A little critique
Jul. 7th, 2010 08:56 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
velvetpageGender gap persists at highest levels of math and science testing
The authors of this study point out that the achievement gap between boys and girls, when testing gifted seventh-graders, has narrowed dramatically in the last thirty years. When it was studied in the eighties, the number of boys scoring above 800 on the math SAT outnumbered the girls 30 to 1, and that gap has narrowed to about 3 to 1. That happened in the first fifteen years - that is, the 3:1 gap has been consistent since 1995.
So the authors are postulating that the persistence of this 3:1 gap indicates a difference in innate ability between boys and girls in math and scientific reasoning (where the same gap is evident.)
I'm not buying it. Here's why.
First, for every elementary school teacher who is well-versed in constructivist teaching methods as they relate to math, there are a bunch more who aren't. The NCTM (National Council for Teachers of Mathematics) put out the original version of their constructivist curriculum in 1989; I suspect if one were to break down the changes further within that thirty-year time span, it would be the years between 1990 and 1995 that would show the biggest change. But the uptake is, at best, piecemeal. Teachers still teach from textbooks, which short-circuit the problem-solving process by their very nature. Manipulatives still start to disappear from ready availability in classrooms as early as grade four. The higher one goes in math, the more likely it is that manipulatives will disappear almost entirely from the classroom, to be replaced with purely abstract problems and procedural methodology - not because those are the end goal of mathematics instruction but because that's how the teachers were taught, and when they get out of the comfort zone of their pedagogical instruction which is generally aimed at the middle of the expected outcomes for their grade level, they tend to fall back on what they know.
In short, how much of this is the fact that girls learn mathematics differently, and their learning styles for mathematics aren't being supported in their gifted classrooms? My gut instinct says that's a huge part of the reason for the gender gap, but of course I don't have the stats to back it up.
Second, their base data is of twelve-year-old gifted kids. Leaving aside the selection criteria for giftedness (which honestly I question, knowing as I do dozens of people who are very clearly gifted academically but were not identified as such in school) there's the question of socialization. Girls are still socialized away from mathematics, more subtly perhaps than they used to be and less often by teachers, but it still happens. Twelve-year-olds are at the point in their lives when they're really struggling to figure out their place in the world. How many of those gifted kids have already decided that math isn't their thing, due to a couple of years of the poor teaching I mentioned above? How many of them will be talked out of that thinking once it starts to establish itself? Or will it simply be seen as her choosing what she's best at, and hey, there are great careers in language-based subjects, too, so what does it matter if she gives up on the highest levels of math?
In short, socialization has been downplayed as a reason in this study, probably erroneously. The cultural myopia of the data selection is in my favour, here: there is no gender gap in several Asian countries when it comes to mathematics, which makes me question why there should be a 3:1 gender gap here. But the study is done entirely on American students using American tests.
Third is the issue of NCLB. It started in 2001. It short-circuits attempted improvements in instruction because so much of the testing is knowledge-based rather than based in a problem-solving model. Because the testing has such very high stakes attached to it, teachers teach to the test, meaning that improvement in instruction has been stymied in favour of getting the test scores up. You'd think that wouldn't affect gifted education, but school culture affects everything, including the kids who otherwise might not have to worry about it. If the teachers' PD is all about getting test scores up, the teacher of the gifted students effectively is getting no PD at all. His kids are going to do just fine. But he's not then getting trained in the enrichment methods which would really serve everyone much better and are absolutely essential for the highest-functioning kids.
In short, if you want to see problem-solving in students, you have to ask for problem-solving on the tests. The US as a whole is not doing that, so the level of problem-solving isn't improving.
Should I email the authors of the study and point out the problems in their methodology? :)
The authors of this study point out that the achievement gap between boys and girls, when testing gifted seventh-graders, has narrowed dramatically in the last thirty years. When it was studied in the eighties, the number of boys scoring above 800 on the math SAT outnumbered the girls 30 to 1, and that gap has narrowed to about 3 to 1. That happened in the first fifteen years - that is, the 3:1 gap has been consistent since 1995.
So the authors are postulating that the persistence of this 3:1 gap indicates a difference in innate ability between boys and girls in math and scientific reasoning (where the same gap is evident.)
I'm not buying it. Here's why.
First, for every elementary school teacher who is well-versed in constructivist teaching methods as they relate to math, there are a bunch more who aren't. The NCTM (National Council for Teachers of Mathematics) put out the original version of their constructivist curriculum in 1989; I suspect if one were to break down the changes further within that thirty-year time span, it would be the years between 1990 and 1995 that would show the biggest change. But the uptake is, at best, piecemeal. Teachers still teach from textbooks, which short-circuit the problem-solving process by their very nature. Manipulatives still start to disappear from ready availability in classrooms as early as grade four. The higher one goes in math, the more likely it is that manipulatives will disappear almost entirely from the classroom, to be replaced with purely abstract problems and procedural methodology - not because those are the end goal of mathematics instruction but because that's how the teachers were taught, and when they get out of the comfort zone of their pedagogical instruction which is generally aimed at the middle of the expected outcomes for their grade level, they tend to fall back on what they know.
In short, how much of this is the fact that girls learn mathematics differently, and their learning styles for mathematics aren't being supported in their gifted classrooms? My gut instinct says that's a huge part of the reason for the gender gap, but of course I don't have the stats to back it up.
Second, their base data is of twelve-year-old gifted kids. Leaving aside the selection criteria for giftedness (which honestly I question, knowing as I do dozens of people who are very clearly gifted academically but were not identified as such in school) there's the question of socialization. Girls are still socialized away from mathematics, more subtly perhaps than they used to be and less often by teachers, but it still happens. Twelve-year-olds are at the point in their lives when they're really struggling to figure out their place in the world. How many of those gifted kids have already decided that math isn't their thing, due to a couple of years of the poor teaching I mentioned above? How many of them will be talked out of that thinking once it starts to establish itself? Or will it simply be seen as her choosing what she's best at, and hey, there are great careers in language-based subjects, too, so what does it matter if she gives up on the highest levels of math?
In short, socialization has been downplayed as a reason in this study, probably erroneously. The cultural myopia of the data selection is in my favour, here: there is no gender gap in several Asian countries when it comes to mathematics, which makes me question why there should be a 3:1 gender gap here. But the study is done entirely on American students using American tests.
Third is the issue of NCLB. It started in 2001. It short-circuits attempted improvements in instruction because so much of the testing is knowledge-based rather than based in a problem-solving model. Because the testing has such very high stakes attached to it, teachers teach to the test, meaning that improvement in instruction has been stymied in favour of getting the test scores up. You'd think that wouldn't affect gifted education, but school culture affects everything, including the kids who otherwise might not have to worry about it. If the teachers' PD is all about getting test scores up, the teacher of the gifted students effectively is getting no PD at all. His kids are going to do just fine. But he's not then getting trained in the enrichment methods which would really serve everyone much better and are absolutely essential for the highest-functioning kids.
In short, if you want to see problem-solving in students, you have to ask for problem-solving on the tests. The US as a whole is not doing that, so the level of problem-solving isn't improving.
Should I email the authors of the study and point out the problems in their methodology? :)
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(no subject)
Date: 2010-07-08 01:29 am (UTC)I was a seventh-grade gifted girl with particular skill in math in 1995, and I GUARANTEE you that sexism and stereotypes were still seriously interfering with girls' math achievement then. It was pretty fucking blatant, and it came from both teachers and fellow students. In fact, resentment from other girls about my math ability (and the fact that I wasn't too tactful about it, a problem exacerbated by my often not receiving adequate enrichment) contributed heavily to my being bullied in both grade five ('93-'94) and grade seven ('95-'96). I experienced sexism from a female teacher who refused to provide me adequate math enrichment, as well, in grade five. There was VERY clearly sexism contributing to the gender gap in math achievement in 1995, so if the gap hasn't changed, I don't see any reason to think its cause has changed.
(no subject)
Date: 2010-07-08 02:18 am (UTC)The US (IMO), outside of single-sex school proponents, is loathe to admit that not only do individual children learn differently, but that there are some significant differences in how girls-in-general and boys-in-general learn. And having teachers call on girls 50% of the time is an insufficient "fix" to the persistent issue that our educational institutions are based on how to teach boys.
(no subject)
Date: 2010-07-08 02:23 am (UTC)Boys tend to deal with abstractions without concrete materials better than girls do, but when given the opportunity to explore through the four stages of mathematical learning, girls can and do succeed just as well as boys. The fact that a large number of math teachers don't know how to teach them that way is not their fault.
(no subject)
Date: 2010-07-08 03:14 am (UTC)OMG, the math teachers here are horrible and the issue starts with the grade school teachers that ADMIT that they never did well in math.
seriously? how the heck is a child supposed to build a mathematical foundation if their TEACHER didn't have a good one? geez.
That said, because I think different than most women and as such am very mathematical (see my other comment), when I tutor my math students I get the same compliment every time, "I never understood math until you taught it to me. Why can't all teachers teach math like YOU do!?"
I have never known what special thing I do but apparently, it's unique and it helps all math students because lord knows, I've tutored many over the years and no two have come with the same learning challenges
(no subject)
Date: 2010-07-08 09:56 am (UTC)I think part of the problem is the pool from which teachers are drawn. In Ontario, education is a second-run bachelor's degree; that is, you have to have a degree in another subject before you can get into the teaching program. Those planning to teach high school need teachables in two subjects, which usually means a major and a minor in their first degree, or a double major. If you're going to teach junior-intermediate, as I did, you need only one teachable (mine is French) and if you're going to teach primary, you don't officially need any. So people who are going to teach primary have first degrees is psychology or English, and probably did quite well in them because it's really hard to get into the B.Ed program. But they took very little math. Most of the math/science people end up teaching high school because that's where they're going to get to teach to their degree subjects. So primary/junior education is full of people who aren't that comfortable with math themselves and have never taken an extra course in how to teach it.
Now, I used to think of myself as a language person. My degree is humanities where it crosses with social sciences (French: language, linguistics, and translation stream, and a minor in history.) I didn't recognize until quite recently that I was subtly disencouraged from pursuing math and science, in part by my teachers.
(no subject)
Date: 2010-07-08 11:01 am (UTC)(no subject)
Date: 2010-07-08 11:11 am (UTC)(no subject)
Date: 2010-07-08 02:44 am (UTC)Not sure if the problem-solving is an issue here, because the SAT itself doesn't really test problem-solving. It tests a very limited range of facts. And only the richest districts even still have gifted programs. Nowhere I've ever taught or attended had one. A few of us got to do self-directed enriched math off by ourselves in elementary school, and then we were placed in year-ahead classes through middle and high school for math and science, which cost the district nothing. In elementary school, I got pulled out for a Great Books reading group twice a week, and my mother-in-law, a retired elementary reading teacher, did something similar herself. Other than that? No gifted classes.
I got a 680 on the SAT when I took it in grade seven. I got an 800 four years later, which would have been right in the middle of this study, and an 800 on the math GRE (which admittedly was a FAR easier feat to accomplish).
Without seeing the study or the methodology, I'd have to go almost exclusively with socialization. Have there been any studies pointing to girls as a group learning mathematics differently? And how much of THAT difference could be attributed to very early socialization itself?
(no subject)
Date: 2010-07-08 10:20 am (UTC)Mathematics instruction has to be grounded in concrete learning and intertwine itself through those stages, back and forth, all the way up. If it's not doing that, the kids whose preferred learning style is to make connections are going to get lost. And yes, the research suggests that that's a more classically female learning style. It can and does lead to the same depth of understanding, even of very high-level concepts - but only if the opportunity to explore the connections is embedded in the instructional methods.
(no subject)
Date: 2010-07-08 11:06 am (UTC)(no subject)
Date: 2010-07-08 11:03 am (UTC)(no subject)
Date: 2010-07-08 03:08 am (UTC)not discounting your thoughts, just saying, yeah - I'm definitely a different thinker than other XX humans.
(no subject)
Date: 2010-07-08 09:58 am (UTC)(no subject)
Date: 2010-07-08 01:34 pm (UTC)Personally, I'm all for teaching from a constructivist approach because a) the abstract, linear representation is there already, and they'll all get that, so it provides built-in differentiation and b) I've noticed ALL kids benefit from it.
And of course, I have a huge concern with how socialization affects performance on standardized tests. I think boys are socialized to do better on multiple-choice tests and girls aren't.
(no subject)
Date: 2010-07-08 04:48 am (UTC)Anyway. It wasn't comprehensive, but I did a study on this a few years ago, based on local school district data (11th and 12th grade scores and participation) combined with state data (4th and 8th grade mandatory standardized tests). It was very interesting to see the statistics.
What I saw was that as age increased, so did the gap. This isn't new information. Some people are quick to say that it's because "oh, 4th grade math isn't hard enough to show a difference in potential. The innate difference comes when you get to higher levels of math, where it's more difficult." But I don't agree; there are plenty of 4th graders who struggle with that level of math, and according to the data, that doesn't seem to be gender-based. The basic thought processes for math are the same up through higher levels, for the most part. If girls really are just not as tuned in to that kind of thinking, not as innately gifted in math, I would honestly expect that to be reflected (I believe the actual data showed that 4th grade girls outperformed 4th grade boys, but not with a statistically significant margin).
What interested me most, though, was from our local school district data. The high school AP classes (college-level courses taught in high school, where students take a test at the end of the year to qualify for college credit) in math and science had a significant skew towards the men--in participation. But not performance. The female mean and median scores were higher than the male mean and median scores, but the sample size was much smaller. There are several possible explanations, but the one that fit with the 4th/8th grade trends was this: mid-level females weren't taking the classes. A male who would likely make a B would much more probably enroll in a class than a female who would likely make a B.
My thoughts on the standardized test gap are related to that concept. Girls are not taking the advanced classes (even as far back as 8th grade, it appeared. Here, math splits in 7th grade between "regular" and "pre-algebra," and again in 8th grade to "regular," "pre-algebra," and "algebra." That split sticks with students until they graduate, with even more splits in high school). When students get to the age to take standardized tests, then, the males are more likely to have had advanced classes in math that would have further prepared them for the test content.
So not only have the girls not been taught in a way that they would learn, many of them have simply not been taught. The girls that stuck around did as well as their high-performing male counterparts; it's hard not to wonder how the mid-range girls would have performed in comparison to their mid-range male counterparts, had they taken the courses. The whole situation makes me a little sick to my stomach, and feels vaguely overwhelming. I presented a paper based on my research at a regional meeting of the Texas Section of the American Association of Physics Teachers, and I did things in college like organize a free weekend math/science workshop for middle school girls, where a group of college-aged female math/science majors showed the girls awesome college-level science experiments and tricks. But it's such a massive problem, and I don't even know where to begin to try and help fix it.
(no subject)
Date: 2010-07-08 10:08 am (UTC)Ontario doesn't split that early; all strands of math are taught in a generic math class until grade eleven, but as of grade nine, classes are divided according to difficulty into three strands. Frankly, I think streaming according to ability is one of the single biggest problems our education systems have, because it encourages all the stakeholders to think that ability IS innate, and furthermore that it can be assessed with accuracy by the age of fourteen, and the research mostly shows that that's not true; given enough parental support of the right kind and really good teaching, pretty much anyone can succeed at a high level.
(no subject)
Date: 2010-07-08 11:17 am (UTC)(no subject)
Date: 2010-07-08 11:25 am (UTC)Streaming makes it possible for teachers to pretend that every kid in their class is at the same level, and to put the onus of keeping up with the teacher on the student. Both of those ideas are wrong. No matter how good the streaming, differentiation is essential if you're going to reach every student, or even most of the students, most of the time, and if a kid doesn't get what's going on, the correct response is not to tell them to work at it harder or drop to the next stream down. Yet you and I both know that that's the response they're going to get in a streamed setting.
As I've said before, I don't discount the potential for streaming for the most advanced and least able students. I'd be surprised if that was more than 5% of kids at the top and bottom, though. Everyone else manages better in a differentiated, mixed-ability classroom.
(no subject)
Date: 2010-07-08 09:46 pm (UTC)I'm remembering my first grade GT class, which met once a week. In regular class, our math consisted of counting and ordering whole numbers, counting by numbers, and talking about math in real words. In my GT class, we used small pill bottles to learn multiplication and division (extension of counting by numbers, with the added concept of new vocabulary and notation). We even got into equations a little (if you multiply one side of an equal sign by three, you have to do the other side, too, etc). It was definitely just an extension of what we were already learning, but the physical pill bottles were the key to my understanding at that age. How would a teacher work with kids who aren't ready for that extension, and would be easily distracted by others playing with pill bottles?
I guess it sort of boils down to the question of how differentiated is "differentiated instruction"? Would all the kids use pill bottles, no matter what they're working on? How general is the learning concept for the day (counting by numbers? finding patterns? stuff with whole numbers?) Does the teacher teach each kid individually, walking around the room? Is there any time where the teacher is at the front of the room, with all the kids listening, and if so, what would he/she say? How do the kids know which "level" they are supposed to be working with?
This got long.
Date: 2010-07-08 11:06 pm (UTC)So, Monday morning. I put up a problem on chart paper at the front of the room: "A spider travels 19 cm per second. How long will it take the spider to travel the perimeter of a room 3m x 4m?" The kids get the standard instructions for group work: they can work with anyone in the class and they can use whatever manipulatives or supplies will help them figure out the problem. If they seem lost, we may discuss a few possible ways of approaching the problem, for example: "Well, if the spider travels 19 cm in one second, how far does it travel in two seconds?"
The kids then start working through the problem. While it seems obvious to an adult that this is a division problem - 3m x 4m = 12 m = 1200 cm, so the answer will be 1200/19 - this is not obvious to the kids and I don't point it out to them. Most will start by adding up, 19+19+19, over and over again. I circulate and ask questions like, "What do these nineteens mean? What part of the answer are you getting here?" and "What strategy are you using?" to get their metacognitive thinking going. Meanwhile, I'm taking notes. Who jumps right to using multiplication - for example, 19x10 - and then adds groups from there? Who uses repeated subtraction instead of repeated addition? Who can't seem to add the number of nineteens at the same time as they're adding nineteens? Who is using an estimation strategy, for example 20x5 = 100?
Over the course of the next hour or so, I'll get different students up to the board to explain their strategies to the other kids. The kids get to ask questions of the person presenting, and if they have a suggestion, they can make it at this point. Usually, a bunch of kids realize that they can use what the other kids said to refine their strategies, because they were doing something similar. I don't reserve this step only for the people getting it right; I'll often get someone up who is missing one key piece to make an otherwise-sound strategy work, in the hope that another student will point out what they've missed.
When we get to the end of the problem - and it might very well take two days - we go back and revisit the strategies we used. I give the kids a chance to point out that the repeated addition worked, but it wasn't very efficient, and could be made so if they added groups instead of individual nineteens.
This got long, part 2
Date: 2010-07-08 11:06 pm (UTC)Now that I've got my groups, I'm going to find two or three problems that are similar but differ in a couple of respects. The lowest group is getting friendly numbers to work with. They won't see anymore nineteens; they'll get twenties and tens and hundreds, numbers I want them to develop skill at working with in their heads. I'll probably work with them first in a guided math lesson, where we go to one space in the room and start tackling the problem together, with lots of manipulatives to model the problem.
Meanwhile, the middle group has been given a similar problem, with less-friendly numbers, and a couple of discussion questions to guide them towards the strategies I want to see them develop. They're working elsewhere in the room, and I'll check in with them once I've got the lowest group well-established at their task and getting help from each other.
The highest group has been given possibly the same problem as the middle group (to facilitate them learning from each other later on, and transfer between groups if someone either gets it really well or doesn't get it as well as I thought.) But their discussion questions are different. I want them to draw connections between different strategies and begin to develop their patterning. When I get to this group - probably the second day of group work - I'm going to be talking about equivalencies and ratios, both of which are beyond grade-five level according to the curriculum, and possibly showing them some simple algebraic equations for the problems they've got in front of them.
Usually, the middle group starts to run into the higher group as the week progresses, and by the time the week is over, fully half the class will have been exposed to a level of algebra more commonly associated with grade seven than grade five. The goal for the lowest group is to develop their understanding that multiplication is a faster way to add groups, and use concrete materials to get to the point where they can use a more advanced strategy to approach the problem.
At the end of the week or the beginning of the next week, I'll give them another problem as a "game time" activity. I may or may not differentiate this problem or give them a choice of problem to tackle; it depends on how the rest of the week has gone. They have to answer this one independently and answer a couple of questions similar to the discussion questions they've been working on, and this activity determines their mark for this part of the unit.
(no subject)
Date: 2010-07-08 11:40 pm (UTC)1) Pre-assessment. I need to know exactly where everyone is, not because they're labeled gifted or LD but because I've seen them work on this type of problem and I've taken notes about what they're doing and how they can progress.
2) The opportunity to work through problems without being shown how to do it; I want them to build on their prior knowledge and use it as the basis for the skills they're developing. It's very, very easy to short-circuit this process, and this is the biggest pitfall that most teachers make when they think they're using constructivist teaching methods: instead of letting kids figure out the next level on their own, they try to jump them two or three levels at once by explaining. It doesn't work.
3) No marks. They are not graded on any of this until they've been working on it for several days, and even then, if I discover that they're not getting it, I'll turn the evaluation into a practice activity and we'll work on it some more. Nobody is well-served if I jump the gun and evaluate them before they've consolidated their learning.
4) Flexible groups based on observation, with plenty of opportunity to try problems that other groups are tackling. I'll generally have a series of problems available so that if a kid gets to the end of a problem before their group, I've got something just slightly harder for them to do. As often as possible, this involves a different way of looking at their work rather than just harder numbers.
5) Clear expectations. I want to be able to tell the lowest group when they've met the grade five expectations (which gets them a B) and I want to be able to tell the highest group that they're doing grade seven work. It's all laid out somewhere and I know exactly where I'd like to steer them next, no matter what level they started at.
6) A wide variety of manipulatives. In your pill box example, I'd be taking that group aside for practice with arrays and basic multiplication, but if another kid wanted to horn in on that lesson and proved they were ready for it, well, the more the merrier. Kids can use whichever manipulatives or resources they want to best model the problem for themselves.
7) Flexible assessments - some kids will be asked to write out an explanation, some will be asked to make connections, some will be asked to create a similar problem for someone else, some will be asked to find the patterns. If possible, they get a choice in how they show their learning. Often, if they can explain it to me out loud, I'll write down a mark without making them write it down.
Congratulations! You just got a crash course in constructivist mathematics at the junior level!
(no subject)
Date: 2010-07-09 12:00 am (UTC)I'd be interested to learn about the social implications of that kind of differentiation. I always understood that one of the underlying reasons behind "streaming" is that they are in a class with people at their own level, no matter what level that is. A negative aspect of streaming is that children know that they are in the "lower level" class, when their friends are in the upper level. Kids may internalize that feeling of inadequacy if it comes up in social situations, but in class, at least, they are on equal par with their fellow students. In a differentiated classroom, you don't have the same social stigma of being in the "stupid class" (or the "nerd class"), but lower-level students will be re-singled-out every day, in front of higher-performing peers. During the initial group work, levels mix (I assume), and I'd worry that lower-level students would either not try at their own level/pace (relying on high-level friends), or try and then feel frustrated when their friends/peers catch on faster and don't struggle.
I guess it comes down to which is worse. In streaming, students may feel labeled as "stupid," but they aren't reminded of it in the learning situation. In differentiation, they aren't labeled as anything, but they will learn to associate the feeling of "stupidity" with the learning environment. I'd think the better of the two options would entirely depend on the student, but you can't structure a school both ways.
(no subject)
Date: 2010-07-09 12:10 am (UTC)I gave out A's to kids who had never gotten an A before in math. I wasn't padding anything; they earned it, and their A meant exactly the same thing that the gifted kid's A meant in terms of knowledge gained. In a streamed situation, an A in a lower stream does not equal an A in a higher stream, so kids are left constantly feeling that there is nothing they can do to improve to that level. Meanwhile, failure is a Really Big Deal to the kid in the higher stream because failure involves leaving the prestige of the higher stream. A fear of failure leads to an unwillingness to take risks, and that's not exactly conducive to good problem-solving.
(no subject)
Date: 2010-07-08 10:11 am (UTC)