Comments

Catherine --- awesome post.

Something to cling to.

-- CarolynJohnston - 28 Sep 2005

I can't believe it took me this long to finally get this up (obsession strikes: I wanted to do it justice.)

There's so much more, too.

But let me tell you, that moment was a turning point.

Your post about having a math brain is the exact same thing.

Ed almost didn't believe me this morning when I was telling him about it. His life, in many ways, was determined by his perception that for a 'math brain' engineering is easy.

-- CatherineJohnson - 28 Sep 2005

I still have to remind myself that this is what I believe.

Because like everyone else in America (just about) I don't really believe it.

I believe in math whizzes & math-isn't-his-thing.

-- CatherineJohnson - 28 Sep 2005

I don't know. I think our problems in math education are a walk in the park compared to what passes for English language instruction nowadays. We might have "fuzzy math," but they have "whole language" and it's evil twin "balanced literacy."

If I knew how to post pictures, I'd post a chart of mean SAT scoes I found going back to 1960 which show a big dip in math scores but a huge dip in english scores. And, while math scores have recovered somewhat in recent years, English scores have not improved one iota. In the 1995 recentering, verbal scores got an across the board boost of something like 80 points (almost an entire standard deviation). So if I want to compare my pre-1995 verbal SAT scores to someone taking the SAt today, I get to add 80 points to my score.

The critical period to watch is grades 4-6 when the students are getting out of the controlled readers and into real reading. That's when the problems start to surface.

-- KDeRosa - 28 Sep 2005

KDeRosa - this is true, but it's also a lot easier for parents to (a) recognize that their kids can't read, and (b) supplement their schooling to teach them to read.

With math, parents seem much more willing to throw their hands up and say, "this is too hard for me to help my kids with," or, "I never understood math either." I work at a very large, prestigiuos public accounting firm, and I'm shocked at how many smart, educated parents here express similar sentiments. I'm never sure how to respond to that; I can't think of anything to say that doesn't have me come off sounding like an egotistical ****head. The best I can come up with is to point them towards the Saxon or Singapore Math websites.

Fuzzy reading is just as bad as fuzzy math, but it seems like the effects can be mitigated just a bit more easily. At least, for educated and involved parents; poor kids get hosed both ways.

-- IndependentGeorge - 28 Sep 2005

I don't know. I think our problems in math education are a walk in the park compared to what passes for English language instruction nowadays. We might have "fuzzy math," but they have "whole language" and it's evil twin "balanced literacy."

Catherine was telling me the other day that whole language was pretty much put to death singlehandedly by a (government?) crusader recently who traveled the country publicizing a large study that showed that whole language sucks.

I think that math ed is the frontier at this point.

-- CarolynJohnston - 28 Sep 2005

Well, from personal experience, I can state that there are young children who love math and would pursue it even when given other options. Both my husband and I were like that as children.

In 2nd grade, my teacher had a supply of "scratch paper" that we could draw on. I flipped a page over, and discovered that it was a math worksheet for 3rd grade. I was so excited! I had great fun struggling through it.

In 5th grade, I was thrilled when my teacher was throwing away old math workbooks at the end of the year and let me keep one. I spent some of my free time during the summer doing fraction and protractor problems just for fun.

I think what I love about math is how orderly, precise, and objective it is. As a small child, I had a very strong sense of what was "fair", and math was consistent and predictable to me, unlike adults.

-- AndyJoy - 28 Sep 2005

Actually, KDeRosa's right about the 4th grade slump; that's exactly the point to watch.

Christopher stopped reading at that age; I've talked about it before.

I think we fixed that with Megawords (which caused me to develop my theory about second-stage phonics, spelling & reading skills....)

I'm skeptical about the increase in math scores, though, partly because of Loveless' report on fractions being taken off the NAEP tests.

Across the board, everywhere I look, I hear & see that 'math scores are rising,' and this always includes schools like KIPP, where they do wonders bringing up the math scores of disadvantaged kids, but don't do so well bringing up their reading scores.

I've come to think this is probably because everyone's math performance is so poor that disadvantaged kids don't have as far to go on math as they do on reading....

Another anecdotal factoid: NY state tests.

In Christopher's class of 19 kids, 2 got 4s on the ELA section. 5 kids got 4s on math. One of the teachers who graded it said the ELA section was much harder than the math.

This is all pure anecdote.....but it's hard for me to believe that 'math scores are rising.'

(He's right about the recentering. My verbal on SAT shoots up to 790 under recentering. Math didn't budge.)

-- CatherineJohnson - 28 Sep 2005

KDeRosa

If you send the chart, I can post it.

I LOVE graphics.

-- CatherineJohnson - 28 Sep 2005

Independent George

I work at a very large, prestigiuos public accounting firm, and I'm shocked at how many smart, educated parents here express similar sentiments.

I hear this from everyone.

It is a huge problem.

There's no one breathing down the schools' necks to improve math ed, because parents are so intimidated themselves.

I'm one of about 3 moms (and dads) here in Irvington willing to tackle the monster head on--and of course I'm so intimidated I felt I needed to re-learn the entire subject A to Z in order to help my kid do his homework!

-- CatherineJohnson - 28 Sep 2005

I'll rustle up something on Reid Lyon & the NIDHD research on reading.

Constructivists all want to continue doing whole language, but it's going to be VERY hard to bring it back full-tilt.

Still, the grade 4 slump is very much with us.

-- CatherineJohnson - 28 Sep 2005

Andy

I met a mom the other day who said the exact same thing. She hates Trailblazers because of the multiple answers. She said when she was a kid she loved getting the right answer.

Everyone loves that; it's universal.

That's one of the things that bugs me most about the constructivists, which is the pride they feel in stripping math of one of its primary pleasures for young children--while calling math worksheets 'drill and kill.'

-- CatherineJohnson - 28 Sep 2005

I'm taking a class entitled "Math for Elementary School Teachers" for personal enrichment, as I intend to home school my children, and want to get some pointers.

My teacher is AWESOME. She seems to have an incredibly balanced view of teaching math. I don't know precisely how others here would define constructivism, but the way she explains it (or her application of it) is very logical and practical. BUT, she also is a big fan of "drill and kill" math as well.

I don't think she knows much about the extremes to which constructivism is currently taken, however. She defines it as building on the knowlege kids already possess. For example, instead of introducing multiplication as facts to be learned by rote, model repeated addition or "3 groups of 4", since children are already familiar with this. Don't introduce the list of facts until after they grasp the concept, then make sure they memorize them and can recall them quickly without having to "build up" to the answer every time.

Can someone explain extreme constructivism to me? Is the problem that proponents never want to introduce the standard algorithim for a problem or make children memorize facts?

-- AndyJoy - 28 Sep 2005

I assure you whole language is alive and well in almost every school district in the US. They just don’t call it “whole language” anymore, they now call it “balanced literacy” which, in theory, is supposed to be a balance of whole language and phonics. They made this concession because the National Reading Panel went through all the ELA research threw out 90% of it because it was junk and the remaining 10% clearly showed that phonics won. So now every ELA curriculum includes “phonics.” As long as you don’t look too close, at least to the untrained ear. There is a good kind of phonics (direct, systematic, intensive) and a bad kind (implicit, embedded). Guess what kind gets taught in most schools.

So when Singapore math finally wins the math wars, be on the look out for “balanced math” – constructivist math with some extra drill worksheets thrown in.

-- KDeRosa - 29 Sep 2005

"Can someone explain extreme constructivism to me?"

no.
it's an eternal mystery like the trinity or something: a
"those who know, won't say; those who say, don't know"
kinda thing. anyhow, all credible commentators
seem to agree on one thing:
it's an epistemological position
and as such, has very little to say about
pedagogical issues (elementary ed, in particular).

if, ghod knows why, you want to tap the source,
my impression is that the name you want is
ernst von glasersfeld; from there on you're on your own.

-- VlorbikDotCom - 29 Sep 2005

Hi Andy

I'll try to get to a post about radical constructivism versus smart constructivism (actually, I think I wrote at least one already).

Smart constructivism does have a strong focus on figuring out where a child is, what he knows (both what he knows that's correct and what he knows that's incorrect) and working from there.

I'm not sure how much emphasis 'smart constructivism' places on discovery learning at all, as a matter of fact.

-- CatherineJohnson - 29 Sep 2005

So now every ELA curriculum includes “phonics.” As long as you don’t look too close, at least to the untrained ear. There is a good kind of phonics (direct, systematic, intensive) and a bad kind (implicit, embedded). Guess what kind gets taught in most schools.

Well...that's depressing, and I hope it's not quite as true as you think.

Although, given our family motto, I probably shouldn't hold out a lot of hope.

Nevertheless, I believe--without having any particular evidence to offer at the moment--that when you change the discourse you do change the practice to some extent.

The words 'whole language' are now illegal, and this is one case in which I heartily endorse speech codes. (There's actually some interesting writing out there about what happens to racism when it becomes illegal to express racist sentiments publicly.....it gets weakened)

Parents universally believe in phonics (I think), and universally say so (I think), and universally expect to hear their Kindergarten & 1st grade teachers Speak Of phonics, AND, last but not least, universally expect their kids to be reading at the end of 1st grade. (That's way more unsupported assertions than I have any business making. sigh.)

The kids here are all reading, that's for sure.

-- CatherineJohnson - 29 Sep 2005

But, yes, when Singapore Math wins the math wars it'll be balanced.

I think we can count on that.

Have you read the AIR report on Singapore Math??

Every five seconds the thing pauses to say that PRIMARY MATHEMATICS doesn't teach enough real-world mathematics.

This is a grave weakness.

-- CatherineJohnson - 29 Sep 2005

"So now every ELA curriculum includes “phonics.” As long as you don’t look too close, at least to the untrained ear. There is a good kind of phonics (direct, systematic, intensive) and a bad kind (implicit, embedded). Guess what kind gets taught in most schools."

"Well...that's depressing, and I hope it's not quite as true as you think."

Our public schools use "balanced literacy" with direct phonics as a last resort. When my son was entering Kindergarten, someone asked whether they use Whole Language at the school. They said: "Oh no! We use balanced literacy." End of discussion.

"So when Singapore math finally wins the math wars, be on the look out for “balanced math” – constructivist math with some extra drill worksheets thrown in."

Balance. They argue with generalities, but then they decide on the details.

-- SteveH - 29 Sep 2005

What they've done with the word "phonics" is both devious and Orwellian. Now, they are able to tell the parents "oh, sure we teach phonics" without really teaching any. Check out www.nrrf.org for the whole story.

I have both a math and a reading anecdote to horrify you with on my son's first month in kindergarten this year. Just remember that the plural of anecdote is not data.

Math: Having seen the dreaded buzzword NCTM on the cryptic kindergarten curriculum hand-out, I knew it was going to be a constructivist laden curruculum. But, I thought that they'd have to start out with some basic arithmetic, like addition within 10. Wrong. His first assignment was graphing the shoe sizes of all the kids in the class. This must be what they mean when the say "real world" math, as long as the kids grow up to be cobblers.

Reading: "Balanced Literacy." First assignment: Kid Writing. Write a sentence about someone -- any words you don't know just put a dash. This is before the kids had been taught a single letter of the alphabet, much less a word. It's like handing a kid a violin and asking him to play a song without ever learning a single note. Two weeks later they learned their first letter -- A -- without learning its sound.

-- KDeRosa - 29 Sep 2005

I've read the AIR study. Did you notice how when they claimed how much better the US curriculum taught real world math and improved creativity they conveniently forgot to provide any supporting data?

It is eerily reminiscent of what was done when Direct Instruction thoroughly trounced all the other ELA curricula in Project Follow Through in all the academic measures. Subsequent reports always stressed however how the other curricula had improved self-esteem or some other nonsense factor. Nonetheless, this was sufficient for the study to recommend all the curricula, even the ones that underperformed the control group – like whole language.

-- KDeRosa - 29 Sep 2005

You must live in our town.

Go home and ask your family what their favorite ice cream is. Draw a picture of each ice cream cone and put the number next to it. Forget the fact that the sample size is meaningless. They never even said a word about why you would want to do this in the first place. I had to explain to my son that if he owned an ice cream parlor, he might use this information for ordering. Rote data collection substitutes for math.

My son's Kindergarten teacher was not happy when I naively commented that I was giving him math worksheets (from SuperKids^?). I would leave them on the table, he would walk by, and sit down to do the problems. He loved it. She probably thought I was harming him.

Kids Writing/Journal! Draw pictures and write some words if you can. You will get a gold star for all of your creative Kids Spelling.

I thought they would teach him how to hold a pencil properly. No. Four years later and it's still a problem.

-- SteveH - 29 Sep 2005

What is it with this infatuation with data collection and graphing?

Of course, the supreme irony is that it is coming from a profession that is incapable of conducting a valid scientific experimentation itself.

-- KDeRosa - 29 Sep 2005

Andy

Here's a pretty useful post (if I do say so myself) on radical constructivism versus smart constructivism:

smart constructivism

Here's a line from the National Research Council's How People Learn:

A common misconception regarding 'constructivist' theories of knowing (that existing knowledge is used to build new knowledge) is that teachers should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves. This perspective confuses a theory of pedagogy (teaching) with a theory of knowing. Constructivists assume that all knowledge is constructed from previous knowledge, irrespective of how one is taught (e.g., Cobb, 1940)--even listening to a lecture involves active attempts to construct new knowledge.**

And here's my favorite radical constructivist line:

It is possible for students to construct for themselves the mathematical practices that, historically, took several thousand years to evolve.

-- CatherineJohnson - 29 Sep 2005