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Monday, May 12, 2014

Summer math class: Solving division problems: long division vs. partial quotients method

By Laurie H. Rogers

[The Betrayed blog is offering spring and summer math exercises, using algebra, "real-world application," satire and humor to illustrate various realities in K-12 public education. The full series is posted here. If you would like to participate by offering a math exercise or by correcting or enhancing an exercise presented here, please write to me at]

Problem #2. A reform method for division provided to public-school students in America is the partial quotients method. A reform method for instruction is "constructivism," where students work in groups to: develop their own strategies; teach each other and themselves; and achieve consensus. A reform method for solving actual math problems is to hand students a calculator.

On a math test, students have 10 division problems to solve. Each dividend contains six digits. Each divisor contains two digits. There is at least one decimal place in each dividend and divisor.
Students are not allowed to use a calculator for this test.

It takes twice as long to use the partial quotients method to solve these problems as it would take to use the traditional "long division" method. It takes 20 minutes to solve these 10 problems using long division. How long will it take students to do these 10 problems using the partial quotients method and constructivism?


Below is a calculation for Problem #2.

Below that is a parody of today's typical math class, related to Problem #2.

Calculation for Problem #2.

x 2

Answer: The students take 40 minutes to solve the 10 division problems using the partial quotients method and constructivism.

This number, of course, is a flight of fancy. The students do NOT take 40 minutes to solve these problems using the partial quotients method and constructivism. Nor do they take 20. They will not be able to successfully use the "partial quotients method" to solve these 10 division problems containing decimal places.


Parody of today's typical math class, related to Problem #2:
** The students are faced with 10 division problems containing decimals. Sadistic people have made them dependent on their calculator for the smallest thing and then refused them the use of a calculator for this math test. 

The students work in groups to try to achieve consensus on answers, using a method that doesn’t deal well with division, much less decimals, and working with classmates who are just as confused, bored and unknowledgeable as they are. They all get different answers (except for those who begin texting and checking their Facebook account and who just write down whatever their classmates tell them to).

Eventually, the bell rings, class is over, soccer practice begins and ends, and the students go home. They describe their math test to their parents, who say, “I don’t understand that method. Let me show you how to do it properly,” whereupon the students say, “My teacher won’t let me do it your way. I have to do it this way,” whereupon the parents say, “Then I can’t help you,” whereupon the students say, “Yeah, the teacher told us you would say that.”

The next morning, students find out that their math teacher is away getting professional development in how to “guide” students in math, and there is a substitute who is actually a social studies teacher. She has no idea of what the class is doing, but she does want to talk about “Decreasing Inequity in Our Society,” which is the title of her research project for her master’s degree in education. The students get nowhere with the math test, but they are a little more depressed about our inability to decrease inequity in our society.

When their teacher eventually comes back from professional development, students ask her how the problems would be done using the partial quotients method. She says, “Work with your partners,” because that’s what she learned last week to say. Students tell her, “They don’t know, either.” She says, “Well sit down with them and see if you can figure it out.” Students say, “Please just tell us.” The teacher, who doesn’t actually know how to solve these problems using the partial quotients method, says, “You have to ask three students before you ask me,” because that’s what she learned last week to say. The students say, “I hate math.”

The teacher says: “Yes, math is hard. I know you’re frustrated, but this is a best practices method, and once you put enough effort into it, you’ll see how fantastic it is. It’s so fantastic, I barely understand it myself, but I know it’s better, and I know that math is just hard and everyone hates it."

The teacher continues: “Maybe math isn’t your best subject. If you would spend less time in soccer and piano, you would do better in math class. You have to be more motivated. You have to learn to get along with your classmates so they can help you learn."

The students tell her: "We asked our parents to explain it to us, and they can't figure out this method."

The teacher responds with what she learned last week: “Your parents can’t help you because this method isn’t how they learned it. They are stuck in an old way of thinking, but what you need are 21st-century skills and critical thinking skills, and this method will give all of that to you."

She continues: "I wish we could have professional development for your parents. If we had enough money, we could reform everything and everyone, but we are so desperate for money, we might have to cut back on heat and light in our classrooms. Besides, math is a societal problem. There’s just too much inequity, and we all know societal problems can’t actually be fixed. It’s all so very, very sad and frustrating."

The students begin to cry, and the teacher feels badly for them because that's what she learned last week to feel. She says gently, "Don't worry about this. Just do your best. I grade on a curve. You’ll be fine. When you get home tonight, please give your parents this flyer and ask them to remember to vote on the levy so we can fix all of our problems in math.”   ***

Each day, the students repeat the process from ** to *** until they drop out and/or become mentally unstable.

Please note: This information is copyrighted. The proper citation is:
Rogers, L. (May 2014). "Summer math class: Solving division problems: long division vs. partial quotients method." Retrieved (date) from the Betrayed Web site:


Bruce Price said...

I conclude that the people in charge of promoting Reform Math are such earnest, serious, indeed humorless ideologues they don't realize that their behavior has become sociopathic.

They are making little children sick (and innumerate) because they themselves are sick. I feel this needs to be pointed out, discussed, analyzed, complained about, ridiculed, and placed in the public stockade.

Anonymous said...

I absolutely agree with Bruce and the sociopathic character of math, that make children sick and ridiculed. It is hard to believe that those that are responsible for planting this curriculum don't see it. To the math problem from this article about how long does it take to solve division problems; I have to add, the solution provided by the author would be worth only 2/4 points as it is lacking a long verbal "show your thinking" explanation to the solution.