Entries from ConstructivistTeaching

What makes this book so interesting is Ravitch's documentation that "Progressive" education has been progressing in the same direction for over 100 years. The same ideas are rediscovered again and again, and those seeking to reform American schools have been fighting the same bogeymen (drilling, teacher as "sage on the stage") with the same rhetoric (teach the student, not the subject) for just as long. The book is at its best in showing that these ideas have been recycled numerous times.

The math wars aren't going to be won; at least, not by us.

The math wars will go on and on, and will always be new, like an episode of The Twilight Zone.

We have to teach our kids ourselves.

And we have to find, or invent, the resources that will help us do it.

Susan just pointed me to the most amazing personal story at Illinois LOOP.

I'm bulletting the main points from the introduction for readability:

• author is a mother of 3 in a state that instituted progressivist reforms in the early 90's.

• she and her husband hold doctoral and masters degrees in non-education fields and provided their children an enriched environment

• all 3 children have professionally-assessed aptitude in the superior range.

• their complete reliance on teaching professionals and progressivist methods resulted in learning difficulties resembling those of the 'disadvantaged'.

• after-school remediation of elementary skills has, over the course of about 18 months, made significant improvement to the children's grade-level achievement and attitudes toward learning.

• family will now homeschool 2 of the children next year using the 'classical' method.

update

Read this:

By the end of elementary, we acknowledged to ourselves that something had gone badly wrong, though the causal link from early elementary instruction was not yet clear. It was easier to place blame on ourselves, on an exaggerated sense of homework neglect. Still, we took the precaution of moving the children to a private school billed as 'traditional' - only to eventually discover it to be an upscaled version of the progressivism offered at no extra charge by the public school next door. That discovery, too, was years in coming; I was so consumed with the career that paid the tuition that I barely took note of the continuing deterioration in scholastic achievement, much less delved deeply into the reasons why.

• parents knowing there's a problem, but not knowing what it is
  
  is it your child? (poor aptitude, 'average' ability, 'math-reading-spelling's not his thing,' watches too much TV')
  
  is it me? (didn't supervise the homework, wasn't paying attention, didn't read the stuff in the backpack)
  
  is it the teacher? (It didn't cross my mind that Christopher's problems in math might be related to the textbook until I tried to teach out of the it myself. And not until this year did I begin to perceive problems with the system (no core curriculum, no articulation between grades & schools, etc.)

• private schools just as pervaded by constructivist philosophy as public
  

update 2

What was it that finally broke through my unquestioning faith and mindless optimism? A recognition that certain elements of a 7th grade math program were badly askew, some research for purposes of a teacher conference, and finding the Mathematically Correct website. A binge of research ensued which continues to this day.

As full understanding of how progressivism had failed my children finally dawned, I was furious - more with myself than anyone else. But, I can no longer spare the emotional energy which anger consumes. It takes all I've got to stay attuned to three children from 3:00 to 10:30 p.m. sufficiently to correct Kumon math, direct grammar remediation, go over their SRA reading comprehension work, monitor the writing process program, and check assigned homework for the knowledge gaps which have undermined so much prior learning...and somehow attend to the non-tutoring aspects of parenting.

That is horrifying.

My perception—and I hope everyone will chime in on this—is that many parents hit the wall at the end of 4th or 5th grade.

I've heard through the grapevine that there are lots of unhappy 5th grade parents here thanks to the TONYSS tests.

(The TONYSS aren't mandated by the state, and aren't the same test everyone has to take in 4th and 8th. They're created by a private testing company, and purchased by individual school districts.)

The TONYSS are graded on a scale of 1 to 4.

Almost no one earned a 4 on the English language arts half. Only 2 children in Christopher's class of 19 kids got 4s, Christopher being one.

(Poor thing. Christopher's glaring, obvious talent in life is not math. It's history & social science. Not surprising given that his father is a historian.)

Back to the TONYSS. There were 4 or 5 kids in Christopher's class who earned 4s on math.

It sounds like a lot of kids who had been getting good grades all school year suddenly came up with 2s & 3s on the TONYSS.

I could be wrong about this.

But that's what I'm hearing.

For me, Christopher's '39' on Unit 6 at the end of 4th grade was a lucky break.

Even Christopher said the same thing last fall.

He actually said, 'If I hadn't gotten a 39 you wouldn't have started teaching me.'

Up til the moment Christopher came home with that 39 I had no clue there was anything wrong with U.S. education that couldn't be fixed by moving to a super-expensive suburb and paying a small fortune in property taxes to get small class size and high per-pupil spending.

When it came to education, the sum total of my sophistication was 'you get what you pay for.'

update 3

I've felt anger, but there are no easy targets. I knew every teacher and administrator involved. I knew that they had cared about my children and appreciated my work on behalf of the district; many of them are my friends. I saw them as well-intentioned, doing their best to use effectively the pedagogical tools to which they were limited by the progressivist reform vision that had been imposed from a policy level, one in which millions in professional development funds were being invested.

This is what I've come to realize: the problem is at the 'system' level...

You can certainly have a bad teacher; I think we've had one so far. (She was a terrific lady; I feel bad saying anything publicly. But she didn't seem to be able to teach math out of the SRA book, something I couldn't do, either.)

I love this, too:

If I have anger left for anyone, it is the educationalists who control accreditation standards that shape teacher training and professional development, and incidental to such, education policy.

[snip]

...for all their power to effect or impede change at the critical level of teacher training, this is the last group to feel the heat of public accountability. They will never have to confer with the parent of a 4th grader who can't read. They will never see a performance review based on the achievements of their students. They will never face the electorate with their records. And they are, in a practical sense, insulated from legal liability for malfeasance.

Moving to a leafy suburb with well-funded schools does not guarantee the best education for your children.

Personal Stories of parents

Can children make up for lost time?

Some of the most hair-raising stories I heard from Carolyn were about college kids who simply could not learn algebra because they didn't get what they needed in grade school mathematics.

Carolyn made me wonder whether there might be a critical period for learning math the way there is for speaking a foreign language without an accent.

I've come to think there isn't, mainly because I find it possible (and pleasurable) to learn math as an adult, and I don't think I'm unique.


I started thinking about this because last night I did an impromptu interview with my cousin who, it turns out, pulled her daughter from public school because of a wretched experience with Everyday Math. (I'll post it shortly.)

Her daughter used Everyday Math for 3 years, from 2nd to 4th grade.

Then it took her 'several years' to make up the lost ground.

She just finished her freshman year in high school, and is doing great in high school math. (Her private school used Saxon.)


I talked to another woman who pulled her son out of the Tribeca schools because they use TERC.

He's now high school age and still doesn't have rapid fluency with his math facts. (She spent a lot of time working with flash cards, too. Another flash card failure.)

How can we remediate kids who've fallen behind because of constructivist math?

two immediate thoughts

To me, it seems like it has to be possible to make up lost ground more quickly than this.

At least, I hope so.

Here are my first thoughts:

• remediation has to mean doing timed worksheets every day, day in and day out, until the child or young adult has his calculations down cold

• remediation also means doing story problems every day, day in and day out (probably a coherent sequence of story problems, like those in the Singapore Math Challenging Word Problems books) [I have no idea how many story problems to do per day]

• finally, remediation may mean that you need to back up to the beginning of math, or close to: back up to content well before the point where the child became lost--and move quickly through a coherent 1st, 2nd, or 3rd grade curriculum, regardless of the fact that the child or young adult already 'knows' most of the material

update: Department of Corrections

Thank you, David! (For everything you do.)



All of us should keep this handy, because none of these programs ever calls itself constructivist, and schools don't seem to advertise this piece of information, either.

When I first raised the issue of TRAILBLAZERS being a constructivist curriculum with a teacher on the textbook selection committee, she looked at me blankly. I got a number of those blank looks before I discovered that everyone in the school knows what the word constructivism means, and knows what a constructivist curriculum is.

The reason I know this is that I finally read the original committee report, which states explicitly that the new curricula must have a constructivist approach with modeling. I was a little behind the curve there.

Elementary school

Middle school

High school

Programs explicitly denounced by over 220 Mathematicians and Scientists:

printable page


Thanks, Jo Anne, for taking the time to do this!



key words:
DavidKlein
listofconstructivisttextbooks
constructivist textbooktitles
NSFfundedcurricula

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MissingKnowledge 25 Jul 2005 - 22:46 CatherineJohnson


More good stuff from Education News:

Today's math lessons, Armbrecht said, focus much more on "inquiry-based learning" than the math of yore. Students are given a problem, then asked to use their understanding of number structure, logic and math concepts to solve it. In Armbrecht's generation, most students were told to memorize facts instead of being challenged to understand the underlying concepts, he said.

Furthermore, today's math students use calculators, computers and hands-on objects more often than their parents did. So, like Wilmington resident LaMere Henderson, even well-educated parents aren't equipped to help their children with math.

[snip]

But math teacher Dawn Olmstead, recently retired from Alexis I. du Pont High School, said so many reach high school unprepared that remediation can't be avoided.

"What we're seeing is the kids don't know how to add fractions," she said. "Some don't even know what fractions are.

"When they come into ninth grade, they're supposed to be prepared for algebra, and they're not."

There are so many topics to cover, she said, it's a burden to teach them all by the time of the test, which is given in March.

"How about probability?" she said. "Why would I teach that in an algebra class? Because it's on the test. I have to do both: algebra and what's on the test."

For many kids, math is a low priority

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HighlyQualified 25 Jul 2005 - 00:48 CatherineJohnson


Some of you may be aware that a second provision of NCLB kicks in next year. Teachers must be 'highly qualified.'

I would be in favor of this provision if ed schools weren't in charge of definining who is and who is not highly qualified.

Case in point: One candidate certified in math submitted his application this month for a job in Howard County - less than two months before classes begin.

"He wasn't worried," Mascaro recalled. "He'll have six to seven job offers wherever he goes. There's a lot of competition."

She added, "For the critical-needs areas, it's absolutely a teacher's market."

Adding urgency to recruitment this year is a requirement under the federal No Child Left Behind Act that all teachers in core subjects - English, reading, math, science, social studies, foreign language, economics, geography and arts - be "highly qualified" by the end of the next school year. Otherwise, schools risk losing federal funds.

In Maryland, recent data show that the percentage of classes not taught by "highly qualified" teachers has declined to 24.7 percent this year, from 33.1 percent in 2004. Suburban school systems tend to fare better than urban systems.

Hiring is tough task for schools

(Another thank you to Education News.)

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XtremeBehaviorismTeachingAndScripts 29 Jul 2005 - 18:34 CatherineJohnson


I just found a wonderful comment after the post on bullying:

smart constructivism

I haven't looked at the book, but I find the concept interesting. I believe that it takes a special skill to remember your own child accurately, through the lens of childhood, and if you can remember it, then you can teach children anything.

You can teach them math or history or art or how to be polite or how to handle a bully.

Teaching is a puzzle. It's a puzzle where you must navigate backwards in a maze. A child is at point K, but they are supposed to be at point Z. If you just show them again how to go from A to Z, you are missing the point of how they got to K.

And usually, kids made a rational mistake: they misunderstood something, or misheard something, and this thing is embedded in their minds. It leads them (Rationally) to this bad position K.

Teaching is about figuring out how someone got into that position, so you can FIX that misunderstanding. It's not enough to tell them that K is the wrong place; you have to help them never follow that wrong path in the first place.

The best way to help kids learn is to remember the typical misconceptions YOU had as a child, and ones similar to it, to try and understand why they would think what they think. Then, you can see how they are really very smart--just misguided.

a child must feel like himself

re: the aspergers/high functioning autism stuff: this kind of description is very similar to what behavioral psychologists teach to help children with anxiety and attachment disorders. I personally believe that there is a high correlation between attachment disorders and what's called asperger's, but I caution people to refrain from just teaching these techniques to children.

The problem with just teaching this techniques is that you need your children to feel like themselves. That may sound silly, but it isn't helpful to teach your child how to act. You may want them to learn how to behave, but they need an emotional makeup capable of backing up the behavior.

For a short term case like a bully, maybe it doesn't matter so much, but in terms of making friends, you need your child to have an emotional makeup that feels these behaviors are natural. If not, the other children will recognize that the behavior is still off, and worse, the child can often feel that they are not capable of making friends by being themselves but have to act like someone else. That's a painful experience for a child, and can do a lot of damage in the long run. Be careful at behavioral solutions that make a child feel that their personality isn't acceptable.

joannejacobs comment thread on bullying

Interesting comments on bullying at joannejacobs.com




how to stop a bully
Comments thread on bullying at joannejacobs.com

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SmartConstructivism 31 Jul 2005 - 13:43 CatherineJohnson


For awhile now I've been noticing that not infrequently I'll read a constructivist text and think: OK, that idea does not sound actually insane.

Then, with a sense of growing alarm, given the fact that I've just spent the last 3 months of my life banging on about constructivism here on the World Wide Web, I'll think: as a matter of fact, that idea sounds like an idea to which I myself subscribe.

Fortunately, the cognitive dissonance never lasts long, because the next paragraphs invariably put forth wing-y observations and grand, looping conclusions that do not follow logically from any known principle governing the natural world. Such as, to quote my number one most demented peer-reviewed constructivist nonsense on stilts prose passage of all time:


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


That's just nuts.

Still, I keep having these moments of recognition, stumbling over, however fleetingly, my own thinking & experience in constructivist texts. And from time to time this will have happened often enough that I'll have to stop and think: Wait a minute. Am I definitely against constructivism?

The answer is yes. As it turns out, there is an obvious and simple resolution to the problem of When Bad Constructivists Say Good Things, which is that there is smart constructivism, and stupid constructivism, the latter, I've just this moment discovered, being known as radical constructivism in the trade, which is what I intend to call it from now on.

Say it together, now:

radical constructivism!

There isn't a parent on the planet who's going to enjoy hearing that his school is implementing a radical constructivist curriculum, which is probably why the words radical constructivism are nowhere to be found on the web site of the NCTM.

So I'm going to be using radical constructivist from now on, and I'm going to say text instead of curriculum, for good measure. MATH TRAILBLAZERS: a radical constructivist text.

That's gonna make me popular.

What is smart constructivism, you ask?

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.**

According to smart constructivism, all knowledge is constructed, period.

There isn't active knowledge & passive knowledge, constructed knowledge and swallowed-whole knowledge, or any other kind of Correctly acquired knowledge versus Incorrectly acquired knowledge. Knowledge is knowledge; to get more of it, you have to build your new knowledge on the foundation of the old knowledge you already possess.

smart constructivism at Kitchen Table Math

Probably all of the commenters on ktm assume or understand this, and have thought about it. Here is Anne Dwyer's wonderful story about connecting a lesson with her daughter's pre-existing knowledge:

Erin is finally finishing up Primary Mathematics 1B. She is working on money. She has always had problems counting money. She can skip count by 5 and she can skip count by 10. But she couldn't skip count by 10 if she was on a number that ended in 5. I tried several methods to help her but nothing worked until we started working on the white board. I wrote out skip counting by 5 and underneath I wrote out skip counting by 10. And finally, in frustration, I suggested that when she had to increase the number by 10, she should skip count by 5 twice. Well, that just totally clicked with her. She got it and has never had another problem counting money. I never would have 'taught' it that way, but it totally worked for her.

And this comment from a ktm guest beautifully expresses the essence of smart constructivism:

Teaching is a puzzle. It's a puzzle where you must navigate backwards in a maze. A child is at point K, but they are supposed to be at point Z. If you just show them again how to go from A to Z, you are missing the point of how they got to K.

And usually, kids made a rational mistake: they misunderstood something, or misheard something, and this thing is embedded in their minds. It leads them (Rationally) to this bad position K.

Teaching is about figuring out how someone got into that position, so you can FIX that misunderstanding. It's not enough to tell them that K is the wrong place; you have to help them never follow that wrong path in the first place.

The best way to help kids learn is to remember the typical misconceptions YOU had as a child, and ones similar to it, to try and understand why they would think what they think. Then, you can see how they are really very smart--just misguided.

*Cobb, P., Yackel, E. & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Mathematics Education, 23, 2-33.

** Bransford, John D., et al. (2000). How People Learn: Brain, Mind, Experience, and School Revised Edition. Washington, D.C.: National Academy Press. (pdf file)

keywords: radical constructivist radical constructivism lost in translation smart constructivism

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FlowChart 04 Sep 2006 - 21:36 CatherineJohnson



Yes, it's a Constructivist Flow Chart!







Actually, this web site is worth taking a look at for a quick overview of educational psychology. On the basis of very rapid skimming, I'd say that the author, Richard Hall, the associate Dean for Research, School of Management and Information Systems at the University of Missouri Rolla, seems to have some horse sense.

Topics covered:
active learning
assessment
behaviorist theory
constructivist theory
information processing theory
learning in groups
learning strategies
learning styles
metacognition
education, hypermedia, and the world wide web

update: definitely worth reading

I've just read the constructivist page closely, and this is quite a nice summary. When you put all 10 of these pages together, this is probably the most useful short, concise comparison-and-contrast discussion of contemporary ed psych topics I've come across.

I'm going to read all of them.

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ConstructivismAsPsychoanalysis 10 Oct 2005 - 22:07 CatherineJohnson


from Ed Berenson:

The radical constructivist notion that students have to develop their own knowledge seems analogous to the psychoanalysts’ conceit that patients have to arrive at insights about themselves, guided only lightly by the doctor. Analysts and therapists routinely say that they can’t just tell you what’s wrong, because what’s told won’t sink in. You need to think and feel your own way into the heart of your neuroses. 

There is, of course, a measure of truth in this idea: if your problem is denial, and the analyst tells you as much up front, you will, well, deny it.  But beyond obvious things like this, you don’t have to be a cynic to see how self-serving such an idea is. It takes longer to come to insights on your own, and that suits the doctor, paid by the hour, just fine. 

Educationists have brought this therapeutic model into the classroom. Teachers can’t just give students information, so the constructivists say; kids have to develop insights on their own. Only then will they genuinely know that material at hand. But arriving at insights takes a long time, and often those insights won’t surface by themselves. To wait for them is to draw out the process, preventing kids from moving on. 

It would be sensible for psychoanalysts to tell the patients certain things when they’re ready to hear them, without having to wait for patients to figure them out. The same holds for teachers and students. Why not present material in a way that builds on prior knowledge so that students will learn new ideas and information when they’re ready? 

One quality of a good teacher is to know when kids are poised to progress. Such readiness happens a lot sooner than the self-generated knowledge that constructivists falsely believe to be the only genuine kind.  

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ConstructivistChecklist 01 Aug 2005 - 16:31 CatherineJohnson






created by Elizabeth Murphy, professor, writer, researcher, and inquirer.
Constructivism: From Philosophy to Practice

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TheInstructivistOnHistoryOfProgressiveEd 01 Aug 2005 - 18:42 CatherineJohnson


A terminological clarification

I gather from comments here and there that there is some confusion about the term "progressive" as in progressive education.

The “progressive” in progressive education derives its name from the Progressive movement (ca. 1890-1920 or thereabouts). It fought social ills and did much good (child labor laws, anti-trust laws, food and drug laws, muckraking...). The term should not be confused with “progressive” as it is used now in the political sense (a euphemism for the far left).

Progressive education was propelled by a laudable desire to humanize the often harsh and unimaginative educational practices of yore but was marred by a profound anti-intellectualism......

read the whole thing at The Instructivist

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AnotherFindForTheInstructivist 02 Aug 2005 - 22:28 CatherineJohnson


via the Instructivist, who, I learned from today's post, attended ed school himself, this list of the Ten Myths of Reading Instruction.

Research has revealed an extremely dangerous phenomenon that has been dubbed the "Matthew Effect." The term comes from the line in the Bible that essentially says that the rich get richer and the poor get poorer. That certainly describes what happens as children enter school and begin learning literacy skills. Over time, the gap between children who have well developed literacy skills and those who do not gets wider and wider. At the early grades, the "literacy gap" is relatively easy to cross, and with diagnostic, focused instruction, effective teachers can help children with poor literacy skills to become children with rich literacy skills. However, if literacy instruction needs are not met early, then the gap widens the rich get richer, and the poor get poorer until the gap gets so wide that bridging it requires extensive, intensive, expensive and frustrating remedial instruction. The gap reaches this nearly insurmountable point very early. Research has shown that if a child is not reading grade-appropriate materials by the time he or she is in the fourth grade, the odds of that child ever developing good reading skills are very slim. It is still possible, but it is much more difficult, and the child's own motivation becomes the biggest obstacle to success.

I'd put money on it that 4th grade is the make-or-break year for math, too.


And, on the importance of good teachers:

Myth #3
Reading programs are "successful." It is extremely common for schools to buy a reading program to address their reading instruction needs, and trust that the program will solve their school's literacy issues. Typically these programs require a great deal of commitment from the school, both in terms of time and money.

However, while reading programs can be "useful," no reading program has ever been shown to be truly "successful" .... And no reading program has been shown to accelerate all children to advanced levels of performance. There have been a few programs that have been shown to improve overall reading scores significantly (especially in low-performing schools), but that improvement is still a long way from what anybody should describe as "success." If 60% of the students in a school are performing unacceptably on the benchmark reading assessments, moving that number to 40% is an improvement, but it is still unsatisfactory.

Research has repeatedly indicated that the single most important variable in any reading program is the knowledge and skill of the teacher implementing the program, so why do we persist in trying to develop "teacher-proof" programs? Some would argue that it is our over-dependence on such reading programs that is preventing us from cultivating more knowledgeable and effective teachers. After all, if you want somebody to become a chef, you can't just hand that person a cookbook and tell him or her to follow a recipe.

I'm coming to the conclusion that not only do we sell our kids short, we sell our teachers short, too.

update

Why do I think Instructivist is a himself?

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SexismInEverydayMath 18 Aug 2005 - 20:27 CatherineJohnson


Christopher has complained for a very long time that, in schoolbooks and on children's television, boys are always the losers. They're dumber than the girls, weaker than the girls, slower than the girls; and they deserve what they get.

My impression has been that he's right.

Then a couple of days ago Instructivist posted a link to an American Educator article showing that at least two different sources have formally banned 'positive stereotypes' of boys in textbooks. I'm sure many more sources have informally and implicitly banned 'positive stereotypes' of boys as well; I'm equally sure that, in practice, 'no positive stereotypes' means 'no positive images,' period.

Certainly that would be the smart way to go. Drop in a positive image of a boy and you risk getting dinged for positive stereotyping. Drop in no positive images of boys and you don't.

Simple.

I'm sure that's the thinking, because when I look at textbooks or watch TV, I see an awful lot of cool girls, but precious few cool boys.

Which brings me to Everyday Math.

Given the well-documented deterioration in the academic performance of boys (Ed tells me that the NYU student body is now 60% girls), I am actively hostile to the inclusion of problems like this one in the Grade 5 E-Math curriculum:






source:
What the United States Can Learn from Singapore's World-Class Mathematics System (and what Singapore can learn from the United States): An Exploratory Study, page 77 (pdf file)


Message: men are rude schmucks, titter, titter.

It's a cliche, but it goes without saying that you could not publish the same word problem about blacks or women or Jews or old people or Muslims or Navajo Indians.

But you can tell 10-year old boys that when they grow up they'll be dopes.





source:
Banned Words, Images, and Topics: A Glossary that Runs from the Offensive to the Trivial

update: you can't say that

Almost 20 years ago, when I was a Contributing Editor at NEW WOMAN, I wrote an article about elementary school and boys. I talked to everyone, major developmentalists, psych researchers, recognized authorities. All agreed that boys and elementary school are a bad fit. Grade schools are run by women, and are predicated upon little-girl behavior, which is demonstrably less rowdy and more organized than little-boy behavior.

When I turned it in, my editor--still a close friend today--said there was no way she could get it through the editorial staff at NEW WOMAN. The message was wrong.

She wanted to see the article in print, so she sent it to a friend at, IIRC, WORKING MOTHER.

The editor there called me up and said, and I quote:

If I even showed this article to anyone else here you would never write for us. No one would look at anything you did.

True story.


So here we have a report that ran in the Detroit News on January 9, 2005:

The nation's boys are slipping and researchers say it's time to worry.

According to the U.S. Department of Education, boys have fallen behind girls in academic achievement. Fewer boys than girls are enrolling in and graduating from college and fewer men have master's and doctoral degrees.

While it may look like girls have won the gender wars, some wonder if something is amiss.

In the last 30 years, more boys than girls have been diagnosed with attention deficit disorder and learning disabilities, and more boys have dropped out of school.

"There is serious concern about what is happening to boys," said Katherine Newman, a sociologist at Princeton University. Experts offer a variety of reasons for the decline.

They say a disproportionate number of boys are diagnosed as learning disabled too early in life, a label that can later prove difficult to shed. Others argue that boys have been neglected in a large-scale societal effort to help girls. Others blame classroom cultures that have developed over time without accounting for the physically active nature of young boys.

"I think (elementary school) matches girls' personalities," said West Bloomfield mom Liz Fellows.

Whatever the reason, researchers agree the trend needs a closer look, in part because it will influence the ability of future men to make a living. "Since the 1970s, this has not been true," Newman said. "This is a serious concern because the possibility of a well-paying job without education has become more of an issue."

source:
Boys fall behind girls in grades

People studying child development knew all this 20 years ago. At least.

So I'm sorry. I can't see this as a case of 'neglecting' boys in a 'large-scale societal effort to help girls.'

When you have the New York City Board of Education formally banning depictions of boys as curious, intelligent, or able to overcome obstacles you're talking about something more malign than a simple oversight.


Here is Tom Mortenson's fact sheet, What's Wrong with the Guys?. (pdf file)


USA Today report on 135:100 boys:girls ratio in college
sexism in Everyday Math
invisible boys
boy trouble (New Republic on boys)
slacker boys, middle school, & forbidden positive images of boys in textbooks
throw rocks at them
please remain seated at all times
Ann Althouse thread sums up classroom change
cooperative vs. competitive learning
the girl show (8th grade graduation awards)
the boy show (character ed)
the other boy show
Where the Boys Aren't

letter from Robert Lerner, former commissioner NCES
Tom Mortenson's research
The Boys Project board
for every 100 girls —

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WhereHaveAllTheStudentsGone 15 Aug 2005 - 22:07 CatherineJohnson


In today's world, I've discovered, there are no more students.

Only learners.

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RuthParkerThread 26 Aug 2005 - 20:14 CatherineJohnson


Chris Adams mentioned Ruth Parker in a Comments thread....

So get your Ruth Parker sources right here!

Ruth Parker thread at Math Forum

Ruth Parker & the Turkey Problem at DARTMOUTH REVIEW

update

I just went looking for a picture of Ruth Parker, and while I found a lot of pictures of various Ruth Parkers, I didn't find a specific picture of a person named Ruth Parker not teaching math to children.

We will have to use our imaginations.

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EdSchoolAccreditation 26 Aug 2005 - 22:11 CatherineJohnson


Charles of instructivist points us to EducatioNation's post on NCATE.

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WeAreTheRadicals 28 Aug 2005 - 17:41 CarolynJohnston


ChrisAdams posted in a comment:

I think Carolyn's unfortunate discovery is an indication of how embedded into our educational system the CMP type math is. My goal with our daughters is simply to limit the damage as best I can.

There's no question that 'progressive math' is deeply embedded into public education in our country, and moreover, has been for decades.

A few months ago, Catherine wrote this post about the start of progressive math education, at Columbia Teachers College in the 1920s.

Since then, I've read Hirsch's book, The Schools We Need (and why we don't have them), about the origins of the thinking behind progressive education (also at Columbia), how it came to totally dominate professional education schools and the public schools they feed, and what some of the reasons are for its continued support by educators.

Here's Hirsch on constructivism, which he claims is only the most recent name applied to the discovery learning method that has been around for years in progressivist education:

In mathematics, [the progressivist] orthodoxy recommends that instead of making students rote-learn the multiplication table and solve a lot of workbook problems, schools should encourage them to work on 'real-life' problems and 'shift toward mathematical reasoning -- away from an emphasis on mechanistic answer finding.' While no sensible person would dissent from the goal of developing students' mathematical reasoning skills, he or she might very well question the claim that the failure of American grade schools to teach math competently stems from their use of traditional practices such as rote memorization of addition and subtraction facts. One of the complaints parents make is that their children are not mastering such facts. Is it possible that the ideas recommended by the NCTM are the very ideas that already pervade the very schools they are to transform?

Constructivist math curricula take the position, in their marketing and with their adherents, that they are maverick programs, transforming boring, traditional, failing, fossilized math programs into an exciting new form. It's a great marketing strategy... but it's really just the same old thing -- diminishing skills and understanding -- wrapped up in a new package with a new name.

Look at all the parent groups, and websites like this one, springing up in order to stand up for higher standards and more content in the math classroom. Aren't the mavericks supposed to be the ones who are on the outside fighting to get in, and the orthodoxy the ones with the power base? Which of us is which?

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MiddleSchoolPart4 19 Sep 2006 - 12:40 CatherineJohnson


Day 2 and we have locker trauma.

Christopher can't open his locker. He spent hours after school trying to open it until finally a teacher came by and opened it with a key.

The reason we have locker trauma, apart from the fact that lockers are apparently not easy to learn when you're 11, is that Christopher's locker was jammed on Day 1, so when they taught the kids how to open their lockers Christopher wasn't able to follow along with the moves, or practice the moves after the demonstration.

No practice, no learning.

It's a Discovery Locker.

Google has failed me

So naturally I was searching all over the web for locker opening instructions....and I came up with these, which are fine, but which apparently are not the instructions for Irvington lockers.

today's advice: before your kid goes to middle school, buy a combination lock and have him practice it 5 gazillion times.


they grow up so fast





parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

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ExtendedResponse 08 Nov 2005 - 22:52 CatherineJohnson


My sister-in-law, a fantastic teacher in central Illinois, says the Big New thing in math is extended response. She's going to fill me in when she finds out what it is.

In the meantime, I found this page of released extended response items on the ISAT.

my extended response to extended response

OK, my initial reaction to extended response is: I'm against it.

Actually, make that mixed. My initial response is mixed.

Here's one of 2 released 2004 extended response gr5 items:

A company makes a wall calendar each year. The company sells ad space
around the calendar to local businesses. The cost of ad space is based on
the number of square units each ad contains. The company charges $40.00
for Ad Space D. Using this information:

Draw an Ad Space that costs exactly $60 in the gridded space on page 10 of
the answer document.


And here's the illustration:




I like this problem, although wiser heads here at ktm may give me reasons why I shouldn't, in which case I'll revise my opinion.

I like it because it's visual & spatial as well as 'numerical' (if that's the right word), and because I've found Christopher to be very challenged by any problem that asks him to combine numerical thinking or problem-solving with spatial 'thinking' or problem solving. And of course I love the Singapore bar models, and this problem reminds me of them.

I also like it because it has 2 steps: you have to figure out how much each square costs & then you have to figure out how many squares $60 would buy.

I like the open-endedness of this particular problem, too. A child could simply count the number of squares in Ad Space D (40) and then divide 40 dollars by 40 squares to get $1/square. Or he or she could notice that Ad Space D is a standard multiplication array, and multiply 4 by 10 to get 40. I'm sure a lot of kids would start out counting & then notice, mid-stream, that they could have arrived at their answer more efficiently by multiplying instead. Which is good. A little Math Object Lesson buried inside a story problem.

I like that!

Last but not least, I kind of like the fact that each square turns out to cost exactly one dollar. I don't know why. It reminds me of a genre of problems in Russian Math, in which you go through all kinds of elaborate, painstaking calculations only to end up with an answer of ONE. Or maybe TWO. Or, when things get really fancy, ONE HALF.

Interestingly, I'm finding, as I work my way through RUSSIAN MATH, that I'm becoming quite attached to the number one. Every time it crops up as an answer I think: I should have seen that coming. An answer of one always seems like a flag, a sign that there was an easier, more elegant way to do whatever it was I was doing.....but I missed it.

Russian Math has all kinds of 'surprise answers,' and I think a surprise answer in the middle of an ISAT could be slightly.....fun?

An answer of one is like a little joke.

What I don't like...

...is the injunction to Explain in words how you got your answer and why you took the steps you did to solve the problem.

That is a terrible, terrible idea for a test.

It's a good thing to do on homework once in awhile, or in the classroom. RUSSIAN MATH asks students to write out explanations, although it doesn't ask students to explain how they did a problem. It asks them to restate the definitions & explanations given in the lesson.

Items like these can't possible be graded well on tests. They are far too time-consuming, and graders will end up scoring on length or number of explanations given. When you have items like these teachers are going to end up devoting all kinds of class time to writing extended responses, as Susan H says is already happening. We're looking at a massive waste of teachers' and students' time.

Last but not least, I'd bet the ranch you learn nothing from the verbal explanation that you didn't already learn by looking at the student's work.

Being able to produce a fluent, intelligible verbal explanation of a mathematical solution is almost certainly important for math teachers.

It's not important for the rest of us.

I really don't like this one

The number of fifth-grade students going to the museum is greater than 30
but less than 50. Each student will have a partner on the bus. At the
museum, each tour group will have exactly 6 students.

How many students are going to the museum?

Show all your work. Explain in words how you got your answer and why
you took the steps you did to solve the problem.

Unless 5th graders in Illinois are doing a lot of prime factor problems, I don't see any reason to include an item like this one on a timed assessment.

First of all, no one should have to be doing discovery ON A TEST.

And second, this problem has two answers (36 & 42, right?), but the wording implies that it has just one answer, and that one answer is findable.

I am DISCOVERING the fact that I don't think red herrings belong in math classes. Certainly not in elementary school math classes.

What is the point? You are teaching children to distrust the English language at the precise moment they're learning grammar & composition. An unreliable narrator in a work of fiction can be a terrific device.

But an unreliable questioner in an examination is just wrong.

I'm against it.

update: I forgot 48!

sigh

(thank you, Dan K)

extended response in 8th grade

Here's the 2004 released 8th grade item:

Peter sold pumpkins from his farm. He sold jumbo pumpkins for $9.00
each, and he sold regular pumpkins for $4.00 each. Peter sold 80 pumpkins
and collected $395.00.

How many jumbo pumpkins and regular pumpkins did he sell?

Show all your work. Explain in words how you got your answer and why
you took the steps you did to solve the problem.


The problem is fine, assuming these kids have actually been taught some algebra.

If they haven't, this is a discovery problem on a timed assessment, and I'm against it.

So, assuming they've learned how to set up & solve equations with unknowns, the problem is good. IMO.

The demand that the student explain each step in words is not.

Russian Math rocks

Instead of writing about Russian Math, I should be downstairs (at the kitchen table!) actually doing some Russian Math.

So I think I'll sign off.

But tomorrow I'll give some examples of what a proper extended response item should be.

A proper extended response item should be a RUSSIAN MATH EXTENDED RESPONSE ITEM.

update: scoring rubric for extended response

'Student Friendly' Mathematics Scoring Rubric

Assuming I'm reading this correctly (I feel a little distrustful), students must get all computations correct in order to earn the highest possible score of 4. They can earn a score of 3 with minor mistakes in computation, which I feel is fair, though others may disagree.

What I reject absolutely is the explanation section:

• I write what I did and why I did it.
• If I use a drawing, I can explain all of it in writing.

This is wrong. I don't believe a 4 should depend upon being able to supply an explanation in any case. But here you have a child who can explain why he or she did what she did in a drawing, which is no mean feat (and I'm in a position to know) and even that isn't enough.

Pace Anne, you'll notice that it's not OK for a child to explain what he/she has done by offering a mathematical demonstration, as the teachers in Liping Ma's book do. Anne's right about that; it struck me, too. Over and over again, when Liping Ma asks a Chinese teacher why he/she teaches an idea a certain way, the teacher responds by writing out a proof-like mathematical demonstration. That's what makes the book incredibly difficult (and incredibly valuable) to read for most of us; the teachers don't translate math into words, and neither does Ma.

For Chinese teachers, math is math.


This drops you to a 3:

• I write mostly about what I did.
• I write a little about why I did it.
• If I use a drawing, I can explain most of it in writing.

A couple of years ago the head of our school board sent out an email explaining the adoption of TRAILBLAZERS that included this line (from memory): In recent years math has become language-based.

I think that would come as a surprise to actual mathematicians.


extended response problem from IL state test
extended response problem 1
extended response problem 2
extended response problem 6
extended response problems 7, 8, 9
direct instruction & the rigor conundrum
Dan's daughter reacts to extended response problem
defensive teaching of Singapore bar models
open-ended problems in math ed
problems that teach - "Action Math"
email to the principal

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ConstructivistMathInWashingtonState 10 Sep 2005 - 00:31 CatherineJohnson


JoanneJacobs links to an article on constructivist math in Washington state:

Erin Bennett doesn't really care that her students can solve 12 x 3 = 36.

When the Columbia Elementary School teacher conducts a math lesson, she's more interested in how her students solve the equation, and if they can explain themselves well. And the right answer doesn't hurt.

"You did it in a really cool way," she told student Jarred Brutscher. "Tell us how you did it."

Brutscher wrinkled his nose and launched into a quiet explanation of his thought process: the fourth-grader knew that 10 x 3 = 30, and 2 x 3 = 6. So using those two equations, he deduced the answer....

Hey!

Isn't that the DISTRIBUTIVE PROPERTY??????

I think it IS!!!!

WAY cool, Jarred!!!!!


Reading on we learn that--

Teachers hope as they, their students and parents adjust to new approaches to mathematics, students' affinity for the subject will grow.

Right. Good luck with that!

Then there's this:

"We're asking students to communicate their understanding," said Jim Carlson, a math teacher at Kamiakin High School in Kennewick. "That's what you need to do to be successful. You have to be able to communicate and to make connections."

I swear, these people are like Stepford wives.

Communicating!

Making Connections!

Robotically Intoning Various Assorted Gerunds that have nothing whatsoever to do with math!


So I'm thinking. If Success in the 21st Century is going to mean a whole lot of people running around Communicating and Making Connections, my best move is to head for the hills now.

Before I go, however, I'm going to take a moment to drop Ms. Bennett a note making a connection between Jarred's cool solution and the standard paper-and-pencil algorithm for multiplication. Seeing as how neither Ms. Bennet nor Jarred seem to have noticed.





Teachers trying to change the image of mathematics

update

aack!

It occurs to me that the reason Ms. Bennett did not make the connection between Jarred's cool solution and the paper-and-pencil algorithm is that Jarred may not know the paper-and-pencil algorithm, because Ms. Bennett may not have taught it.

I wonder.
keywords: making connections communicating 21st century future

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ConnectedMathProjectList 14 Sep 2005 - 16:58 CatherineJohnson


I'm going to have to pace myself.

One week into the new school year and I'm already fuming. The Connected Math page Carolyn found hasn't helped.

It's worth reading the whole thing.

Here's a project that caught my eye:

Bits and Pieces II
Ordering from a Catalog
Students select items from a catalog and fill out an order form, calculating shipping, tax, and discounts.

That's special.

Susan S says....

Boy, they seriously need to update to more 21st century skills. A better world application might be to go to Amazon.com and click on your own special one-click button. Why should life be so complicated?

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KleinOnMultiplicationTablesInLA 02 Mar 2006 - 22:14 CatherineJohnson


via NYC HOLD,