Tuesday, March 31, 2009

Making after-school clubs non-competitive

I learned at today's meeting that our principal feels that all after-school clubs should be non-competitive, in the sense that they shouldn't select students based on test scores. (Tryouts for the school musical seem to be another matter).

Rather, all clubs should select students on a first-come, first-served basis (except for the school musical).

While this spares students the very real pain of rejection (except when they try out for the school musical), it has what I believe is an unintended consequence. Like so many well-meaning measures intended to level the playing field, it replaces meritocracy with something far worse: namely, insidocracy.

In the case of after-school clubs, this means that children with the best-connected, best-informed, most organized and on-top-of-it parents will get in.

In the name of not widening the achievement gap between the most capable and everyone else, our school thus further widens the achievement gap between those with certain types of parents and those without.

Sunday, March 29, 2009

On Grade Reversal: They didn't publish this letter

I wrote this letter to the NY Times in response to their recent article on the 1-4 grading system that more and more schools are using instead of letter grades:

The new numerical system distracts from the real issue, which is what it now takes to earn top grades--especially in math. "Performance goes beyond standard" and "Independently explores ideas and topics" are two of the criteria listed on the Philadelphia School System's standards-based report card. But the Pennsylvania math standards are so low, and the standards-based curriculum so easy, that students have no opportunity to exceed the standards by doing harder problems. If they want top grades, rather, they must explain and illustrate their answers to today's easy problems as elaborately and neatly as possible, and, as one of our teachers puts it, "solve problems in multiple ways without being told to." The more mathematically inclined you are, the more inane you will find these requirements. Top grades no longer go to those who are best at math, but to those who are most eager to game the system.
I discuss a specific instance of this grade reversal in a previous post. Where will it lead, and why aren't more people up in arms about it?

Friday, March 27, 2009

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

A. From this week's 2nd grade Investigations homework:

My Own Comic Strip

Family Connection
Students have been creating their own story problems. Here your child is being challenged to write and illustrate a story in which an unknown part (or amount) is being added to a known part (or amount) to create a given total. Being able to visualize what is given in a problem--and what is missing--is an important skill.

1. Write a story for this problem:
36 + ____ = 52
Your story can be funny or silly or serious!

2. Draw pictures that show how your story starts, what happens, and how your story ends.

3. Show or tell how you solved your problem.

B. From a similar point in the Singapore Math curriculum, Primary Mathematics Workbook 2B, p.85:

1. Ben bought a snack from a vending machine that cost 55 cents. He put a one-dollar bill into the machine. How much change did he get?

2. Sam had $8. He bought a toy car for $5.35. How much money did he have left?

3. A toy robot costs $5.90. A doll costs $3.85. How much cheaper is the doll?

C. Extra Credit

Draw a comic strip that shows a child drawing a comic strip to solve each problem set. Your strip should illustrate how comic strip visualization skills help the child solve math problems, and how the child feels about the math that is "given" and the math that is "missing" in each curriculum. Your story line can be funny or silly or serious!

Wednesday, March 25, 2009

Autism Diaries VIII: time traveling full circle

Ever in search of new avenues for mischief, J delighted when landing on "I've got a gun in my pocket." What a satisfying reaction that earned him at school.

I tend to find the professionals' reactions less satisfying than J does. That is, I prefer descriptive reports, with their implicit assumption that we parents will handle things appropriately, to the usual well-meaning advice & lecture: "Could you please tell him that that's it's totally inappropriate to threaten his classmates. He can get suspended for this." But what really gets my goat is the occasional interrogation: "Has anything changed at home? Has he been watching violent TV shows?"

People keep forgetting that, with autism, the usual rules don't apply. And that, when it comes to individual members of this highly heterogeneous population, the parents really are the experts.

Besides telling J how important it is not to threaten people in school, casting it in part, as usual, in terms of self-interest ("Do you want to get into a good high school in two years so you will later be able to get a good job and earn lots of money?"), I decided to go out of my way to make quality time that evening.

Homework dispensed with, we spent over an hour discussing galaxies, black holes, and time travel. Before I had a chance to describe to him the "grandfather paradox" (what happens if you go back in time and kill your grandfather before he meets your grandmother, such that you no longer exist as his murderer), J came up with a related puzzle all on his own, inspired by his fascination with 9/11 (an event of which he'd only become aware within the past year). What if, he asked, he took a picture of the "New York Cemetery," traveled back in time to the morning of 9/11, photograph in hand, and locked all the doors to the World Trade Center before anyone could enter. "Then would the pictures of the graves disappear?"

Duly impressed, I had him look up "grandfather paradox" on Wikipedia--along with galaxies, black holes, and time travel.

The next day at school pickup, I found him sobbing. He'd had a very bad day, they told me. He'd started to make death threats again.

"I didn't threaten anyone," he sobbed, inconsolably.

Now I don't trust J anymore than the next guy does, but I do trust his hot, swollen, tear-stained face. So I embarked on an interrogation of my own, and the dust gradually settled.

The threats weren't oral, but in writing. He'd written them not as actual threats or notes-to-self (a la Dylan Klebold), but as part of his literacy class "free write." The someone in question wasn't someone from school, but the 9/11 hijackers. And, no, he wasn't "going to kill" people who were already dead; rather, he was going to travel back in time and kill the hijackers before they got on their airplanes--"New York Cemetery" photograph in hand.

Monday, March 23, 2009

Cooperative learning?

Today's educators credit cooperative learning with teaching children the virtues of team work, and with exposing them to diverse ways to solve problems.

I got a slightly different take on cooperative learning from my daughter this past weekend. She told me that she received a "1" (the lowest possible grade on the 1-4 scale) because her partner kept erasing her correct answers and replacing them with his incorrect answers.

I'm curious what this experience has taught my daughter about the virtues of team work, and about diverse ways to solve problems.

Do the benefits of mandatory cooperative learning really outweigh the costs? Or is "mandatory cooperative learning" an oxymoron in more ways than one?

Saturday, March 21, 2009

Today's false dichotomy: special education vs. general education

Some superintendents, I recently learned from an insider friend, spend the bulk of their time on issues relating to special education. Especially time-consuming are the increasing numbers of court cases in which parents sue schools for failing to accommodate special needs children. All of this, of course, also costs huge amounts of money: an ever higher proportion of school district spending. The more so as more and more kids are getting special diagnoses, along with the I.E.P.'s (Individual Education Plans) that require schools to accommodate them.

A fair amount of this expense, I believe, is attributable to today's right-brain classroom practices: child-centered, group-centered, hands-on learning; the avoidance by teachers and textbooks of explicit instruction; the watering-down of the math and science curriculum with arts & crafts and "creativity"; and the rise of open-ended questions and large-scale/interdisciplinary projects.

How does all this relate to special education labels?

1. Making children work in groups redflags more and more unsocial children as having Asperger's Syndrome, PDD, and social anxiety.

2. The lack of structure of both the child- and group-centered classroom, and the open-ended questions, redflags more and more structure-craving children as having Asperger's Syndrome or PDD.

3. Insufficient explicit instruction in phonics yields more and more children with dyslexia.

4. Nonexistent penmanship instruction, together with grades based on "neatness," yields more and more children with dysgraphia.

5. Insufficient explicit instruction in arithmetic, together with the organizational demands of large-scale/interdisciplinary projects, yields more and more children with Nonverbal Learning Disabilities.

6. The noise and chaos of child- and group-centered, hands-on learning yields more and more children with sensory integration and attention deficit disorders.

7. The dumbing down of math and science and points off for lack of showy graphics, deficient "creativity," and explanations that are insufficiently verbose propels increasing numbers of parents to seek mentally gifted diagnoses so that their children can receive more challenging material and better grades.

Many of the resultant I.E.P's require schools to provide additional structure, more explicit instruction, quieter learning environments, exemptions from group work, exemptions from visual "creativity" requirements, fewer large scale/interdisciplinary projects and open-ended questions, and/or more challenging math problems, to the children in question.

If schools were to provide these basic accomodations to everyone from the get-go, perhaps we wouldn't have nearly the numbers of students labeled with Asperger's Syndrome, PDD, social anxiety, dyslexia, dysgraphia, Nonverbal Learning Disorders, sensory integration disorders, ADD/ADHD, and mental giftedness.

...And schools would save some time and money that might be better spent elsewhere.

Thursday, March 19, 2009

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

1. This week's 2nd grade Investigations (TERC) assignment:

Guess My Rule Questions:

NOTE: Students use the given data to figure out additional information

1. A Grade 2 class was playing Guess My Rule. There were 21 students in the class. 8 were wearing stripes. How many students were not wearing stripes? Show your work. Write an equation.

2. A Grade 3 class was playing Guess My Rule. 6 students were wearing glasses. 18 students were not wearing glasses. How many students were in the class? Show your work. Write an equation.

3. A Grade 2 class was playing Guess My Rule. 12 students were wearing sneakers. 10 students were not wearing glasses. How many more students were wearing sneakers? Show your work. Write an equation.

2. From a similar point in the 2nd grade Singapore Math curriculum (Primary Mathematics 2B, p. 114):

Mrs. Coles bought 18 mangoes. Mrs. Lambert bought 28 mangoes. How many more mangoes did Mrs. Lambert buy than Mrs. Coles?

Matthew learns to spell 7 words every week. How many words does he learn to spell in 5 weeks?

The students in a class borrowed 26 books from the class library. There were 34 books left. How many books were there in the library at first?


3. Extra Credit:

Given that all math problems have students using given data to figure out additional information, discuss why the Investigations problem set, but not the Singapore Math problem set, includes an explanatory note about this for parents.

Tuesday, March 17, 2009

When dumb stuff makes you dumb

It's a no-brainer that, in the long run, dumbed-down stimuli (as in a dumbed-down curriculum) dumbs everyone down.

But lately I've been thinking about how this true even in the short run. That is, when our immediate environment is under-stimulating, we become dumber then and there.

I first started noticing this after I had kids. For all the intellectual and emotional stimulation that children bring, there are also those deathly boring routines where you're trying to get your five year old to put her empty bowl, spoon, and cup in the sink, put on her jacket and backpack in that order, look where you're pointing when you tell her where her bike helmet is, and put on her hat on before she puts on her helmet.

On those situations, I find myself fumbling for words. I say "plate" instead of "bowl," "counter" instead of "sink," and "helmet" instead of "backpack." I'm so bored by these exchanges that my brain seems to shut down.

On the other hand, in a grownup conversation about math education, words seem to come easily. For example, I don't confuse "algorithm" with "algebra" and "digit" with "decimal."

Speaking of math education, my daughter seems to experience a similar mental shutdown in her classroom. "School math is so hard," she keeps telling me.

"How can it be so hard," I ask, "When the stuff you're doing at home is so much harder, and you don't think that home math is hard?"

(She's in 2nd grade, doing 3rd grade Singapore Math at home, so we're talking about school problems like this 2nd grade Investigations Problem, as compared with home problems like this 3rd grade Singapore Math problem.)

"It's boring," she eventually clarifies.

Boring kids makes them dumb, it turns out.

But too many teachers don't recognize this phenomenon. Instead, its effects encourage them to keep things boring and easy. After all, if it takes my daughter, staring into space and pretending to be "thinking," half an hour to complete an Investigations problem like this one, then surely she can't handle anything more challenging--despite what her pushy, deluded, helicopter parents might claim to the contrary.

Sunday, March 15, 2009

Let's rename the PTA, PTO, and HSA

Leaders of Parent Teacher Associations and Organizations and Home and School Associations tell me that it's not their role to hear, let along act upon, parent concerns about the school curriculum.

Some of these leaders seem surprised that we parents even think we should have any influence over the curriculum.

It seems that many of us are laboring under antiquated impressions of the parent-teacher organizations that date back to that era when our own parents were involved: those long-ago days when such organizations dared to let parents express concerns about what children were learning in school.

If they now want to quell such awkward remarks at their public meetings, PTA, PTO, and HSA leaders should rename their organizations to make their 21st century missions entirely clear. If these missions consist, entirely, of baking cookies, stuffing envelops, chaperoning field trips, helping teachers manage child-centered, cooperative learning groups, and organizing teacher-appreciation days, then a better name might be: Parent Volunteer Organization.

In other words, let's stop pretending that parents have any role in public education other than to further enable teachers to do what they and their supervisors have already decided is the best way to educate our children.

Friday, March 13, 2009

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

1. From "Bit and Pieces II" unit of the 6th grade Connected Mathematics curriculum (Bits and Pieces, II. p. 48):

Problem 4.4

Work with your group to develop at least one algorithm for adding fractions and at least one algorithm for subtracting fractions. You might want to look back over the first three problems in this investigation and discuss how each person in your group thought about them. Look for ideas that you think will help you develop algorithms for adding and subtracting fractions that always work, even with mixed numbers

Test your algorithms on a few problems, such as these:

5/8 + 7/8 3/5+5/3 3 3/4 + 7 2/9
3/4 - 1/8 5 4/6 - 2 1/3 5/6 - 1/4

If necessary, make adjustments to your algorithms until you think they will work all the time. Write up a final version of each algorithm. Make sure they are neat and precise so others can follow them.

Problem 4.4 Follow-Up

1. Exchange your addition algorithm with that of another group. Test the other group's plan. Write a paragraph explaining how your algorithm and the other group's algorithm are alike and how they are different.
2. Exchange your subtraction algorithm with that of another group (a different group from the group you exchanged with in part 1). Test the other group's plan. Write a paragraph explaining how your algorithm and the other group's algorithm are alike and how they are different.

2. From the "Fractions" unit of the 6th grade Singapore Math curriculum (Primary Mathematics 6B, p. 14):

Exercise 7

1. A shopkeeper had 150 lb of rice. He sold 2/5 of it and packed the remainder equally into 5 bags. Find the weight of the rice in each bag.

2. Peter had 400 stamps. 5/8 of them are U.S. stamps and the rest are Canadian stamps. He gave 1/5 of the U.S. stamps to his friend. How many stamps did he have left?

3. 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?

4. 2/3 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. Extra Credit

Work with a group and write a paragraph about (1) which problem set involves more higher level thinking, and (2) which one is more irritating. Then exchange your answer to the first question with one group and and your answer to the second question with another group, and write two paragraphs explaining how your answers are alike and how they are different.

Wednesday, March 11, 2009

Continental Math League update: let no good deed go unpunished

Breaking news: the principal is faulting our Continental Math League for "widening the achievement gap."

It's been suggested that, instead of running a math club for gifted students, I instead run one for struggling students.

But I kinda tend to think that it's the school's job, not mine, to educate struggling students.

A first step for the school would be to follow in the footsteps of the following school districts and drop the Investigations math curriculum: Framingham (Massachusetts), Inner Grove, Little Falls, Staples-Motley, Stillwater, & Waconia (Minnesota), Columbia (Missouri), Fairport, Greece, Penfield, Pittsford, & Syracuse (New York), Lebanon, Painesville, Three Rivers, & Wickliffe (Ohio), Gervais, Sutherline, & Chariot (Oregon), Arlington, Bellevue, Clover Park, Eastmont, Lake Stevens, Oak Harbor, & Richland (Washington), Black River Falls, La Crosse, River Falls, & Superior (Wisconsin).

If the Powers that Be have the guts to do this, I will be so grateful that I may, indeed, be willing to sacrifice additional time in the name of math education.

Monday, March 9, 2009

Update on computer programming instruction

I'm still waiting on whether a friend can help me figure out how to make SCHEME work interactively; I've downloaded Scilab but haven't figured out how to run it (when I click on the icon, nothing happens); I haven't yet tried out Python and Scratch.

In the meantime, I'm using what's already up and running--namely, javascript. I introduced this to J. years ago, and he's learned how to create basic html pages with buttons that make calls to simple js code. But now I'm attempting to teach him, systematically, some more basic programming, and thought I'd share his assignments as I make them up.

Assignment 1: write program that prints out numbers 1 to 20; 5 to 30; 100 - 150 (introduces alert() and for-loops)
Assignment 2: write a program that asks for two numbers and prints out all the numbers between them (introduces prompt() and variables)
Assignment 3: write a program that prints out all the multiples of 5 between 1 and 100 (introduces multiplication operator)
Assignment 4: write a program asks for a low number, a high number, and a factor and prints out all the multiples of that factor that are between the low number and the high numbers (combines tools from assignments 1-3).
Assignment 5: write a program that determines whether a give number is odd (introduces if...else)
Assignment 6: write a program that determines whether a given number is prime (introduces "break" for breaking out of loops; applies all the above tools to a mathematical problem). This one was a challenge; we had to spend time going over the value of the looping variable at different points within the loop and at the exit point.
Assignment 7: (next one on the agenda) write a program that lists all the factors of a given number. Stay tuned!

Friday, March 6, 2009

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

1. The totality of this week's (TERC) 2nd grade Investigations homework:

Fingers and Toes at Home

NOTE: Students practice counting by groups of 5 and 10.

Figure out how many fingers and toes there are in your home. Use numbers and pictures or words to show your thinking.

[1/4 page of white space]

Can you also use tally marks?

[1/4 page of white space]

Enough for the class

NOTE: Students compare two amounts and find the difference.

There are 21 students in Ms. Tom's class. Each student needs an eraser. Ms. Tom has 13 erasers.

1. Are there enough for the class? YES NO
2. Are there any extra erasers? YES NO
How many? _________
3. Does Ms. Tom need more erasers? YES NO
How many? _________
4. How did you figure it out? Use this space to show your work.

[1/5 page of white space]

2. Two out of 9 problems in a 2nd grade Singapore Math assignment from a similar point in the curriculum (Primary Mathematics 2B, p. 61):

Mrs. Rossi sold 402 concert tickets in 2 days. She sold 382 tickets on the first day. How many tickets did she sell on the second day?

[1/5 page of white space]

A boat can carry 5 people. How many boats are needed to carry 43 people?

[1/5 page of white space]

Extra Credit:

Compare the amounts of math in the two problems sets and estimate the difference. Use numbers and pictures or words--or tally marks--to show your thinking. Be creative :)

Thursday, March 5, 2009

Interactive Computer Programming Environments--essential yet elusive

In an earlier post on the disadvantages of using calculators in lieu of long division, I wrote about how calculators don't give feedback about wrong answers, and how feedback seems essential to learning.

The more I think about it, the more convinced I am that continuous feedback loops speed learning.

And the more convinced I am that the best and fastest way to learn to program computers, in particular, is by doing so in an interactive environment--one in which you test out a short function or procedure by typing it out on line, hitting 'Enter,' and getting immediate feedback.

Only certain programming languages/platforms allow such interactivity--for example, LISP. And it was only in learning LISP, interactively, that I felt like I was finally getting the hang of programming.

Now I want the same for J, who may well find his calling in computers.

But so far I've come up dry. Even the MIT Open Courseware SCHEME software suggested to me by someone who commented here does not work interactively, at least on my computer.

It somehow seems emblematic of today's technology featuritis and today's anti-analytical education fads that there's a super-abundance of software tools and "interactive learning" schemes, while something as simple as an interactive programming platform is apparently impossible to find.

Any suggestions?

Tuesday, March 3, 2009

Grading for Creativity in Social Studies

Exhibit A-- 25% off for deficient creativity in a Social Studies project
(yielding a 3 on a 0-4 scale):

Can anyone out there give me one good reason why grade school teachers should be rating their students for creativity?

Sunday, March 1, 2009

Why More Mathematicians Don't Oppose Reform Math: and why we desperately need them to

Yesterday's NPR Weekend Edition Saturday featured an interview with Stanford University professor Keith Devlin on the importance of Algebra, and while I listened to it, it suddenly occured to me why more mathematicians don't oppose Reform Math.

Here's what I posted on the NPR website:

Keith Devlin suggests that, given calculators, students should focus less on accurate arithmetic calculations, and more on algebraic reasoning. But, as Devlin's fellow mathematicians (e.g., Howe, Klein, & Milgram) have argued, mastering the basic algorithms of arithmetic is essential preparation for algebra. And while the most mathematically inclined students--including Devlin himself--may be able to master these algorithms without much hands-on, numerical practice, the vast majority do need lots of practice, and striving for correct answers is an essential part of that practice.

Today's arithmetic, unfortunately, has been seriously watered down by the new "Reform Math". More mathematicians need to examine this curriculum and speak out against it; ironically, because they can get by without much arithmetic practice, and because so many of them found arithmetic boring, too few mathematicians have considered the potentially dire consequences that the latest trends in grade school math present to the rest of the population (and to the country as a whole).

When our most prominent, accomplished mathematicians, who themselves may well have gotten by without developing accurate arithmetic skills, discount the importance of teaching such skills to the general population, they do a terrible disservice to elementary school math education (and may themselves be horrified by the results, years later, when today's grade school students enter their classrooms).

Consider what one other NPR poster has taken away from the Devlin interview. As she writes in her post:

I want to thank Dr. Devlin for a great quote that I plan to post at the front of my classroom. “Mathematicians often make mistakes in elementary arithmetic because we have our minds on higher things." That will come in very handy!