## Gobble-de-gook Disguised as Math

From the good folks at The Daily Riff comes this amusing anecdote that isn’t all that funny when you realize the author is a physics professor and he was left confused by what was being taught in his daughter’s 3rd grade math class. Probably because what was being taught in math wasn’t math. Maybe he would have understood if the teacher had drawn a few squirrels…….

Why I Would Fail Third Grade Math

By Joseph Ganem, Ph.D.
Published at The Daily RIFF on August 18, 2011

During American Education Week one year, I visited my daughter’s third grade math class. Five minutes into the class I realized that if I were a student, I would have a tough time passing. The teacher went over problems on a test she had just given. She read a problem out loud.

“If Johnny has \$88 and spends \$32 on clothes, write a number sentence that shows how much money Johnny has left.” She then wrote on the board the following: \$88 – \$32 = \$56

Then she turned to the class and asked, “Is that a number sentence?”

Not to interrupt, but when did we stop teaching the language of Mathematics? Mathematics has a language that is unique and uniform to it. It’s one of those things people who enjoy Math like about it. Addition is addition. Subtraction is subtraction. And an equation is an equation. Number sentence is not a Mathematical concept and we do our children a disservice when we refuse to call things what they are.

At this point I realized that I would be in trouble in this class. I had no idea how to answer her question. In my line of work, this kind of expression is called an “equation.” The class came through. In unison they yelled, “Yes.” The teacher wrote a second equation on the board:

\$88
– \$32
——-
\$56

“Is this a number sentence?”

Again I had no idea, but the class in unison yelled, “No.”

“All of you know what a number sentence is. The directions on the test were to write a number sentence. But I just looked at the papers, and 10 out of 28 of you wrote this.”

She pointed to the second, the column method of subtraction on the board. “That is not a number sentence so I had to mark all of those papers wrong.”

A child raised his hand. “But I got the right answer.”

“I know you got the right answer, but you didn’t follow directions. The directions were to write a number sentence.”

A second child raised her hand. “But I got the right answer.”

“I know you can do the problem. But when we take the state exam in the spring, they won’t know that you can do the problem. The graders will want to see a number sentence. It’s important that you follow directions because we want to show them what smart students we have at our school.”

A third child raised her hand. “But I got the right answer.”

“But, I just explained. You didn’t write a number sentence. If I mark that correct now, you will do that again in the spring. The people grading the state exam want to see a number sentence. They won’t know that you know how to do the problem.”

None of the children looked convinced. More hands went up. Exasperated, she cut off further discussion with an old parental standby. “It’s for your own good.”

Not to interrupt again, but since when is \$88 – \$32 = \$56 correct but
\$88
– \$32
——-
\$56 incorrect when the only difference is how the equation is presented?

We had this debate a while back when the math textbook adoption criteria were being discussed in our school board meeting. One of the criteria was “Develops mathematically powerful ways of thinking”. I’d asked what makes one way of thinking more mathematically powerful than another? The answer was that 6 + 8 = 6 + 4 + 4 = 14 is more mathematically powerful than 6 + 8 = 14. I have no clue why and think that answer is malarkey.

###

Joseph Ganem, Ph.D., who can be found at JosephGanem is a professor of physics at Loyola University Maryland, and author of the award-winning book on personal finance:

The Two Headed Quarter: How to See Through Deceptive Numbers and Save Money on Everything You Buy. It shows how numbers fool consumers when they make
financial decisions.