Thursday, December 31, 2009

Favorite comments of '09: Marcy on math games

Marcy on math games and Asperger’s

Re Op-ed in yesterday's Philadelphia Inquirer, Marcy writes:

One of the things I have a real problem with is the math games. They are really pushed "all the kids have fun playing math games!"

But my AS son doesn't play turn-taking type games. They drive him crazy. So when all the other kids are working on their math facts by playing math games, my son is really left to fend for himself.

Since this is a boy who read Edwin Abbott's Flatland in 3rd grade, I know he has a good head for higher math. Why should he not be allowed to learn math in a more concrete way? Why should he sit around while everyone else plays games?

Wednesday, December 30, 2009

Favorite comments of '09: Obi Wandreas the Funky Viking on “real world” problems

Re Why do our top math & science students defect?, Obi Wandreas writes:

The primary problem with "real world" problems, is that in order for them to require only the math you are trying to teach in the lesson, you have to set up a problem so contrived that it ceases to bear any actual resemblance to the real world.

The other issue, of course, is that it requires a great deal of time and effort to set up a problem and story only to find that your students will refuse to donate any airborne intercourse.

It's great to show students that math has real applicability. For the most part, however, what they are doing simply builds the foundation for the stuff that's really useful. A coach doesn't show athletes how they could use a sit-up to help them in life. When the athlete does something that requires the use of their abs, however, they will be glad to have done them.

Tuesday, December 29, 2009

Favorite comments of '09: Beth on the worst of both worlds

Re Myths about left-brain schooling, II: media complicity, Beth writes:

The tragic reality is that our schools don't do anything well. The fact that the humanities are suffering doesn't mean that mathandscience is taught well. The fact that the schools don't have the rigorous content and skills of the traditional approach doesn't mean that they encourage true creativity like the progressive approach.

They just don't do anything right. They've somehow managed to weld together the authoritarian, anti-creative, carrots-and-sticks approach of the worst kind of traditionalism, with the hollowed-out content and mushy thinking of the worst kind of progressivism.

Monday, December 28, 2009

Favorite comments of '09: Dawn on art activities

Re myths about left-brain schooling, Dawn writes:

I think even though art gets into math and English these days by way of projects it's degrading art as well as those other subjects. Art is as much based on skills and work and practice as math. Expressing yourself is something you can only do after you've acquired the skills to do this. And I say this as someone for whom drawing has always been tremendously important.

Perspective, light, structure, tools, exercises, etc. THAT's what makes art. This half-assed stuff they incorporate into math or english not only cheapens those subjects but cheapens art.

It's a strategy. Maybe if more kids WERE encouraged to bite their teachers when bored....

Sunday, December 27, 2009

Favorite comments of '09: vlorbik on two plus two

Re Postmodern math: does 2 + 2 always = 4, vlorbik writes:

the right answer to
"what is 2+2?"
is of course
"why do you ask?".

unless it's implicit.
a four-year old?
one thing maybe.

somebody testing a piece of computer code?
another maybe.

somebody trying to catch you out
in some pseudophilosophy?
maybe still another.

sure and it's empty to posit that
"properly" defined, correct symbol
manipulation yields correct results.

owen by the way

oh... and by the way...
i was created a doctor
of philosophy [for my
sins] in '92 and have
professed maths.

so here goes an experiment.
these SOB's downtown
have decreed that push
these damnable calculators.
let's see what happens when
i put "2+2=4" [the whole string]
into the command line.
wow. 1.
that means true.

okay. you win this one. sort of.

put it into google then.
let's see.
pretty interesting.
would't call it "true" though.
is google now "not mathematically
well-defined" or some such
weaselword dodge? of course not.
(everybody knows that there are
always *undefined* terms and
other such conventions; this
isn't at all when we're doing math
and seldom when we philosophize).

PS
2+2=5 is the symbol in 1984
of the kind of "truth" that can
only be beaten into you.

mathwarriors split on whether
2+2=4 is of the same type.
i myself do not claim
to know the answer to this.

Saturday, December 26, 2009

Favorite comments of '09: Niels Henrik Abel, Cheryl van Tilburg, and Beth on math projects

Re Summer math projects, grade 5 and Summer math projects, grade 4:

Niels Henrik Abel writes:

As you prepare your game "Package" be sure to include...A colorful and creative game board

So in other words, were a kid to design a game like chess that was challenging yet had a dull & boring game board, he would be marked down?

I guess that's an indication as to what's truly "important."

Cheryl van Tilburg writes:

Instead of ignoring the assignment (which just causes your child grief at the beginning of the school year), I alter the assignment to make it more appropriate for my child. For example, instead of the board game, I would have my student complete several multiplication worksheets and complete a weekly timed test of multiplication facts.

Then, my son brings the completed worksheets and time tests to school, along with a note from me explaining the "differentiated assignment." I include my phone number so that the teacher can call if he/she has any questions. To date, I haven't received any calls.... (I use this same approach when it comes to poster projects in my kids' English class.)

Is this a pain in the neck? Yes. But the way I figure it, things won't magically change without input from parents and other educators who understand that projects based on creativity aren't appropriate for all children.

It's also important to talk about this option with other parents in your child's class/grade. Other families also struggle with these creative summer projects and would welcome some advice how to handle them. (And there's something comforting about knowing that other parents are in the same boat!)

Things won't change until parents band together and demonstrate that they mean business. It's hard to be the only one to speak up (you and Catherine over at KTM are great role models in this regard -- and many others!) If five children come to class with a "differentiated" summer project, that sends a powerful message to the teacher (that hopefully will be passed on to administrators).

And Beth writes:

How do I hate this project? Let me count the ways:

1.) Like a lot of elementary school homework, it's really Mom-work. There's no way your average 9-year-old could complete this without massive assistance from Mom. From locating the grocery store, to buying the poster board, to getting a flyer, to nagging the kid into doing the work, this is one more headache for Mom.

2.) Most of the effort involved is pointless. For a bright child who balks at pointless work, "imagine you're planning a picnic ... now make a poster ..." is the beginning of existential despair. I wish I was kidding, but I'm not. I've seen this happen.

3.) This is a huge time waster. An extremely well-organized Mom might be able to get her child through this in about 3 hours, but that's a bare minimum. Remember there's a trip to the grocery store, and a trip to buy poster board.

4.) Public school is supposed to provide a free education. As soon as you require poster board that you don't provide, you've violated that. In this recession, people are really pinching pennies, and for some families, this is asking too much.

5.) It's called summer vacation because it's supposed to be a vacation! Hello!

I don't see this as a left- or right-brain problem. This is about the schools thinking they have a right to tell me what to do with my kids in our own time. I don't agree.

Friday, December 25, 2009

Favorite comments of '09: Beth on “be creative”

Re Summer Reading Project, 3rd grade, Beth writes:

"Be creative!" No. A child can either be creative or follow the teacher's directions, but he can't possibly do both at the same time.

It's like another old favorite, "Have fun!" usually encountered at the end of a long list of instructions.

So much of the stuff that goes on in school just seems half-baked. The teachers got the message that learning should be creative and fun, which I agree with, but nobody was willing to do the deep thinking and reform that would actually make that possible. So we wind up with stale porridge which is not creative, or fun, or learning.

Thursday, December 24, 2009

Favorite comments of '09: Joanne Jacobs on art projects

Re: Portfolios are coming home: insights into grade rationing, Joanne Jacobs writes:

A friend of mine hired a high school student to help her fourth-grade son produce dioramas. She reasoned that no educational purpose had been advanced for the art projects so it didn't matter who did them. She has a lot of artistic skills herself, unlike her son, but has a full-time job.

Wednesday, December 23, 2009

Favorite comments of '09: ChemProf on pressure for “innovative teaching” in college

Re: Pressure for "innovative" teaching in colleges, ChemProf writes:

It's definitely ed school related. My college is on an assessment kick, driven in part by the accreditation agency. The problem is that the assessment system is being driven by the ed schools and social sciences, so we get lots of blather about "rubrics", but my numerical assessment system (based on percentages) doesn't count. They've yet to try to dictate how I teach my class, but I wouldn't be surprised if it comes to that eventually.

Tuesday, December 22, 2009

Favorite comments of '09: VickyS and Obi-Wandreas the Funky Viking on cooperative learning

Re Cooperative learning?, Vicky S writes:

My son had a similar experience. In 5th grade math they did a lot of cooperative work, and this particular day he was appointed to give the group's answer. They haggled over the answer, and the kids insisted a wrong answer was right. My son knew the right answer so he stood up and reported the right answer. He was given a poor grade because he did not present the group answer. When challenged, the teacher said my son failed to convince the group of the rightness of his answer, so failed in that way as well.

And Obi-Wandreas the Funky Viking writes:

This has indeed been a very valuable teaching experience for your daughter. She has learned several crucial life lessons, including:

1) Who you can, and can't trust

2) What happens when responsibility for your success is placed in hands other than your own, and you sacrifice your individuality for a group

3) The difference between theory and practice

4) How not to run a lesson.

Monday, December 21, 2009

Favorite comments of '09: bky on invented algorithms

Re: Math problems of the week: 6th grade Connected Math vs. Singapore Math, bky writes:

When the curriculum has students invent algorithms for basic mathematical operations, to me the message is this: none of this really matters -- that's why we're letting 10-year olds make the decisions.

What if you teach them how to add fractions and build it up by: (1) giving a good foundation of what a/b means (b partitions of [0,1], count up a of them), (2) using that foundation to show, very common sensibly at this point, how to add fractions with like denominators, then (3) give a good foundation for understanding equivalent representation of fractions (e.g. why 2/3 = 4/6), and then (4) very naturally lead to the general algorithm for adding fractions with different denominators ...? (that sentence started out as a question) Then the message is that adding fractions is so important (and the students are so important) that we want the kids to really be able to do it and understand how it works.

Sunday, December 20, 2009

Favorite comments of '09: vlorbik on computer programming

re Interactive computer programming environments: essential yet elusive, vlorbik writes:

everything got hugely harder with "windows".

in the DOS environment, one had BASIC
right there, ready to go,
on every box on every desk.
you'd open it up, find a program that runs,
and start banging on to see what happens.

also "BAT" files. anything you kept doing
over and over the same way? just write it out
once and run it whenever you need.

right there at the top level directory
where you can't miss it. and self-explanatory.

i can't do the exercises you set a few posts
from now at all now; noplace to start.

..."but you *just* have to..."
download this, install that,
buy the other.

yes. if you happen to *own*
the computer you're working on
and have a fast connection
(and probably some free access
to competent tech support
and god knows what else).
so it looks easy to whoever it is
telling me it's easy.

meanwhile, if i want a list
of pythagorean triples
(beyond the famous 3,4,5
and 5, 12, 13 that everybody knows)
i'll have to (re)-write the code
on my f--ing graphing calculator to do it.
thanks a lot, GUIs.

Saturday, December 19, 2009

Favorite comments of '09: Anonymous and bky on key words in word problems

Re Ideas on Helping Children with Hard Word Problems, Anonymous writes:

Looking for key words is not a good idea. Things are not necessarily going to be written with key words meaning the same thing.

There are 15 candies altogether. Two are outside the jar. How many are in the jar?

Students taught to look for the "key" word altogether might add. What makes them key words anyway? the textbook writer?
...

If a student understands the problem and what it is asking, "key" words are irrelevant. If a student is dependent on key words, and cannot solve the problem correctly without them, then any time in life when a problem is worded without those so-called key words, or the words are used differently, as in the examples above, that student will not be able to solve the problem. It is an ineffective "tool". Better to give students tools they can use in all circumstances.

and bky writes:

I think that Anonymous' last remark about keywords is on the money: if kids know to read a problem and get the mathematical content, keywords are irrelevant. Therefore the goal should be to get kids to read for understanding -- it is as much about literacy as about arithmetic. It is also not something that can be done in one lesson, it needs to be the ongoing framework in which word problems are addressed.

Friday, December 18, 2009

Favorite comments of '09: TerriW on open-ended assignments

Re: Against open ended assignments: evidence from psychology, TerriW writes:

Well, as a parent of little ones still, this is a no-brainer.

"Go get ready for bed."
vs.
"Go pee on the potty"
"Okay, now wash your hands."
"Okay, now brush your teeth."
"Okay, now put on your jammies."
"Okay, now pick out your nighttime book."

Which version gets the job done quickly and which one causes the parent to get angry and drives the child to tears?

Parent-teacher conference!

I just had my first ever parent-teacher conference from which I did not come away with the sense that there was something wrong with my daughter. No mention of IEPs; of uncooperative, fidgety behavior; of deficiencies in expressive writing. All good. All wonderful, in fact.

Dd has made tremendous developmental strides over the years; I wonder how many others like her are simply following their own idiosyncratic time tables.

But there's also this year's wonderful teacher. All of her teachers, in fact, have been wonderful-- but in different ways. And what for some people is pathology for others is quirky creativity. Perhaps it depends on who you are, what you grew up with, or what you hold nearest and dearest. Whatever it is, would that other left-brain children were as lucky as dd is this year.

Thursday, December 17, 2009

Favorite comments of '09: Obi-Wandreas the Funky Viking on science and science fairs

Re School Science Fairs: Right-brained obstacles to left-brainer recognition, Obi-Wandreas writes:

Given the fact that sensationalism has trumped fact and inquiry in some of the most famous fields today, this would seem to be an accurate representation of today's scientific climate.

Although left-brain work in science tends to be that which endures, that's a small consolation to those having to deal with science as a popularity contest today.

Wednesday, December 16, 2009

Favorite comments of '09: bky on why teach long division

Re: why teach long division?, bky writes:

There are two good reasons for teaching the standard algorithm for dividing integers, if that's what you mean by long division:

(1) so kids can calculate the quotient of two numbers(and have an exact form for the remainder if that is wanted, rather than a decimal expansion), and

(2) it is an introduction to algorithms. It is odd that many people who deride the teaching of the traditional algorithms cite the availability of calculators as a reason not to learn the algorithm. I find it useful to regularly (every 6 months or so) have my kids (homeschooled) go over the operations of it, with the idea of helping them not only have confidence that what they are doing makes sense but also preparing them for them to understand the concept of algorithm by familiarity with a few specific examples (also on the list: standard stacking algorithms for multiplying, adding, subtracting).

A good idea is to practice occasionally with something like money: show 734 as 7 dollars, 3 dimes, 4 pennies. If you divide by, say 3, you start with 3 piles, each with 2 dollars; the left-over dollar is exchanged for dimes; etc. It is also useful to do the same problem on paper based on writing out the expansion 734 = 700 + 30 + 4 and then successively dividing each place value with remainder, and throwing the remainder downhill:

734 = 7x100 + 3x10 + 4
= 3x(2x100) + 1x100 + 30 + 4
= 3x(2x100) + 13x10 + 4
= 3x(2x100) + 3x(4x10) + 14
= 3x(2x100) + 3x(4x10) + 3x4 + 2
= 3x(2x100 + 4x10 + 4) + 2
= 3x244 + 2

This is "doing it by hand". The algorithm is a formalization. The algorithm is based on repeated division-with-remainder; you never really need to know what place value you are working with, or which side of the decimal point -- just divide and throw the remainder on the next lower place value. If kids understand this for integers, then dividing in the presence of a decimal point is just as easy. Note also how distribution is vital to long division, and since distribution is difficult for grade school kids this also gives practice recognizing and using that vital aspect of arithmetic.

Some critics say that the LD algorithm doesn't teach place value. Of course, it's not suppose to: it's supposed to divide numbers. But looking at it as an algorithm does indeed reinforce the concept of place value. Long Division is a keeper.

Tuesday, December 15, 2009

Favorite comments of '09: lgm on schools’ demands on parents

I have so many favorite comments that, to fit them in before the year turns, I must start posting them now. I'll do so in chronological order.

Here's the first, from lgm:

(re: parenting the the 21st century)

When I was a child, my school clearly defined the parent's teaching responsibility. It was to send a note in with the undone homework and notify the teacher if the child was struggling. The teacher would do the actual teaching. My district (Dept of Defense Europe) still has this policy.

In my child's public school district in NY, I am to make up whatever the class didn't get to. The penalty for not doing so is ineligibility for college prep courses. If I want my child to have the education I did I must tutor on the side and pay the community college for the senior year courses as it would be elitist to offer Calculus at the high school. I went to small schools. My kids have over 600 in their grade and so many specialists and paras that the principal has to develop a parking lot schedule to go along with the staff schedule. Academics was not the focus until NCLB came along.

Monday, December 14, 2009

7th grade holiday math project: Just Because I Care About You

A Just - Because - I - Care - About - You MATH PROJECT!

You have been given $2,000 to buy gifts for ten different people in your life. You must decide who you want to give a gift to, what you want to buy them, and why you want to buy them this particular item. You must find a picture of this item with the price. Every item you select has a discount. You must find the discount for each item, calculate how much you will save, and how much the item will finally cost you.

Each student must complete a booklet consisting of 13 pages
Page one is your title page. This must include your name, and title of this project.

Pages 2 - 11 will display:
* A picture of a gift
* The original price
* The discount
* The final price with calculated sales tax ***
* Your math work
* Who the gift is for and why you chose this item for this person

Page 12 will show the price you spent for each item, how much money you spent all together, and how much you have left.
On page 13 you will donate the remaining money to a charity of your choice and explain why you chose this charity.

DISCOUNTS
20% off all major appliances (refrigerator, washer)
...
50% off all jewelry and clothing

***Please remember, there is a 8% sales tax on everything but clothing.

...Your project will be judged on creativity, accuracy, and neatness.

Sample


[Picture of Lamp]

A lamp for my friend Nancy.
My close friend, Nancy, just got married. At the Craft Show last month, she admired a lamp which bears a resemblance to this one. She said it was the perfect lamp for her foyer. I could not pass it up.

[Various calculations]

[Final price]

Saturday, December 12, 2009

How not to handicap students with Asperger's

Reading this article from yesterday's British newspaper, the Daily Mail, I was struck not just by the impressive accomplishments of its subject, but by the following points, which I've put in bold face:

A schoolboy is studying for a maths degree at the age of 12.

Cameron Thompson has been accepted by the Open University on its BSc Honours course and expects to graduate when he is 16.

The child prodigy already has A* grade GCSEs [a standardize British subject exam] in Maths and Additional Maths.

The youngster, who has a form of autism called Asperger syndrome, scored 100 per cent in all of those tests, so his teachers decided to put him in for the exam proper last May.

Cameron's father said: 'He is in the second year of the course and in the first unit last year he had a final score of 89 per cent.

'That unit usually starts in October and ends the following June - Cameron finished it a couple of weeks ago.

'The second unit starts in February and he says, quite seriously, that he is going to have letters after his name by next October.

'He also plans to have graduated with a BSc [Bachelor of Science undergraduate degree] honours degree by the age of 16 and he is on course for that.'

Mr Thompson, who works in IT, added: 'His abilities are remarkable but all this does have its challenges as we have thought for some time he has Asperger Syndrome.

'This means he has trouble dealing with other children and tends to lock himself away for days.

'He has never been officially diagnosed but we are thinking of having that done.

'However, Maelor School have been brilliant with him and have provided well for his special needs.'

My question is, how likely are similar children to experience similar recognition and accommodations in present day American schools?

And what does this mean for the future of American children with Asperger's Syndrome?

Thursday, December 10, 2009

Math problems of the week: 6th grade Everyday Math vs. Singapore Math

1. The final arithmetic problem set in the 6th grade Everyday Mathematics Student Math Journal 1, p. 161:





2. The final arithmetic problem set in 6th grade Singapore Math Primary Mathematics Workbook 6B, pp. 14-18:




Wednesday, December 9, 2009

Autism Diaries XIV: More erudition

"Wilson! Wi-i-i-lsON! I will save you!" says J, smiling goofily as he chases the basketball he kicked off the court down the grassy slope.

Yes, a basketball; not a volleyball; and yes, the force of gravity; not an ocean current. But nonetheless, an endearing reference to, and partial reenactment of, a scene from one of the few adult he really enjoys and understands.

And one of the most non-mischievous, "neurotypical" jokes we've seen from him.

Monday, December 7, 2009

Feedback loops or vicious cycles?

Suppose you're in a position to design and disseminate K-12 academic curricula, and that you believe strongly that this curricula should teach students skill X. Suppose, furthermore, that data shows that students are deficient in skill X. Suppose, finally, that you believe that emphasizing A, B, and C will teach skill X. So you design and disseminate a k-12 academic curriculum that emphasizes A, B and C. New data then emerges that shows that students are still deficient in skill X; some of the data suggests that the problem is getting worse.

What do you do at this point?

1. Reform the curriculum so that it puts an even greater emphasis on A, B, and C?

2. Question your initial belief that emphasizing A, B, and C will teach skill X, and try a new strategy?

Hints:

X = "higher level thinking skills"
A = explaining how you solved problems
B = "reflecting" on your learning process
C = "inquiry" and "argumentation" over specific content
"You" = a member of the current education establishment

Saturday, December 5, 2009

Education and the needs of businesses

An article in this week's Education Week reports on concerns that "the push for ‘21st-century skills’" by the Partnership for 21st Century Skills, or P12, "is an attempt by technology companies to gain more influence over the classroom."

The article notes that, "for Ken Kay, the president of P21, such criticism amounts to a 'cheap shot' by those who don’t believe that the education system should be more responsive to business needs. "

This prompted me to post the following comment:

There are two sorts of "business need" that come to mind. One is the need of technology companies to sell their products to schools. The other is the need that companies in general have for a skilled workforce.

I can't help wondering to what extent the P12 group has surveyed actual businesses. The last time I checked in, businesses were bemoaning the scarcity of those with basic numeracy and literacy skills.

The only relatively new skill that I can think of that schools should be teaching is computer programming--and by this I mean actual programming courses; not courses in Power Point, Photoshop, and Excel. Why do so few schools teach, for example, Basic, Pascal, C, and Java?


In defense of p12, a subsequent commenter wrote:
Included [in necessary 12st Century Skills] are team building and project management, skills that help workers in am [sic] ever expanding workplace with ever shrinking human interaction.

Are businesses really crying out for K-12 schools to teach "project management" and "team building"? My suspicion is that they're more interested in "team players," in the sense of players who are skilled enough to get their part of the job done properly, without other team players having to do it over again for them.

Thursday, December 3, 2009

Math problems of the week: 6th grade Connected Math vs. Singapore Math

1. The final fractions calculations problems in 6th grade Connected Mathematics 2, Bits and Pieces I: Understanding Fractions, Decimals, and Percents, p. 52:

Extensions:

For exercises 55-60, find an estimate if you cannot find an exact answer. You may find that drawing a number line, a hundredths grid, or some other diagram is useful in solving the problem. Explain your reasoning.

55. What is 1/4 of 12?

56. What is 2/9 of 18?

57. What is 1/4 of 3?

58. What is 3/4 of 8?

59. What is 2/9 of 3?

60. What is 3/4 of 3?

2. The final fractions calculations problems in 6th grade Singapore Math Primary Mathematics 6B Workbook, p. 13:

Find the value of each of the following:

(a) 1/2 + 1/2 × 1/4 - 3/8

(b) 2/5 × (5 - 3) ÷ 7/10

(c) 2/3 ÷ 4 × 3/4

(d) 2 ÷ (1/2 + 1/4) × 3/8

(e) (1 - 3/8) ÷ (1/2 + 1/3)

(f) 1/6 + 5/6 ÷ 5/6 - 2/3

3. Extra Credit

Which problem set involves more mathematical "extensions"?

Find an estimate if you cannot find an exact answer. You may find that drawing a number line, a hundredths grid, or some other diagram is useful in answering this question. Explain your reasoning.

Tuesday, December 1, 2009

Digesting my Op-Ed responses

The emails reacting to my November 9th Op-Ed have stopped coming in, and so it's time to sum up the 40+ responses.

The biggest contingent were parents and educators of autistic spectrum children who agreed with me that Reform Math is shortchanging their children.

Nearly as numerous were those who agreed with my points, but felt that Reform Math shortchanges a much larger group of kids. (I agree. My focus on autistic spectrum children was partly a matter of news topicality, and partly because I think that these are among the most vulnerable of affected children.)

Less than five people wrote in defense of Reform Math. Those most angered by my piece were a couple of teachers who have autistic spectrum students in their classrooms and claim that Reform Math works just fine for them. ("Please check your facts before writing articles," wrote one.)

This got me thinking about how it is that some teachers can come to believe, based on actual classroom experience rather than ed school indoctrination, that Reform Math is better than traditional math for their most vulnerable students.

What I think is going on here is that people are confusing success with Reform Math with success in math. As should be apparent from my Problems of the Week posts, Reform Math, in comparison with non-Reform Math, offers a much smaller number of easy problems and leaves out all sorts of difficult concepts and procedures. Issues of speed, accuracy, and mathematical challenge do not arise very much.

Therefore, if you are a teacher working with students who struggle with actual math--as many lower-functioning children on the autistic spectrum do, for all the strengths that higher functioning autistic children have in math--and if you confuse Reform Math with actual math, you may come to believe that Reform Math serves your students much better than non-Reform Math does.

That's why we desperately need measures of actual math achievement, instead of all those state tests that, designed (as one follow-up letter to the editor points out) in lockstep with Reform Math, simply measure Reform Math achievement.

Sunday, November 29, 2009

Echolalia or erudition?

"You may have won the battle, dude, but you have lost the war."

Those were the words J belted out after a chess game we played today in which I foiled his attempts to checkmate me in four moves, only to lose the game, badly, about 25 moves later.

"Where did you get that from?" I asked him, incredulous at how apt his quotation was. He coyly refused to tell me. So I went up to the computer and googled it.

J's source? Home Alone 2.

This makes me think about how we judge people along a socially constructed scale that ranges from "erudite" allusion to "mindless" echolalia, with academics quoting from Shakespeare at the top, nerdy adolescents quoting from Monty Python in the middle, and, at the bottom, children with autistic spectrum disorders quoting from children's movies and TV shows. This scale often fails to appreciate the degree to which a given person, whatever his/her "rank," is cleverly making connections vs. mindlessly opting out of using his/her own words.

Sometimes a Home Alone allusion from a 13-year-old with autism is more mindful than a Hamlet allusion from a forty-something-year-old neurotypical professor.

Friday, November 27, 2009

Math problems of the week: 3rd grade Trailblazers vs. Singapore Math

1. The final addition and subtraction word problems in the addition and subtraction chapter of the 3rd grade Math Trailblazers Students Guide (p. 87):

The students held a bake sale to raise extra money to pay for the scenery and costumes. Students in Mr. Sullivan's and Ms. Angelo's classes brought in cookies for the bake sale. Ms. Angelo's class brought in 194 cookies and Mr. Sullivan's class brought in 235.

A. If Ms. Angelo's class brought in 100 more cookies, would they have more cookies than Mr Sullivan's class?

B. How many extra cookies would Ms. Angelo's class need to have the same number as Mr. Sullivan's class?

The bake sale earned $253. Students used $185 to buy material for the costumes.

A. After buying the material for the costumes, did the students have more or less than $100 left from the bake sale money?

B. Exactly how much money did they have left?

2. The final addition and subtraction word problems in the addition and subtraction chapter of the 3rd grade Singapore Math Primary Mathematics 3A (p. 61):

A factory has 2000 workers.
1340 of them are men.
The rest are women.
How many more men than women are there?

The total cost of an oven and a refrigerator is $2030.
The oven costs $695.
Find the difference between the costs of the oven and the refrigerator.

3. Extra Credit

Which is more likely to draw your child into a math problem: a connection to his or her daily life (e.g., school plays and bake sales), or straight forward language with no excess verbiage?

One problem set turns one-step problems into two step problems; the other offers two step problems whose steps aren't spelled out. Which strategy offers a more meaningful mathematical challenge?

Tuesday, November 24, 2009

What does it mean to be a team player?

"Learning to be a team player" is an oft-cited goal of today's classrooms, and the reason why so many students spend so much time working in groups.

Most of the time, most of these groups will be unsupervised: a classroom teacher with 28 students divided into 6 or 7 groups can only monitor a fraction of what's going on within these groups at any given moment in time. Meanwhile, groups of students, whether they are 6 years old or 16 years old, have trouble staying on task. They may argue, they may goof off, and some of them may opt out and free-ride on their groups mates. The result, in comparison with solo learning environments, is reduced academic achievement.

Is it worth it? Do the social skills obtained by group learning outweigh the academic sacrifice?

I asked a friend of mine who regularly engages in team work at a large law firm.

"Team work," she explained, "means dividing a big task into subtasks, and being able to do your subtask well enough that I don't have to do it over for you."

She's sick and tired, she explained, of the many new hires who know how the schmooze, banter, and charm, yet lack the rigorous analytic training that they need to function as competent team players.

Monday, November 23, 2009

Sociability and feline adoption


A left-brain friend visited this weekend, and recounted to me her trials of adopting a cornish rex. A month after filling out her application, the breeder called her up to say the following:

"I've determined that you would be an unfit mother."

After my friend asked for more information, the breeder explained that all the other prospective "parents" had called up several times a week to inquire about how their cats were doing. My friend, she pointed out, hadn't called once.

"That's because I'm much more comfortable dealing with cats than with people," my friend replied.

Epilogue:

Six months later, my friend received a call from the breeder offering her a cat. "I realized I made a terrible mistake," she explained.

Friday, November 20, 2009

Math problems of the week: 4th grade Mathland vs. Singapore Math

I. The final word problems in Mathland's 4th grade Skill Power, p. 219:

Choose the Answer

Gloria scored 12 points in last night's basketball game She scored 1/6 of her team's points. How many total points did the team score?

A. 24 points
B. 36 points
C. 72 points
D. 84 points

Explain your thinking.

-----------

Which size?

Corn Crunchies are on sale. The 10-oz size is $1.60. The 24-oz size is $3.36. Which size would you buy to et the most for your money?

Show how you know.

-----------

True or False?

A can of cat food costs $1.20. True or false? You can buy 9 cans with a ten-dollar bill.

Explain how you know.

-----------

II. The final word problems in Singapore Math 4th grade Primary Mathematics Workbook, 4B, p. 161-2:

A tank can hold 30.1 gal of water. A bucket can hold 1/7 as much water as the tank. Find the capacity of the bucket.

Neil saved 15 quarters in January. He saved 35 nickels in February. He saved 21 dimes in March. How much money did he save in the three months?

How many quarters are there in $116.75

-----------

III. Extra Credit

Which does your child prefer: doing easier problems and explaining his or her answer, or doing harder problems?

Show how you know.

Wednesday, November 18, 2009

Left-Brain Child book talk tomorrow night in Boston

...specifically in Waltham, north of Boston, at Back Pages Books.

We'll discuss concerns and anecdotes about Reform Math, social classrooms, projects and "personal reflections," and grades, as well as strategies for parents and teachers.

Please spread the word to parents, friends, and teachers of shy, unsocial, analytical, academically gifted, math-inclined, science-inclined, and/or Aspergian children.

UPDATE: EVENT CANCELED!

Fire-induced flooding hit the bookstore while the owner was away for a family emergency, which my publicist only found out about today because she herself is out sick.

Monday, November 16, 2009

Everyday Math author defends his program against Katharine Beals

In today's Philadelphia Inquirer Letters to the Editor, excerpted here:

Katharine Beals' article on the use of "reform math" with students with autism contains many misperceptions about Everyday Mathematics that, as the program's coauthor, I want to clarify ("The 'reform math' problem," last Monday).

Everyday Mathematics was designed for general education students, but it has been effective in special education, including with students with autism.

Beals' claim that students spend large chunks of time working in unsupervised groups is untrue. A teacher supervises student group work at all times. While some assignments are "open-ended and language-intensive," many are not. A balanced curriculum needs simple exercises to build basic skills, as well as more difficult problems.

Beals writes that students "lose points for failing to cooperate in groups, explain their answers, and comprehend language-intensive problems." While decisions about how to grade students are made at the local level, many people believe it's reasonable to require students to work cooperatively, explain their work, and understand word problems.

Everyday Mathematics is not just a "sequence of themes," but a carefully organized sequence of lessons resulting in mastery of a specific set of goals. Its approach is well supported by research, the authors' experience, and decades of classroom experience.

Naturally, accommodations for teaching children with autism must be made, and that's what professionals always do. As with any tool, Everyday Mathematics must be used with professional judgment.

Andy Isaacs

Chicago

Saturday, November 14, 2009

Dysgraphia, dysteachia, dystopia

For some of the prototypically left-brain children I write about in my book, penmanship problems are common. They are worsened by the dearth of penmanship instruction in today's schools. One can ask the same thing about dysgraphia as more and more people are asking about dyslexia: how much of this is merely dysteachia?

Just as dyslexia (or dys-phonics-teachia) ultimately impedes higher-level reading comprehension, so does dysgraphia (or dys-penmanship-teachia) ultimately impede higher level writing. In struggling hands, ideas quickly bottleneck, choking off fluency.

Precisely this kind of writer's block is plaguing a gifted third grader I know. So his mom had him evaluated by an occupational therapist, who confirmed "dysgraphia." Mom brought this diagnosis to the school and asked penmanship tutoring. The answer? "No."

As it turns out, our school district (5th largest in the country) is not obliged to provide support for penmanship instruction... because penmanship isn't part of its official curriculum.

This, despite the fact that, in their many hand-written projects, students are routinely marked off for deficient "neatness."

Thursday, November 12, 2009

Math problems of the week: 2nd grade Everyday Math vs. Singapore Math

I. A sampling of problems from the 2nd grade Everyday Math Student Math Journal, Volume I, "Addition and Subtraction Facts," pp. 20-50.

Use > , <, or =.

6 + 7 ___ 15 - 4
5 + 8 ___ 8 + 5
18 - 9 ___ 5 + 4

-------------

Today is ________________
(month) (day) (year)

The date 1 week from today will be ____________

-------------

Use a number grid.

How many spaces from: 17 to 26? 49 to 28?

-------------

Which is heavier: 1 ounce or 1 pound?

-------------

Write an addition story.

-------------

Play Broken Calculator.
Show 17. Broken key is 2.
Show three ways.

-------------

Draw a rectangle around the digit in the tens place

349
406

-------------

Follow the rule. Fill in the missing numbers.

Rule: + 6

___in___out___
___2____8____
___3 ____9____
___5 _________
___9__________

-------------

Subtract. Use the -9 and -8 shortcuts.

13-9 = ___
14 - 8 = ___
...

II. A sampling of problems from the 2nd grade Singapore Math Primary Mathematics Workbook, Volume I, "Addition and Subtraction," pp. 31-68.

-------------

Compare two sets.
[squared-off picture of 11 flowers, labeled "A," next to squared off picture of 6 flowers, labeled "B"]

11 - 6 = ___
Set A has ___ more flowers than Set B.

-------------

Add

3 + 4 =
30 + 40 =
300 + 400 =

-------------

Subtract
7 - 3 = ___
70 - 30 = ___
700 - 300 = ___

-------------

Subtract.

689
- 32

786
- 73

-------------

Add
7 + 6 =
27 + 6 =
527 + 6 =

-------------

Add

264
+ 36

486
+ 54
...

-------------

A watch costs $167.
A camera costs $48 more than the watch.
What is the cost of the camera?
What is the total cost of the camera and the watch?

The total cost of the camera is $ ____
The total cost of the camera and the watch is $ _____

-------------

Add or subtract.

251
-170

358
+416

-------------

David collected 930 stamps.
He had 845 stamps left over after giving some stamps to his friends.
How many stamps did he give to his friends?


III. Extra Credit:

Discuss the phrase "a mile wide and an inch deep."

Everyday Math tells people to "trust the spiral." Do you?

Tuesday, November 10, 2009

Op-Ed in yesterday's Philadelphia Inquirer

Here.

Be sure to check out the comments that appear below the article.

For all the talking points that Reform Math proponents deploy in response to the general criticisms, I haven't yet seen any talking points that respond to concerns about children on the autistic spectrum. Has anyone else?

Since it's well-documented--and generally agreed--that AS children require structure, direct instruction, and discrete tasks, and that many of them have the potential to excel in math, and since the education establishment's purported missions include (1) mainstreaming and (2) catering to different learning needs, I believe this is a fruitful message to keep plugging.

Monday, November 9, 2009

Gifted Exchange

Laura Vankerkam of Gifted Exchange has honored me with an interview here.

She's also got a great piece on the BASIS Schools in Arizona. As Vanderkam notes, "the schools explicitly model their curricula on the best practices exhibited in other countries that routinely trounce the US in international comparisons."

Sunday, November 8, 2009

Mitosis, rote memorization, and the unchanging traditions of grade school biology

Before mitosis begins, the chromosomes and other cell materials are copied. [are copied? Who or what does the copying???] The pairs of centrioles, which are two cylindrical structures, are also copied. [Besides being cylindrical, what is a centriole, and what is its significance for mitosis???] Each chromosome now consists of two chromatids. [Remind us what a chromatid is!!!]

Mitosis Phase 1
Mitosis begins. The nuclear membrane brakes apart. [Why?] Chromosomes condense into rodlike structures. [Why is the new, rodlike structure important and significant?] The two pairs of centrioles move to opposite sides of the cell. [Significance?] Fibers form between the two pairs of centrioles and attach to the centromeres. [Remind us what a centromere is and why it is significant!]

Mitosis Phase 2
The chromosomes line up along the equator of the cell. [How??? and Why???]

Mitosis Phase 3
The chromatids separate [How?] and are pulled to opposite sides of the cell by the fibers attached to the centrioles. [This crucial event should be the centerpiece of the whole discussion of mitosis].

Mitosis Phase 4
The nuclear membrane forms around the two sets of chromosomes, and they unwind. The fibers disappear. Mitosis is complete.
From Cells, Heredity, and Classification (Holt, Rinehart and Winston), with my queries in brackets.

With all the questions it begs and explanations it lacks, this is little more than a list of terms and series of steps to memorize, with no obvious general concepts to guide or interest you. This approach seems to have a long history. It includes my own biology book of a generation ago, which is why I never pursued biology after 9th grade.

But now that my autistic son is studying it in middle school, I need to understand it better.

Only after multiple readings of the passage above did I sort of figure out what the underlying concepts were. (Perhaps if I were a more visual thinker, it wouldn't have taken me so long.)

Assuming that I'm more or less on target, it strikes that a more engaging introduction to mitosis might go somewhere along these lines (ideally generated by some sort of Socratic dialog, with accompanying illustrations):

We already know that cells consist of crucial elements, for example, the mitochondria and the chromosomes. We also know that for organisms to grow, their cells must divide. But is cell division as simple as a cell dividing itself into two? Bear in mind that each "half" of the cell must have all the crucial elements. This means that each element must be copied, and each half must end up with one copy of the element.

Making sure that each "cell half" has exactly one copy of a given element is particularly complicated when it comes to the chromosomes. Is it enough for each chromosome to make a copy of itself? Imagine what would happen if the chromosome copies simply swam around in the cytoplasm while the cell divides. Then what's to stop one half from ending up with two copies of chromosome 1 and no copies of chromosome 2, or vice versa? We already know how each chromosome contains different sets of crucial instructions for the cell, so the results of this kind of lopsided split would be disastrous.

So how can a cell make sure that exactly one copy of each of its dozen or more chromosomes ends up in each "cell half" before the division? Since the cell has no "brain" or other centralized information processor, as soon as the chromosome copy separates from its original, there's no way for the cell to "know" which copy goes with which original, and therefore no way to guarantee that each cell half gets exactly the right number of copies.

Well, suppose each chromosome copy remains attached to the original up until right before the cell divides. This preserves the information about which copy matches up with which original. Then suppose the chromosome pairs (original plus copy) all line up in such away that a simultaneous, symmetrical force emanating from each cell half can pull them apart, so that each original copy ends up in one half while its copy ends up in the other half.

Let's picture how this could happen. Imagine if the chromosome pairs line up along the equator of the cell, with one pair member on each side of the equator. Now imagine tentacles reaching out from the middle of the edge of each cell half and pulling at each chromosome pair from each side. If these tentacles are equally strong, and strong enough to separate the chromosome pairs, the result is just what we want: exactly one copy of each chromosome pulled into each cell half.

Friday, November 6, 2009

Math problem of the week: 5th Grade Trailblazers vs. Singapore Math

I. The first place value/multiplication problems in Math Trailblazers Student Guide 5, pp. 48-49:

Reach for the Stars

Mr Moreno's class is about to begin a unit on the solar system. Irma, Alexis, and Nila thought it would be fun to decorate the classroom. Mr. Moreno allowed them to stay after school to work on this project.

[Illustration of three girls in front of a blackboard and the following cartoon-bubble dialog]

Irma: Let's make a banner of stars.

Alexis: Great idea. We can make a banner with 2 rows of 30 stars.

Nila: Then how many stars do we need to cut out?

Irma: Since 2 × 3 is 6, I know 2 × 30 is 60.

1. A. Explain in your own words how Irma solved 2 × 30 = 60.
B. How would you solve 2 × 30 = 60? Explain your method to a friend.

[Illustration of the three girls in front of a blackboard that now has two long rows of stars on it, and the following cartoon-bubble dialog]

Nila: How about putting stars on the ceiling? Maybe we could get a parent to help us put them up?

Irma: First we need to know how many stars we need. Let's put a star on each ceiling tile. I counted 20 tiles wide and 30 tiles across. How many tiles is that?

Alexis: Looks like we have to multiply by numbers ending with zeros again!

2. Irma learned to look for patterns when multiplying numbers that end in zeros. Find the following products. Use a calculator if needed. Describe the patterns you see.

A. 2 × 3 =
B. 2 × 30 =
C. 20 × 3 =
D. 20 × 30 =
E. 20 × 300 =
F. 200 × 30 =
G. 200 × 300 =

II. The first place value/multiplication problems in Singapore Math Primary Mathematics 5B, p. 16:

Multiply.

(a) 254 × 10 =

(b) 692 × 100 =

(c) 93 × 40 =

(d) 57 × 1000 =

(e) 43 × 600 =

(f) 392 × 800 =

(g) 728 × 5000 =

(h) 8056 × 3000 =

III. Extra Credit:

1. Which activity leads to deeper mathematical understanding: calculator-facilitated pattern recognition, or pen and paper calculation? Which of these is a more important 21st century skill?

2. Estimate the reading comprehension skills necessary to identify the numerical typo in the second Trailblazers problem.

3. Enumerate the math skills necessary to do the Trailblazers vs. the Singapore problem sets.

4. Which problem set is more accessible to:
-Children with autism and/or language delays
-Children learning English as a second language
-Children with attentional delays/disorders

Wednesday, November 4, 2009

Is the world right-brained or left-brained?

Or, put another way, why is my book, Raising a Left-Brain Child in a Right-Brain World, "frequently bought together with" Left-Brain Children in a Right-Brain World?

In an earlier post, I discussed how author Jeffrey Freed and I ascribe overlapping characteristics to "right-brain" and "left-brain." In particular, both his "right-brain" and my "left-brain" characteristics include:

-being good at puzzles
-shying away from hugs
-performing better on one's own than when working in a group
-unusually dependent on structure

But what about the world? Is it left-brain, as Freed claims, or right-brain, as I do?

Like my "world," Freed's "world" mostly encompasses the education system. This, he argues, "has been fine-tuned to accomodate and encourage the kind of thinking that happens in the left hemisphere of the brain." In particular, he claims:

-"Lectures and reading assignments--left-brain teaching methods--are still the norm."
-"Homework is repetitious and a left-brained effort to hammer concepts into children's brains."
-Teachers rarely "use spatially dominant activities as anything but a passing fancy in the classroom."
-Students frequently say things like "I've never met a teacher who isn't a total geek."
-Subjects are "compartmentalized" rather than integrated.

Freed's perception of the education system leads him to advocate for such changes as:

-"hands on activities and experiential activities such as building models, measuring things, performing science experiments, and going on field trips."
-more use of color
-less use of phonics in reading instruction
-interdiciplinary project-based learning

But as anyone who spends any time in the classroom knows, such practices are commonplace, particularly in our model schools, while lectures, textbooks, geeky teachers, and compartmentalized assignments are becoming rarer and rarer.

So there are two possibilities.

Either Jeffrey Freed, like too many other authorities who dabble in education (cf here, here, here, and here), hasn't spent enough time visiting actual classrooms.

Or the education system has changed drastically since 1997, when Freed's book was published--perhaps because more and more schools have been following his advice.

Either way, when it comes to the grade school classroom, it's an increasingly right-brain world--so much so that even many of Freed's right-brainers are in trouble.

Monday, November 2, 2009

Book Talk, Thurs, Mount Airy (Philadelphia)

I'll be discussing "Raising a Left-Brain Child in a Right-Brain World" at the Big Blue Marble (551 Carpenter Lane) this Thursday at 7:00 pm.

If you're a Philly-area parent, teacher, and/or left-brainer, please come and/or spread the word. Right-brainers are welcome, too. I'm hoping for a really lively discussion.

Sunday, November 1, 2009

Why do our top math & science students defect?

This week's Education Weekly reports on a new study suggesting that the problem isn't that America's K12 schools are producing fewer highly qualified math and science graduates. The problem, rather, lies with:

...the top high school and postsecondary students, as measured by ACT and SAT scores and college grade point averages, who choose other studies and occupations, a trend that appears to have begun in the 1990s, the authors conclude.
Lack of STEM (science, math, engineering, and technology) ability, the new study concludes, "is not what is driving many students away." The implication: K12 math and science education is not at fault.

But aptitude tests like the ACT and SAT may not be the best measure of how well prepared American-born college students are in comparison with their peers from other countries, a much higher proportion of whom don't defect from STEM. Perhaps one reason why American-born students do defect is that they are ill prepared to compete, as Allison reports on kitchentablemath:
The kids with natural math talent who are not utter prodigies DO NOT come from behind at a school like Harvard, MIT, Caltech in the math or sciences. They are completely outclassed by the Russians, Czechs, Estonians, Koreans, Japanese, Singaporeans, etc.
The watered-down Reform Math that also began in the 1990's only makes matters worse.

Besides poorly preparing its best math and science students--along with everyone else-- our K12 schools, thanks largely to Reform Math, are also turn many of them off to math and science. As one defector who eventually returned to STEM comments on the Education Week article:
As a teen, science and math were easy and not challenging, even higher level AP courses. Music and the arts encouraged creativity and offered tasks that continued to challenge me.
It's certainly tempting for certain people to believe, as the Education Week study proposes, that it's simply that "that top-tier students may regard non-STEM careers—in health care, business, and the law—as higher-paying, more prestigious, or more stable." But it may ultimately be their K12 experiences that pull them away from STEM.

Thursday, October 29, 2009

Math problem of the week: 7th Grade 1920's math vs. Connected Math

1. From the last graphing problems in Hamilton's Essentials of Arithmetic: Higher Grades, Chapter II, "graphs" section (intended for "year 7"), p. 131:

Trace a curve to illustrate the following changes in temperature for a certain day: 7 A.M., 400; 9 A.M., 420; 11 A.M., 460; 1 P.M., 500; 3 P.M., 530; 5 P.M., 490; 7 P.M., 460

2. From the last graphing problems in 7th grade Connected Mathematics Variables and Patterns: Introducing Algebra, Investigation 5, "Using a Graphing Calculator," p. 68:

Write a letter to a friend explaining how to use a graphing calculator to make graphs and tables. Use a specific example to illustrate your explanation.

Tuesday, October 27, 2009

Sunday, October 25, 2009

"Left Brain Child:" Two Book Talks in Western New England

I'll be giving two talks about my book this week:


On Tuesday, 10/27, at 7:00 PM in Pittsfield, Mass (Chapters Bookstore).

On Wednesday, 10/28 at 7:00 PM in Manchester, Vermont (Northshire Books).

Please spread the word to anyone you know in the area who works in education, or who has a shy and/or unsocial and/or socially awkward and/or analytical and/or mathematically inclined child. I'm hoping for lively discussions.

Friday, October 23, 2009

Math problems of the week: 3rd grade Investigations vs. Singapore Math

Two ways to learn about the number system by "making numbers":

1. From the beginning of 3rd grade Investigations (TERC) Landmarks in the Hundreds booklet, p. 11:

Ways to Make ___

Choose a number to write in the blank above.
Find equal groupings that make your number.
Record your results in the chart.

Note: In class, we use cubes to make groupings. At home you might use beans, popcorn, pennies paper clips, pebbles, coins, or dots drawn on paper.

The number I am making is ____
---------------------------------------------------------------------------------------

Number of cubes in each group: ____
Picture of how you made your number with these groups


Skip count by the number of cubes in each group.
----------------------------------------------------------------------------------------

Number of cubes in each group: ____
Picture of how you made your number with these groups


Skip count by the number of cubes in each group.
----------------------------------------------------------------------------------------

Number of cubes in each group: ____
Picture of how you made your number with these groups


Skip count by the number of cubes in each group.
----------------------------------------------------------------------------------------

Numbers I tried that didn't work
----------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------

2. From the beginning of 3rd grade Singapore Math, Primary Mathematics 3A, Standards Edition, "Numbers 1 to 10,000" unit, p. 13:

Use these cars to make six different 3-digit numbers.

[3] [9] [2]

The three digit numbers are:

----------------------------------------------------------------------------------------
Use these cards to make different 3-digit numbers.

[7] [2] [8]

The greatest number is __________.
The smallest number is __________.

----------------------------------------------------------------------------------------

What is the greatest 4-digit number that you can make using all the digits 1, 0, 3, 8?


____________________

----------------------------------------------------------------------------------------

What is the smallest 4-digit number that you can make using all the digits 7, 5, 2, 6?

____________________

----------------------------------------------------------------------------------------

3. Extra Credit:  

Compare the ratio of time expenditure to learning in each problem set.

Wednesday, October 21, 2009

Caging birds: the worst of both worlds

Beth’s comment on Monday’s post really captures the sad irony of today’s schools:

The tragic reality is that our schools don't do anything well. The fact that the humanities are suffering doesn't mean that mathandscience is taught well. The fact that the schools don't have the rigorous content and skills of the traditional approach doesn't mean that they encourage true creativity like the progressive approach.
They just don't do anything right. They've somehow managed to weld together the authoritarian, anti-creative, carrots-and-sticks approach of the worst kind of traditionalism, with the hollowed-out content and mushy thinking of the worst kind of progressivism.
Beth’s words returned to me last night, when I was marveling at some wildly creative white-on-black drawings that my daughter had recently produced at home: scenes teeming with ghosts, birds in flight, and worried children.“Do you ever get to draw this kind of thing at school?” I asked her, suddenly wondering whether the realism requirements that have persisted since kindergarten extend beyond writing (“realistic fiction”) to art.

“During indoor recess we can draw whatever we want to.”

“What about during regular class time?”

“Then we can’t draw imaginary stuff.”

“So during class time, ever since kindergarten, you haven’t been allowed to draw or write imaginary stuff?”

Apparently at the very end of 2nd grade they were allowed to write (and illustrate) a work of “imaginative fiction,” but my daughter ran out of time before she finished her story.

Further constricting her, most of the realistic fiction she’s tasked with producing is supposed to be about her personal life--a requirement she increasingly resents.

“Why do they want to spy on us?”

“They” may know something about her personal life, but her creative potential remains a well-kept secret.

Monday, October 19, 2009

Myths about left-brain schooling, II: media complicity

Mark Slouka's recent Harper's article about the supposed dominance of math and science in our schools prompted me to write the following letter to the editor:

If Mark Slouka [“Dehumanized”] were to visit an American grade school classroom, he would see that math and science do not rule the school. While classes called “math” and “science” still exist, they contain far less actual math and science than they did a generation ago. Indeed, Slouka’s observations about today’s reading assignments apply as well to assignments in math and science: intended, in Slouka’s words, to “provide students with mirrors of their own experience,” they have students connecting math and science to their personal lives rather than doing challenging problems. This worries many mathematicians, scientists, and parents, not because they want children, in Slouka’s words, to be “hired by Bill Gates,” but because we’re raising a generation of innumerate, scientifically illiterate citizens and turning off our brightest young lights in math and science.
But Harper's declined to publish any letters challenging the article's key assumption that math and science control our schools. Of the three letters they did publish, only one mentioned math education. Its author, a longtime "teacher of mathematics," writes:
I... choose to teach mathematics with reading assignments, art projects, oral presentations, even poetry--all to encourage critical thinking in my students, and to cultivate questioning minds.
Harper's doesn't seem to recognize that, thanks in large part to the many teachers like this one, math and science don't rule our schools.

Friday, October 16, 2009

Math problems of the week: 1930's Algebra vs. Interactive Math Project

1. The final problem in the pure algebra portion of A Second Course in Algebra (first published in 1937), from the "Binomial Theorem" chapter (which is followed by a chapter on logarithms and another on trigonometry), p. 335:

A man can travel from town A to town B by plane in 2 hours and 10 minutes, or by car in 6 hours and 30 minutes. Bad weather forces him to land when he is 65 miles from B and he completes the trip by car. If he traveled the same length of time in the car as in the plane, how many miles is it from A to B?

2. From the final homework assignment in the final algebra chapter of Interactive Mathematics Project Integrated High School Mathematics Year 4, "The World of Functions," p. 345:

Personal Growth

As part of your portfolio, write about your personal development during this unit. You may want to specifically address this issue.

How do you feel you have developed during this unit in terms of your ability to explore problems and prove conjectures in mathematics?
You should include here any thoughts you might like to share with a reader of your portfolio.

[The "conjectures" in question involve comparisons among the graphs of certain minimally modified functions, e.g., f(x), f(x) + b, and f(x+b)]

3. Extra Credit:

If your daughter is interested in a career in mathematics or science, would you worry more about the male perspective in the first problem, or the ratio of effort to learning in the second problem?

Wednesday, October 14, 2009

Right-Brain Children in a Left-Brain World, or Left-Brain Children in a Right-Brain World?

Checking out my book's Amazon page, as I can't help doing from time to time, I've learned that Raising a Left-Brain Child in a Right-Brain World is "frequently bought together" with Right-Brained Children in a Left-Brained World.

From such a sales paradox, two obvious questions emerge:

1. Why?
2. Is the world in question Right-Brained or Left-Brained?

Re question 1, one possibility is that people are simply satisfying their curiosity--e.g., about how these two books could co-exist. Or about how things could have changed so dramatically in the dozen years between the publication of Right-Brained Children in a Left-Brained World and that of Raising a Left-Brain Child in a Right-Brain World. Or, if things haven't changed, about whether it's right-brained or left-brained children who are more at sea in today's world.

Another possibility is that the two books appeal to overlapping groups of readers. To explore this, I acquired a copy of Right-Brained Children and read it last night. My conclusion: yes, there is indeed some overlap--in fact, quite a bit.

Right-Brained Children is about children with ADD. Author Jeffrey Reed, who has been working with such children since well before the term "ADD" became a household label, has long considered his clients as quintessentially right-brained.

But Reed's definition of "right-brained" not only differs mine, but overlaps somewhat with my "left-brained." Traits that he calls "right-brain" and I call "left-brain" include:

>being good at puzzles and mazes
>shying away from hugs
>being better at thinking of ideas if working alone rather than in a group
>being a late bloomer
>at the extreme, being on the autistic spectrum

I don't disagree that these traits are associated with ADD. Some researchers, indeed, have hypothesized that there's an overlap between autistic spectrum disorders and ADD. Nor do I believe that all children on the autistic spectrum are what I call "left-brain."

However, while Reed is basing his terms on what little has been scientifically concluded about brain hemispheres and personality traits (not much!), I'm basing my terms exclusively on the everyday vernacular, which commonly associates "left-brain" with puzzle skill, introversion, and working best independently rather than in groups.

One problem with Reed's dichotomy is that it raises more questions than it answers about the autism-ADD connection. He claims that the typical child with ADD is:

...extremely sensitive to your moods and expressions, reading your body language tone of voice, and look in your eyes far better than do most people. He can tell the moment you walk in the door if you had a good or a bad day at the ofice. If you're happy, he'll pick up on your giddiness; if you're on edge, he's apt to act out and show anger as well.
But for children with autism, such empathy is an area of weakness--indeed, it is a core deficit of autism. Nor do the ADD children I know strike me as more empathetic than their peers. Is it really the case that most of them are unusually right-brained in their ability to empathize with others?

As to the question of whether the world is right or left-brained, stay tuned for an upcoming post.

Monday, October 12, 2009

Right-brained science and disembodied facts

An article in last week's Education Week enthusiastically reports on an interactive science program in which scientists conducting research in the Phoenix Islands share their blogs entries, and correspond by email, with students in a marine biology class at a New Hampshire high school. The blog entries, says Education Week, provide:

--"first-person descriptions of topics they cover, such as coral-reef ecology and damage caused to them by pollution"

--"underwater photos and descriptions of abundant aquatic life—gray reef sharks, moray eels, giant clams, bohar snapper, and barracudas."

--"descriptions of scientific processes, like making observations and collecting data"

--"musings on life at sea: how to avoid the bends while diving, how to guard against infection, what the scientists are eating, and the researchers’ offhand reflections—on a rare species of bird or fish, or a glimpse of the Southern Cross in the night sky."

What could possibly be wrong with presenting such compelling material in such an interactive, real-time fashion? The problem is that this is a huge gamut of topics--from coral reef ecology to the bends--that emerged haphazardly in whatever order they happen to come up in blog entries and email mesages. Your typical high school student, meanwhile, is unlikely to have sufficient background knowledge to organize them systematically in long term memory.

Nor do the classroom follow-up activities appear to deepen students' systematic understanding. According to Education Week, their teacher, Ms. Mueller-Northcott, used the various blog entries to:

--"begin discussions and to prompt students to record journal observations about the scientists’ expedition. "

--"pose experimental-design questions to the teenagers: How could you study humans’ impact on coral reefs? Where would you do your research? What data and equipment would you need?

Journaling about a scientific expedition doesn't do much to deepen one's knowledge or conceptual understanding; as for experiemental design, this is something for experts, not novices, and involves questions far more subtle (and analytical) than desired location and equipment.

However, as Education Week reports, this particular venture is "just one of many aimed at connecting students through technology with scientists doing research in the field, an increasingly common practice in schools." The goals? To:

--"mak[e] scientific studies and careers more attractive to young people"

--"quash the stereotype of the scientist conducting obscure research in dreary isolation."

In other words:
The value for students does not come from scientists’ answering factual questions—that can be covered in class—but rather from the excitement of seeing a scientist at work: struggling, making breakthroughs, documenting joys and frustrations.

It's unfortunate that what the article brushes off in an easy aside--that facts "can be covered in class"--is happening less and less in today's classrooms.

But the real agenda of all of these interactive ventures isn't to teach scientific knowledge in any systematic way, but to promote science as anything but systematic (and analytical, and left-brained). As NASA engineer Heather Paul, a leading advocate for such programs puts it: “We need to work hard to dispel the myths.. [that] we’re brainiacs who sit in the lab all day... [In science] you have to be passionate about what you want to do. ... It’s not just a job, it’s a way of life.”

Like so many other well-intentioned but misguided right-brain fads in education, if only mere passion were all it took to make progress...

Saturday, October 10, 2009

Tae Kwon Do and the linear learning style

Of all recent situations I've been in, the one that reminds me most of what a linear, one-thing-at-a-time kind of person I am is when all three black belts, all zero red belts, all zero blue belts, and the one other green belt are all absent and I'm called upon to teach Tae Kwon Do class. This has happened twice so far, and will happen again soon.

As anyone familiar with martial arts classes knows, teachers typically take the class at the same time that they teach it. So here I am, simultaneously trying to kick and punch out the best kicks and punches I can model, count out each kick or punch from 1 to 10 in Korean, and scan the row of students facing me to make sure everyone's more or less "on target." I can practically feel what I imagine to be the unsually narrow bandwidth of my brain's intake circuitry straining to the breaking point, ready to short out at the slightest additional distraction.

In his "Why Students Don't Like School," Dan Willingham argues convincingly that there is no such thing as an auditory vs. visual learning style. But what about linear vs. holistic learners? I'm convinced I not only perform better, but also learn better, when things are presented to me one at a time, and I've heard many other self-identified "left-brainers" say the same thing.

But I'm still waiting to hear whether any empirical research backs this up. Or is it possibly the case that everyone learns better when things come one at a time?

Of course, when teaching (or taking) a martial arts class, one thing (or one muscle) at a time isn't really practicable.

Thursday, October 8, 2009

Math problems of the week: Systems of Equations in CPM vs. 1900's math

1. The only systems of equations that students are required to solve algebraically in the CPM (College Preparatory Mathematics) Algebra Connections "Systems of Equations" chapter (published in 2006):

y = 1160 + 22x
y = 1900 - 15x

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y = 6 + 1.5x
y = 2x

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y = 2x -3
y = -x + 3

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y = 2x -3
y = 4x + 1

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y = 2x - 5
y = -4x - 2

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y = -x + 8
y = x -2

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y = -3x
y = -4x + 2

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y = 2x - 3
y = 2x + 1

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y = -4x -3
y = -4x + 1

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2. A subset of the over one hundred systems of equations in the Wentworth's New School Algebra "Simple Systems of Equations" chapter (published in 1898):

5x + 2y = 39
2x - y = 3

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x/3 + y/2 = 4/3
x/2 + y/3 = 7/6

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x + y - 8 = 0
y + z - 28 = 0
y + z - 14 = 0

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6x - 2y + 5z = 53
5x + 3y + 7 = 33
x + y + z = 5

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2x + 3y + 1 = 31
x - y + 3z = 13
10y + 5x - 2z = 48

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1/x + 2/y - 3/z = 1
5/x + 4/y + 6/z = 24
7/x - 8/y + 9/z = 14

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2/x - 3/y + 4/z = 2.9
5/x - 6/y - 7/x = -10.4
9/y + 10/z - 8/x = 14.9

3. Extra Credit:

(a) Discuss why CPM, but not New School Algebra, has to stipulate that the simultaneous equations be solved algebraically (rather than graphically or by "guess and check").

(b) Discuss the arithmetic and algebraic skills required by each problem set.

(c) Relate your answer in (b) to the final assignment in CPM's "Simultaneous Equations" chapter, the TEAM BRAINSTORM:

With your team, brainstorm a list for the following topics. Be as detailed as you can. How long can you make your list? Challenge yourselves. Be prepared to share you team's ideas with the class.

Topics: What have you studied in this chapter? What ideas and words were important in what you learned? Remember to be as detailed as you can.

Wednesday, October 7, 2009

How to ration high grades, part IV (addendum to Part III below)

3. Make sure that even the homework directions are clear only to someone who was paying attention in class.

Tuesday, October 6, 2009

How to ration high grades, part III

In addition to the strategies enumerated in Part I and Part II, there's also the strategy of making successful completion of homework dependent on paying attention in class:

1. Expect students as young as 8 to follow oral directions about which worksheets to rip out and put in their bags for homework. Anyone who fails to pay proper attention can then be given an incomplete.

2. Rather than basing homework questions on the material in a textbook, article, or information sheet that goes home in the student's backpack, base these questions on material that was only addressed during class time (e.g., "What did we learn in class today about rocks?"). That way, anyone who failed to pay enough attention during class will under-perform on the homework.

By favoring those who pay attention in class, you can keep high grades from certain students who might otherwise have earned them, specifically:

1. The bright kid who is bored in class and tends to space out.
2. The dreamy, developmentally skewed math/science/computer buff whose analytical skills far exceed his or her organizational skills and ability to pay attention.

Saturday, October 3, 2009

Actual scientific uncertainty

...as opposed to the post modern notion that science (and math) is fraught with uncertainty:

Michael Brooks' 13 Things That Don't Make Sense: The Most Baffling Scientific Mysteries of Our Time

Just finished reading this fascinating, wonderfully researched book.

Yes, there are scientific mysteries--among them, some true bafflers. But that doesn't mean that there isn't a scientific explanation out there somewhere.

Another source of scientific uncertainty: fringe positions have sometimes proved correct. Much as we non-scientists would like to defer to the expert majority, this majority doesn't always get it right. As in all fields, there are egos, fads, and bandwagon effects.

But what's truly special about science as a discipline is that, eventually, errors are revealed and something closer to the truth emerges. Wouldn't it be nice if all human endeavors were like this?

Thursday, October 1, 2009

Math problems of the week: 2nd grade Investigations vs. Singapore Math

I. The entirety of the 2nd grade Investigations "Assessment: How Many More?" (session 2.6, "How Many Tens? How Many Ones?"), administered at the end of May:

1. Jake collects wizard stickers.
He has 46 wizard stickers.

How many more does he need to have 60?

a. Write an equation that represents the situation.

b. Solve the problem and show your work.


2. Sally has 76 marbles.

How many more marbles does Sally need to have 100 marbles?

a. Write an equation that represents the situation.

b. Solve the problem and show your work.


II. Two of the 15 problems in the second-to-last Review in 2nd grade Singapore Math, Primary Mathematics 2B (Standards Edition), p. 162:


9. There are 120 boys at a concert.
There are 85 more girls than boys.
19 girls and 16 girls wear glasses.
(a) How many girls are there at the concert?

(b) How many children are there altogether?

(c) How many children do not wear glasses?

13. Kelly has $6.80.
She wants to buy a photo album that costs $8.50.
How much more money does she need?


III. Extra Credit:

Compare the level of higher-level thinking involved in writing an equation that "represents" the situations described in the first problem set with the higher-level thinking involved in doing the multi-step problem and the three-digit problem in the second problem set.

Why does the first problem set, but not the second, explicitly require students to show their work?

Tuesday, September 29, 2009

Out today: "Raising a Left-Brain Child in a Right-Brain World"

While this book is most obviously for parents of left-brainers, it originated as more of a general education critique. That is, I've always used lay terms "left-brain" and "right-brain" (with the concepts they casually denote as organizing principles), but initially spent more time arguing that "right-brain" trends--the emphasis on sociability and uninstructed visual "creativity" over analytical essays and mathematically challenging math problems for example-- are bad for all students, left- and right-brained.

But focusing, specifically, on the very real needs of left-brain students gives me a more personal, specific-child-focus that should bypass some of the political polarization of the education debate. And I do strongly believe that left-brainers, in particular, are being shortchanged by The System--in all the ways I've discussed in this blog as well as in the book.

On the other hand, I continue to believe that the "right-brain" trends I talk about are bad news for all students.

On the third hand, if you know anyone with a bright, quirky, and/or social awkward child who is frustrated and/or under-performing at school, I certainly won't discourage you from mentioning this book to them.

Saturday, September 26, 2009

Reading "all about me" replaces analytical reading

...codified as early as second grade in this Text-to-Self Connections T-Chart, duly completed by my daughter:

Making Text-to-Self Connections T-Chart

The author said: Tom and Lucy got lost in a dark cave.
That reminds me of: I got lost at the beach because I couldn't find my grandma.
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The author said: The Littles went on a hike. It was so far.
That reminds me of: I went on a hike that was faraway too.
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The author said: The Littles got stuck in a fridge.
That reminds me of: I got trapped in my room before but not in a refrigerator.
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Figuratively trapped in her room by the many assignments like this one, not to mention uninspired and resentful ("Why do they want to spy on us?!"), my daughter nonetheless earned a ☺on this T-Chart.

Thursday, September 24, 2009

Autism Diaries XIV: The Wikipedia Entry Thought Experiment

Last night, J informed me that he'd managed to hack through the firewall blocking our household computers' IP-addresses from Wikipedia--a ban that resulted from J's repeated "Wiki-vandalism" of their pages over the last school year. (No sooner had I shown him Wikipedia as a great source on black holes, time travel, and the Grandfather Paradox than he figured out he could edit it, thereby entering a whole new arena for mischief--and earning us a 6-month ban).

Once again able to edit Wikipedia articles--at least temporarily--he cautiously added a line or two to the ceiling fan entry about ceiling fan chains (if you pull them too hard, they might break), to the beach house entry (some beach houses have ceiling fans), and to the restaurant entry (some restaurants have ceiling fans).

I'd be surprised if any of J's edits are still there--we've seen how alacritous Wikipedia's established editors are about damage-control. But what is surprising is that J would be surprised as well.

I know this because of the Wikipedia Thought Experiment I conducted on him during the long hikes we took on our summer vacation. One of the things he'd carry on about was his Wiki-vandalism, and after dozens of conversations about this it finally occurred to me to ask him about which of his proposed Wikipedia edits would survive Wikipedia's administrators. For edits like "I am going to kill you," he already knew the answer; but right away he also realized that obvious entries ("some fans are on fast"), trivial entries ("some fans have five blades"), or entries that aren't of general interest ("Ari's house has 10 ceiling fans") also wouldn't endure.

So here's yet another Theory of Mind/perspective-taking exercise for children on the autistic spectrum: along with the Sally-Ann and Smarties Tests, the Wikipedia Entry Thought Experiment.