Saturday, May 30, 2009

Reversing home and school

Is this just our school, or is it schools in general?

Today yet another local parent reported to me how her child's teacher, while acknowledging the importance of arithmetic drills, states that there simply isn't enough time during the school day to conduct them. Apparently group-centered, hands-on, discovery learning, and 40-minute-long sharing of multiple solutions to single problems, leaves little time for multiplication tables and such.

Since at least the beginning of this school year, the abiding message from our school's teachers and math specialist has been: You parents should be teaching kids the addition, subtraction, and multiplication facts at home.

To this, I have several reactions:

1. Why do schools have less time to teach these things than they did back when we parents were kids?

2. This seems like a great way to widen the achievement gap between kids from different home environments.

3. It's also yet another way in which schools are attempting to reverse the roles of home and school. Schools continue to assume more and more responsibility for children's social and emotional development, and for the informal application of academic skills, while handing off more and more hard-core academic responsibilities to parents (arithmetic facts, penmanship, phonics).

4. Has anyone bothered to ask us parents whether we'd rather spend time drilling our kids on multiplication facts and teaching them phonics and penmanship?... Or whether we'd perhaps prefer to have their classroom teachers do this so that we have more time to take them to museums, do hands-on activities with them, and attend to their social and emotional development?

Thursday, May 28, 2009

Math problem of the week: 5th grade Trailblazers vs. 1920's Math

Higher Level Thinking Problems from the end of the 5th grade curriculum:

I. Hamilton's Essentials of Arithmetic Higher Grades (published in 1919), "Problems Without Numbers," p. 155:

How can you tell, by means of a scale on a map, how far it is from one city to another?

If you know the dimensions of a hall, how can you find the number of square yards of plaster needed to cover the walls and the ceiling?

If you know the first three terms of a proportion, how can you find the fourth term?


II. Math Trailblazers Student Guide, "Grass Act," p 508:

Manny: I can't believe how long it took me to cut the grass in our yard Saturday. There must be a zillion blades of grass there.

Felicia: There's no such thing as a zillion.

Manny: I know. It's just a way of saying there's a whole lot. Still, I wonder how many blades of grass are in my yard? It would be really interesting to find out. I wonder how we can.

1. Think about how Manny and Felicia can estimate the number of blades of grass in the yard. Work with your group to develop a plan that can be used to solve this problem.

2. Record your group's plan. Use the Student Rubric: Solving to help you as you write your plan.


Extra Credit: Work with your group to develop a plan to estimate how far U.S. grade school math has come since the 1920s.

Tuesday, May 26, 2009

Left-brain epiphany: incidental, hands-on learning yields disembodied facts

This struck me during some recent visits to local museums.

Playing with pendulums, I witnessed how periodicity relates to length. Moving on to levers, I witnessed my muscles working harder when levers got shorter. Moving on to rotating platforms, I saw my son spin faster as he drew his legs in. Wandering on into the aerodynamics room, I quickly forgot these details and witnessed how paper airplanes with different shapes followed different trajectories. But there were too many variables for me to draw firm conclusions. In the meantime, I forgot the specifics of pendulums and levers. By the end of the visit, all I could remember were vague impressions and a few fragmented details I've since forgotten.

It's not that I wasn't interested; it's that I no longer have active recall of a structured knowledge base--e.g., in basic mechanics and aerodynamics--in which to store these facts and find meaning in them.

Imagine a child who never gets this foundation. Imagine a child whose classroom science instruction eschews the structured facts provided by decent science textbooks and dynamic science teachers, and instead resembles that provided, in an incidental, hands-on kind of way, by a science museum.

Incidental learning is great, but it only works atop a foundation of structured knowledge. Today too few classrooms provide this, and the sad result are fragmented, and therefore meaningless and ultimately forgotten facts...

...of the sort that people who tout incidental, hands-on learning love to say they hate.

Sunday, May 24, 2009

Pressure for "innovative" teaching in colleges

This past week, on three separate occasions, three college professor friends of mine recounted how their respective universities have recently heightened scrutiny of classroom teaching methods. Part of this involves professors filling out forms describing and justifying their teaching strategies.

It turns out that some teaching strategies are preferable to others: namely, "innovative" ones.

It turns out, furthermore, that some strategies are inherently more "innovative" than others: namely, Constructivist ones.

Thus, to increase their chances for tenure, or, once tenured, for salary hikes, professors must use the same "innovative" teaching techniques that have become the norm in more and more grade schools around the country: hands-on, student-centered, cooperative learning.

Does this indicate an unprecedented influence of education schools over the universities that house them, or does it reflect the needs of Constructivist high school graduates, who no longer know how to listen to lectures and work independently?

Friday, May 22, 2009

Math problems of the week: 3rd grade Everyday Math vs. 1920s Math

I. The final word problems in the 3rd grade Everyday Math Student Math Journal 2, p. 317:

1. Rule: × 3

in out
0 ___
1 ___
2 ___
3 ___
4 ___

2. A brachiosaurus is 72 feet long, a diplodocus is 90 ft long, and a stegosaurus is 23 ft long. If they get in line behind one another, how long is the line?

The line is ___ feet long.

Number model:

3. Bary ran 800 meters. Kristen ran 628 meters. How much farther did Gary run?

He ran ___ meters farther.

Number model:

4. I bought a beach ball for $1.49 and a sand toy for $3.96. How much change will I get from a $10 bill?

$ ____

5. Write 3 ways to say 8:45.


6. Complete the Fact Triangle. Write the fact family.

[picture of a triangle with 16 and 2 in two corners, and × and ÷]

___ × ____ = _____
___ × ____ = _____
___ ÷ ____ = _____
___ ÷ ____ = _____

II. The final word problems in Chapter IV, the final chapter for 3rd grade of Hamilton's Essentials of Arithmetic, published in 1919, p. 122:

1. Robert had a plot in a school garden 10 feet long and 8 feet wide. How many square feet were there in his plot?

2. He planted two rows of tomatoes from which he raised 96 pounds. How much did he get for them at 9 cents a pound?

3. He planted two rows of beans which he thinned out to 3 plants to the foot. How many plants did he then have on the 20 feet?

4. How much did he get for 15 pounds of beans at 8 cents a pound?

5. He planted 35 turnips 7 to the foot. How many feet of turnips did he plant?

6. He raised 28 pounds of turnips which he sold at 3 cents a pound. How much did he get for them?

7. He also planted beets, carrots, and Swiss chard. He received 30 cents for his beets, 20 cents for his carrots, and 25 cents for his chard. How much did he get for these vegetables?

8. He raised and sold 10 heads of lettuce at 5 cents apiece and 8 bunches of radishes at 5 cents a bunch. How much did he get for them?

III. Extra Credit:

Discuss the level of higher level thinking in the 1920s.

Wednesday, May 20, 2009

Autism Diaries X: following the directions:

J is really good at math, but has trouble following directions--so much so that he received failing grades on his first few math quizzes. I've therefore asked for school accommodations to include verbal clarifications that ensure that he understands the directions.

Whether this accommodation is met, of course, depends on the ability of the supporting staff to deduce whether J understands the directions. Sometimes, this may be quite a challenge.

However, when a child is seen using a ruler to measure shapes that implicitly aren't drawn to scale (implicit in "Suppose each figure has a perimeter of 24 centimeters"), you'd think it would be pretty obvious. Consider this:

When J's failure to follow directions is due to the school's failure to follow its directions, who should receive a failing grade?

Monday, May 18, 2009

Gladwell's Outliers: more "everything but the math curriculum?"

Teacher quality; inadequate education funding; anti-nerd stereotypes; the digital revolution; religious fundamentalism; the triumph of self-esteem and self-help; existential aimlessness. Pretty much everything under the sun has been held responsible for the mediocre math and science skills of the average American gradeschooler. Everything under the sun, that is, except the actual math and science curriculum.

At first glance, Malcolm Gladwell (Outliers), appears to join the chorus of intellectuals blaming everything but the curriculum. Addressing the problem of America's below-average TIMSS scores--the international test that compares gradeschoolers in math and science--he cites cultural differences and attitude as more influential than anything else.

This message is sure to resonate with the many American education experts who've been claiming for decades that culture and emotion are way more important than actual academics.

A more careful read, however, reveals that what Gladwell is talking about is work ethic. In discussing culture, he specifically cites cultures that have a long legacy of hard work; by attitude, he is specifically talking about attitudes towards hard work.

But we tend to remember best what resonates with our preexisting assumptions. Thus, many readers, I'm guessing, will come away thinking that Outliers further justifies the popular view that education is all about culture and attitude--just as many readers came away thinking that Gladwell's Blink further justifies the popular view that intuition matters more than rigorous analysis.

One of Gladwell's observations that I suspect many readers won't remember points implicitly to the importance of curriculum content:

One of the questions asked of test takers on a recent math test given to students around the world was how many of the algebra, calculus, and geometry questions they had previously learned in class. For Japanese twelfth graders, the answer was 92 percent. That's the value of going to school 243 days a year. You have the time to learn everything that needs to be learned--and you have less time to unlearn it. For American twelth graders, the comparable figure was 54 percent.
The problem is that Gladwell (like many, many, many, many others) appears not to have visited enough math and science classes to have noticed how poorly American schools use the time slated for math and science. He mentions neither the logistical inefficiencies discussed in books like The Learning Gap, nor the curricular inefficiencies of today's discovery-based learning and multiple solution-centered problem solving, nor the pervasively low level of actual mathematics found in today's Reform Math.

In other words, Gladwell is implicitly assuming that if American schools were simply to spend more time on math and science instruction, they would spend that time well enough to cover all the material that Japanese classrooms cover.

Saturday, May 16, 2009

Autism Diaries X: If it's negated and in quotes, is it still a threat?

J, explicitly barred from making death threats at school, is testing the linguistic limits of what constitutes such a threat in the "daily free-write" he does in literacy class. Writing about the Grandfather Paradox didn't pass muster; neither did his latest venture:

There was a community where the children are in charge. They made a law "Only children 8 or over can drive." They sell games with Gryffindor Challenge and game that I get billion of beans. They trap adults between floors. They remove a sign saying "I am going to kill you. I am going to murder you." They vandalize wikipedia. They tell adults to build houses.
Somehow, the broader scenario conjured up by this paragraph didn't attract as much concern as the M- and K-words.

Meanwhile, I've just learned that the summer reading assignment includes Lord of the Flies.

Thursday, May 14, 2009

Math problems of the week: 3rd grade Everyday Math vs. French Math

1. The last five addition problems in the second (and final) Everyday Math 3rd grade workbook, Student Math Journal Volume 2, p. 316:

2,384 + 1 =
2,384 + 10 =
2,384 + 100 =
2,384 + 1,000 =
2,384 + 10,000 =

2. The last five addition problems in a French 3rd grade (CE2) math workbook, Cahiers d'activites mathematiques, p. 22:

57 + 19 =
84 + 29 =
164 + 19 =
315 + 29 =
36 + 39 =

3. Extra Credit:

What do these problems suggest about who learns more about place value by the end of 3rd grade?

Tuesday, May 12, 2009

Comic book project is back!

J received a 20 out of 24 overall, having removed the offending elements.

Full points for Dialog/Text and Title Page.

Here's where he fell short:

3 out of 4 for Creativity (measured by number of "creative details and/or descriptions that contribute to the reader's comprehension and enjoyment of the project").

3 out of 4 for Illustrations (measured by how "original" and "detailed, attractive, and related to the text on the page" the illustrations are).

3 out of 4 for Originality (measure by degree of "originality and inventiveness" and how "interesting" the content and ideas are).


3 out of 4 for Grammar and Syntax. (This last one, at least, is self-explanatory--not to mention objective, as well as relevant to aptitude in English).

Yes, this is an English class assignment, even though you lose a point for Dialog/Text if "there is too much dialogue and text in this story."

Also of interest is how the grading rubric factors in some expectations that aren't included on the list of requirements in the original assignment.

Presumably this is because top grades require going above and beyond expectations.

Sunday, May 10, 2009

The pleasures of parenting left-brainers

When our 15-year-old sets up his own orthodontist appointments and plans bus-to-train-to-trolley routes across the city to get himself there.

When our 8-year-old figures out how to use Power Point to write and illustrate stories about her imaginary friends.

When our 12-year-old (J) discusses space-time curvature and imagines time redoubling upon itself in ways that don't imply repetition of particular moments.

It's moments like these, however unrepeatable, that make me especially happy to be a parent of left-brain children.

Friday, May 8, 2009

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

1. The first two problems in Bits and Pieces II, More About Percents, the second chapter on percents in 6th grade Connected Math:

A survey asked cat owners, Does your cat have bad breath? Out of the 200 cat owners surveyed, 80 answered yes to this question. What percent of the cat owners answered yes?

Try to find more than one way to solve this problem. For example, you might begin by asking yourself what fraction of the cat owners surveyed said their cats have bad breath. Be prepared to explain the different methods you use to solve the problem.

If 80 out of 400 cat owners surveyed said their cats have bad breath, what percent of the cat owners is this? Is this percent greater than, equal to, or less than the percent represented by 80 out of 200 cat owners. Explain.

2. The first two word problems in Primary Mathematics 6A, Percentage, the only chapter on percents in 6th grade Singapore Math:

There are 25 girls, 18 boys and 7 adults on a bus. What percentage of the people on the bus are adults?

Ben, Mingli and Samy shared $180. Ben received $45, Mingli received $63 and Samy received the rest. What percentage of the money did Samy receive?

3. Extra Credit

For each problem set, estimate the percentage of time spent on higher level thinking, as in logical and mathematical reasoning.

Wednesday, May 6, 2009

Grade Reversal

I'm collecting anecdotes!

Specifically about cases in which smart students are getting lower grades than their classmates. 

Perhaps they aren't explaining their answers to math problems.

Perhaps they don't do well with the arts & crafts/"creativity" components of English and social studies assignments.

Perhaps they don't cooperate well in group assignments.

Perhaps they participate insufficiently in class discussions.

Perhaps their classrooms are too cluttered and chaotic for them to concentrate.

Perhaps they are overwhelmed by big, interdisciplinary projects and multi-step directions.

Perhaps they are too uninspired to "go that extra mile" that top grades require.

And perhaps the actual academic requirements in math, science, writing, etc., are so low that they have no way to exhibit their strengths.

Whatever your child's story is, please share it here.

Tuesday, May 5, 2009

Rebellious artists and rebellious parents

I was never much of a rebellious child, and hadn't planned on becoming a rebellious parent. But then my left-brain children entered our right-brained schools.

Fresh out of last week's contentious meeting about my son's backpack, I finally pulled out the latest assignment out of my daughter's backpack.

The dreaded diorama. It's only 2nd grade, and the dreaded dioramas are already upon us.

My daughter loves arts & crafts. She spends hours per day on her own projects--paper dolls dressed up in paper clothes and laminated with clear packaging tape; a tiny family made out of meticulously molded, painted clay, complete with pet bunny.

But assign her a project and her enthusiasm vanishes, along with her artistic talent and her ability to execute complex directions.

So, after three hours of screaming and crumpled papers, and after our last shoe box was rendered unusable, I rebelled once again.

And this morning, my daughter walked into school empty handed, her depiction of her favorite scene of her favorite book rendered not in 3-D cardboard, but in words on two sides of a sheet of paper tucked neatly into her backpack, along with a note from yours truly.

Sunday, May 3, 2009

Autism Diaries IX: punishing children for organizational disability

If my son earns low grades in English, it should be because of his difficulties with English, not his difficulties with organization.

And yet, a pile of papers has come back full of low grades based on work J didn't hand in and quizzes he didn't study for. Once again, it turns out he's not turning in all the work he's completed, and not taking home all the quiz notifications and study materials that his teachers are giving out.

At the last meeting two months ago, I thought we'd resolved this. We agreed that I could re-organize J's backpack into a series of two-pocket, "in"/"out" folders, color-coded by subject. We agreed that one of the two people assigned to work specifically with him during the school day would ensure that assignments, notifications, and study materials make it into and out of that backpack.

Last week's meeting was a completely different story. It was as if they'd all gotten together ahead of time and decided they'd had enough. In any case they informed me, repeatedly and at high volume:
1. that J needs to take more responsibility and so those low grades are appropriate.
2. that they've done all they can at their end.
3. that they've already made a tremendous number of accommodations for J.
4. that every time J gets a grade I dislike, I ask them to change it, and I need to stop doing this.
5. that it's my job to call in when things don't come home.
6. that I should mark my calendar to call up the school every Monday if the vocabulary words don't come home.
7. that I need to take more responsibility.

No matter how often I returned, at equally high volume, to my points:
1. Organizational skills are part of his disability that should be accommodated in his IEP.
2. No kid should be dependent on his mother's memory in order not to get a 2 out of 8 on a vocabulary quiz.
3. How hard is it to make sure J puts things in his backpack and takes things out of his backpack?
...the English/home room teacher repeatedly interrupted me with with shouts and gestures of "Stop, Stop!" followed by a verbose repetition of her points.

Her lack of professionalism is understandable, in that this is the same teacher who:
1. gave J a D on a Personal Timeline assignment because she didn't think the events he chose were sufficiently "important."
2. (or so eyewitnesses tell me), walked into the classroom at her first Back to School night wearing flipflops and chewing gum, and then told the parents that their kids shouldn't come to school wearing flipflops and chewing gum.

But lack of professionalism can be expensive. For the first time in about 6 years, I will be calling on my disability lawyer.

Friday, May 1, 2009

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

1. From the "Patterns in Multiplication" unit, Unit 7 of the Math Trailblazers grade 4 Discovery Assignment Book, p. 80:

For the following problems, make a prediction of what you think the answer will be. Then, do the problem on your calculator to check.

A. 6 × 70 = ____
B. 8 × 400 = ____
C. 800 ×6 = ____
D. 7000 ×4 = ____
E. 800 × 8 = ____
F. 60 × 4 = ____

2. From "The Four Operations of Whole Numbers" unit, unit 2 of the 4th grade Singapore Math Primary Mathematics 4A, p. 60:

Estimate and then multiply.

218 × 37 =
⇓ ⇓
200 × 40 =

× 37

483 × 59 =
⇓ ⇓
___ × ___ =

× 59

372 × 64 =
⇓ ⇓
___ × ___ =

× 64

648 × 78 =
⇓ ⇓
___ × ___ =

× 78

3. Extra Credit Question:

Need I say more?