"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.
Sunday, November 29, 2009
"You may have won the battle, dude, but you have lost the war."
Friday, November 27, 2009
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
"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
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.
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
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.
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
...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
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.
Saturday, November 14, 2009
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
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
Follow the rule. Fill in the missing numbers.
Rule: + 6
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.
3 + 4 =
30 + 40 =
300 + 400 =
7 - 3 = ___
70 - 30 = ___
700 - 300 = ___
7 + 6 =
27 + 6 =
527 + 6 =
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.
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
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
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
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!!!]From Cells, Heredity, and Classification (Holt, Rinehart and Winston), with my queries in brackets.
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.
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
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:
(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
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
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
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.