mental math question

Kumon asks kids to do multi-digit multiplication problems without writing down any of the 'carried' digits:

Students master the multiplication tables by practicing until they can answer immediately. Next, students learn up to 4-digit by 1-digit multiplication with mental carryovers.

What do you think?

Interesting post on the subject of mental maths here.

All Children Are Capable of Greatness

From the Kumon website:

At the heart of the Kumon Method is the belief that all children are capable of greatness. With the help of their parents, family and friends, children can develop in ways that will humble and amaze you.

Kumon’s founder, Toru Kumon, believed every child has the potential to learn far beyond his or her parents’ expectation. “It’s our job as educators,” Kumon said, “Not to stuff knowledge into children as if they were merely empty boxes, but to encourage each child to want to learn, to enjoy learning and be capable of studying whatever he or she may need to or wish to in the future.” Children who learn through the Kumon Method not only acquire more knowledge, but also the ability to learn on their own.

Last week Catherine and I visited the Kumon headquarters.

I bring back some Kumon lore:

• Kumon started in 1954, when 2nd grader Takeshi Kumon came home from school with a crumpled up math test stuffed in his backpack. I find it hilarious, by the way, that the "crumpled math test" is this universal experience that transcends continents and generations.

• Mrs. Kumon told her husband Toru, a high school math teacher, that he needed to help their son with math, and voilá, the Kumon worksheet was born.

• Today, there are 4.2 million children studying Kumon in 46 countries.

Turns out, there's also an adult Kumon workbook, Train Your Brain: 60 Days to a Better Brain, and it has sold millions of copies. From the introduction:

Through my research, I found that simple calculations could activate the brain more effectively than any other activity. I also discovered that the best way to activate the largest regions of the brain was to solve these calculations quickly.

Cross-posted on Perfect Score Project

in Borders today

We picked Andrew up at camp today and learned that he had a fantastic week --- he was the best camper in the place, his counselor said.

Then he added, gesturing to his chums sitting under the canopy, "They would all say the same."

Wow!

He did pretty well in the car until we stopped at Office Max to pick up poster board for the Big Calendar that's going to change everyone's life around here.

Big tantrum at Office Max & then in the car 'cause he'd spotted a Borders and wanted to go there. But since he'd managed to pull himself out of it by the time I'd made my purchases, we decided to go to Borders after all.

And guess what I found in the school section?

A Frank Schaffer Singapore Math 6B Math Practice workbook.

Plus a lot of terrific Kumon workbooks (those are the two next to Singapore Math Practice.)

The cover of the Singapore math book says, "Activities based on the leading math program in the world--Singapore Math!"



introduction to Singapore Math - Level 3 (pdf file)
Andrew comes home from camp - July 2008

instructional practice

I was looking for an old ktm post about Kumon this morning, and when I found it I rediscovered the concept of instructional practice, meaning practice that teaches.

I think that's probably what the Arlington Algebra Project's sections on probability provides.

Barbara Oakley at ktm-1

Here she is!

ideologically-motivated intellectual gatekeepers

easy is better

from Steve:

My son has a teacher who is known for making her 7th grade social studies class hard. The idea is to toughen the kids up for high school. The assumption is that real learning is a difficult process. I feel like telling her that any teacher can make a class hard. It's more difficult, however, to make the class easy. There seems to be the idea that if you make learning easy, kids will never learn to do it on their own. You have to take an indirect, or discovery approach to really remember the material.

What if you came up with a direct, easy approach that could teach kids about fractions, percents, and decimals. Would you not use it? [answer: no] Thematic, real world, group discovery learning is supposed to be fun, interesting, and effective in both what you learn and how your learn. Too bad it doesn't work and wastes a lot of time. That's OK, because they want to emphasize the process and not the results. Perhaps that's why they don't like tests. Answers are not as important as the process.

I have no patience with educators who pride themselves on being "hard."

Hard work: yes, if (and only if) the kids are learning a lot. Hard to understand, hard to learn: no.

Ditto for the idea that a school's job is done once students have been "challenged." As I once told the now-retired science chair here: If I wrote challenging books, instead of books on challenging subjects that people can read and understand, we wouldn’t be living in Irvington. As a general rule, people don't like hard stuff. They like easy stuff, and rightly so:

Hyunjin Song and Norbert Schwarz wanted to see if they could motivate a group of 20-year-old college students to exercise regularly—not an easy task. They gave all the students written instructions for a regular exercise routine, but they used a simple but ingenious method to make the how-to instructions either cognitively palatable or challenging: Some got instructions printed in Arial typeface, a plain font designed for easy reading. Others got their instructions printed in a Brush font, which basically looks like it’s been written by hand with a Japanese paintbrush; it’s unfamiliar and much harder to read.

There are a lot of ways to make something mentally palatable, or not. You can used clear and simple language, or arcane vocabulary words; simple sentences or convoluted sentences with lots of clauses. The psychologists chose typeface because it’s easy to manipulate in the lab. After the students had all read the instructions, they asked them some questions about the exercise regimen: how long they thought it would take, whether it would flow naturally or drag on endlessly, whether it would be boring, and so forth. They also queried them on whether they were likely to make exercise a routine part of their day.

The findings were remarkable. Those who had read the exercise instructions in an unadorned, accessible typeface were much more open to the prospect of exercising: They believed that the regimen would take less time and that it would feel more “fluid” and easy. Most important, they were more willing to make exercise part of their day. Apparently, the students’ brains mistook the ease of reading about exercise for ease of actually doing the pushups and crunches, and this misunderstanding motivated them to actually think about a life change. Those who struggled through the Japanese brushstrokes had no intention of heading to the gym; the reading alone tired them out.

A Recipe for Motivation
by Wray Herbert

If schools were accountable for results, you'd hear a lot less twiddle-twaddle about "challenge" and "hard." Just ask KUMON. Or Fluenz. Or Pimsleur. Or hell, just about anyone trying to sell you an educational product of any kind. Do book publicists write ad copy telling folks, "Buy this book. It's hard"?

No. They don't.

Even Jay Mathews has modified his approach to the "Challenge Index." In the past, all schools made it onto the list if they had a high number of students taking AP courses & the AP test. How students actually did on the test wasn't part of the index; hence the term "Challenge." The Challenge Index measures challenge, not achievement.

[pause]

Remind me again.

Exactly what are we paying these people to do?


make them struggle
education professors: students must struggle
KUMON: "work that can be easily completed"
handing it to the student

Happy 50th Birthday Kumon!

Kumon Math & Reading Centers, the world's largest after-school education program, turns 50 this year .

[…]

"The Education industry is burgeoning," says Deven Klein, vice president of Kumon franchising. "Tutoring is a widespread option for an increasing number of families in the United States."

Gee, lucky for us that we have this option.

Over the past five years, the average Kumon Center enrollment in the United States increased by 55 percent, and overall, the company has 80,000 more U.S. students than in 2002.

Kumon opened 84 new US centers last year, and expects to open 120 in 2008. Business is booming.

Chocolate Pecan Pie & Fractions

I have been baking chocolate pecan pie almost every Christmas for over 20 years. Tonight my 5th grade daughter helped me with this recipe:

CHOCOLATE PECAN PIE
1 pie shell, unbaked
Filling:
1/4 cup (1/2 stick) unsalted butter
2 ounces unsweetened chocolate
3 large eggs
1 cup sugar
3/4 cup dark corn syrup or sugar cane syrup
1/2 teaspoon pure vanilla extract
3 tablespoons bourbon or rum (optional)
1/4 teaspoon salt
1 1/2 cups pecan halves
Preheat the oven to 350 degrees F.
To make the filling: melt the butter and chocolate in a small saucepan over medium-low heat, remove from heat and let cool. Beat the eggs in a large mixing bowl until frothy and then blend in the sugar. Stir in the syrup, vanilla, bourbon, salt, and the melted butter mixture until well blended.
Arrange the pecans on the bottom of the pie crust and carefully pour the egg mixture over them. Bake until the filling is set and slightly puffed, about 45-50 minutes. Test for doneness by sticking a thin knife in the center of the pie, if it comes out pretty clean, you're good to go. Transfer the pie to rack and cool completely before cutting.

We made two pies because we’re having 15 guests for dinner on Christmas Day. My daughter instantly converted all the fractions to the quantities needed for two pies. She was faster than I was. It may not seem like such a great achievement to some, but to me it was wonderful.

Thank you, Kumon!

Mr. KUMON

comment left by Tex:

Copying sentences can be especially helpful for improving writing skills if done as Ben Franklin did -- from memory.

My 5th grade daughter is in her second month of Kumon reading, and this week’s worksheets include copying sentences from memory. First, she is instructed to read a short paragraph from a story. Then, she is given a few related sentences to write from memory. The instructions are: “Read the sentence until you can remember it. Then write the sentence.”

I had no clue about the value of this exercise, and I don’t recall that she ever had this in school. Now, I’m starting to understand how this can be beneficial. I’ll ask “Mr. Kumon”, (that’s what my daughter calls him) next time about this.

I don't know why I bother.

Obviously KUMON has already figured the whole thing out. Talk about reinventing the wheel.

I thought "text reconstruction" sounded like a good idea the first time I read about it in The First American by H. W. Brands. But until I saw C's results, I had no idea how useful this technique might be.

It certainly didn't cross my mind that text reconstruction would give me so much insight into what C. needs to work on. It's not just an instructional technique; it seems to work as a diagnostic tool, too.

This fall Ed and I are going to ask to see C's state ELA exam. I mentioned the vagaries of the ELA assessment in a Comment on another thread. C.'s score was 10 points below the cut-off for a 4, but he has a 95% "percent correct" average on the test. Apparently you need 97% or 98% correct to get a 4.

This sounds like a distinction without a difference.

Still, because of the number of multiple choice items, I assume C. had to have lost points exclusively on written responses, which makes sense. His writing isn't remotely as good as his reading. So we need to see his test.

I also assume the state isn't going to be able to tell us why he lost the points he did. The school probably won't be able to tell us, either, because they seem to be pretty much tearing their hair out over the whole thing, and rightly so as far as I'm concerned. The year before last -- the first in which the test was administered -- kids they thought had passed turned out to have failed instead, and scores on the front of a student's test report sometimes didn't match up with scores on the back of the report. Twice I was told the department had "calls into" the state and were waiting to hear back.

Maybe I'll put a call into the state.

I've got the number.

Point is: the whole thing is shrouded in mystery, as my friend M. would say, only in this case the mystery is coming from the state, not the school.

I think the text reconstructions will help. We'll have a more "granular" sense of C's writing when we see the scored test; we'll be able to look at his written responses and either spot what the state rubric found problematic or spot what we find problematic.

We'll see.

In any case, it's clear to me that cohesion devices are going to be a focus around here for the foreseeable future.


The Paragraph Book

Susan S has been using The Paragraph Book with her son this summer. I ordered it, too, on the strength of her recommendation, and while I haven't had time to dig into it, it looks terrific.

I especially like this piece of advice the author gives students about the structure of a paragraph:

FIRST
NEXT
THEN
FINALLY

acronym: FNTF

I'm going to teach this acronym to C. I'm not sure it will help with cohesion devices per se, but I do think it gives one a mental guide to paragraph structure.

Besides, the difference between "NEXT" and "THEN" is cool.


update from le radical galoisien re: cohesion devices--

Well I am sure the material must be very competent, it seems slightly ironic when a summary about text comprehension requires several re-readings to be comprehensible.

I wish I'd said that.

KUMON & the components of long division

anonymous left this comment:

I'm running out of patience with Kumon. They keep making my daughter repeat the same workbooks. She already knows the stuff, she's not moving forward and it's not helping her. There's an opportunity cost to making her do all these Kumon books when she should be forging through Saxon Math.

On the other hand, if I let her drop Kumon, will she ever master long division?

I have a friend who's had the same experience. Her daughter is stuck in a Level and can't get out!

I'm guessing that the Morningside people wouldn't allow a child to be stuck on anything. I think they'd drop the child back to the component skills and practice those skills to mastery. Then you'd hope to see contingency adduction - you'd hope to see the child take a soaring leap up to the complex, composite skill.

So: what are the component skills of division?

estimation?

multiplication?

or....subtraction, estimation, multiplication....?

should learning be a "struggle"?

from Tex:

I love Kumon! The anti-struggle way to learn.

The Kumon method, Step 1:

Students begin at a comfortable starting point—determined by our placement test—with work that can be easily completed. This way your child will master the basics and gain complete proficiency with each successive step. Kumon students develop better concentration and study habits because they don't get frustrated by our learning process.

Also, from Step 5:

Your child’s individualized program is never compromised by the needs of a group or a prescribed teaching agenda.

make them struggle
education professors: students must struggle
KUMON: "work that can be easily completed"
handing it to the student