Monday, June 29, 2009

Writing from a prompt: problems for left-brainers

I used to think I had little facility for creative writing. Eventually I realized that I could write, even creatively, but only on my own terms.

Even more recently, in recent discussions with those who teach creative writing, I've realized that much of my writing insecurity stemmed from the standard writing exercises I encountered in school--and that continue to this day. This is where the instructor places some sort of object in front of the room, or writes some sort of quote on the blackboard, which serves as a prompt for 15 minutes of open-ended, impromptu writing.

Staring at the closed metal box, or "the left hand of darkness," and listening to the pens of my classmates scribbling away, I'd sit there feeling empty, stupid, and thoroughly uncreative.

Only later, as I saw these frustrations repeat themselves in my own children, and considered the clustering of learning differences that characterize left-brainers in general, did I fully realize how antithetical the "write from a prompt" assignments are to what make our creative juices flow:

1. Unless the original inspiration comes from us (and not from a prompt chosen by someone else), we require structure, and the open-endedness of the typical writing prompts doesn't provide nearly enough.

2. Impromptu writing shows us at our very worst--both absolutely and in comparison with others. In order to produce anything that doesn't embarrass us (and that doesn't erect a barricade of psychological blocks that completely shuts us down), we require much more time than others do to plan, structure, and revise.

What, then, is a writing teacher to do? Perhaps all "writing from a prompt" exercises could be accompanied by the option to instead write about whatever currently interests you, and/or to revise your last in-class writing exercise.

Lacking such alternatives, too many left-brainers may conclude, as I did, that they have no aptitude for creative writing.

Friday, June 26, 2009

Math problem of the week: 19th century algebra vs. Contemporary Math in Context

1. From the first algebra problem set in New School Algebra (George Wentworth), published in 1989, p. 22, "Simple Equations":

A man has x dollars and y dimes and z cents. If he spends a half-dollars and b quarters, how many cents has he left?

A train is running at the rate of a miles an hour. How many miles will it travel in m hours?

A rectangular floor is a feet long and b feet wide In the middle of the floor there is a square carpet c feet on a side. How many square yards of the floor are bare?

2. From the second to last algebra problem set (the one that precedes graphing and the "Spiral Reviews") in Core-Plus Mathematics Contemporary Mathematics in Context, "Algebra: Variables and Expressions," p. 40:

Evaluate each expression if x = 7, y = 15, and z = 8

xz - 2y + 8

z2 + 5y - 20

3y(40x) - 1000

3. Extra Credit: Which century most favors rote computation?

Wednesday, June 24, 2009

A model school's selling points: everything but the math

A year of activities: Spelling Bee | Talent Shoe | Musical | Science Fair | Fall Festival | 100 Days | Opera Company | Reading Buddies | Spring Concert | Valentine's Dance

So goes the text along the margin of the glossy school newsletter that came home yesterday on the last day of school--along with color photographs of smiling students and staff, and articles about the school and the community.

You'd never know that one of the school's activities was the Continental Math League club, run by yours truly and another parent volunteer, and attended 1 1/2 hours a week from October to March by 20 eager 2nd and 3rd graders.

Especially since, despite the principal's earlier assurances, the information sheet about next year's Continental Math League club (and ways to practice for it over the summer) somehow didn't accompany the above newsletter into students' backpacks.

Concerned that this might happen, I had sent said principal an email reminder the day before the last day. Then, when I bumped into her on the morning of the last day, I'd asked her about the email.

"I deleted it," she said, a big grin on her face.

I guess she's happy it's summer vacation.


For those who are interested in ways to polish up their math skills for Continental Math League, or for any other reason, here's what I spent several hours compiling for students at our school. Perhaps other schools and other principals will find this more compelling than ours did:


Monday, June 22, 2009

Portfolios are coming home: insights into grade rationing

Weighing down my kids' backpacks in this home stretch of school are large quantities of homework and classwork, some dating all the way back to March. Assignments that could have been part of a productive feedback loop between home and school instead spend months accumulating inside classroom portfolios, selectively becoming part of the "portfolio assessments" that dominates today's grading. As a recent post by SteveH on kitchentablemath suggests, our school is not alone in its practices.

I've come to believe that portfolio assessments and delayed handbacks play an integral role in rationing top grades and ensuring that they don't favor the traditional "egg heads" and "math buffs" (for that, of course, would be elitist).

The strategy, as far as I can tell, is as follows. Rather than give children conceptually challenging material and reserve high grades for those who show mastery (which would favor the eggheads, math buffs, and other left-brainers), schools assign easy stuff where most kids ceiling out at the conceptual/analytical level, and then use rubrics biased towards subjective or trivial dimensions like "creativity," "effort," "neatness", and elaborateness of explanation--a.k.a. "going beyond the standard".

Of course, the more parents catch on to the preeminence of neatness, colorful drawing, verbose explanations, and purple prose, the more those of us who worry about grades play by the game, and the harder it is for teachers to ration top grades appropriately.

This is where portfolio assessment plays its key role--beyond its loftier rationale as "more authentic" than traditional grading systems. Delayed hand-backs ensure that not too many parents wise up to what's going on, or remember to do something about it--until it's too late.

Friday, June 19, 2009

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

1. Connected Math, p. 78, final word problems in Covering and Surrounding, "Unit Reflections," p. 85:

How would you explain the difference between area and perimeter to a younger student who has not yet studied those mathematical ideas?

Describe calculation strategies that can be used to find the area of each shape and be prepared to justify each procedure.

a. Rectangle (picture with width and height shown)

b. Triangle (picture with height and base shown)

c. Parallelogram (Picture with height and base shown)

d. Circle (Picture with radius and diameter shown)

2. Singapore Math, final problems on area, Primary Mathematics, 6B, p. 93 and 93:

3. Extra Credit

At what point in the curriculum does Connected Math present problems as challenging as the Singapore problems above?

Wednesday, June 17, 2009

Left-brain meditation

I'm wrapping up our summer vacation plans, and therefore contemplating the prospect of relaxation.

Which leads me to the topic of meditation. Many of us left-brainers fail at the standard meditations, thanks to that incessant chatter in our brains, which seem to especially abhor the vacuum of quiet meditation. Has anyone considered the possibility, however, of a left-brained approach to meditation?

This first hit me when I saw how Gelfand's Algebra problems could calm down my autistic son J, and heard how his breathing would slow, deepen, and regularize as he factored or completed the square.

Then it occurred to me that some of my calmest, in-the-zone moments occur while I'm extensively tweaking my software.

My other two left-brainers are likewise at their calmest and most content not when trying to sit still and quiet their minds, but when engaged in logic puzzles or physics problems. Again, there's that slow, deep, regular breathing, suggesting an inner calm that others get by meditating.

So wrapped up are we in the right brainers' notions of meditation that it doesn't occur to us--or at least to me--that for some, the equivalent of an Ashram is a math camp.

Monday, June 15, 2009

Left-brain routes to social skills

In autism, there are fundamental deficits in the ability to read and use mental-state information available from faces, voices, or body gestures... Nevertheless... a small percentage of children with autism develop the ability to pass false-belief tests via language.

In autism, language is the single most significant prognostic factor for long-term cognitive, social, and adaptive outcomes... Some children with autism, the minority with normal or near-normal linguistic ability, can use language to reason logically through false-belief tasks...
--Helen Tager-Flusberg and Robert M. Joseph, "How Language Facilitates the Acquisition of False-Belief Understanding in Children with Autism."

By the same token, I wonder, how many of us left-brain neurotypicals tend to use language to reason through social situations for which we lack the right-brainer's gut social instincts?

And might left-brain children best develop social skills not by the baptism-by-fire approach of peer group immersion, but by the armchair approach of social analysis?

Saturday, June 13, 2009

Artsy science: what about sciency art?

The second annual World Science Festival is underway in New York City. Today's New York Times reports the following highlights:

an investigation of the effects of music on the brain with a performance by Bobby McFerrin

a quest for a long-lost mural by Leonardo Da Vinci at the Metropolitan Museum of Art

The science behind "Battlestar Galactica" with actors from the show
"The idea," the Time goes on, "is to mix up art, theater and music with the inevitable talking heads and professional interlocutors like Charlie Rose or Alan Alda..." In Alda's words, "Art needs rigor and science needs creativity."

But if art needs rigor, how come we never see an arts festival correspondingly infused with science and/or rigorous analysis? E.g., something billed as an arts festival that includes lectures on the mathematics of African polythythms, the geometry of Cubist painting, and the poetics and discourse analysis of David Mamet dialogs.

Wouldn't this be an equally effective way of interesting people in science? Or is this perhaps low on the agenda of those who run arts festivals?

Thursday, June 11, 2009

Math problems of the week: 4th grade Trailblazers vs. 1920's math

End-of-year word problems for 4th grade:

I. Hamilton's Essentials of Arithmetic Lower Grades (published in 1919), p. 200:

1. George bought a camera costing $6.12 and 6 rolls of films for $.24 each. How much change did he receive from a $10 bill?

2. Each picture was 2 inches by 3 1/4 inches. What was the number of square inches in its surface?

3. The pictures were mounted on cardboard, with a margin of 1/2 inch on each side. What was the length of the cardboard? the width? the number of square inches in the surface?

4. It cost $.18 to develop the roll of films. How much was this for each of the 6 exposures?

5. A roll of films having 6 exposures cost $.24, the developing for 6 exposures $.18, the printing of each picture $.03, and the mounting $.02. What was the total cost of each picture?

6. A picture 2 1/4 inches by 3 1/4 inches was mounted in the middle of a card 4 3/4 inches by 5 3/4 inches. What was the total cost of each picture?

7. How large a card would be needed to mount a picture 6 1/2 inches, leaving a margin of 3 1/2 inches on each side?

II. Math Trailblazers Discovery Assignment Book, p. 215:

Choose an appropriate method to solve each of the following problems. For some questions, you may need to find an exact answer, while for other questions, you may only need an estimate. For each question, you may choose to use paper and pencil, mental math, or a calculator [italics mine]. Be prepared to tell the class how you solved each problem.

1. Nila has $585 in her savings account. On her birthday, she deposits $75 she got for birthday gifts. How much money is in her savings account after her birthday?

2. Jackie and her family are taking a 23-mile ferry ride to an island in Lake Michigan. A round-trip ferry ride ticket costs $29 per adults and $15 per child. If 4 adults and 3 children purchase tickets, how much will the ferry ride cost the entire family?

3. John's older brother is in college. His brother and his three roommates want to buy a new stereo that costs $764. If they split the cost of the stereo evenly, how much should each student pitch in?

4. Ming built a house of cards. Before the house came tumbling down, he used 2 full decks of cards. The house also contained all but 15 cards from a third deck. About how many cards were in Ming's house of cards. (A deck of cards has 52 cards).

5. On vacation, Shannon's family took 3 rolls of 24 pictures and 2 rolls of 36 pictures. How many pictures did the family take in all?

6. Roberto is driving with his family to visit his grandmother. After driving 144 miles from Chicago, the family stops or lunch. They drive 89 more miles and stop for gas. Then, they stop for a sot drink after driving 123 more miles. Roberto's grandma lives 275 miles from Chicago. About how many more miles must they drive before they reach their grandmother's house?

7. If one year is 165 days, how many days old will you be when you are 16 years old?

3. Extra Credit

1. Estimate the ratio of words to numerical complexity in each problem set.

2. If Trailblazer's 4th graders were to time travel back to the 1920s, back before students had calculators, how well would they do in math compared with their 1920's classmates?

Tuesday, June 9, 2009

Temple Grandin on lack of mentors for autistic children

Watching a recent presentation by Temple Grandin on Youtube, I was struck by her increasing concern about the lack of mentors for school-aged children on the autistic spectrum. Rarely do such kids encounter teachers who encourage them to develop their strengths. Rather, most spend their school years attempting to remediate their weaknesses.

The result, Grandin observes, is that all too often people on the autistic spectrum end up as janitors rather than as engineers or computer programmers.

Grandin suggested that things are worse than they use to be, and I suspect that she is right. This first occurred to me a couple of years ago when I met Mr. X, a teacher at an alternative school in New Haven, CT--an eccentric engineering type whose classes had attracted large numbers of children with Aspergers. As I listened to Mr. X, who must be just a few years away from retirement, discuss the engineering projects he does with his Aspie students, I became increasingly certain that there isn't anyone like him anywhere in the Philadelphia public school system, where my children attend school.

There certainly isn't anyone like Mr. X at their specific school, where science class is all about communiating about science, and "technology" class is all about powerpoint and photoshop. And, unfortunately, this sort of science and technology curriculum--or lack thereof--appears predominate at Philadephia public schools in general. Nor do the Philadelphia charter schools appear to offer much of an alternative.

And, since current trends in math and science also permeate the training of math and science teachers--as a visit to any number of math, science, or technology "methods" classes will confirm--most Aspie-friendly eccentrics will never make it past a single week of teacher certification training.

For years I've been longing for a Mr. X in J's school--as Grandin observes, all it takes is one such person--and for years I've been increasingly concerned I'll never find one.

Sunday, June 7, 2009

Reversing home and school, II

SwitchedOnMom from TheMoreChild just alerted me to the following Principal's Letter (Montgomery County Public Schools, 4/09):

The Homework policy, which is sent home at the beginning of the school year, calls for nightly practice of basic facts in addition to the homework that is a review of concepts taught in school. The school doesn’t “teach” math facts daily… what it really is memorization. My staff spends some time on supporting students with the facts, but it would be impossible to teach the curriculum and carve out time daily for students to memorize. Although memorization of facts is considered a lower-level skill, it is so important in students being able to successfully master the more complex mathematical concepts we teach. We know time is a barrier; however, the review really is important

And which sorts of households are most likely to be able and willing to provide this "important" review?

This letter reminds me of one the observations I just encountered in Outliers, the latest book by Malcolm Gladwell. Apparently, the achievement gap between students from different socioeconomic backgrounds tends to rise during school vacations. The reason, Gladwell proposes, is that vacations are when gaps in educational opportunities are greatest. In general, disadvantaged students have far fewer opportunities for extracurricular academic enrichment--both inside and outside their homes.

As more and more schools abdicate responsibility for teaching basic academic skills to mastery, and become more and more like summer vacations in their effects on students (at our local school, in addition to whatever it is that actually goes on during math class, we've got movies during "library" and computer games during "technology") the more we can expect this achievement gap to widen.

And, equally perversely, the more we can expect schools to deny enrichment opportunities to the most academically advanced students--because, after all, this would only further widen the gap.

Thursday, June 4, 2009

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

End-of-year addition and subtraction word problems.

1. From tonight's 2nd grade Investigations "How Many Cubes?" worksheet (Unit 6, Session 2.3):
Jake and Sally were playing Roll-a-Square. They had 27 cubes and then rolled a 9. How many cubes do they have now?

Kira and Franco were playing Roll-a-Square. They had just received 53 cubes, but they landed on the space that says "Oh No! Give back 6 cubes." How many cubes do they have now?

Jake and Franco were playing Roll-a-Square. They had 46 cubes and then landed on the space that says "Great! Take 5 more cubes." How many cubes do they have now?

2. From 2nd grade Singapore Math, Primary Mathematics 2B "Review 15", (p. 188):
Jen made 240 cupcakes. She made 405 muffins. How many more muffins than cupcakes did she make?

Wendy made 153 cookies. 89 of them were chocolate cookies. The rest were wheat cookies. How many wheat cookies did she make?

Samantha saved $10.40. She saved $3.95 more than her sister. How much did her sister save?


3. Extra Credit:

1. Discuss the levels of respect accorded to Singaporean vs. American math learners, considering such things as mathematical tasks, games like Roll a Square, and the number of explanation points per problem set.

2. Do Singaporean school children follow different developmental time tables from their American counterparts?

Tuesday, June 2, 2009

The politics of education reform: map the institute to its ideology

Institute X, Mission Statement:

The X Institute is a non-profit think tank dedicated to advancing educational excellence. We promote policies that strengthen accountability and expand education options. Our reports examine issues such as the No Child Left Behind Act and school choice.

The X Institute believes that all children deserve a high quality K-12 education at the school of their choice. Nationally and in our home state of ---, we strive to close America's vexing achievement gaps by raising standards, strengthening accountability, and expanding education options for parents and families.

Our work is grounded in these convictions:

• all parents should have the opportunity to select among a variety of high-quality schools for their children;
• the path to increased student learning is to set ambitious standards, employ rigorous assessments, and hold students, teachers and schools accountable for performance;
• every school should deliver a content-rich curriculum taught by knowledgeable teachers; and
• schools exist to meet the educational needs of children, not the interests of institutions or adults.

We advance the reform of American education by:

• engaging in solid research and provocative analysis;
• disseminating information and ideas that shape the debate;
• supporting quality schools and organizations in Dayton, in Ohio, and across the nation;
• sponsoring charter schools in Ohio and building their academic excellence; and
• informing policy makers at every level about promising solutions to pressing education problems.

Institute Y, Mission Statement:

We are tired of a state that focuses on divisive side issues while our schools [and other things] suffer. [Our state] is great when we have [various other things and] quality schools.

[Institute Y] delivers accurate policy research with a focus on smart, effective progressive messaging through a multi-media platform. We are framing [our state's] public policy debate. Through our communications strategy, we've compelled legislative and executive branch policy change. We link academic and traditional foundation research to achieve tangible, demonstrable solutions.

Question: Guess which institute (X or Y) accuses which institute (X or Y) of "masquerading as 'thoughtful think tank discourse'" while actually "espousing right-wing educational policy"?

Follow-up: Check your answers by googling each site using extracts from the above mission statements. Then see if you can determine one good reason why one institute should draw conclusions about the political characteristics of the other institute's educational ideology.