kitchen table math, the sequel: end brain-based education now

Saturday, June 7, 2008

end brain-based education now

Paula V sparked my interest in reader Comments on the algebra-in-8th story.

Here we go again:

Here's the thing. According to Piaget, the formal operational stage doesn't even begin to develop until students are of high school age or even older for some. Oh, and formal operational means that a person can think abstractly. And the ability to think abstractly is important if you are going to learn algebra because algebra is all about abstraction. So what are we really teaching? If a child is not yet ready to think abstractly, are we really teaching anything or are we doing harm? We are asking students to learn things they are not ready to learn. How can that be good? Oh, and here's another thing, not everyone ever enters or completes the formal operational stage of development. So how much algebra will that person ever learn?
6/5/2008 6:22:50 PM
Its amazing that people are able to make statements like these without reference to actual living, breathing, math-learning (or not), flesh and blood children.

Supposing Piaget did say 8th graders can't learn algebra.....(did he?)....shouldn't we ask ourselves how it is exactly that 8th graders everywhere else on the planet are able to learn algebra while American kids are not?

How long ago was Piaget debunked, anyway?

News travels slow in the edu-world.

The belief that children of particular ages cannot learn certain content because they are "too young" or "not ready" has consistently been shown to be false.
National Math Panel Fact Sheet

this one's fun:

Welcome to America....where people are actually having a serious discussion about whether teaching kids advanced math as soon as possible is a bad thing. Is it any wonder our country lags behind in math/science?

and this one:

It's surprising to me that it pushing to take Algebra I in the 8th grade is thought of as acceleration and that some parents in Montgomery county are resisting it. My dad went to an inner city black school in a southern city in the 60's and he took algebra in the 8th grade and took calculus before he graduated high school. Yet, Algebra I wasn't available to me in the 8th grade in a rural school many years after integration, and I ended up having to double Algebra II and Geometry my sophomore year in high school in order to take Calculus. Somewhere along the line we slid backwards. None of this stuff is advanced math. Just the basics American students will need to be competitive on the world scale in Engineering and Science.


here we go, "freakshow stage parents" -- good one!

This all seems analogous to the freakshow stage parents who pressure their kids to succeed in spelling bees and beauty pageants so they can brag on their kids to their friends. Seriously, do any of you out there remember anything past Algebra II who aren't currently in an engineering field. I use high-end statistics daily and got very limited exposure to it until grad school. My thought, pipe down a bit on the rush to calculus...there is plenty of time for that in college; rather focus on stats since it seems like analyzing data has permeated into lots more fields than in the past. Performance indicators and measurement are the next trend in management and should receive more attention than calculus in my opinion. Many old school managers rarely used math to make decisions whereas now managers are responsible for developing systems and metrics which can quantitatively track progress toward stated goals and objectives.

reading right along.... another Piaget comment from a physics teacher, no less. I'm not cutting and pasting any more from JP.

sigh

Piaget has a lot to answer for.

from France:

I went to a French boarding school through 10th grade (troisieme in their parlance). Upon returning to the United States I spent two years reading French novels in the back of the class, raising my hand and going to the blackboard only when others couldn't solve problems being discussed in class. I didn't do any homework either, and graduated only because the teacher who announced a week before the end of my senior year that he was going to grade us 50% on the year's homework got called to a conference, and ended up grading us only on tests.

I can't see that allowing students to take more demanding courses is a bad thing.

Here's the one Paula quoted:

So Prince William county is slowing their kids to a crawl with Investigations while the neighboring counties are moving their kids ahead at a faster pace.
We really need a national math curriculum.

Slowed to a crawl. Yup.

The help-with-homework issue rears its ugly head:

Many decades ago, I minored in math. I can still use the stuff, too. But I work with lots of people educated in social science and humanities who can't deal with fractions or proportions, let alone scientific notation or long division of polynomials.

Given that these educated people are parents, what are the chances that the average parent will be qualified to help their kids with math homework in the grades?


I know the answer to that one.

Slim to none.

Next:

"Accelerated Math Adds Up To a Division Over Merits"

Yes, you're so right, I just think that Albert Einstein kid was a little too "smart for his britches" and should have been held back a couple of years!

That would have made it much fairer for the other students in his classes.

Another Stop Manic Moms and Dads! sentiment:

The issue here is not whether children should or shouldn't be in accelerated math programs, it's whether parents should be allowed to pressure teachers and administrators. Children should be placed based on performance only to prevent manic moms and dads from pushing their children beyond their level.

This is a big one around here.

For years we were told that the accelerated math class was filled with "kids who don't belong" and got in thanks to "pushy parents" etc.

That particular meme went splat after the district clamped down on the pushy parents and required all the kids to test into the class. The first placement test was Top Secret; the middle school refused to show a copy to the 4-5 teachers in order to prevent them from prepping their students. The goal was to cut kids from the track, not help kids get into it, so the grade school teachers had to be kept in the dark.

Lo and behold, the kids who tested in fair and square also had a he** of a time of it.

C. was one of them.

Moving right along:

american grade school math has always been a sad joke. Europeans learn algebra+geometry in 7th grade. I support accelerated math.
and:
The advanced part isn't what is new, it is the quotas (80% of 8th graders are expected to be in Algebra) that are new.

Pushing the regular kids into advanced math is just as bad as keeping the advanced kids in regular math.

Why can't we just teach them what they are ready for? (because we don't have the time or money to teach individuals in our school system)

That's sure my beef.

Next:

Back in the 1950's I went through an accelerated math program like the one described here. The idea can't be all that new.
Things went downhill fast after the 1950s. See: The Race Between Education and Technology.

old chestnut:

I would forewarn the stories from Japan with their relatively high suicide rate of children from the pressure brought to bear on them to excel, mostly for the parents sake rather than the childs.

There isn't any higher teen suicide rate in Japan.

There is a higher teen suicide rate here. (see: Stigler, The Learning Gap)

"My wife is a teacher. Everyday, she sees pushy parents who insist that their kids are "gifted." It's a disgusting conceit on the part of loser parents who want to pretend that their failures can be fixed by their kids"

I think it works both ways. Teachers will hold truly gifted children back. My daughter was tagged as "gifted" through testing and I put her in an accelerated math program outside of school (loving it doing well too), but her school is refusing to commit to placing her in the high level math class. This is private school and they are control freaks. I'm thinking of putting her in public school where it sounds like she'll get more of an appropriate education.

And really, most parents want what's best for their child so your comment is rather inflammatory and I'm sure untrue.


Pushy parents! Holy moly, life would be good without pushy parents, for sure.

Having taught pupils of many nationalities and from widely varied backgrounds, I would affirm that children from the U.S.A. are extremely backward compared with others around the world, resulting in widespread adult ignorance. Some pushing along would certainly not come amiss!

Here's the full version of the pushy parent quote:

According to the article:
"I think parents of what I call above-average to gifted kids . . . were all saying, 'Our kids are bored,' " said Louise Epstein, a Fairfax mother and president of the Fairfax County Association for the Gifted.

My wife is a teacher. Everyday, she sees pushy parents who insist that their kids are "gifted." It's a disgusting conceit on the part of loser parents who want to pretend that their failures can be fixed by their kids.

Get a grip--suck it up. If your kid can hack it, all the better. I'm concerned that teachers, beaten down to nothing, will submit, merely to survive to the next paycheck.

I for one am not remotely concerned that teachers will "submit." They won't. History tells us this is true.

Will they feel beaten down & survive from one paycheck to the next? Yes. Algebra in 8th grade will, like everything else in the edu-world, be implemented from the top down with teachers being handed heterogeneous groups of kids half of whom won't remotely be ready to learn algebra. It will be a miserable experience.

That's not because of pushy parents.

That's because of pushy administrators.

Pushy parents have even less control over the administrative practices of public schools than teachers do.
Grade level math might be better termed decelerated math. I remember 4th-7th grade math as utterly boring and repetitive. Algebra got me interested again--in the 8th grade. I would have enjoyed an earlier shot at it.

and, last word:

Isn't there time in high school for advanced math? I don't remember doing much algebra in grade school (grades 1-8), but in my prep school we were required to take algebra I, algebra II, geometry, trigonometry, calculus I, and calculus II. In other words, I was always in a math course, all the way through high school. I didn't like any of it, but I had no choice.

Still, I guess it was good for me, as I could always count on a 99th percentile score in any standardized test I took. SAT, GMAT, etc. Isn't that good enough?

I say let the parents/kids chose, at least for the grade school kids.

20 comments:

Tricia said...

What we know from current research is that experience, not age, is what allows students to move on to more sophisticated concepts. They simply must be exposed to the ideas, and the earlier the better.

We may not call it algebra in first grade, but those missing addend problems require algebraic thinking. The empty box in the problem stands in for the more traditional variable ("x"). It's not as abstract, but no different in approach. We solve by subtracting, just as we do when we isolate the variable.

Tricia said...

Sorry, I must add a post script to my last comment, particularly after reading all the comments about this issue.

I work with a grant funded program that provides five week of intensive summer study to urban middle school kids in an effort to prepare them for algebra and earth science in grade 8. Putting them on this "accelerated" track is the only way to prepare them for A.P. classes in high school, particularly if we want them to consider studying math and science once they get to college.

There is simply no reason for postponing algebra instruction until high school, and for kids with college aspirations, it's simply a bad idea.

ChrisA said...

Well I don't know whether to laugh or cry, but I am glad I took my blood pressure pill!

I would like to point out that there are similar idiots over in the UK that want to stop teaching academic subjects that are "middle class".

http://joannejacobs.com/2008/06/06/unsustainable-schooling/

You just can't make this stuff up. Speaking of making stuff up, this is slightly off topic but still illuminating...

http://rightontheleftcoast.blogspot.com/2008/06/id-have-canceled-play.html

Is there a way to make these links show up as "clickable"?

Instructivist said...

[I would like to point out that there are similar idiots over in the UK that want to stop teaching academic subjects that are "middle class".]

This prof who is advising the government doens't want any academic subjects taught. Why the government would hire this clown to advise them is a mystery.

Link here:

Brain-dead education now

Read the comment from soneone from "Teacher Leaders Network." This leader thinks the ignorance-peddling prof is a visionary. She uses Schopenhauer to make her case. Hilarious!

Anonymous said...

Mathematics is a continuum!

I think we'll wake up one day to find that lumpkin school oganization is the greatest crime of the 21st century.

Each kid should be delivered individualized instruction that empowers him or her to go at her own pace, wherever it goes. We were able to do it in the 19th century. In the 20th century we blew the model up. In the 21st we have technology to help us get back to that model but we only use it to make more lumps.

Anonymous said...

One aspect of algebra that is entirely missing in this and other threads is the importance of algebraic notation. It's also entirely absent in Investigations and most of CMP (parts come into play in grade 8).

I've always understood math as a language. It has its vocabulary and spelling (arithmetic), sentences (equations), and composition (problem solutions). Early algebra should focus on the syntax that is the notation used to communicate a solution. I'd be happy if any algebra course spent more time on this. I don't see teachers that know how to do proper notation in pursuit of a solution and it certainly isn't in texts (they don't have real text anyway).

This results in solutions that are unreadable mush. Not surprisingly kids struggle with the 'math' in algebra when they don't have the composition tools. The lack of tools imposes a lack of organization, death in higher mathematics.

This is a fundamental skill that is not taught unless you luck out and get a teacher that is passionate about it.

SteveH said...

The greatest crime is low expectations.


"We were able to do it in the 19th century."

Really? Everywhere?


"In the 21st we have technology to help us get back to that model but we only use it to make more lumps."

I guess I don't have the same optimism that you have about technology. Lumps don't bother me. The problem is that K-8 schools are eliminating lumps and redefining education.

A main theme in many of the comments to the article is that schools get to decide what constitutes a proper education, not parents. Schools don't even want to allow (internal) choice in K-8. Will technology change this mindset?

I've commented before that this might happen under the guise of providing all students with an IEP. If schools (like ours) are big into differentiated instruction and teachers as guides on the side, then perhaps they would allow parents to select an individualized, computerized learning path that meets the needs of the child and the goals of the parents.

The problem is that one of the major goals of our school is socialization and working together in child-centered, mixed-ability groups. This is not impossible with individualized IEPs and computerized curricula, but many educators will just dismiss this model. They have different goals and they get to decide.

Then there is the issue of technology replacing the role of a good teacher and direct instructon. Is there any technology that can do that? I'll buy that software. Actually, there are a lot of good printed books and training material, but what is the educational overhead required per student? Technology can reduce that overhead, but how much educational burden does it place on a child without parental support? Schools will still be sink or swim models of education. Kids will be allowed to go at their own speed, but it will be really, really slow.

Technology is not going to change their assumptions, expectations, and desire for control.

Anonymous said...

The quote below is from the article "Why the Best Math Curriculum Won't Be a Textbook"

http://www.edweek.org/ew/articles/2008/05/07/36patton.h27.html?tmp=1040308925

"Given the action agenda set forth by the National Mathematics Advisory Panel, the time is now right to consider alternatives to the traditional publishing model. In an unchanged publishing environment, and with the same pressures to meet the needs of 50 states in a one-size-fits-all book, we should expect the same outcome: bloated, incoherent texts. Only by going digital can we integrate what Singapore does best—maintaining a tightly engineered, coherent core curriculum—with what America does best—inventing adaptations that better cultivate the mathematical genius of a large, diverse population."

There are some other VERY interesting points in the article with GREAT potential (imho) for improving mathematics education.

Correcting our failed "delivery system" in a transparent and non-profit way could provide many more opportunities for our children.

Maddy said...

This the crux for me -

"
Pushing the regular kids into advanced math is just as bad as keeping the advanced kids in regular math.

Why can't we just teach them what they are ready for? (because we don't have the time or money to teach individuals in our school system)"

That at the irony that 'the richest country in the world can't afford it,' I always love that one.
Best wishes

Anonymous said...

Maybe I was being too obtuse with my previous post. When I referred to lumps I was not refering to kids. I was refering to the lumps caused by arbitrary placement models. The lump is a group of 30 kids with a huge standard deviation put in an environment where a single teacher is assumed to have the superhuman ability to get to ALL of them ALL the time.

When I refer to technology I am not proposing some kind of robotic teacher. I am proposing tools that allow a single teacher to grasp where each kid is at, in real time, while at the same time having a means to present, over and over if necessary, professionally prepared 'lessons' on an individaulized basis.

The teacher's job is to uncover misconceptions, devise alternative representations, and perform the ongoing analysis to maximize the time kids spend in their own ZPD instead of the ZPD that was created for the median child who is not in the class.

The 19th century model that worked is the one room school house. Kids were moved along at their own pace. There were no arbitrary grade groupings. The older kids helped the younger ones (a fantastic learning paradigm). Most kids went just through grade 8 and I would bet large sums of money that most would blow away today's high school students in the three Rs.

Ari-free said...

High school math in America used to involve proofs. That part of math has also been watered down. It doesn't seem that even Singapore cares either. American math today is not so good but maybe we need to dig up our own old textbooks.

Barry Garelick said...

Gee, maybe somebody can ask Jerry Weast, the Superintendent of Montgomery County why they dropped the piloting of Singapore Math in that County. (See here. )

As for the elimination of proofs, you would think that the clamor for critical thinking would increase the demand for the teachng of proofs, but like everything else in edu-land, it's "critical thinking appreciation" rather than the real thing. As for using older textbooks, see here.

While there is some objection to the older texts as also having problems and being poorly written
they at least had some content, and time on task for basic skills and concepts by the way--not merely rote. Where they were lacking, they could be repaired, filled in, by a good teacher, even by the student himself if he was willing to think. Many of today's
books--even the traditional ones, not just the NSF-EHR grant-fed atrocities--force ignorance, on the teacher and student alike.

Ari-free said...

The philosophy of today's reformists is that everyone should be the same. There must be no competition. The higher skills are watered down so that *everyone* would have a claim to them and even parents of students with higher math ability are on board because they think they are getting a modern 21st century math education. The strategy of equalization works when you can even fool the best and brightest to give up their advantage.

ElizabethB said...

"Its amazing that people are able to make statements like these without reference to actual living, breathing, math-learning (or not), flesh and blood children."

I always joke about really poorly designed education products--that they must have been designed by someone who never even saw an actual child, let alone taught one.

Most of the best phonics programs were designed by people who had been working with ACUTAL CHILDREN and teaching them for years, observing what worked and what didn't and changing their program to reflect this.

Blend Phonics: free online at Don Potter's webpage, designed by a lady who taught for many years and was forced to come up with a good phonics method that would work in large (40+) classrooms.

Phonics Pathways: reasonably priced, designed by a lady who has been tutoring reading for 30+ years.

Pollard's Synthetic Series: free online at Google books (linked from my webpage,) a really fun method with songs and great pictures and explicit instruction on how to use it, designed by a lady who taught for many years.

Right Track Reading: Developed by a lady who tutored for years, reasonably priced online.

We All Can Read: Uses nonsense words! Developed by a man who taught many remedial adults.

I also like to joke that my phonics lessons are on version 10.2.6. (I actually don't keep track, they're always changing based on new students and new ideas. I'm in the middle of another revision now.)

And, an ACTUAL CHILD did great with Webster's Speller, it does get amazing results. He must have seen an actual child sometime, and maybe even taught one, or at least watched others teach with his Speller. One of his later Spellers talks about a decision to go with syllable division that reflects pronunciation instead of common dictionary division in his spellers, a decision made to help children learn to read and spell easier although they would not get the exactly correct syllable division that way.

ElizabethB said...

"Given that these educated people are parents, what are the chances that the average parent will be qualified to help their kids with math homework in the grades?"

"I know the answer to that one.

Slim to none."

The 3 most popular math programs for homeschoolers are Saxon, Singapore, and Math-U-See. Math-U-See has great DVDs to go along with the program. In the upper grades, most of the programs that are popular have some kind of DVD or CD-ROM.

I'd rather have a good program on DVD than a fuzzy math program taught by a real person who doesn't know much about math.

Although I'm qualified to teach up to Differential Equations (with a lot of brush-up) and worked as a statistician for 6 years, we're currently using Math-U-See with our daughter because it's working best for her. Next year we'll supplement Math-U-See with Singapore.

Note: we looked at our ACTUAL CHILD and selected a method that worked best FOR HER. If you had asked me when she was 2, I would have said, "we'll be using Saxon." (I hadn't seen Singapore Math then.)

I'm thinking Saxon/Singapore for our son, but he just turned 3. Right now, he likes to put the green units pieces from his sister's Math-U-See blocks on his fingertips and pretend he's a red-eyed tree frog. (Actually, she like to, too! It's quite funny, for some reason.)

Anonymous said...

In our district, the mathematically talented kids take algebra in 7th grade. This is about 14% of the population. The kids who are above average in ability take algebra in 8th grade. The below average students take it in 9th grade. I'm not sure about the kids who are right in the middle.

This seems to work well. Sometimes parents try to get their kids moved up or down a level, but most seem okay with this method of offering algebra.

Catherine Johnson said...

We may not call it algebra in first grade, but those missing addend problems require algebraic thinking. The empty box in the problem stands in for the more traditional variable ("x"). It's not as abstract, but no different in approach. We solve by subtracting, just as we do when we isolate the variable.

I'm glad to get your opinion on this.

I've always thought those problems were a VERY good idea. I first saw them in Saxon Math (though I believe Math Trailblazers has them).

C. learned inverse operations from these problems. He also segued easily to the idea of a variable.

His pre-algebra course was a miserable experience, but that was because of problems on the school's side, not the kids'.

Ari-free said...

Hi elizabeth. I've never heard of those programs before. I have just started using Zig Engelmann's "Teach Your Child to Read in 100 Easy Lessons" as it teaches everything involved in the reading process.

ElizabethB said...

Ari-

Teach Your Child to Read in 100 Easy lessons is good, one of the best conventional phonics programs out there, but it doesn't teach your child to read 3 and 4 syllable words like A Beka or Webster's Speller. (Webster's is free, the copyright has been expired for ages!)

My just turned 6 year old is now spelling at the 3rd grade level and reading out the KJV Bible after working through Webster's Speller this year, you can find out how to teach it here, it's really easy, 16 year olds taught it in the days of one-room schools:

http://www.thephonicspage.org/On%20Reading/webstersway.html

The Pollard series is from the late 1800's, most people haven't seen it! It's great, free online from Google books.

Blend Phonics was published in 1980 and is not commercially available, it is free online only, from Don Potter's Website, www.donpotter.org.

The rest of the programs are more recent, but most of them are not as well known as they should be, they're more effective than most phonics systems that cost far more.

Unknown said...

Not a problem, If your worry about Math then don’t worry about it, we learn Math with different very easy tools and methods. We have Online free Math Website for kids – to learn & Practice math skills. 2nd Grade, 3rd Grade,6th Grade kids for Add, Subtract,Math Multiplication, Multiply,Division, Algebra, Word problems, Worksheets and more which you want