Sunday, January 31, 2010

Mathematically gifted boy finally gets what he needs

Shortly after I published an Op-Ed in the Philadelphia Inquirer on how Reform Math programs like Everyday severely shortchange children on the autistic spectrum, the grandmother of an extremely gifted eleven year old boy (IQ: 180) wrote to me about how gifted children, too, are shortchanged by the current system. With her permission, I share her story here:

I loved your editorial. You are so, so, so right about how math is taught today. But, not just for autistic children--for all kinds of kids.

As to your statement about autistic children losing points for not explaining their answers and future engineers languishing--you are so right! Not only are the autistic children's futures being stunted--the gifted kids are, too. We've been fighting for my g.son to be taught at a level commensurate w/his abilities ever since pre-kindergarten when he taught himself double digit math and could do it in his head. He's now 11 and not one school (he's been in 4) have deigned to put him where the heck he belongs. He might as well spend his time drooling on his desk for all the good school has done for him so far.

Finally, this year in 7th grade, with pre-algebra (7th grade) and algebra (8th grade) in one building, we thought we had a shot at having him put in 8th grade algebra. He passed the requested pre-algebra test, but even so, when we asked the principal to put him in Algebra, the response was, "We've never had an 11 y.o. in Algebra I. I don't know how we could do that."

These are the people in charge of your math and science gifted autistic and non-autistic children. People so bereft of imagination that they cannot figure out they could let a kid walk down the hall to the Algebra class instead of keeping in pre-Algebra class. But, I guess no worse than the "upper school" administrator who wouldn't let my g.son (during first grade) go into third grade reading because he wasn't 8 yrs. old. Didn't matter that he could already read at the third grade level.

Not only are gifted children being penalized for being smart, they're penalized for not making more work for themselves. As you said, they get zeroes when they have the right answers, but are able to do it in their heads and don't show their work.

But, also, the schools' solution for "challenging" these kids is to give them extra work after they've done the regular work--and most of the time the "challenging" work is also stuff these kids already know. Who wants to do extra boring work? Not these kids! And then the teachers say they can't possibly be advanced 'cause they're not doing the "challenge" work, which is nothing more than busy work offered to make teachers and administrators think they're accommodating these advanced learners.

In my experience, no one cares about extremely gifted children who could be advanced ahead of their peers were there a framework in place. Some statistics show that 50 percent of dropouts are gifted children (and I'll bet some of them are autistic or Asperger's), yet not one single person I've spoken to or written to sees the connection between boring our children to death and dropout rates. Everyone thinks these kids can learn advanced subjects on their own outside of school (a fallacy), they will fail when placed with older children (another fallacy) and ought to sit down and shut up while in school--oh, except for that hour every week they're pulled out for gifted class--never mind that they're gifted 24/7.

I've contacted Rowan Univ. to talk about setting up a weekend program like Montclair, written to Jill Biden (VP Biden's wife) because she is in the teaching profession, and to Colin Powell because he recently made a speech about education, and no response at all except for Mrs. Biden who wrote back thanking me for my thoughtful message and then never even mentioning what my thoughtful message was about (I think it was a form letter). Even the people in the state gifted organization tell me not to bother, no one cares.

I've contacted all kinds of fancy schools asking if they would place my g.son according to his ability and not his age and the answer is always no. Heck, there are only a couple of universities in the country that actually offer degrees in gifted education, let alone gifted and disabled by something like autism.

Last week she wrote me again with a wonderful update that should inspire everyone who works with gifted children to see that appropriate settings are not only attainable, but can bring about fantastic improvements and unexpected miracles:
After speaking with the dean at the local community college, they allowed him to register for a math class. We are now two weeks into the class and a transformation has taken place in Christian that can only be attributed to magic.

When he entered school at age 4 years, he changed from an almost perfect kid (which was ironic 'cause his mother was the hardest kid on earth to raise!) into a child just filled with anger and frustration that spilled over into his life at home. My Lord! This child has been anything but pleasant between pre-kindergarten and two weeks ago. He gave Lord Voldermort a run for his money!

Now he's apparently in the proper educational setting (even tho' he's only 11 and in college) and the 4-year-old we had the day before he started pre-kindergarten has returned! He's happy, he's content, he's polite, he's empathetic, he can't wait to get to class. No more angry outbursts, no more fights with his brother (his 8-year-old brother is stunned and keeps asking, "What happened?"), no more defiance (we love that part!) , no more sulking, no more impulsive behavior, no more begging him to do his "home schooled" work (or like we used to do, beg him to do his regular school work during the times he was in public school).

He says he doesn't need his ADHD medicine anymore and he's right. We stopped it, expecting something awful to happen, but nothing did. He's with his intellectual peers and, most importantly, learning at the pace at which his brain works. The whole family is astonished at how changing his learning environment has changed his whole life. We are willing to sacrifice small animals to whatever god made this happen. He's happy--is there anything better in life?
Readers, please share this story as widely as you can; it's imperative for all gifted children that we disseminated its messages as widely as possible.

Friday, January 29, 2010

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

1. The final fractions word problems* in the fractions chapter ("Rational number Uses and Operations") of the 6th grade Everyday Math Student Math Journal (volume 1, p. 160):

Sean bought 3 5/8 yards of fabric to make a dress. The pattern for the dress calls for only 2 1/3 yards of fabric. How much fabric will be left to make something else?

Martin is building two picture frames. He used 4 1/2 feet of lumber for one frame and 2 3/4 feet for the other frame. How many feet of lumber did he use in all?

*not including the final two problems, which use bar modeling diagrams.

2. The final fractions word problems in the fractions chapter ("Fractions") of the 6th grade Singapore Math Primary Mathematics Workbook (6B, p. 15):

Kyle gave 2/7 of his money to his wife and spent 3/5 of the remainder. If he had $300 left, how much money did he have at first?

3/5 of the beads in a box are red, 1/4 are yellow and the rest are blue. There are 42 more red beads than blue beads. How many beads are there altogether?

3. OILF's Extra Credit:

Which problem set involves multiple applications of inversion, addition/subtraction, and multiplication of fractions, along with algebraic reasoning, and which problem set involves single applications of fraction addition or subtraction?

How might this relate to the fact that the Singapore Math workbook clearly indicates which grade it is for, while nowhere on the Everyday Math workbook is the intended grade level indicated, even in the fine print*?

*though one can look it up online, for example, here.

Wednesday, January 27, 2010

How to turn off left-brain writers from writing--and possibly some right-brainers as well

Selected lesson plans from ReadWriteThink, which partners with the National Council of Teachers of English, and whose mission it is to "provide educators, parents, and afterschool professionals with access to the highest quality practices in reading and language arts instruction by offering the very best in free materials."

1. "Langston Hughes was Born in 1902"

Provide students with a copy of Hughes' poem "Dreams" Each stanza of the poem is one sentence, and each sentence contains a metaphor for a dream. Tell students that a metaphor compares two objects or ideas that are not generally associated with one another. Have them identify the metaphor in each sentence, and then ask them to think about what Hughes was trying to convey about dreams by using these metaphors. What kind of dream would a "broken-winged bird"represent? How about a "field frozen in snow"?

Brainstorm with the class some other metaphors for dreams that Hughes might have considered for his poem. Conversely, have the class brainstorm metaphors for dreams that people may have that they hope will come true. Working in groups, students can then compose poems using metaphors for dreams coming to fruition.
2. "Book Report Alternative: Creating Careers for Characters"
Students first explore resumes using the internet. They then work as a class to construct a sample resume for a character in a book they have all read. Next, they explore want ads and online job sites for possible jobs for a character from a book they have read on their own. They write a letter of application and create a resume for their character for the selected job.
3. "Cooking up Descriptive Language: Designing Restaurant Menus"
Students explore the genre of menus by analyzing existing menus from local restaurants. After establishing the characteristics of the genre, students work in groups to choose a restaurant and then create their own custom menus. They then analyze the use of adjectives and descriptive language on sample menus before revising their own menus with attention to descriptive phrasing.
4. "Author Lois Duncan was Born on This Date in 1934"
Share with students some of the mysteries from Ken Weber's Five Minute Mysteries series and test their sleuthing abilities. After students have had a chance to solve a handful of mysteries (the solutions are in the back of the books), ask them to brainstorm the critical attributes of a good mystery. What elements do mysteries share? What do authors need to do to write a compelling mystery for readers?

Once the class has completed this part of the activity, place them in small groups and ask them to compose some short mysteries themselves. They can plan their stories using the interactive Mystery Cube. Groups can then exchange and attempt to solve one another's mysteries. The mysteries from each group can also be compiled and shared with other classes as well.
5. "Writing about Writing: An Extended Metaphor Assignment"
This lesson asks students to reflect on their writing process, and helps the teacher learn more about students' habits and techniques as writers. Students begin by reading and analyzing the poem "The Writer" by Richard Wilbur, particularly discussing the use of extended metaphor. Students then reflect on their own writing habits, compare themselves as writers to the writer in the poem, and brainstorm possible metaphors for themselves as writers. Finally, students complete one of several recommended projects to extend the metaphor describing themselves as writers. Throughout the process, students share their work in small groups.
6. "Draft Letters"
Draft letters ask students to reflect on a single piece of writing that they have completed, thinking more deeply about their writing and how they work as writers. This process of deep reflection helps students improve as writers. Dawn Swartzendruber-Putnam explains:

“Reflection is a form of metacognition—thinking about thinking. It means looking back with new eyes in order to discover—in this case, looking back on writing. As Pianko states, ‘The ability to reflect on what is begin written seems to be the essence of the difference between able and not so able writers from their initial writing experience onward’ (qtd. in Yancey 4)” (88).

Beyond the importance of critical thinking, active learning allows students to take ownership of their work while increasing their engagement with the activities at hand. Activities such as draft letters encourage students, rather than teachers, to “direct . . . every action and decision about their writing” (88).
Note what counts as justification for the last lesson: not empirical findings on how children learn to write, but a tendentious "statement" by one person embedded in a tendentious "explanation" by another person--neither of whom knows how to write a coherent sentence. Has either Swartzendruber-Putnam or Pianko consulted with anyone who can?

Monday, January 25, 2010

Are right-brainers really quirkier than left-brainers?

In the title review of my book (which no longer appears on Amazon), one reason the reviewer was convinced my title was wrong was that she was sure that quirky, creative kids must be right-brainers, not left-brainers. A similar reaction is seen in a comment about my book on Wrong, a site for adults with Asperger's Syndrome: "I was under the impression that most people WERE left-brained. I thought right-brained people were very creative types, artists."

I've already addressed the creativity issue. But what of the notion that most people are left-brained, such that what's quirky and special are right-brained traits? The popularity of this notion, I maintain, is evidence that there's in fact a widespread right-brain bias that marginalizes left-brainers. People seem to forget that left-brainers aren't merely boring accountant types, but also those with extreme focus and drive, who often develop encyclopedic knowledge and preternatural skills in specific areas--whether in math, music, physics, design, or engineering (to name just a few of the more stereotypical areas).

And people seem to forget that a quintessential left-brain trait is resistance to working in groups and insistence on marching to one's own drummer.

Surely these are quirky traits? But too many people (too many right-brainers?) either forget about them, or are reluctant to give them their due.

Saturday, January 23, 2010

Book talk feedback: where are the teachers?

At my last book talk someone asked whether I had had any discussions with math educators vis a vis my concerns about Reform Math.  In reply, I had to say that I'd had a few, but that, unfortunately, those discussions hadn't been very satisfying.  At some point I'd raise some topic, e.g., a comparison of specific Singapore Math problems with specific Reform Math problems, or the needs of children with autism, or the possibility of surveying grade school students to find out what percentage of them find school math class too hard/easy, at which point the math educator stopped responding to my emails.  

I've also noticed that very few teachers attend my book talks, and that those who do are predominantly special ed teachers.  Only one math teacher, as far as I know, has appeared (he defended Reform Math on the grounds that it covers more statistics than overseas programs do).

A number of teachers do read my blog (or, at least, there are a number of visitors from servers like and, including local teachers who could easily have conversations with me if they wanted to, but only a couple of self-identified teachers have ever posted comments here.

My experiences would seem to be typical, or so I hear.  Perhaps others have thoughts on this, including teachers? If so, please do share!

Thursday, January 21, 2010

Math problems of the week: final high school math problems

1. The final problem in Interactive Mathematics Program: Integrated High School Mathematics, Year 4, p. 454:

It's the News

The central problem of this unit concerns election polls. Polls are used in many situations to get information about what people think and do. Such polls appear in newspapers regularly, although reports on the polls sometimes don't give as much information as they should.

Your first task in this activity is to find a newspaper or magazine article that reports on a poll.

Then summarize what the report says and discuss any shortcomings or weaknesses you see in the report. In particular, comment on any information that you think should have been included that would have helped you understand better what conclusions you could draw from the poll.

2. The final problem in Mallory's A Second Course in Algebra (first published in 1937), p. 477:

Find the area under the curve y = x2 - 8x + 12:
a. From x = 0 to x = 2; b. from x = 2 to x = 6.

3. Extra Credit:

A Second Course in Algebra entirely omits statistics (e.g., election polls); the Interactive Mathematics Program entirely omits calculus (e.g., area under the curve). Discuss the ideal ratio of statistics to calculus in high school mathematics.

Tuesday, January 19, 2010

Discovery learning and politeness

One theme of this blog is how discovery learning (aka Constructivism, aka experiential learning, aka incidental learning) particularly disadvantages children on the autistic spectrum. AS children are less able than other kids are to pick things up incidentally from social context, and depend on direct, structured instruction--whether the subject is turn-taking or fractions.

One subject I haven't addressed is politeness. But now, reading up on the wisdom of Temple Grandin for an online course I'm designing on high functioning autism, I've realized that the same issues arise here. Especially since politeness has gone the way of reading (Balanced) writing (Workshop) and arithmetic (Reform). Here's a quote from Grandin:

Fewer and fewer parents are taking the time to instill manners and teach proper social etiquette to their children. It's having a ripple effect. Young parents today aren't even conscious of some of Miss Manners' rules, which used to govern society when I was young and growing up.

Typical kids are able to deal with this shift in emphasis on teaching social functioning skills--they have the brain capacity to learn by watching other kids and still pick up manners if they need them, despite not being directly taught. But the Asperger kids can't learn by observation; they need direct teaching, direct experiences--they need that structure that used to exist in the social world. It's not there at home or at school, and they're lost as a result.

(From the Unwritten Rules of Social Relationships: Decoding Social Mysteries Through the Unique Perspectives of Autism.)
Of course, each society at any given time strikes a different balance between how formulaic vs. spontaneous and heart-felt our interactions with others should be, and different people have different personal preferences. For those on the autistic spectrum, however, there's a distinct downside when the rules become too spontaneous, unstructured, and untaught.

Sunday, January 17, 2010

"Raising a Left-Brain Child" book talk:

This Tuesday, January 19th, 7:00-8:00 at the University of Pennsylvania book store.

If you are a Philadelphia-area parent or teacher, I'd love to hear your questions and comments on how to help bright, quirky, socially-awkward children (including, but not limited to, children on the autistic spectrum) thrive at home and at school--especially where Everyday Math, Investigations Math, big summer projects, working in groups, and other new trends in education are concerned.

In other developments, I recently did an interview with Dr. Teena Cahill, author of The Cahill Factor, which now can be heard as a podcast.

The podcast of my interview on the Parent's Journal with Bobbi Conner is also available for download.

The title review of my book that appeared on Amazon last week has been deleted (I believe the only person who has the power to do this is the author of the review).

Friday, January 15, 2010

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

I. The last three multiplication/division word problems in the 3rd grade (TERC) Investigations Student Activity Booklet Things that Come in Groups, p. 79.

3. Spiders have 8 legs.

How many legs are on 2 spiders?
How many legs are on 4 spiders?

4. There are 28 legs, and they all belong to cats. How many cats are there?

*How many cats would there be if there were 144 legs in all?

5. We counted 3 insects, 2 cats, and 4 people in the house. How many legs are there altogether?

II. The last three multiplication/division word problems in the 3rd grade Singapore Math Primary Mathematics 3A, pp. 138-139

3. Tim printed 900 pamphlets. He packed them equally into 8 boxes. How many pamphlets were there in each box? How many pamphlets were left over?

4. A florist has 145 yellow roses. She has 8 times as many red roses as yellow roses. How many more red roses than yellow roses does she have?

5. 8 students sold 272 concert tickets at $3 each. Each student sold the same number of tickets. How much money did each student collect?

III. Extra Credit:

Which students, TERC students or Singapore students, are more likely to be using calculators to solve these problems?

Estimate the number of the Singapore Math problems above that an exclusively TERC-educated 3rd grader, armed with a calculator, would be able to solve correctly (no partial credit for "explained" but incorrect answers).

Wednesday, January 13, 2010

Is the world right-brained or left-brained?, II

I just came across a new Amazon review of my book that raises this question again.

I should clarify that this is actually not a review of my book, but a review of my book's title (the first exclusively title-focused review I've encountered in all the many reviews I've read on Amazon or anywhere else). Indeed, the author makes it pretty clear that she hasn't actually cracked open the book. She's sure, however, that the title contains a serious error:

The title is supposed to be Raising a RIGHT-BRAIN Child in a LEFT-BRAIN World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School. Hence, it is the creative, brilliant RIGHT BRAIN that these kids use the most, while too much of the population utilizes too much of the LEFT BRAIN. Interesting and kinda scary that no one is catching this mistake.
This title review (what I've excerpted above is about half of it) doesn't give me too many lines to read through--though, to its credit, it contains perhaps six times as many words as those in the title it reviews. I'd venture to guess, however, that there are two reasons why the reviewer thinks my title is wrong.

One I'll discuss in a later blog; the other is seen in her implicit assumption that creativity and brilliance are right-brain traits. The problem with this assumption is that, even if we take the term "right brain" not to denote the actual right hemisphere of the brain, but (as I do in the book) as it's used in the popular culture--i.e., to denote intuition, holistic thinking, social skills, and artistic creativity--it's still not a reasonable assumption. It is, however a widespread one.

Too many people, including too many K-12 teachers, forget that not all creativity is artistic. In my book, I discuss, in particular, the left-brainer's creativity in "abstract ideas and strategies, abstract representations, abstract connections between ideas, and reworking of abstract paradigms":
These are the kinds of creativity it took, in the extreme, Darwin to formulate his principles of evolution, or Einstein his general relativity--the sort of creativity, in other words, that finds little inspiration or opportunity in today's concrete, conceptually easy assignments, and that few of today's teachers are either trained to appreciate or encouraged to reward.
Indeed it's precisely because so many people equate creativity with a certain kind of (predominantly visual) artistic creativity that, as I argue in my book, our world, especially the world of K-12 education, is right-brained, not left-brained.

Monday, January 11, 2010

Enlightened exchanges with Reform Math defenders, IV

Final installment:

(Exchange between yours truly (KB) and Michael Paul Goldenberg (MPG), a Lecturer in Mathematics Education at University of Michigan-Flint, who seems to think I operate out of Ridgewood, New Jersey).


Scores of bright math students--from moderately to extremely gifted--are bored out of their minds by the level of challenge offered by Reform Math classes in public, private, and parochial schools alike. I know this because I interviewed them for my new book. Their parents know it as well. And other people would know it, too--if they simply bothered to listen to what these children have to say.


Well-crafted inquiry-based curricula (and I don't mean books per se) challenge all students at whatever their entry point may be. Creating such programs and teaching them requires a level of commitment and knowledge that may be rare, but is not impossible to help teachers achieve.


Given that inquiry-based programs require "a level of commitment and knowledge that may be rare, but is not impossible to help teachers achieve," a more realistic bet is a teacher-proof curriculum like Singapore Math. This is what large numbers of bored kids I know (about 1/3 of the 3rd and 4th graders at our local school, for example) are doing at home with their parents.


Yeah, well, any thought that you might have anything useful to contribute to mathematics education just went out the door. There are no teacher-proof curricula.


I know many students who are learning mathematics not from teachers, but from Singapore Math at home with minimal supervision from parents.


While I'm not going to denigrate what Singapore Math is or was intended to be, or how it's done in Singapore, or analyze the strengths and weaknesses of the program itself regardless of the concomitant pedagogy (which is open to adjustment here by every teacher who uses it in the United States, where we don't HAVE a Ministry of Education or the threat of caning if someone chews gum or doesn't toe the line), or go over once again the insanity of believing that ANY curriculum can be adopted to massive, diverse public school education in the United States from a homogeneous, tiny, affluent country that doesn't educate its working class (because it IMPORTS its working class daily and sends them back where they came from at the end of the day, leaving the kids of THOSE folks to be educated elsewhere),


No working class students reside in Singapore and attend its schools? References, please.

Singapore Math resembles math in other East Asian countries, Russian Math and Unified Math (continental Europe). The approach is not specific to Singaporean society; it's used with quite a diverse group of students, from a multitude of cultures, societies, and socio-economic classes. Singapore Math appeals to Americans over the various other overseas math curricula because it's written in English. The only element I know to be unique to Singapore Math is bar modeling, which doesn't strike me as particularly connected to homogeneity, small populations, wealth, or consequences for chewing gum.


I will suggest that anyone who believes there are teacher-proof curricula (not to mention the crazy idea that Singapore Math pretends or aspires to be one of those), has lost all credibility in my eyes (and likely in the eyes of the vast, vast majority of educators).


See above.


And the notion that you'd sacrifice real, inquiry-based education on the altar of something ostensibly "teacher-proof" gives the game away even more nakedly than the rest of what you've posted to this list.


Are you retracting your earlier comment about how rare the skills are that effective inquiry teaching requires?


The red herring that we're going to lose future mathematicians is equally absurd. We still have a glut, last I checked.


The graduate students in our top math programs were disproportionately educated in countries that use the math programs I cite above.


Every lame argument in the book against trying to teach the majority of our population to be numerate, inquisitive, self-reliant, challenging of the status quo, etc., seems to be in your repertoire. You are likely a wonderful pupil of the Gospel According To Mathematically Correct and NYC/HOLD, (as I know you are, having visited your site and put two and two together regarding your role in trying to undermine progressive mathematics education in the Atlantic states), but you're going to find a little more resistance to received doctrine here than in, say, Ridgewood, NJ.


I'm not familiar with Ridgewood NJ, but I am familiar with inner city Philadelphia, where Everyday Math and Investigations are widening the achievement gap between those who do Singapore Math at home with their parents, and those who do not.


Too bad you didn't interview kids in my high school, right next door to Ridgewood, back in the sixties. No reform math to blame. Just crappy, uninspired, traditional math pedagogy at its "finest." Some kids did well enough in spite of that. But how many LOVED mathematics who didn't already come to school inclined (perhaps because of "left-brainedness") to do so? How many very, very bright kids got so turned off to mathematics, in fact, that they came to loathe it? I have occasion to be in NYC every month these days, and I have reconnected with a number of old acquaintances from FLHS c. 1965-1970. Want to know what they feel about mathematics? It isn't pretty. It's downright depressing. If I even start to talk about math in any specific way, they get very uncomfortable.

How about the number of people I meet in Ann Arbor and vicinity of my generation, many of them graduates of such institutions as University of Michigan, Michigan State, Wayne State, etc., whose eyes swim when mathematics is mentioned? I'm hardly alone in knowing that this obvious fear and loathing is a plague upon the land. And what you propose is to return as much as possible to the approaches to mathematics teaching that created their feelings and beliefs? Whom do you hope to fool? Perhaps the same folks you're selling "Left-brained" children to?


Some people will never like math, no matter how it is taught. Of the mathematically inclined of your personal connections, how many of them have seen the latest trends on math ed and say that they actually prefer the new curricula to what they went through? I'm personally connected to many mathematicians, and not a single one has expressed such a preference. Most, in fact, express the exact opposite.

As for credibility, you might increase yours by editing out certain phrases that make you look angry and therefore untrustworthy. For example: "any thought that you might have anything useful to contribute to mathematics education..."; "lame argument"; "Gospel According To"; and "Whom do you hope to fool?". Just a thought.

Saturday, January 9, 2010

Did Humpty Dumpty have Asperger's Syndrome?

It's become a parlor game to "out" various famous personalities as Aspie--Mozart, Einstein, Andy Warhol, for example. But what about fictional characters, I wondered the other night, as I continued through Alice Through the Looking Glass with my daughter and came across Humpty Dumpty. Consider this:

1. He won't get down from his wall:
a rigid, restricted behavior, if there ever was one.

2. His eye contact is minimal:

"And how exactly like an egg he is!" she said aloud, standing with her hands ready to catch him, for she was every moment expecting him to fall.

"It's very provoking," Humpty Dumpty said after a long silence, looking away from Alice as he spoke, "to be called an egg--very!"

"I said you looked like an egg, Sir," Alice gently explained. "And some eggs are very pretty, you know," she added, hoping to turn her remark into a sort of compliment.

"Some people," said Humpty Dumpty, looking away from her as usual, "have no more sense than a baby!"

Alice didn't know what to say to this: it wasn't at all like conversation, she thought, as he never said anything to her; in fact, his last remark was evidently addressed to a tree...
3. He's very direct:
"Don't stand chattering to yourself like that, Humpty Dumpty said, looking at her for the first time, "but tell me your name and your business."

"My name is Alice, but--"

"It's a stupid name enough!" Humpty Dumpty interrupted impatiently.
4. He takes everything literally and is quite pedantic:
"How old did you say you were?"

Alice made a short calculation, and said, "Seven years and six month."

"Wrong!" Humpty Dumpty explained triumphantly. "You never said a word like that."

"I thought you meant 'How old are you?'" Alice explained.

"If I'd meant that, I'd have said it," said Humpty Dumpty.

"I mean," she said, "that one ca'n't help growing older."

"One ca'n't, perhaps," said Humpty Dumpty; "but two can. "

"In winter, when the fields are white, I sing this song for your delight--

"only I don't sing it," he added, as an explanation.

"I see you don't," said Alice.

"If you can see whether I'm singing or not you've sharper eyes than most," Humpty Dumpty remarked severely.
5. His words have private rather than public meanings:
"and that shows that there are three hundred and sixty-four days when you might get un-birthday presents... and only one for birthday presents you know. That's glory for you!"

"I don't know what you mean by 'glory.'" Alice said.

Humpty Dumpty smiled contemptuously. "Of course you don't--till I tell you. I meant 'there's a nice knock-down argument for you!'"

"But 'glory' doesn't mean 'a nice knock-down argument," Alice objected.

"When I use a word," Humpty Dumpty said, in rather a scornful tone, "it means just what I choose it to mean--neither more nor less."
6. Quite the egghead, he has a large vocabulary and a certain idiosyncratic intelligence and imagination:
"'slithy' means 'lithe and slimy.' 'Lithe' is the same 'active.' You see it's like a portmanteau--there are two meanings packed up into one word."

"'mimsy' is 'flimsy and miserable (there's another portmanteau for you). And a 'borogove' is a thin shabby-looking bird with its feathers sticking out all round--something like a live mop."

"'outgribing' is something between bellowing and whistling, with a kind of sneeze in the middle."
7. He can read things upside down:
e.g., Alice's calculation for how many un-birthdays in a year.

8. He is obtuse about conversational pragmatics
supplying uninformative answers to questions, declining to respond appropriately to compliments, and closing conversations abruptly:
"Why do you sit here all alone?" said Alice, not wishing to begin an argument.

"Why, because there's nobody with me!" cried Humpty Dumpty.

"What a beautiful belt you've got on!" Alice suddenly remarked...

Evidently Humpty Dumpty was very angry, though he said nothing for a minute or two. When he did speak again, it was in a deep growl.

"It is a--most--provoking--thing," he said at last, "when a person doesn't know a cravat from a belt!"

"And when I found the door was shut,
I tried to turn the hand, but---"

There was a long pause.

"Is that all?" Alice timidly asked.

"That's all," said Humpty Dumpty. "Good-bye."
8. He's got prosopagnosia:
This was rather sudden, Alice thought: but, after such a very strong hint that she ought to be going, she felt that it would hardly be civil to stay. So she got up, and held out her hand.

"Good-bye, till we meet again!" she said as cheerfully as she could.

"I shouldn't know again if we did meet," Humpty Dumpty replied in a discontented tone, giving her one of his fingers to shake: "you're so exactly like other people."

"The face is what one goes by, generally," Alice remarked in a thoughtful tone.

"That's just what I complain of," said Humpty Dumpty. "Your face is that same as everybody has--the two eyes, so--- (marking their placed in the air with his thumb) "nose in the middle, mouth under. It's always the same. Now if you had the two eyes on the same side of the nose, for instance--or the mouth at the top--that would be some help."
9. He may have gross motor difficulties:
"...of all the unsatisfactory people I ever met---" She never finished this sentence, for at this moment a heavy crash shook the forest from end to end.
That's glory for you!

Thursday, January 7, 2010

Math problems of the week: 5th grade Investigations vs. Singapore Math

I. From the 5th grade Investigations (TERC) Student Activity Book, the last two fractions problems (in Unit 4: What's that Portion?, p 68):

More moves on the Fraction Track

Suppose that you are playing the Fraction Track game with the board that goes from 0 to 2. All your markers are on 0. Find diferent combinations of ways you can move on 2 tracks, 3 tracks, or 4 tracks.

NOTE: Students have been playing a game in which they find different sums that equal a given fraction.

For example, if you draw 7/8, you can move:

On two tracks: 1/2 + 3/8

On three tracks: 1/2 + 1/4 + 1/8

On four tracks: 1/3 + 1/6 + 1/4 + 1/8

Find some different ways you could move if you got these fraction cards.

1. Your fraction card is 9/6. What are some ways you could move?

On two tracks:

On three tracks:

On four tracks:

2. Your fraction cars is 12/10 What are some ways you could move?

On two tracks:

On three tracks:

On four tracks:

II. From the 5th grade Singapore Math Primary Mathematics 5A Workbook, the last two problems on fractions (in Unit 4, Multiply and Divide Fractions, pp. 98-99):

3. After giving 1/3 of his money to his wife and 1/4 of it to his mother, Mr. Li still had $600 left. How much money did he give to his mother?

4. Lucy spent 3/5 of her money on a purse. She spent the remainder on 3 T-shirts which cost $4 each. How much did the purse cost?

Tuesday, January 5, 2010

Enlightened exchanges with Reform Math defenders, III

Whew! I'm done posting my favorite comments of the year, and it's time to start using my own words again. I thought I'd begin with a recent exchange I had with an individual from my recent past.

The Drexel University Math Forum recently had a discussion about the plight of mathematically gifted children, to which I posted the following comment:

KB: Scores of bright math students--from moderately to extremely gifted--are bored out of their minds by the level of challenge offered by Reform Math classes in public, private, and parochial schools alike. I know this because I interviewed them for my new book ("Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School"). Their parents know it as well. And other people would know it, too--if they simply bothered to listen to what these children have to say.
This lead to the following back-and-forth between myself and a lecturer in mathematics education by the name of Michael Paul Goldenberg (not to be confused with E Paul Goldenberg), who spends much of his time defending Reform Math against "Reform Math haters," including yours truly (cf here and here):
MGP: I was so fascinated with the notion of "left-brained" and "right-brained" children that I went to Ms. Beals' web site to learn more. There I found the following: "A note on left-brain, right-brain, and brain hemispheres Here left-brain and right-brain are used in the informal, everyday sense. They do not refer in any way to left and right brain hemispheres. Left-brain: logical, systematic, analytical, one-at-a-time, abstract, verbal, introverted. Right-brain: emotional, incidental, intuitive, holistic, relational, nonverbal, social." Boy, am I confused.
KB: Please don't be; these are fuzzy categories, as I make clear in my book (where there's more space to elaborate than on my website) and it goes without saying that many people have "left-brain" and "right-brain" traits.
MGP: ...while at the same time just happening to come down along the lines of some of our most preciously-held gender stereotypes.
KB: Not my personal stereotypes: I'm left-brained and female. But, I'm open to the possibility that more males than females are left-brained. Simon Baron-Cohen has interesting data on this.
MGP: ...Along with the fact that one of the authors who praises Ms. Beals' work is the author of a book entitled THE MINDS OF BOYS.

KB: Guilt by association?

MGP: Now along comes Ms. Beals to argue that not only are progressive curricula and pedagogy in math education boring the bejeezus out of a bunch of budding math geniuses, but it turns out that there is an actual brain-based reason
KB: How can you attribute to me a "brain-based" reason when you just quoted me as saying that 'left-brain' and 'right-brain' "do not refer in any way to left and right brain hemispheres."
MGP: ...for kids (mostly boys, I gather) to be nerds who are, of course, gifted in mathematics to some degree or other (it's a little hazy how wide a swath giftedness cuts, exactly, but I'll not quibble over such niceties).
KB: Plenty of girls, too.
MGP: ...So does this mean we DO have to find different ways to teach different "flavors" of child? That we can neatly categorize some/many/most/all kids into either right-brained (the darlings of progressives, I guess, especially because they sound like what are usually thought of as feminine) or left-brained (future NASA dudes in white shirts with pocket protectors: see the control room scenes in APOLLO 11 and THE RIGHT STUFF if you can't conjure up the image yourself)? Not sure what to make of people with graduate degrees in, say, literature AND mathematics education,
KB: Please don't conflate graduate degrees in mathematics education with graduate degrees in mathematics. The coursework involved in the one vs. the other is extremely different.
MGP: ...but are always a few of us around to make neat dichotomizing a little more difficult than it should be.
KB: These are fuzzy categories (cf above), and I'm not the one assigning gender stereotypes here.
MGP: ...Really puzzled at how the MC/HOLD cadre will respond to Ms. Beals' work. After all, she seems to suggest we need different sorts of content and methods for different kids.
KB: In my book, I argue (chapter 3) that left-brain kids are *especially* shortchanged by the reform curricula, but also (chapter 6) that children in general are also ill-served.
MGP: Boys will be nerds and girls will be housewives and people of color will learn their rightful places toting and cleaning, and all will be Right and White with the world.
KB: I'm sorry you see it this way.

Monday, January 4, 2010

Favorite comments of '09: Deirdre Mundy on 7th grade holiday math project

Re 7th grade holiday math project: Just because I care about you, Deirdre Mundy writes:

Wait-- is the lamp considered a major appliance (you plug it in!)? or is it a piece of clothing? (You can wear the shade!)

Will the booklet be graded on neatness, or just the quality of arithmetic? What if my family doesn't HAVE any catalogues or junk mail? What if I don't have 20 people? Is it OK to make some up?

Can I say, "This is a load of @#%@" and then just count on the final exam to make sure I get at least a B in the class? Heck, I'll even settle for a C if I can skip all the cutting and pasting and just do the math instead!!!!

(Projects like this are why I home school. Seriously--why take 30 minutes worth of math and turn it into 3 hours of tears????)

Sunday, January 3, 2010

Favorite comments of '09: TerriW, Beth, and Niels Henrik Abel on Everyday Math problems:

Re this and this

TerriW writes:

If only they would play "Broken Calculator" all year...

Beth writes:

If this is the final exam, what happens to a kid who checks off "needs lots of practice" in all the categories? Will the child be given additional help and practice, or just sent out to summer vacation and the next year of math, which he isn't prepared for?

The emphasis on performance and grades rather than actual learning is a big problem, and it doesn't get better when you have the kids grade themselves. The "grade yourself" portion of this test is huge. It supports the message that the entire function of a year's worth of math classes is to finally pass judgement on the child.

And Niels Henrik Abel writes:

"Does it matter"?

What is the antecedent to the pronoun? There are two possible ways to imagine what the intended question is:

Q1) Does it matter whether you prefer to do operations with fractions or decimals?

A1) No, it doesn't matter what you prefer - you need to learn to do both anyway.

Q2) Does it matter whether operations are done with fractions or with decimals?

A2) Yes, it matters. Fractions are always exact, and you need to be proficient at manipulating them, particularly if you want to succeed at algebra (think: rational expressions).

Saturday, January 2, 2010

Favorite comments of '09: Joanne Jacobs on educational feedback loops

Re Feedback loops or vicious cycles?, Joanne Jacobs writes: 

You left out the third option:

Argue that skill X can't be measured by tests and therefore may be improving invisibly.

The fourth option:

Argue that skill X is irrelevant for 21st century students. They really need skill Z.

Friday, January 1, 2010

Favorite comments of '09: Julia D on algorithms vs. conceptual understanding

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

When I was a kid, all they did was teach us algorithms (or what I thought were "tricks") to finding answers to math problems. We were just supposed to memorize the steps, but they never explained why the steps worked. I think where we've gone wrong with all these visuals and explanations (number lines, hundredths grid, etc.) is that we are encouraging students to use them *instead* of memorization, when we should be using them only help students understand why the quick algorithms work. As an adult, I absolutely use the memorized "math facts" and algorithms that were drilled into me, and I could not function without them. But I also like that I now know why they work.

If I see one more GED student try to add 1-digit numbers by drawing a bunch of dots (in the middle of a multi-step algrebra problem), I'm going to scream.