The Algebra Revolution: How Spreadsheets Eliminate Algebra 1 to Transform Education

By Art Bardige

A little over a year ago I made a discovery that changed my life. I found that eliminating Algebra 1 was a magic wand that not only enabled us to bring new problem solving mathematics into our schools, but would revolutionize both our curriculum and pedagogy. I cannot begin to tell you how excited I am about this discovery.
Eliminating Algebra 1, the algebra of equations, removes the greatest roadblock to achievement, a seminal, obsolete and now irrelevant course. It is made possible, indeed required, by bringing spreadsheets and their algebra of functions into our schools. It opens the door to questioning the entire math curriculum, to rethinking the disciplines generally, and to reimagining the pedagogy we take as canonical, which fundamentally changes how, what, and why students learn.
The result greatly surprised me. I believe you too will find it startling. Yet, this revolution based on a new educational paradigm will assuredly happen. I hope you will download this ebook, spread the word, and use the magic wand I hand you to help transform education.

• Language: English
• Publisher: BookBaby
• Release date: Nov 8, 2022
• ISBN: 9781667868752

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Copyright © 2022 by Art Bardige

Cover by Ryan McQuade

Images not referenced were created by the author or found in Wikipedia

All rights reserved. This book or any portion thereof may not be reproduced or used in any manner whatsoever without the express written permission of the publisher except for the use of brief quotations in a book review.

ISBN: 978-1-66786-875-2

Contents

Preface

Past

The Call

A Magic Wand

Spreadsheets

Function Machines

A Revolutionary

Tradition Tradition

Leonardo’s Algebra—The 1st Algebra Paradigm

Equations

Functions—The 2nd Algebra Paradigm

I am amazed

FAQ’s

Present

Spreadsheets transformed business

Spreadsheet Math—A 3rd Algebra Paradigm

Parameters

Amazing How Small It Is

Algorithms are not Concepts

The Ladder

Do We Need Algebra 1 and 2?

Do We Need Geometry?

Do We Need Precalculus and Calculus?

9 Reasons for Spreadsheets:

FAQ’s

Future

Eliminate Algebra 1

The Proper Question

Math as Problem-Solving

What is the Purpose of School?

Not by Direct Instruction

Tools of the Web

Share

What if Math Labs

Discovery

Explorations: Curriculum of the Future

Equity Diversity Inclusivity

Revolution

Is this a Solution for you?

FAQ’s

Acknowledgements

For Betty

who always imagined

a better future

Some of us, who have enjoyed the excitement of being alive for the digital revolution, are beginning to realize that truly seismic changes are still ahead. Education is a critical aspect of society where the digital transformation is still largely in the future. Art combines a lively memoir of how personal computing has begun to impact schools along with a bold vision for the true revolution to come. An unexpected solution to a universally perceived problem.

Chuck Olson

Edtech development executive since the ‘80’s

Member of the Bank Street Writer development team

I have never made a significant proposal but what there was a crowd who said, ‘Ain’t so, can’t possibly be,’ If you do something new or innovative, expect trouble. But think critically about it because if you’re wrong, you want to be the first one to know that.

Professor Eugene Parker

My high school mentor, discoverer of the solar wind,

leading astrophysicist.

I think, however, that there isn’t a solution to this problem of education other than to realize that the best teaching can be done only when there is a direct individual relationship between a student and a good teacher... It’s impossible to learn very much by simply sitting in a lecture, or even by simply doing problems that are assigned.

Professor Richard P. Feynman

The Feynman Lectures on Physics June 1963, who I sought to emulate.

Paradigms… I take to be universally recognized scientific achievements that for a time provide model problems and solutions to a community of practitioners.

70 years ago, Thomas Kuhn transformed the vision of scientific progress in his masterwork, The Structure of Scientific Revolutions, with a single word: paradigm. He taught us that the sciences periodically undergo revolutionary change driven by a radical new way of thinking. Such a paradigm shift is occurring today in education, enabled by technology.

Thomas Kuhn,

The Structure of Scientific Revolutions, 1962

This Abstract, which I now publish, must necessarily be imperfect. I cannot here give references and authorities for my statements. I can give only general conclusions at which I have arrived, with a few facts in illustration.

Charles Darwin,

On the Origin of Species, 1859

P

reface

It seems such a straightforward idea. Education should be about preparing our children for their future, for what they will do next. Yet, so much of formal education prepares children for our past. They study for tests in which they are told to take out a piece of paper and a pencil, turn off their phones and computers, not cheat by talking to other students, and take an hour or so to write the answers to questions that demand they know facts or show skills required in the past.

They do not show their proficiency for working with others, use the Web to find what they need to know, engage their creativity to solve problems, or use skills to analyze complex real-world data. Their curriculums, like their tests, are separated into subject silos (math, history, science, English) no longer segregated in the world they will inherit, live, and work. The content and skills they are required to master they know to be no longer relevant, because they constantly ask, Why do I have to learn this?

Our students are, in the main, still taught as if they are empty vessels to be filled with information passed from teacher to students, in classes of modest size, separated by individual desks aligned in rows and columns facing forward to maintain eye contact with the teacher and not each other, a fashion from the Middle Ages. In these classrooms, the main speaker is the teacher and listeners are the students who raise hands in salute to be recognized to speak, expected to show common decorum, pay proper respect, and exhibit constant attention.

The school day and year remain agricultural era vestiges with little respect for sleep, physical exercise, or the stress of daily bus rides. Those considered to be learning too slowly or not challenged enough are given even longer, more intensive, and more rigorous days. From the earliest grades they are divided into robins, bluebirds, swallows, and cardinals, grouped to learn at the longitudinal rate commensurate with their intelligence, energy, and concentration.

This division solidifies in middle schools when the groups are placed into homogeneous classes with curriculum and instruction either less rigorous or more demanding. These inequities perpetuate through high school where the college bound are distinguished from the non-college bound, and college were we again segregate our children into those who, get a two-year degree, a four-year degree, and do graduate work to become professionals. We prepare students to be 19th century workers, unskilled, skilled, managerial, professional. So rarely do they cross those borders that we celebrate success by labeling them, The first in their family to go to college.

We are so embedded in this education of the past that like fish in water we do not even see other possibilities. We cannot imagine an educational system that makes it possible for the vast majority of our population to attain the learning level we associate with a college degree. We cannot imagine a system that enables us to educate the vast majority of our children from their early months through college at costs that do not bankrupt our nation or our children. We cannot imagine classrooms and schools that focus from the very beginning on communication, collaboration, creativity, and problem-solving even though these skills are considered the highest priority for the 21st century workforce. We cannot imagine enabling every child to reach their dreams and to thrive in this new century even though we claim this to be our goal. We cannot imagine an equitable education system because we remain wedded to a paradigm and a learning technology nearly a thousand-years-old, a technology based on paper and on the skills required for working on paper.

Paper was an amazing invention. It came to Europe from China in the late 11th century as a decorative material, a precious trading commodity. When Europeans applied their waterpower technology to its manufacture, paper became the standard medium for conveying information. Gutenberg printed 3/4 of his Bibles on paper.¹ From that time on paper was the tool of choice for books and necessity for tracking trades. Reading, writing, and calculating on paper became the skills young children learned in schools to prepare for work. Paper remains our prime tool for learning, the skills demanded