kitchen table math, the sequel: Preconceived notions about place value

## Thursday, October 28, 2010

### Preconceived notions about place value

(Cross-posted at Out in Left Field--with some great comments)

One thing that struck me about the math talks given at this weekend's New England Conference on the Gifted and Talented was the emphasis on manipulatives and the concerns about whether children understand place value. Are these the most appropriate things to be focusing on when it comes to students who are gifted in math? The mathematically gifted kids I know grasp place value and other aspects of arithmetic with only minimal exposure to manipulatives, and quickly advance to higher levels of abstraction by the time they hit first or second grade. But the education establishment seems bent on convincing itself that children--however gifted--don't understand place value.

Why would you want to convince yourself of this? Because it gives you an excuse not to teach the standard algorithms of arithmetic. If children don't understand place value, then they can't understand borrowing and carrying (regrouping), let alone column multiplication and long division. And unless they understand how these procedures work from the get-go, educators claim (though mathematicians disagree), using them will permanently harm their mathematical development.

So, given how nice it would be not to feel any pressure to teach the standard algorithms (because, let's admit it, they are rather a pain to teach), wouldn't it nice to convince ourselves that our elementary school students, however gifted in math, don't understand place value?

But how do you convince yourself of this? As that ground-breaking math education theorist Constance Kamii has shown, it's child's play. All you have to do is ask a child the right sort of ill-formed question. Here's how it works:

1. Show the child a number like this:
27
2. Place your finger on the left-most digit and ask the child what number it is.

3. When the child answers "two" rather than "twenty," immediately conclude that he or she doesn't understand place value.

4. Banish from your mind any suspicion that a child who can read "27" as "twenty-seven" might simultaneously (a) know that the "2" in "27" is what contributes to twenty-seven the value of twenty and (b) be assuming that you were asking about "2" as a number rather than about "2" as a digit.

Allison said...

Sometimes math ed is just Alice-in-Wonderland compared to reality. The question they ask is poorly phrased, and could confuse anyone, gifted or not. Most normal people would use a statement that "these children don't understand place value" as a reason *to* teach them the standard algorithms, so they could learn the procedure and then learn its meaning.

So it's hard to make sense of nonsense.

The conference sounds about like everything else: G&T teachers know no more math than any other teachers do. Why would they? They are still taught in education school.

But to the issue of gifted kids learning place value, I think I may disagree with you in general. Bright children may "get it" immediately, as they do many things. The problem is since math ed is so poor, all they get, however quickly, is the procedure/pattern/symbol manipulation. It doesn't necessarily mean they get the reasons why. Bright children are poorly served by acceleration when it is acceleration of shallow content.

Here's another example: if no one teaches the notion of equality, and instead the first algebraic expressions are all about "solving for x", the bright child can easily learn all of the patterns, successfully solve for every x. "Here, move that term over to the other side; point-slope formula works here; that's pascal's triangle" etc. It doesn't mean she has spent even two seconds thinking about WHY it's valid (or what property permits you) to "move that term to the other side", or why any pair of points on a line has the same slope (without resorting to circular reasoning), or that polynomials aren't just squiggly graphs, but apply to actual numbers, or why someone would want to know the roots of an equation.

I realize these issues aren't likely the depth of problem the conference considered. But I do think most bright kids only realize much later (at a time too late for many to handle the failure) how thin their knowledge is. A good G&T program would spend more time teaching why to these children, just as a good elementary program would in general.

bky said...

My experience with teaching my kids math at home is that place value is something they understand (like everything else) in stages. To get to any given stage they need to do work with numbers. The process of doing arithmetic is the ultimate teacher. The other day my 7-year old had a subtraction problem that was something like 805 - 305. He looked at it and said "5?" How diagnostic. Yes, 5 something, but not 5. It's one of those things where the student has to get into and out of (minor) trouble. He gets out of trouble with more understanding. Likewise, subtraction with borrowing is a good arena for really understanding place value. If you want to wait until kids "really understand" place value, in a deep and mystical way, before having them learn subtraction, then you are building in pointless long-term delays in learning.

By the way, isn't the 2 actually a two? Is 2 ever a 20? Or don't I understand place value? A well known curriculum repeatedly asks young kids questions like "what is the value of the 2 in 27"? It's still a 2, but its value in 27 is 20.

SteveH said...

Were the people at the conference mostly K-12 educators? Did they have a position on whether the G/T kids were to be taught with differentiated instruction or with pull-out or tracking?

Our state does not allow tracking or pull-out. This means that any discussion of G/T is constrained by that limitation. Individual schools determine how to handle the issue with some form of differentiated instruction. The schools KNOW it doesn't work for G/T. I used that to get my son to skip 6th grade EM and go directly to pre-algebra. That's much better than what they were talking about in one breakout session on "Schoolwide Cluster Grouping Model". It's described as:

"Serving the learning needs of gifted students in a full-time program that delivers consistent curriculum compacting and differentiation opportunities without major budget implications"

There is compacting and differentiation, but no acceleration. Did anyone talk about acceleration at the conference? When I looked at the breakout sessions, all I saw was traditional educational thought applied to the gifted and talented.

Allison said...

The number 2 is always the number 2, no matter how you write it. But symbols aren't numbers.

Usually, we refer to the symbols we type or write as digits, and the places in the place value tells us what the digits stand for.

The digit 2 in 27 stands for (the number) 20. The digit 7 stands for 7.

In 203217, the digit 2 in the leftmost position stands for the number 200000. The digit 2 in the position 3rd from the right stands for the number 200.

Allison said...

If your child says 805 - 305 out loud, would he get the problem right?

Eight hundred and five minus three hundred and five is ....

simplify it for him: "what is eight hundreds minus three hundreds?" His answer should not be 5 question mark. It should be immediate 5 hundreds.

Children should be shown that the ones/tens/hundreds are units, and you only add like units. what is 3 apples plus 4 apples? apples. what's 3 hundreds plus 4 hundreds? 7 hundreds.

then you teach that you can find common units to add unlike things.
What's 3 apples and 4 oranges? It's 3 apples and 4 oranges. or, it's 3 pieces of fruit plus 4 pieces of fruit is 7 pieces of fruit.

Anonymous said...

The digit "2" in "27" represents "2 tens."

SteveH said...

The "2" could mean 2 8s or 2 times base^1, assuming that the base is greater than 2. For "27", you would have to assume that it's at least octal. What if you were given the number 2F? How about the number "&X"? I just made that one up. (It could be a machine address.) How about the complex number 3 + 2i?

There are many levels of understanding, so what is their point with raising this issue? Understanding is fine. Just define what you want for a particular grade and get on with it. The assumption seems to be, however, that with some magic level of unknown understanding, mastery of skills becomes less important.

My impression after looking at the conference web site is that although it's about gifted and talented kids, the level of educational thought is not gifted or talented.

Katharine Beals said...

@Allison: how quickly bright kids pick up place value and equality is an empirical one. My guess, anecdotally from the ones I know, is that very brief demonstrations are all that are necessary for enough (preliminary) understanding for the procedures to be meaningful, and for the child to get jump-started into meaningful adventures in arithmetic and the gradually deepening understanding that those adventures facilitate.

@Becky--"the process of doing arithmetic is the ultimate teacher". Very true, and very well put.

@Steve: It was a combination of parents and educators. My talks had 50:50, or perhaps slightly more parents. The other math talk I attended was overwhelmingly educators, and you could definitely feel the intellectual and ideological differences between the audiences.

As for differentiation, "differentiation", and acceleration, no overall philosophy was apparent to me. The conference drew people from all over New England, so it included states that do allow tracking and pullout (yours doesn't?? sweeping and shocking!). As you noted, the conference was not terribly academic (and there was much more on soft stuff like emotions and creativity). I tried to make my talks as academic as I felt I could get away with.

SteveH said...

Our state (RI) spends \$0.00 on G/T. It's all supposed to be done in the context of differentitated instruction(DI), and that is left up to the individual schools to implement. The state has an "advisory" group, but they just talk, and by the looks of their web site, they haven't done that in years. There is another advocacy group, but it looks like they stopped meeting last year.

Just because some people advocate for G/T, it doesn't mean that they advocate for anything like the content and rigor pushed by those at KTM. Since acceleration is "off the table", they focus on issues like some vague sort of deep understanding, as if that's the way differentiate and avoid acceleration.

In music, the gifted get the best teachers, a faster pace, more competition, and are grouped with other top kids. Somehow, that isn't allowed for academics. When my son went to Interlochen last summer, it was an amazing experience for him. He also couldn't believe that someone else in his cabin was reading the same book on string theory.

Hainish said...

Re: G/T

Would it be possible to provide G/T education via an outside provider offering a no-cost afterschool enrichment program to a district?

(The provider may or may not decide to label the program "G/T" but would of course have final say over who could enroll.)

Anonymous said...

Hainish -- maybe. But my G/T did not want more school, they wanted school that wasn't boring. Although realistically, your solution may be the only possible one.

Crimson Wife said...

I agree that it's a horrible question. The better one is to do what Singapore does and ask the child to write out in expanded form that 2305 = 2000 + 300 + 5.

LynnG said...

Parents tried to push for g/t programming, but ran into a wall. The best the school would offer was after school and that would be open to anyone without respect to ability.

When it looked like it was going to devolve into cheap after school day care with a "creative" angle, the parents backed off and it never happened.

Our schools are philosophically opposed to g/t programs of any sort. Differentiation and peer tutoring is the only nod they give to the g/t students.

Peer tutoring is nothing more than the kids further ahead help the slower kids. It doesn't do much for either group.

Hainish said...

More school vs. less boring school: Ideally, the enrichment program would be able to siphon kids out of 1-2 class periods daily to replace *some* of the boring school.

Still, stealth G/T might be the only way to go in a lot of places.

Anonymous said...

i had a teacher in elementary school...
and i've forgotten who or i'd tell you...
who was talking about what "opposite"
means and told us that the opposite
of a "frog" is a "tadpole". naturally
i knew she was completely full of it.
so did most of my classmates i guess.

but i didn't speak up because i knew
that it wouldn't do any good: the *real*
lesson, as it *usually* is, was "never mind
the truth; authority does what it wants".

this was, evidently, a pretty good school
(and a very different time from the present)
so we didn't encounter this kind of thing
in math class. it's no accident that i was
a math major...

nowadays of course if there's any clarity
emperor will object. if the student can
be right and the teacher wrong, one had
better change the subject pretty quick.

why would anybody expect otherwise?

jtidwell said...

@Hainish, isn't what you propose basically a pull-out program? I thought SteveH said that wouldn't fly where he is.

@Katharine, from what you could see at the conference, is there any discernible movement towards rigor, rich content, high standards, etc. (all that good stuff) among New England gifted parents? If there's any other parents around here thinking like I am, I'd love to have a conversation with them.

Our school district just eliminated most of the G/T pullouts, and the class sizes are so big that no realistic differentiation happens. Budgets are too tight for these poor teachers to do anything except classroom management and teaching to the middle. Still thinkin' that gifted-only school may be our best solution, whatever its flaws may be...

SteveH said...

A separate school might be the only way, but you may not get what you expect, as with the Anova school.

Now that my son is in a good (?) high school, I'm happy enough. It's kind of scary, but I don't have much to do with his math or any other subject anymore. As for extras, we can add things outside of school, as needed.

The bigger problem is in K-8, where parents have to struggle just to keep their kids happy and up to an ordinary grade level. I would have been happy with a K-8 school that did this well, and not necessarily a specialized G/T school. However, I don't see that changing any time soon at our local schools. We tried to find it at a private K-8 school, but ended up bringing him back to the public school in 6th grade, where we used "differentiated instruction" to allow him to skip a grade in math.

Another family in our town kept going at our old private school as a pipeline to send all of their kids off to Phillips-Andover, and then, presumably, to Harvard, if possible. We weren't too interested in that much of a programmed fast-track, but it might be just the thing for some kids. Besides, even with just one child, that path is hugely expensive. When we took our son out of the K-8 private school, the headmaster said that he would do well anywhere. Gee, why were we there in the first place paying \$16K/yr for Everyday Math?

Hainish said...

jtidwell: It's a pull-out program if the district runs it and funds it and calls it a G/T program. If it's sponsored by an outside provider and labeled something else, then maybe it's something more acceptable.

Anonymous said...

Would someone be willing to provide brief compare/contrast definitions for what you all mean by acceleration, differentiation, enrichment, G/T, pullout, and whatever else you think ought to be defined in this namespace? When you say you were looking for X but all they offered was Y, I'd like to know what you wanted, and what you got instead (and maybe a bit of the reasons why?)

Thanks.

Allison said...

Here in MN, there is a state requirement that "Gifted and Talented education" be funded, but implementation issues -- what that education is--are left up to the district. Different districts conduct different tests and observational evidence, but usually by the end of 2nd grade, some students have been identified as "gifted". What happens then again varies by district.

In Saint Paul, there is an aptitude test given in K, and students scoring in the top 5-8% percent of it are offered placement in a school for the gifted, though preference is given to cetain acceptable minority groups, so some don't get it. Those students are then supposed to be accommodated in other St Paul schools using "gifted pullout", where a teacher who, by some criteria counts as a gifted ed teacher, try to provide some special services to these kids who are removed from their normal classes during those hours in order to receive this special instruction.

(cont)

Allison said...

So, by state law, kids' needs are supposed to be met, and "acceleration" is allowed. Acceleration in this context means the child is promoted from their current grade to another grade for either this specific subject or as many as necessary, including all subjects. A 3rd grader in 4th grade math is accelerated. A 6 yr old in grade 2 is accelerated.

Some school districts (and some principals) make parents jump through enormous hoops to allow their child to be accelerated. "compacting" is a word for acceleration within the year--teaching that year's material faster.

Differentiation is another tactic. The idea is that while the student is in the same room as their age peers, the content they are given per lesson is taught at "a variety of levels", so all children are met at their need. That's the concept.

Enrichment is the idea that you teach new and different material, outside of the curriculum, in order to keep these students engaged. Enrichment can either mean more depth or more breadth--deeper probing of why certain things are true, or using primary sources, etc. would constitute more depth, while teaching about a new group of countries other than the ones taught in that year, or teaching sudoku, etc. would count as breadth.

So, what's wrong with differentiation? It is crazy to think that a teacher or two can really teach highly disparate groups of students all at their "zone of proximal development". It means that in practice, students are often mindless "tic tac toe assigments" where children can choose any 3 of 9 assignments, some of which are more effortful than others by some criteria. Can it work? In extremely skilled and knowledgeable teachers, with some ability grouping in the first place, and an enormous amount of prep time for a tiny amount of actual class time, it could. Ask yourself whether that could happen in your school.

What's wrong with enrichment? There's still no good defn of what a gifted teacher should be doing, so they are often either hamstrung by their district's curricula, or they have to figure it all out for themselves. Often "enrichment" devolves into time spent playing games--not doing anything that actually builds, no coherent curriculum. It's a waste.

So what's wrong with acceleration? What's wrong with GT schools, or with pullout?

Like enrichment, all of the above depend on the quality and knowledge of the teachers, and the curriculum that gets to be used: if all you are doing is moving a kid up a year in Everyday Math, they aren't going to learn anymore. If all you are doing is putting gifted kids all together in a school that still does Everyday Math, "balanced literacy", and Writer's Workshop, they are learning nothing. If all you are doing is pullout, and all pullout ends up being is "enrichment" games, they are learning nothing. (Worse, many teachers don't like how pullout disrupts their class, and may end up taking it out on the student, causing them more pain than if they'd not done it.)

Fundamentally, elementary ed is in crisis, because the bulk of teachers don't know the content in the subjects that used to be taught, and the curricula used has precious little content too. This is still true in gifted ed--because there is nowhere these teachers would be taught content. And what programs in "gifted ed" worry about are all pedagogical and psych issues, not content.

Glen said...

Allison, that was useful for me, too. Thanks for the summary.

SteveH said...

"...if all you are doing is moving a kid up a year in Everyday Math..."

I remember thinking that when my son was in first grade and the school was using MathLand. When we put him into a private school looking for more, we got Everyday Math.

"And what programs in "gifted ed" worry about are all pedagogical and psych issues, not content"

That was my impression of the G/T conference in Hartford.

But this raises the issue that it's not just about teaching them more content. They believe that education is some other kind of animal. Back when my son was in first grade, I told the school committee that they should hand out the Core Knowledge series on "What Your First (Second, Third, etc.) Grader needs to know", and tell parents that this is NOT the education they will receive. Even without more content knowledge, schools could follow a more Core Knowledge approach.

Things change for our middle school (and high school) teachers who have to be certified in the area they teach. Most don't show the low content and low expectation issues of the K-6 classes. However, would more content education change things in K-6? I understand that there is talk in some places about using certified math teachers for math in all grades, but would this end up being just training in how to teach Everyday Math?

The hope is that content knowledge will cancel pedagogical views, but it's not clear that will happen. Besides, I don't think they will ever give it a chance.

Allison said...

-- Even without more content knowledge, schools could follow a more Core Knowledge approach.

Not really, though, because they don't know how to write a lesson for the content. They don't know what they don't know.

--would this end up being just training in how to teach Everyday Math?

It depends. Certainly, a teacher who has been taught enough about math to know what is wrong with Everyday Math's "explanation" :
"Students will probably be puzzled by this procedure (invert and multiply), since it doesn’t make sense intuitively. To help them accept its validity, ask them to use the procedure to solve the same problems they solved earlier by the common denominator method..Suggest they solve the problems on their calculators.”"

has a better chance of working around the textbook, and not relying on it. Such a teacher could actually motivate fraction multiplication because they know it DOES make sense if you teach it properly. Think about how PalisadesK manages to actually teach some English even though she's got all the buzzwords right. Think about how she admits that even parents can't tell she's teaching real content from what can say to them.

But if your school district requires that you "teach the text to fidelity", and everyone in the whole district is supposed to be on the same page on the same day, there's not really much chance that you can get away with throwing out Everyday Math's awfulness, is there?

Curriculum is not enough. Content knowledge is not enough. Teachers need to be professionals, and need to be in a school that treats them like professionals. Such a school needs an excellent curriculum, and teachers with knowledge enough to teach it.

SteveH said...

It sounds like you are talking about fixing ed school requirements, not trying to fix what comes out of ed schools. For K-6, I don't know if any other solution comes close. There is the question whether K-6 ed school philosophy and content knowledge are incomptible. At best, what I've seen are a few K-6 teachers who might want to provide more rigorous content education, but the system makes it very difficult to do that. Schools claim that they do it all and point to the successful kids even though they know they get help at home.

If teachers had more content knowledge, they would still be required to make it work with full inclusion. Schools claim that it works; that all they need to do to fix problems is to work harder or smarter. Our schools would love to see teachers come up with differentiated lesson plans that helped the more able kids. It's not so much that they are against more depth, they just want it done within the current setup. We are stuck trying to prove that it can't work or somehow figuring out how it can work.

There is also the issue of expectations. In high school, we have two worlds; the NCLB world and the AP/SAT world. In K-8, there is only the NCLB world and the slope is too low. There is nothing (even optionally) to calibrate or drive the slope needed to match up with the AP/SAT curve and slope in high school. Our schools pushed out (finally) CMP in middle school, but something has to drive the higher expectations into the lower grades.

Differentiated Instruction almost guarantees that there will never be the required upper slope of K-6 education. They talk about compacting, but the overall K-6 slope is still the same. They talk about enrichment, but the content slope is still the same.

Is there a solution that will work? The only one I can see (politically and philosophically) is one where all kids are in the same room, but there is more ability grouping. It would be kind of like pull-out without the walls. It's more like pull to the other side of the room. With some mixed ability, hands-on group projects, a balance (of philosophies) could be achieved.

Perhaps more content knowledge will make it clear that they need to carefully define this upper slope for K-6. However, I still think too many K-6 teachers would balk at that level of expectation; that it would too clearly show that there are differences between students. It's fine if it's hidden at home, but they don't want to see it in the face.

Allison said...

--It sounds like you are talking about fixing ed school requirements, not trying to fix what comes out of ed schools.

I don't really understand what you mean by the former, but I don't think it's possible to do the latter.

--For K-6, I don't know if any other solution comes close. There is the question whether K-6 ed school philosophy and content knowledge are incompatible.

Right now, they are incompatible.

We've eaten the seed corn for K-8 education. That's already happened. The majority of people in education have no idea what content works, what content used to be taught, or how to teach it to mastery. They don't know what synthetic phonics is. They don't know what grammar and rhetoric are. They don't know enough mathematics to teach even elementary math--they have no understanding of why arithmetic, fractions, decimals, etc. work the way they do. And they have already become the masters teaching the new apprentices, so the lore of what needs to be done is gone except for a couple outposts here and there. Those outpost can't fix what's wrong though.

For an individual school to fix these issues is possible. A school with high expectations, high skill and knowledge by its teachers, a willingness to admit the problems and fix them, a willingness to pick good textbooks, and a shared vision of success can do it.

I don't think any larger unit can fix itself.

It will take several years after the ed schools collapse and real people with real knowledge enter the schools for them to notice that they need to find out how to teach reading and math. Then, they may be able to reinvent or rediscover synthetic phonics, grammar, rhetoric, handwriting, coherent mathematics curricula, etc.

I don't think we have that much time.

Glen said...

If you could create your own school, staffed by teachers trained in your own ed school, free of external political limitations, what would you teach and how would you teach it?

kcab said...

Katherine, I'm curious about the same thing as jtidwell - did you see any tendency toward rigor, rich content & high standards? I know a few parents of G/T kids in my district (in CT) who push for those, but most seem happy with just the pullout enrichment.

Katharine Beals said...

"did you see any tendency toward rigor, rich content & high standards?"

Not in the talks themselves (and none of the talks were given by people who identified themselves primarily as parents). The conversations I had with parents were specifically about math, and here there was at least some concern about higher standards.

But again, the conference was overall more psychologically than academically focused, and this may have created a selection bias among attendees (as well as in the membership of this organization).

I've also wondered whether the more academic of children are less and less likely to be identified as gifted as there's more and more priority given to things like sociability, "creativity," emotional maturity, and organizational skills in the admissions process for gifted children. If those most invested in gifted programming--the insiders-- have children who are in these programs for reasons other than academic achievement, academics may not be their top priority, and some of them may want to keep out those for whom academics is a priority.

It's interesting how there doesn't seem to be a national organization for parents of gifted children that is academically focused. I think that says a lot about our society and its priorities. (It's interesting to compare NAGT with its Canadian counterpart).

SteveH said...

There is also the low end cutoff point for the "T" in G/T. This is not some magical point of academic discontinuity, so maybe people try to find other, fuzzy justifications for a separatate educational path. I might agree with this for the truly gifted, but for those, I would recommend carefully-selected individual tutors or mentors. For all others, I see a need for academic speed, rigor, and depth that should not stop at the low end of "T". It should be integrated in with the normal K-8 curriculum. If most schools are crippled with full-inclusion and low NCLB goals, I don't see a solution.

"I don't think any larger unit can fix itself."

The only potential solution I can see is if a school brings in math specialists for K-8. This was mentioned once at KTM. Does anyone have a link to a school system that has done this? This doesn't guarantee that EM won't be used, but there might be a better chance of eliminating those K-6 teachers who create problems.

Anonymous said...

"It's interesting how there doesn't seem to be a national organization for parents of gifted children that is academically focused. I think that says a lot about our society and its priorities."

Or about the willingness of parents to join such an organization.

-Mark Roulo

jtidwell said...

"I've also wondered whether the more academic of children are less and less likely to be identified as gifted as there's more and more priority given to things like sociability, "creativity," emotional maturity, and organizational skills in the admissions process for gifted children. If those most invested in gifted programming--the insiders-- have children who are in these programs for reasons other than academic achievement, academics may not be their top priority, and some of them may want to keep out those for whom academics is a priority."

Gah.

I'd love to find the K-6 "steep slope" that SteveH talks about -- I was lucky enough to have it, and I want it for my kid.

I'm almost willing to make the following commitment: if I can find 10 to 20 Boston-area parents of young gifted kids who want a rigorous and content-rich academic program, I'd like to talk to them about a homeschooling coop. (Or not even gifted, but at least motivated and somewhat quick at reading and math.) In my daydreams, I'd like to hire a very experienced old-school teacher for such, one who can put together a terrific curriculum for these kids and manage their individual paces.

(Either that or hunt down a classically oriented private school that's not outrageously expensive.)

Crimson Wife said...

Isn't there already a gifted co-op called Voyagers near Acton, MA? At least there used to be several years ago.

Bostonian said...

Katharine Beals wrote:

'I've also wondered whether the more academic of children are less and less likely to be identified as gifted as there's more and more priority given to things like sociability, "creativity," emotional maturity, and organizational skills in the admissions process for gifted children.'

If you admit children to gifted programs based primarily on scores of well-established IQ tests such as the WISC or Stanford-Binet, the gap of 1 standard deviation between whites and blacks and 2/3 SD of between whites and Hispanics means that whites (and Asians) will be greatly "over-represented", as will children of parents with college and graduate degrees. The fuzzier criteria you listed are easier to fudge in order to get "diversity" in a gifted program. Lots of strange educational practices make political sense as ways to avoid the reality of The Bell Curve.

Allison said...

--Isn't there already a gifted co-op called Voyagers near Acton, MA? At least there used to be several years ago.

Yes, but I wouldn't call it a coherent or rigorous curriculum. It might be engaging, but it won't make up for gaps in depth of math, reading, writing, history, or science in elementary grades.

http://www.voyagersinc.org/wiki/bin/view/Fall2010/WebHome?sortcol=2&table=1&up=0#sorted_table

D said...

Have to agree with Bostonian, but beleive the schools are deliberately setting up the scenario. What if the incoming preK children with good memory skills, high visual/spatial ability and low math knowledge were allowed into a real K-5 math course instead of the inclusion course? The result would be children who were competitive with the privately tutored children who do have less ability but more resources. As it stands now, in districts like mine, the poor lose out because they have no access to most of the grade level curriculum. It's no suprise that honors is filled with teachers' children....their parents have the in on the curriculum, the testing, and the bucks to provide the qualified tutor.

lgm said...

ooops, that was me, lgm not used to this laptop and touchpad....apologies.

lgm said...

Back to the original post.
Students that understand place value can use other bases. Back in the days of New Math, this was opportunity was offered to everyone in reg ed upper elementary , not just those politically chosen for G&T. Wish I had those textbooks.

Perhaps we need to campaign for a Mars Mission to restart Math & Science education as a serious essential. Up here, IBM made an attempt to get their math competent scientists/engineers into public school teaching..they were soundly rebuffed. That tells me that parents are on their own if they want a real math education.

http://www.howtoons.com/?page_id=1310

Katharine Beals said...

"Up here, IBM made an attempt to get their math competent scientists/engineers into public school teaching..they were soundly rebuffed."

lgm, please tell more! How were they rebuffed, and what reasons were given?

SteveH said...

Give me a high 31. How about a 132. This should be good for a week of wasted "hands-on" math class time.

lgm said...

An attempt was made at an offical alternative path to teaching certification, since many engineers and scientists do have the content knowledge to teach many of the science and math courses NY requires at the high school level and many have taught the same courses as adjuncts at community colleges. Some also teach classes such as intro to statistics and economics within the company. Answering the question of 'why do I need to study algebra? what good is it?' certainly would not be a problem.

The rebuff was that content knowledge is not enough and OJT in adolescent behavior is not good enough..certification -- i.e. a full blown M.A. or M.S. in teaching is req'd. This was seen as a money grab and union block as a practicing physicist would not be allowed to teach a 17 year old high school physics, despite years of teaching 18 yr olds in night CC physics courses and cutting edge knowledge of physics (which certainly isn't what a typical high school physics teacher can offer).

Right now in NY there is no fast tracking an engineer or scientist into teaching via an alternative certification program. The legislature earlier this year gave alternative programs a little more freedom:http://www.nytimes.com/2010/04/19/education/19regents.html?pagewanted=2

Hainish said...

NYS does have a sort of alternative certification where you take 21 credits and get an "Initial Certificate." It's not exactly a *fast* track--It took me a year, including a summer--but it isn't a full-blown M.S., either.

Of course, NYS doesn't make it very easy to figure out what your options are if you want to teach.

lgm said...

A NYer with a BS or BA can also step into a classroom and begin teaching right away as long as the principal wants him & he begins a program toward the master's degree in teaching. I've known a few people to segue into a second career this way via Western Connecticut's grad offerings. I've met a few also that have decided that it's not for them, and are glad they were able to get into the classroom and find out early in the career changing process.

K9Sasha said...

We've eaten the seed corn for K-8 education. That's already happened. ... And they have already become the masters teaching the new apprentices, so the lore of what needs to be done is gone except for a couple outposts here and there. Those outpost can't fix what's wrong though.

I just got back from an International Dyslexia Association conference. These are the people who believe in direct, systematic, intensive, explicit, and comprehensive instruction in reading. As I looked around, I saw almost no 20 and 30 year olds, and very few younger than about 50. Explicit instruction is going the way of the dodo.

K9Sasha said...

I've also wondered whether the more academic of children are less and less likely to be identified as gifted as there's more and more priority given to things like sociability, "creativity," emotional maturity, and organizational skills in the admissions process for gifted children.

I thought things like sociability (with average IQ students who do not think as quickly), emotional maturity, and organizational skills are some of the things truly gifted students, as opposed to high achieving students, don't do well. Hoagies website talks about this, among many other things, and is a wonderful resource on giftedness.