privileging of the conceptual in constructivist math is that it is misleading and even hypocritical: in my experience, constructivist textbooks do not encourage conceptual understanding at all. Indeed, my main problem with reform math is that it does not promote mathematical understanding, full stop.
The note from my daughter with which I started this post, in which she expresses her ongoing frustration with math, was sparked by a revealing instance of the true non-conceptual nature her constructivist math text. The problems my daughters were working on for their homework that night involved perimeter and area. In certain questions, they had to compare perimeters given in different metric units. To do that, they had to convert, for instance, metres to centimetres or vice versa in order to figure out which of two given perimeters was bigger. My daughters had no problem with this, but then they were confronted with a problem in which they had to compare the areas of two rectangles—one measuring 8400 centimetres squared and the other measuring .84 metres squared—and, again, indicate which was bigger. Their first instinct was simply to multiply .84 by 100 in order to carry out the comparison. This was my first instinct as well, but something (a residual spark of mathematical reasoning?) told me that in the case of area, it didn't quite work this way. Confused, I flipped back a page or two to see if any explanation of this type of problem had been given. I found no explanation, but I did find, in a coloured bubble in the margin of the previous page, these instructions:
When you convert an area in metres squared to centimtres squared, each dimension is multiplied by 100. So, the area is multiplied by 100 x 100, or 10,000.So there it was: a formula! No verbal or visual exposition, just an easily-missed bubble telling the kids what to do. You can't get any less "conceptual" than that. My daughters read the instructions and understood them, but they wanted to know why the formula worked. I asked them if the teacher had explained it, and they said he had not. I tried, unsuccessfully, to explain it. I then enlisted the help of my computer-scientist husband. He drew diagrams, and took my daughters, step-by-step, through the hows and whys of the formula given by the textbook; in doing so he was able to teach the girls how to carry out conversions from any metric unit squared to another—which the textbook formula, restricted as it was to conversions from metres squared to centimetres squared, was unable to do.
My point here is neither to ridicule my daughters' math textbook nor to blame the school for choosing it; it is, after all, one of a handful of textbooks approved and financially supported by the provincial government. My purpose, rather, is to demonstrate that this so-called constructivist, "conceptual" textbook is neither. It's just poorly-presented, pedagogically dubious, bad math. Which is why I concur with my daughter: THIS MATH DEPRESSES ME.
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