Killing Aunt Sally: Unteaching Bad Math

By Jon A.S.

"PEMDAS" is wrong. More importantly, it matters that it's wrong. Killing Aunt Sally peels back the covers on mathematics education in the United States. Author Jon A.S. offers criticisms of the common approaches that have been used for decades and longer, and presents a better way. From the very first numeric relationships we encountered to the last time we sat through a math class, we were likely subjected to an archaic approach that left us with the all too common, teacher-dreaded, yet completely justified question, "Why are we learning this?" But it's not too late to turn things around. Killing Aunt Sally delves into what needs fixing, how we can fix it, and why it is urgent that we do.

• Language: English
• Publisher: Jon A.S.
• Release date: Mar 10, 2020
• ISBN: 9780463215876

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KILLING AUNT SALLY. Copyright 2020, by Jon A.S.

All rights reserved. Printed in the United States of America. No part of this book may be used or reproduced in any manner, stored in any retrieval system, or transmitted or shared without written permission, save the case of brief quotations embodied in critical articles and reviews. For information, address Jon A.S. at [e-mail].

No public information is available for this publication.

A Timely Educational Proposal

Killing Aunt Sally

Unteaching Bad Math

Jon A.S.

And you do Addition? the White Queen asked. What's one and one and one and one and one and one and one and one and one and one?

I don't know, said Alice. I lost count.

She can't do Addition, the Red Queen interrupted.

-Through the Looking Glass (Lewis Carroll)

Table of Contents

Introduction

Chapter 1: I'm Bad at Math

Chapter 2: Quantities and Relationships

Chapter 3 Aunt Sally

Chapter 4: The Root Symbol

Chapter 5: The Answer Doesn't Matter

Chapter 6: Equations

Chapter 7: FOIL

Chapter 8: Some poorly named terms, and terms that should have names, but do not

Chapter 9: Functional Math

Honorable Mention

Conclusion

About the Author

Introduction

It's pronounced pimped ass. That's me, correcting a student who responded to a question I posed to the class: How do we know which operation to do first? And of course, the student eagerly volunteered Pim Dahs, a.k.a. PEMDAS. Please Excuse My Dear Aunt Sally. I explained that we pronounce it pimped ass, because that's how a student of mine said it a few years ago, not even jokingly, and it's just too good to go back to the old pronunciation. It doesn't really matter though, I tell them, because we're getting rid of it, it's garbage.

Let me start by saying that in this book, I am not going to cite other works or studies, reference other books, or use a lot of data. Sounds hypocritical for someone writing a book about math. Well, excuse me, it's not hypocrisy, it's laziness. I don't want to have to add a reference page or give people credit for things. But I am going to do the most mathematical thing I can: use logic to support, maybe even prove, the ideas I put forth.

In reality, math is born of laziness. Math only exists as a way to say complicated things in a concise manner. Would you rather explain the location here where this line meets this line and the location where this line meets this other line are further apart than the location where this line meets this line and the location where this line meets this other line or AB > CD? That second one takes so much less work. Ok, I should clarify. The LANGUAGE of math is the lazy part. The practical part, really. The fewer the symbols, the more math we can do. Math itself is not created, only discovered. Then taught. And we've been teaching it wrong.

The title, as you are likely familiar, references the oft used mnemonic, Please Excuse My Dear Aunt Sally. This is how the mathematical order of operations is generally taught. It is one of several fundamental notions in math that we teach wrong. And we start so early. We give students bad tools and bad reasons and bad motivations. Are we really confused as to what is causing the almost universal fear/hatred/hyperventilation among grade-schoolers when they hear their least favorite 4-letter word, math? My aim is to identify the early points at which we derail and offer suggestions to better stay on course. Ultimately, we owe our kids better.

Chapter 1: I'm bad at math

It was day one, a few years ago. Even after over a decade of teaching, I'm never ready for day one. I'm taken back to my own high school days, when I played on the basketball team. Before the games I'd don my knee-high white socks with stripes matching our jersey color. I'd slide my wrist band onto my left arm, exactly 1.5 inches from my elbow. I'd drink a Surge soda spiked with 5 Pixie Sticks. I always pictured the game in my head, the moves I would make, the crowd's reactions, the score, the possible game winning shot. No matter how much I had prepared, when I stepped onto the court for the opening tip, hundreds of people in the stands, I was always nervous, never felt ready for that moment. But once the ball was put in motion, I was all business and the nerves were gone. Now, talking to the students on the first day of class is my jump ball. It's not so much that I'm nervous before they arrive as much as I have no feel for my job, like I've never done it before. I feel completely unprepared for their arrival. Once they enter my room, however, and I start getting to know them, and let them get to know me, we're good. I'm all business.

On this particular day one, the very first interaction I had with one student was him telling me I suck at math. I merely asked are you sure? He proceeded to tell me about his past grades in math, and all the reasons for his failures. He then proceeded to become the most successful student in my class. He even used his mathematical skill to help others on a daily basis. Why did he genuinely believe he was bad at math? He clearly wasn't. Or was he actually right? He really was bad at math before, but he just hit a brain spurt that year, like we hit a growth spurt. Probably not that. Brain spurts aren't a thing. He probably just wasn't actually bad at math.

When any of us believe we're bad at math, there is probably some truth to it, in a purely relative sense. I'm bad at gymnastics, if I'm comparing myself to Nadia Comaneci or Simone Biles. And it is very likely that I had no chance from birth at being as good as they are. If I work really hard at stretching, I can get my legs to do a 90 degree angle. That's as far apart as they're going. If you need to plot a rectangular concrete foundation for a house and forgot your square, I'm on it. Spread my legs and let's go. Please don't use that last quote out of context.

Just like my un-stretchy legs, and the rest of the human body, the brain is a physical organ. There is inherent variance in people's brains, which means inherent differences in their academic abilities. But if I'm trying to learn gymnastics, focusing on my relative limitations doesn't really lead to success. I could be damn good at gymnastics if I put in time and effort. I'm certainly not inherently BAD at gymnastics. In the same way, I don't think anyone is inherently bad at math, even if some are more naturally inclined to be really good at math. Also,