kitchen table math, the sequel: 6/17/07 - 6/24/07

Saturday, June 23, 2007

Quote of the Day

I attended Parent Orientation today at the small, midwestern liberal arts college that my daughter will be attending this fall. The professor leading one of the break-out sessions said, at one point, "I hate the term 'helicopter parents' because it's so derogatory towards parents. The reality is that it's your child and you want them to succeed."

In general, the theme of the day seemed to be that they recognized that college involved a transition process, and that these 18 year old freshmen are "emerging adults. Also, that parents and the university have a joint relationship and it is essential to keep an open line of communication because while they may be students, they are also still somebody's child.

Help Desk – Singapore bar modeling

I will be starting to teach my 9-year old daughter how to solve word problems using Singapore bar modeling. I purchased Challenging Word Problems 2 & 3. We have never used Singapore before, only Saxon and Kumon. She has difficulties with reading comprehension and word problems are hard for her.

To prepare myself I’m practicing doing problems in the book. I’m also going to practice with the problems on Thinking Blocks, a wonderful interactive website that enables users to practice with bar diagrams.

I’ve searched for help, and found this scripted prompt that appears useful:
STEP ONE: What do you know already? - Can you draw a bar (or two) to show what you already know?
STEP TWO: What do you need to find out? - How are you going to find that out? - Does the bar(s) you have set up/drawn give you any clues as to what kind of question (operation) this is and what you need to do with the numbers?
STEP THREE: Now DO it and find the answer(s)!

I have virtually no teaching skills, and I’m feeling challenged by the prospect of trying to explain how to solve word problems. Typically I have found myself tongue tied when helping with homework word problems.

Any advice for me? Any resources you would suggest?

Diane Ravitch Misguided Arugments against the Pay-the-Student Plan - Politics on The Huffington Post

Diane Ravitch: Bloomberg's Misguided Pay-the-Student Plan - Politics on The Huffington Post

Via Edwize, I just read Diane Ravitch's critique of NYC's pay the student plan.

She says:
Nowhere in the article does Diane Ravitch make the argument that the plan won't improve achievement, instead she complains that poor inner-city students should suck it up, ignore reality, and learn for the sake of learning.

I don't know if this program will work. All I care about is that if it does work, that it's more cost effective than any other plan to raise achievement by the same amount.

Diane's argument is petty, unrealistic, overly-idealistic, and represents whats wrong with our holier than though education system.

By her arguments since teaching is a truly valuable and critical profession, in fact it is a noble profession and a higher calling, perhaps we should all oppose any attempts to increase teachers pay, since increased pay devalues "the value of intrinsic motivation, or the rewards of deferred gratification, or the importance of self-discipline for a distant but valued goal."

Note: I like a lot of what Diane has to say on other subjects, but on this I don't agree.

Living Environment Regents in 8th grade - Results

Probably, I do lack a middle school mentality. After all I never experienced "a lay back" attitute from my teachers nor exhibit it myself.

My students from 3 honor classes took the REgents exam in Living Environment on Wednesday. Since I followed the rules accepted in HS (a student who passed the class with 65 or higher, completed 2000 minutes of laboratory work and 4 state mandatory labs are allowed to take the exam), only 2 students from all 3 classes were not allowed to take the examination due to absences (both were suspended many times during the year, and didn't pass my class). So, out of 77 students who took the exam, 81% passed it. The rest will have to repeat the class over in HS.
Comparing to citywide percentile, we did great. This exam (though difficult because of the phrasing of questions and answers) was a perfect final point for my class, there was no concepts that we didn't study in class! Students who studied and worked all year - passed it, students who were slacking off - didn't.
But what did I get from admins (not from Science AP though) - 14 students failed, that's bad, very bad! You should have selected before the test, they will have an F in their record untill they pass this exam...
This attitude kills me. Oh, poor child will have an F... That child is given a second chance in HS, and should work better next time. (After all, I told them that they have a right not to come for the exam this year - they still will have to take it in HS.
Oh, well. My AP defended me (thanks!), blaming the inappropriate placement in the first place. Will anything be done about it? (As I learned recently, in my school parents have no say in their childrens placement, and I was advised not to tell the children what class they will be in next year!!!)
The only calming thought in this is that the students who passed my class and my exam LEARNED biology well, and can proceed to other science classes in HS.
(In the 8th grade yearbook, I was named "Ms.Quiz", and the advice to future students in my classes read "Hold on, you are going to STUDY!")

Summer Suggestions

The schools sent home their usual advice on how we parents can keep our kids skills up over the summer -- I'm supposed to encourage my kids to look for patterns, keep a journal, do estimation at the grocery store, and of course, read.

I figure KTM readers have far better suggestions for long car rides and rainy days at the beach.

Here is one of our favorites to get things going:

Stump Mom Dictionary Game -- you need 1 dictionary per person playing. Everyone thumbs through the dictionary looking for a word you don't think the other person knows. Write it down, trade papers, and see who can define their word first. My kids have gotten amazingly fast at finding words in the dictionary. They were very cool on this one at first, but now it's one of our favorites, especially since Mom chooses words that kids love -- bodily function and gross humor. It adds a whole new level to their vocabulary (latest cool find -- haruspex). To make it harder, the older kids have to use the word in a sentence.

"You're going after people's jobs."

From Peyton Wolcott’s website:


I can't take credit for the origin of this insight,
which comes from a wise friend
(who wisely chooses to remain anonymous)
who cautioned me years ago:

"You're going after people's jobs."

In some cases we are--with wasteful high-priced
administrative positions--and in some we aren't.
In either case, our public schools consider our
questions and searches personal attacks and
respond accordingly.

Be forewarned and stay positive.

Perhaps the defensive responses we frequently get when we ask questions of our schools can be explained by this. I have never thought of it in those terms. However, there may be a mindset within the educationist culture that views questions as challenges to their “public service” jobs.

Friday, June 22, 2007

Peyton Wolcott

from Niki Hayes, a website on taking back the schools

how to file a public records request

and lots more

Association of Math Teachers defends dumbing down the math

Cross-posted from The Eclectic Educator:

In the June 22, 2007 Ridgewood News (Ridgewood, New Jersey) is an article about the math wars. It states that at the recent Board of Education Meeting, an executive board member of the Association of Math Teachers and a consultant to the Ridgewood Public Schools went to the microphone.

Barbara VanDenBerg, says the article, "fired off a string of credentials as a math expert in support of reform math."

And this is what she said:

"Balance is by far the most important thing. Because we're all so diversified, we all can't be the disciplined mathematicians...that's just not reality."

If this is not an admission that reform math is dumbed down, I don't know what is.

Mathscape help!

Anchorage school district has just adopted MathScape: Seeing and Thinking Mathematically.

Should I be worried?

place value makes the "short list"

cross-posted to Beyond TERC:

terrific post on place value:

Place value is one of those things non-mathematically trained grownups tend to take for granted (at least, I did).

The Singapore Math series teaches place value year after year. Singapore Math has a "true" spiral curriculum in that kids learn to mastery in year one, then study the same topic in more depth in year two and master that material, too, then study the same topic in still greater depth in year three and, again, master the material. Place value is one of the spiraled topics.

I didn't quite understand this, even though Christopher's brilliant 5th grade teacher (I don't use the term "brilliant" lightly) told me how important the topic was. She said she'd asked her friend, who had a Ph.D. in math education, what were the most essential & fundamental topics for K-5 kids to master.

He said "place value."

I wish I could remember what Ed said about it the other day. We were talking about some "guess and check" problem-solving situation that was supposed to be a model of higher order thinking.

Ed said, "The way these kids are solving the problem shows they don't understand place value, and if they don't understand place value they don't have conceptual understanding."

One of the things that would be SOOOO helpful to parents like me (to most parents, that is) would be to have a list of the CORE topics you MUST make sure your child knows.

For instance, the other day Vicky said that decimals aren't as important as fractions.

I sort-of knew that already, but only because I've spent 2 1/2 years of my life immersed in K-12 math & math education. But, otoh, I didn't know it with conviction.

Most parents can't teach math on the side; even parents who have the capability to teach math on the side are going to find that their kids won't cooperate past the age of 10. (You can still teach a middle school child on the side - I've done it - but the amount of time you have to spend wrangling with them to get their attention steeply reduces the amount of time on task.)

What we need is a short list of THE essential skills our kids MUST have.

My list, so far, is:

  • fractions
  • place value
  • long division
  • measurement

from Lynn:
  • automatic recall of basic facts

from independent george:
  • order of operations
  • properties of arithmetic

from instructivist:

  • In addition to total mastery of math facts, I would put equivalent fractions on top of the list. Equivalent fractions directly leads to an understanding of proportions, percentages and all the other good stuff (scaling, unit rates...)

from Mr. Person:

I've had a list for a long time of core concepts/skills that are emphasized at each grade level.

1: Place Value
2: Addition/Subtraction Facts
3: Multiplication/Division Facts
4: All operations with whole numbers
5: All operations with fractions
6: Ratios and proportions

from Susan J:


Common sense. (Such as if you subtract a positive number the result should be smaller.)

[question: do the reform math programs do a decent job with estimation and common sense? do we know?]

update: it strikes me that the list already exists. It's the TOC for the Primary Mathematics series.

I'll pull it & post.

don't teach Shakespeare

To teach Shakespeare effectively, a strong teacher needs to direct her entire class, a teaching strategy frowned upon in a system that demands group work using a strategy called the "workshop model." Shakespeare is content. I recently heard about a staff developer who wrote the word "content" on the blackboard, and then proceeded to put a big X through it.

"You are not to teach content, ever," he warned. Students should choose their own books, and discuss them in groups and thus "construct their own knowledge."

"What about ‘Romeo and Juliet'?" asked one teacher, who has taught the plays of Shakespeare in her class for years. "Why would you want to teach that?" replied the staff developer.

Mrs. Badillo and the Bard
Andrew Wolf
NY Sun
June 22, 2007

Do bus drivers drink Starbucks coffee?

In a conversation with an elderly relative, I mentioned that I had purchased Starbucks gift cards as end-of-year gifts for my daughter’s school bus drivers. She remarked that I should have given them Dunkin Donuts cards, because she didn’t think bus drivers go to Starbucks.

When she said that, my reaction was annoyance. Why was I annoyed? Was it because she was right? Or, was it because this remark betrayed a certain type of prejudice, elitism or plain old ignorance?

Should I have gone to Starbucks to buy my teacher gifts, and to Dunkin Donuts to buy my bus driver gifts?

Gift giving can be very complicated.

Thursday, June 21, 2007


school's out!!!

making meaning

Here at ktm-2, we've been behind the curve.

We've been thinking constuctivism was about constructing knowledge.

It's not.

Constructivism is about constructing meaning.

  • D.C. Philips: Thus, von Glasersfeld's epistemology.... leads him argue that each individual science and mathematics student is responsible for building his or her own set of understandings of these disciplines;....teachers cannot assume that all students
    have the same set of understandings, or that their own ways of understanding are shared by their students. The Good, the Bad, and the Ugly: the Many Faces of Constructivism (pdf file) by D.C. Phillips Educational Researcher, Vol. 24, No. 7, pp. 5-12

  • According to [constructivist] theory, learning occurs only when students make an effort to construct their own understanding out of a problem situation. Constructivist-Compatible Beliefs and Practices among U.S. Teachers (pdf file) by Jason L. Ravitz, Henry Jay Becker, Yan Tien Wong Center for Research on Information Technology and Organizations U. California Irvine July 2000

Naturally all this stuff is driving parents crazy, especially seeing as how constructivist educators have stopped teaching for mastery but have carried right on testing for it. Well, everywhere except Scarsdale, that is.

Unfortunately, our plight doesn't elicit much interest from policy wonks and education journalists, most of whom* apparently believe that a quarter century of constructivist training in our schools of education has little to do with the achievement gap. (Interesting, isn't it, how it never seems to be progressive educators who make any headway narrowing the gap...I wonder why that is?)

So naturally I've been enjoying the spectacle of eduwonk getting the constructivist treatment:

OK, I am increasingly convinced that there is a reading crisis in our schools. On his blog, Fred Klonsky, a teachers' union head in Illinois, writes about the article(s) that Rick Hess and I have done on the competition - equity tension. But he ascribes a conclusion to us that is not in the article...and then he further tries to muddy the issue when called on it. Klonsky says that what he did is "make meaning" of what we wrote. Oh brother, try just reading what it says. It's an article, not a work of political philosophy.

That was Tuesday, June 19.

Today is Thursday, and eduwonk hasn't recovered: lame, pseudo post-modern BS, attempt to spin out of this, “make meaning” from it as though this is a political theory seminar and we’re debating Montaigne....


Let's have more of that!

update from Linda Seebach:

When I was a graduate student in mathematics (decades ago, that was) a significant part of the first-year courses was intended to develop students' intuitive understanding of the unfamiliar and abstract object that populate the mathematical universe, and you'd better believe that the professors expected all of us to acquire "the same set of understandings" they themselves had.

constructivist lollapalooza (thank you, instructivist)

* with a few notable exceptions (see: Linda Seebach, Debra Saunders, Andrew Wolf)

teaching writing during the summer

fantastic series of ideas on the Comments thread for Writing website. I'll try to get them posted on the front page later...

Also, three resources left by ktm readers:

from Ester:

Write Source Eval-U-Write
Write AtHome (homeschoolers like this)

from Vicky S:

very important: scored writing samples of student work from the University of Oregon

I am constantly looking for scored samples of student work; they're very hard to find.

I also have 3 models for book reports (one from Susan):

TimeforKids sample book report, check list, and graphic organizer (beautifully laid out)
expository book report (includes annotated book report - very nice, though graphically confusing)
Writer's Model Book Review (Susan's find - Holt - annotated - well laid out - pdf file)

Writer's Choice above average, average, and below average student work, grades 6-12

Grade 6
Grade 7
Grade 8
Grade 9
Grade 10
Grade 11
Garde 12

light bulbs for the SmartBoard

re: how much does the lightbulb for a SmartBoard cost?

Most projectors come with a two-year warranty and a bulb that should be replaced after 3,000 hours of use. To estimate how long your projector bulb will last, do a simple calculation. For example, if you use the projector 20 hours a week for approximately 40 weeks of the year, you get 800 hours of use per year, and the bulb will last for just over three years. One bulb can typically be replaced for approximately US$400.

Evaluating Total Cost of Ownership for SMART Board Interactive Whiteboards (pdf file)
January 2006
SMART Technologies

how much does a light bulb for the SMART Board cost?
replacement light bulbs for the SMART Board
budget vote
more and ever more SMART Boards

re: hiring a new superintendent

This comes from Thinking Out Loud, an attorney for the school board association in another state (not CT, NY, or NJ):

What the community should be asking [the school board] is process questions:

  • HOW are you going to go about doing a superintendent search?
  • HOW are you going to involve the community?
  • What is the vision of the board for this school district?
  • What steps has the board taken to see if the board's vision for the school district is the same as the community and staff's vision for the school district?
  • How will these visions be reconciled into a comprehensive vision that works for all players?
  • What would the characteristics be of the right leader to make the vision happen?

superintendent to retire
re: hiring a new superintendent
why was the budget defeated? (student study)

Superintendent To Retire

Last night, our Superintendent for the past 12 years announced her intention to retire at the end of the next school year. The Supt has proven herself to be an adept politician, bringing in Everyday Math is sure to be one of her claimed successes; also pushing for "professional learning communities" and the demise of the gifted program, also she ended norm-referenced testing.

So, I'm not shedding any tears here, but I expect we will begin searching for a new Supt., and I'd like to figure out how to keep things from getting any worse. On the downside -- I suspect we are going to have to pay a lot more for a new Supt. This one got $153,000 per year, and that is low for Conn.

So, any suggestions on what parents can do to influence the choosing of a new leader? I'm going to assume that no one is going to invite me onto the committee that will choose a successor.

Let's hope that guy from Ridgewood, NJ doesn't apply for the job!

superintendent to retire
re: hiring a new superintendent

Wednesday, June 20, 2007

Earth Science

The good news from here is: Christopher was invited to take Earth Science next year.

When the letter arrived we were elated.

That probably sounds ridiculous, but it's true. We were elated. Next year, in 8th grade, Christopher will take two high school courses: Earth Science and Math A (algebra 1 & part of h.s. geometry).

Yes, he'd probably be doing more advanced work at Hackley or Horace Mann or wherever, but still: this isn't bad.

Not bad at all.

I was happy, too, because I've been "working on" the Earth science situation for over a year .... "working on" meaning taking every opportunity that came my way to push for two reforms:

  • transparent placement process
  • offering the course to all comers

The first of these happened; the second didn't.

However, the first - the creation of a (reasonably)* transparent placement process - is a significant change. I didn't know how significant until I asked "Thinking Out Loud," the school board attorney I'm hoping will find time to write some posts.

Here's what Thinking Out Loud had to say:

You are in an area called "student assignment," to assist you in your research. Typically, student assignment is wholly up to the school administration, and there is NO recourse beyond the central office/superintendent level if you are dissatisfed. This makes sense, if you back up and think about it objectively: professional educators have the knowledge and background and the objectivity to make decisions about where to place students--and this is NOT something appropriate in which to involve the school board. In our state, schools can retain students over the objections of the parent. In some cases, I have had calls from parents who wanted children with perfectly decent grades--Bs and Cs--retained, and the school refused, knowing full well that the motive was athletic! So, as a general rule, the decisions at the building level are final. Central office has a strongly vested interest in not overturning the building level decisions, or a long line would form for appeals from parents who didn't get the answer they like.

When I asked whether the issue of student assignment in the abstract was a policy issue, Thinking Out Loud replied that:

It absolutely IS a policy issue to discuss placement, but in truth, these policies are deliberately kept vague even when there is a good policy in place to avoid problems and potential litigation--the idea is to preserve maximum discretion for administrators, who mostly want to do the right thing, in my experience.

This was a revelation.

I had been assuming that the extreme vagueness of Irvington placement and tracking procedures was a bad situation that had evolved over the years, not a perfectly normal, intentional school practice.

This is one of the obstacles to working on school reform; parents have no idea why educators do the things they do.

If, as Thinking Out Loud says, student assignment practices are everywhere shrouded in mystery as a matter of course, this is a major reform for a school to institute in one year's time. (It's possible I should increase the number of years to 3 or 4; the middle school has been offering a high school science course to roughly 1/3 of the 8th grade class for 4 years now, I believe. NOT FACT CHECKED I assume that a handful of parents have been complaining about the placement process for all 4 years - although I was led to believe that none has asked that the course be opened up to all students who wish to take it.)

I'm not quite sure whom to thank, though I believe the new head of the science department is responsible.

Good for her.

news from nowhere part 14
news from nowhere part 16
news from nowhere part 17
news from nowhere part 20
tracking in "high-performing" schools
Earth Science reform
email to the guidance counselor, 2007 edition
email from the guidance counselor
Earth Science

* I say "reasonably" because I assume some parents would say that the department could take things further than they did this year. I don't think any parents would say that the selection process isn't radically more transparent than it has been.

parents are the problem

Fascinating new poll on NCLB reauthorization out today (via eduwonk).

from the executive summary (pdf file):

All groups agree that a lack of parental involvement is the biggest problem facing schools. Teachers (61% select it as one of their top two problems), administrators (53%), the public (39%) and even parents themselves (38%) say the lack of parental involvement is the central challenge to our nation’s schools.

So.... I guess this has something to do with the booming business in tutoring and parent reteaching in high-performing districts.

moving right along...

Lack of discipline in the classroom was mentioned second by the public and parents (26%). Teachers (31%) and administrators (50%) point to inadequate funding as the second greatest challenge schools face.

Don't get your hopes up on the inadequate funding percentages, which I initially took as an indication that the public may have stopped believing money = good education:

The public overwhelmingly rejects blanket solutions for schools that perform poorly on state tests in favor of solutions tailored to individual schools. From a list of possible consequences for schools that perform poorly for several years, the most popular solution is the most flexible — requiring administrators to develop a comprehensive school improvement plan that offers a sharp departure from the school’s current approach. [ed.: preferably a strategic plan! (scroll down)]

The public believes funding should be increased for schools that fall short of their AYP objectives on state tests. [ed.: why has this never been tried?]* The second most popular consequence for poorly performing schools, gaining support from 57% of the public in all or most cases, is increased funding so struggling schools can hire more teachers, reduce class sizes and improve classroom conditions. Naturally, this is most popular among teachers (71%).

Other proposals receive far less support. A school takeover, in which school administrators are replaced, is viewed as the right move in all cases of poor performance by just 13% of the public and, in most cases, by only 12%. While 48% say it’s the answer in some cases, 24% believe that it should never happen. Not surprisingly, school administrators line up firmly against this idea (56% never, 40% some cases and only 4% in all or most cases).

The proposal that earned the least support in “all or most cases” is firing teachers and replacing them with new ones. Only 12% of the public believe this should be the consequence in all or most cases (46% some cases, 40% never). Teachers join them, of course (4% all or most, 33% some, 62% never).

I don't know why we don't just take all that money and give it directly to the parents, seeing as how they're the problem.


Interestingly, while 39% of respondents said that "lack of parental involvement" is "one or two [of the] biggest reasons for public schools' problems," only 27% thought that increased parental involvement was "one or two [of the] best changes to solve public schools' problems."

So... 30% of the people who said the biggest problem was lack of parental involvement don't believe it themselves.


CA Math Frameworks: "responsibilities of parents" (scroll down)
why do we have so many tutors?
parents are the problem

* Judge clears way for state-wide intervention of city schools 6-14-2007

E-mail to the powers that be

This morning, I sent this e-mail to the Supt., Dir of Curriculum, and all of the Board of Ed members.
As part of the Board's review of professional development and curriculum this evening, I was wondering if you would consider focusing at least one full day of professional development next year to the needs of gifted learners in our schools?

Since the demise of [our] well-regarded gifted learning program four years ago, which directly served about 100 students in grades K-8, very little has been implemented to ensure that every child's learning needs are being met.

Add to this the disturbing conclusion of a 2005 study that found 68% of Connecticut teachers hold erroneous beliefs about the characteristics of gifted students. Moreover, a disturbingly small percentage of teachers in Connecticut believe that they have received adequate pre-service and in-service professional development to teach a differentiated curriculum to gifted students in the regular classroom. I've attached a short synopsis of current research that supports these conclusions.

Even when teachers are given some training in differentiation and curriculum modification, they are reluctant to implement these practices in their classroom, according to a 2003 study. In fact, the study found that teachers are unwilling to eliminate previously mastered curriculum material for fear that student achievement on State tests could drop. This, despite research that shows high ability learners show no decline in achievement test scores even when 40-50% of the curriculum is eliminated in at least one subject area.

The 2003 Minnesota study recommends that teachers receive not only professional development targeted to gifted learners, but also follow-up support so that they can actually make improvements in their classroom instruction. Stephanie Hirsch, Deputy Executive Director of the National Staff Development Council stated, "Training without follow up is malpractice."

I urge you to consider a more aggressive teacher training and support program to better meet the needs of gifted learners. We are fortunate to be quite close to the National Research Center on the Gifted and Talented, located at the University of Connecticut at Storrs. We need only take better advantage of the resources located close to home to improve the quality of education for our most able students.
I don't hold out a lot of hope on this one. But it's probably good just to keep things from falling to far off the radar screen. Here's a link to the research synopsis that was attached to the e-mail.

writing website

Susan's find:

TOEFL-Prep Writing Practice Site

how to decide

So I was arguing with Ed about CO2 and global warming.

When he flew back from Brussels not long ago, he sat beside some international science type who told him there is a near-absolute consensus that CO2 is causing global warming, and "the only interesting question" is what to do about it. The economists are figuring it out.

Ed reported this to me as settled truth. (Settled enough.)

Naturally I took it amiss.

I don't happen to have the first clue whether CO2 is causing global warming. Normally I assume CO2 is causing global warming because of the aforementioned near-absolute consensus.

However, if you made me bet money on CO2 being the cause of global warming, I wouldn't bet the ranch.

The reason I wouldn't bet the ranch is the aforementioned near-absolute consensus. My rule: in cases where everyone believes X, and where, more importantly, everyone fervently believes X, it's best to take a step back.

I don't know why I think this, exactly. Emotion per se isn't the problem. I believe, with Damasio & c., that emotion and reason are allied.

If you want to know why I have this decision rule or what role other people's emotions plays in it, you'll have to ask my cognitive unconscious. All I can say is that when emotion has led to dissenters being called "deniers" and the like, I assume we've left Damasioland.

Ed took that amiss.

I kept trying to say, "It's a writer thing," (which it is, for me at least) but that got me nowhere until I invoked Bayesian reasoning. Citing Bayes sounded good and it worked: "worked" meaning Ed decided to stop seeing my position as "they're in it for the (grant) money" and to start seeing my position as the logical result of a nonfiction writer applying a semi-conscious Bayesian heuristic to the problem.

So this morning I picked up Daniel Willingham's collection of classic articles in cognitive science, and found this: The benefit of additional opinions by Ilan Yaniv.

Lots of fun, and directly apropos:

  • in a study of inflation forecasts, the aggregate prediction was "more accurate than most ...individual forecasts, though not as good as the best ones. The best forecasts, however, could not be identified before the true value became known."
  • you only need 3 to 6 extra opinions to gain the full value of aggregated opinions
  • Condorcet's jury theorem, when applied to "categorical, binary judgments," is the exception that proves the rule - with binary judgments, the more experts the better
  • experts whose opinions you seek need to be independent to give you the benefit of opinion aggregation [score one for me]
  • otoh, "gains of appreciable size can be observed even when there are low or moderate positive correlations between the judgments of the experts." [one for Ed]
  • people are biased in favor of their own opinions (roughly: 70% favoring own opinion, 30% favoring advisor's opinion)
  • people are biased against dissenters [no kidding]
  • being biased against dissenters makes sense when there is a range of opinion on a subject ("fat tails")
  • I assume, though Yaniv does not say so, that the opposite is true: being biased against dissenters does not make sense when there is a near-absolute consensus

Which would mean that my "writer's rule" is a good one. In cases of near-absolute consensus buttressed by high emotion it's best to take a step back.

Naturally I apply this principle to constructivism (though not to instructivism - no, never!)

Joking aside, my Bayesian rating scale tells me that when a Stanford University School of Education professor publicly - and sympathetically - characterizes constructivism as a ruling ideology, I have just been told everything I need to know about whether constructivism is a correct model of the world.


I have to learn grammar.

I have no idea whether "Joking aside, my Bayesian rating scale..." is or is not grammatical.

Have I just said that my Bayesian rating scale has set joking aside?

I don't know.

I'm going to have to learn how to diagram a sentence, too.

Ilan Yaniv homepage

why do we have so many tutors?

This really is the mystery of affluent, "high-performing" schools.

I was talking to my Scarsdale friend yesterday. She said Scarsdale has an earth science teacher so bad people hire tutors as soon as they find out their kids are going to be in his class.

Why is that?

Why has such a situation been allowed to develop, and why has it been allowed to persist?

why do we have so many tutors?
parents are the problem

absence of instructivism

In the past couple of weeks I've had the belated revelation that one of our problems here in Irvington isn't constructivism per se, but, rather, the absence of instructivism.

Example: few educators in our district are alarmed by the high levels of tutoring going on. Not only are few educators alarmed, but school personnel refer parents to Irvington teachers when children need tutoring.

Parents seem readily to make the connection between high levels of tutoring and fairness (no disadvantaged kids enrolled in accelerated classes) not to mention tax revolts; Irvington administrators do not.

Instead our administrators apparently see tutoring as a superior form of instruction, the ultimate class size reduction to a teacher-pupil ratio of 1:1. Thus wealthy parents hiring tutors when their kids have problems in school, or teaching their kids themselves, are simply purchasing (or providing) elite instruction.


Obviously this analysis is off the mark, but it isn't constructivism. Constructivists don't believe that a tutorial with an Oxford don is the pinnacle of educational excellence. Constructivists don't believe in dons.

This isn't constructivism.

So what is it?

And where does it come from?

Arguably, it comes from the absence of instructivism in schools of education.

When you talk to younger teachers and administrators, you find that the vocabulary of explicit instruction - breaking material down into smaller units of material, teaching the units directly, providing distributed practice of material until it is mastered (i.e. lodged in long term memory), building up connections amongst the parts, performing frequent formative assessment - simply do not come up in conversation.

This is why the core moment for me in my 100 Years War with the math department was the "If students need distributed practice, parents can find worksheets online" exchange. The words "if students need distributed practice" could not come out of a direct instructivist's mouth.

The math chair, a woman in her 30s, is interested solely in student understanding; the word "understanding" is the term she uses exclusively when discussing the math instruction for which she is responsible.

"I've visited the class, and the students understand."

"If they don't understand, they need to come in for extra help."


The 6th grade teacher talks the same way. When a student does badly on a test, she tells parents the student "doesn't understand" the material.

But then, when the tutor rides in to the rescue, the tutor says the opposite. A math tutor hired by a friend of mine told her that her son understood the material well enough. The problem was that he couldn't do the math on math tests quickly and accurately enough to earn an A or a B on a test.

Of course, David Labaree would say that the math chair is not a "real" constructivist. And David Labaree would be right.

But nor is she an instructivist.

As a result, when a student fails to learn math, the only available explanation is that the student has failed to understand the material. That is the fallback and the default. The student doesn't understand.

Therefore the only logical solution is for the student to "come in for extra help" and have the material explained again.

From what I can see, extra help is all about re-explaining the material, not about diagnosing the missing skills and providing the missing practice.

once again with feeling

This reminds me of Michelle Weiner-Davis' book, Divorce Busting. Weiner-Davis says most people assume that if what they're doing isn't working, they should do the same thing more often and louder. Once again with feeling.

Which reminds me of the great story I heard about a legendary professor at Columbia medical school, a man who trained many of the most important research physicians working today.

His fundamental axiom, the central principle he drilled into all of his future Nobel prizewinners:

If what you're doing isn't working, try something else.

One of his former students told me that story.

from Steve H:

While I was writing this post, Steve & Susan were beating me to the punch:
You have to get to the details to see what's going on. Constructivism has a great influence on education, but it does not mean that content and skills are not taught. The ideology is costructivism, but schools are pragmatic at some level. This provides a certain amount of "balance" or plausible denial. We all know what balance means - the school decides and the parents go away.

I've always thought of it as the difference between a top-down approach versus a bottom-up approach. Modern constructivists never implement pure constructivism. They know that content and skills are important. The big difference is that they want to achieve the results starting from a thematic and real-world view of knowledge and having the kids work down to the basic skills. They can talk the talk, but this approach does not guarantee that basic skills and content ever get done. This is OK because they see little linkage between mastery and understanding. Only conceptual understanding is necessary.

The justification for limited content and lack of mastery is based on constructivism. Just because you can't see child-centered learning when you walk into a classroom doesn't mean that it isn't having a big impact. My son's Everyday Math class wasn't done in groups. they did the student math journal pages in class. It doesn't look constructivist, but it is top down with little emphasis on mastery.

I sometimes get the feeling that constructivism is just pedagogical cover for a dislike of hard work, mastery, memorization, high expectations, and accountability. They just can't come out and say that, so they hide behind discovery and conceptual understanding. When pushed, they talk about balance and hope you won't look at the details.

from Susan S:

Yup. That's it in a nutshell.

The odd thing is that they either don't seem to care that the basic skills didn't get mastered, or they believe that the kids that never learned the foundational blocks just aren't able to learn them.

I was talking to a friend this morning. She's been helping one of her son's high school friends review for his math final, and came out saying that both boys have difficulty doing long division. Neither of them is very good at long division, and both avoid it.

Also, both try to get by estimating answers and leaving it at that.

Neither of these kids spent a second learning math from Math Trailblazers.

David Klein has long said that all U.S. textbooks have "constructivist elements."

By now it's probably the case that all or nearly all U.S. classrooms have constructivist elements, too - constructivist elements that are so "natural" and taken-for-granted that no one connects bad grades on tests with unexamined, taken-for-granted constructivist practices.

spilt religion - Hirsch on progressive education & Romanticism
David Labaree on the 2 factions
Labaree on constructivism
Hirsch on Labaree

Hirsch, E.D., "Romancing the Child," Education Next, 1 (Spring 2001).
Labaree, David F., "Progressivism, Schools, and Schools of Education: An American Romance," Paedagogica Historica (Gent), 41 (Feb. 2005), 275–89. (pdf file)

Tuesday, June 19, 2007

Labaree on constructivism

Today progressivism means pedagogical progressivism. It means basing instruction on the needs, interests and developmental stage of the child; it means teaching students the skills they need in order to learn any subject, instead of focusing on transmitting a particular subject; it means promoting discovery and selfdirected learning by the student through active engagement; it means having students work on projects that express student purposes and that integrate the disciplines around socially relevant themes; and it means promoting values of community, cooperation, tolerance, justice and democratic equality. In the shorthand of educational jargon, this adds up to ‘child-centered instruction’, ‘discovery learning’ and ‘learning how to learn’. And in the current language of American education schools there is a single label that captures this entire approach to education: constructivism.

As Lawrence Cremin has pointed out, by the 1950s this particular progressive approach to education had become the dominant language of American education.2 Within the community of professional educators—by which I mean classroom teachers and the education professors who train them—pedagogical progressivism provides the words we use to talk about teaching and learning in schools. And within education schools, progressivism is the ruling ideology. It is hard to find anyone in an American education school who does not talk the talk and espouse the principles of the progressive creed.

This situation worries a number of educational reformers. After all, progressivism runs directly counter to the main thrust of educational reform efforts in the US in the early twenty-first century. Reform is moving in the direction of establishing rigorous academic frameworks for the school curriculum, setting performance standards for students, and using high stakes testing to motivate students to learn the curriculum and teachers to teach it. Education schools and their pedagogically progressive ideals stand in strong opposition to all of these reform efforts. To today’s reformers, therefore, education schools look less like the solution than the problem.3

Progressivism, Schools and Schools of Education: An American Romance (pdf file)
David Labaree
Paedogogica Historica
Vol. 14, Nos. 1 & 2, February 2005, pp. 275-288

what does an actual teacher teaching in US public schools have to say?

buzzword education

spilt religion - Hirsch on progressive education & Romanticism
David Labaree on the 2 factions
Labaree on constructivism
Hirsch on Labaree


today's factoid

One theory to explain how human altruism evolved involves the way we interacted as groups early in our evolution. Towards the end of the Pleistocene period – about 12,000 years ago – humans foraged for food as hunter-gatherers. These groups competed against each other for survival.

The archaeological and ethnographic data [Bowles] used showed that 13% to 15% of foragers died from wars, which were common between groups.

Why altruism paid off for our ancestors

I find this oddly comforting.

factoring is unmultiplying

Is that correct?

I think it's correct, but I have no idea whether what I think is correct is correct.

If it is correct, I'm looking forward to briefing Christopher on this. Depending on what mood I catch him in, I'll get enthusiasm or eye-rolling, either one. Doesn't matter, though; he's going to like this idea whether he rolls his eyes or not.

Boys love it when their moms teach them math.


Unfortunately, I don't remember which website published the "factoring is unmultiplying" line, so I can't credit it.

it's always worse than you think, part 3

an email from Niki Hayes:
We're seeing it everyday in public education, where few of the accountability programs are worth their time and effort.
So.... I guess I shouldn't be pinning my hopes to value-added.

Monday, June 18, 2007

shotgun wedding


I was on the board of the National Alliance for Autism Research for 7 years. People used to bug me about internecine warfare all the time.

All the time.

I finally started saying, nicely, "You can put your energies into bugging CAN & NAAR about internecine warfare, or you can put your energies into raising money to fund research."

I remember that having a big effect on a couple of people, and rightly so.

This morning Ed was reading snippets of the autism article out loud.

When I read it myself, I'll probably have something to say.

summer reruns, part 2

tour de force

worst project ever, part 2

from Lynn:

I nominate everything my son did this, his first year, of high school.

1 -- poem on inhalants (he wrote an "Ode to Air")

2 -- build a model home for geometry

3-- create a "solar cooker"

4 -- build a self-powered rubber band car

5 -- build a bridge out of random objects supplied by the teacher (mostly popcicle sticks and string)

6 -- a poster on global warming for spanish class

I'm sure there's others. If this had been 4th grade, I wouldn't be so upset. But it is high school and he has now lost one whole year.

from Cassy:

We had 2 unique dilemmas in 3rd grade this year. One child was unable to prove gravity by dropping 2 kids of fruit from a ladder and the other found that Jupiter had its own atmosphere and was warmer than mercury, making the sun irrelevant to planet temperature.

On the minus side, they were totally incorrect. On the plus side, we knew there was no parent involvement. At least we gave the parents the benefit of the doubt.

from Molly:

I nominate my daughter's fourth grade math project, to which several weeks of class time where dedicated.

1. Select a sport. Research the history of the sport and determine when and where it was first played. (My daughter selected swimming and determined it was first played when someone fell into a body of water and didn't drown.)

2. Print (from your web search) or draw 5 pictures of people engaging in the sport you selected.

3. Make a chart showing how many calories per hour are burned during this sport, and compare it to two other sports. Work with classmates on this part.

4. Write 5 word problems about your sport. (AHA. Actual math! But wait...the example given was "Sally runs the 100 meter dash in 6 minutes. Anne runs the 100 meter dash in 7 minutes 20 seconds. How much faster is Sally than Anne?" A better question would be why are Sally and Anne so amazingly slow?)

5. Draw or collect pictures of the equipment used for you sport. List the cost of each piece of equipment and how often it is used in each game.

6. Create a poster containing all of the information about your sport.

Can I also nominate my daughter's fourth grade social studies assignment - putting the major battles of the American Revolution into alphabetical order, because we all know that history makes much more sense when studied alphabetically rather than chronologically.

from exo:

Oh, gosh... that's terrible! (those parents of 120 students of mine SHOULD BE eternally greateful to me - I don't do projects in science!!! )

Well, in factI did one this year with my students - all done in class in a week and a half, including three lessons on ethograms, data clllection, design of the data tables, and research of background info including proper referencing. That was or exit project. Two of the best projects went for the city-wide Urban Advantage Science Expo at the museum of Natural History.

And here's the funny one: a child made a project in science (8th grade) researching the best place to hide the money on a person. She found that to be a pocket on tbe inside of the bra cap! Beat me, I don't know what kind of science is that, and what kind of teacher would take it for the city-wide expo!

from nbosch:

My oldest son did a science project in 8th grade that consisted of drawing a Kansas animal on a paper plate and writing 5 interesting facts on the back. Oh fine. I'm hoping things have gotten better.

from Karen A:

Sunflower Greetings to nbosch from a native Kansan now living in Illinois:

My report on the Wildcat--a Kansas animal:
1. Indigenous to the Manhattan area (that's Kansas, not New York).
2. Synonymous with Purple Pride.
3. Worst enemy is a Jayhawk.
4. Will answer to the name of Willie.
5. Likes to hang out in Aggieville.

[ed.: wait! that's not a project! that's a report]

from Vicky A:

Where to start!

All the animal talk has me thinking about this one (did I post this already??):

Integrated project between Science and Language Arts (amazing, isn't it?).

6th grade

Pick an animal.

Research its physical adaptations to its environment.

Write a "rap" verse about this animal and its adaptations.

Dress up as this animal (with three of the physical adaptations) and perform the rap verse in front of the class.

This was one of the weirdest but I have to admit, it was actually kind of fun (I had to really help with the rap though, LOL! Should I post it? You guys might get a kick out of it.) The dress up thing, however, was over the top, for my guy at least.

The illustrated bookmarks with the revolutionary war biographies that were required in social studies were not nearly as exotic, but much worse to do.

from lsquared:

I'm going to nominate the two weeks my daughter spent in both language arts and social studies making crafts for an end of the year fiesta (6th grade). The excuse was that it was a capstone for covering central and south america, but since the kids couldn't tell you where the objects they were making came from or what their significance was, I have a hard time buying into it.

from Tracy:


I have to know - how did she arrive at this result? Was it theoretical or empirical?

from smartest tractor:

At first I thought I should send the "winner" a prize, a bottle of wine and Advil perhaps. But now I am thinking if we get a bunch more, maybe the Kitchen Table Math Collective should send out an offical award every year to the teacher with the Worst Project Ever.

I'm game.


I am.

Keep 'em coming.

more t/k

just say no

yours for $3.95 at Zazzle

foiled again

So after my "cowboy gene" post yesterday, Ed and I drove up to the Jacob Burns Film Center to see The Good, the Bad, and the Ugly.

number one: I had no idea the movie is 3 hours long.*

number two: can you spell homoerotic?

Not that there's anything wrong with that!

Still, 3 hours of homoerotic, anti-war, Italian ("Blondie! Blondie!"), cowboy movie isn't my idea of a bonne Father's Day.

* "Don't miss the reconstructed full-length English-language version of Leone's three-way Mexican standoff, "the ultimate rush in Spaghetti Westerns" (Time Out New York), in which a bounty hunter (Lee Van Cleef), a Mexican bandito (Eli Wallach), and a con man (Clint Eastwood) search for buried gold. With Morricone's masterful score and Leone's over-the-top storytelling—and more than 15 minutes restored to the already-classic original U.S. release."

Sunday, June 17, 2007

Math Humor of the Day


My 14 year old shared that with us at lunch today.

Happy Father's Day!

Boys to Men
June 15, 2007; Page W11

...But what makes a good father? This question holds more than philosophical interest for me. Though my father left when I was young, and my stepfather found me uninteresting, I now have three sons of my own (ages 7, 5 and 2). Not knowing any better, they think I have fatherhood figured out. They believe Father's Day is rightly my day.


I could really use a restful Father's Day, but recently I found my sons huddled over a book on traps, which makes me fear that they're planning for my gift to be something live. Already this spring they've captured a snake, a bullfrog and at least one deadly spider. While other men think about golfing or napping tomorrow, I'm praying I can weather the day without getting bitten.

There's more than a little irony in the fact that I have three sons. I'm not what you'd call a master of the manly arts. I can't start a fire without a match, or track a deer, or ride a horse. I don't know how to fix cars, and my infrequent forays into home repair usually necessitate medical attention. But these are the things little boys want to learn -- I remember wanting to learn them myself. Or maybe it's that boys yearn to do things with fathers, and those things usually involve a little danger. A new wildly popular book of essential boy knowledge recognizes this in its title: "The Dangerous Book for Boys." My oldest has dog-eared nearly every page.

I'm allergic to most danger. I get a stomachache at the thought of confrontation. I'm grouchy and self-centered, and have few of the traits that William McKeever, in his curmudgeonly 1913 classic, "Training the Boy," considered essential to manhood: "courageous action in the face of trying circumstances, cordial sympathy and helpfulness in all dealings with others, and a sane disposition toward the Ruler of All Life." I'm hardly qualified to be a role-model for three boys.










Father's Day, in our house, won't entail golfing or napping or watching a game. I'll probably have to contend with some trapped and irritated reptile. There's that cannon made of PVC that my oldest boy has been pestering me to help him finish. And the youngest two boys are lately enamored of climbing onto furniture and blindsiding me with flying tackles. Father's Day is going to be exhausting. But it will be good, because in the midst of these trials and joys I find my answer to the essential question on Father's Day. What makes a good father? My sons.

foiled again

Liberate the public schools

Steven Greenhut asks this interesting question.

Would you trust the production of food, clothing or shelter – even more important to our well-being than education – to the same people who are producing education in Washington, D.C., Los Angeles and even wealthy Capistrano Unified? I didn't think so.


An elite group plans and directs a one-size-fits-all system. There are few choices. There are no consumers. This is a top-down, government-controlled monopoly system, with more than a little bit of coercive force at its disposal. How could a system such as this take root in a society that is supposed to pride itself on freedom and the market economy?

Increasingly, this argument makes so much sense to me.

The article is Liberate the public schools.

Worst Project Ever

I stopped the "at home" project crap in my second year of teaching. The "this is really studid" moment came during a science fair for the school. The grade four project goal saw cars soaring down a ramp and traveling as far as possible along the gym floor. The top three cars went to the district's regional science fair.

It was quite exciting to see cars made out of Lego, balsa wood, Cub Cars outfitted with washers and bolts. Happy kids sized up the competition. They complimented each other on their choice of marker colour or the way the attached extra weight to the front of the block of wood.

There was one car that was absolutely incredible. This little fella, with proud papa close behind, had a car made from cast aluminum. The wheels spun for a day and a half with a simple flick of one's finger. I can't even speculate how long it took to design and fabricate. It came forth!

In the interest of fun, shall we start a little collection of "Worst Projects Ever"?

worst project ever
worst project ever, part 2