Mastering the quadratic formula has long been the culmination of the high school algebra courses, the capstone of “Algebra I and Algebra 2”. We endeavor to prepare our students for it by teaching them arithmetic to do its operations, and algebra to solve linear equations, graph linear functions, factor special quadratic equations, and cap off their introduction to algebra with this magical formula. The intent is to show our students the power of algebra to use a sequence of symbols to find the values for x that make any second order polynomial equation true.
The Quadratic Formula is a big deal. If a student can use the Quadratic Formula to solve an equation, we deem them worthy to graduate high school and ready to learn college algebra, the algebra of functions. It involves not just the use of symbols to represent known and unknown quantities but makes use of imaginary numbers along with real numbers they learned on the numberline. It is no wonder movies and TV shows that put math symbols in blackboard background shots almost always include this iconic equation. Thus, it has long seemed obvious that this pinnacle idea should be a fundamental mathematical concept that every student should prepare for, learn, and master.
But… let me ask you a question. “When will any of our students ever use the Quadratic Formula?” Unless perhaps, they are in the 1% who finish college with a Bachelor’s Degree in mathematics or who minored in math, and now teach middle or high school, the answer has to be never! Unless, perchance, they have to solve a quadratic equation to get off of a desert island. (When they can always google it.) And if they can’t get on the Internet then, wouldn’t you suggest they treat the equation as they would any function, graph it and approximate x-intercepts? In all likelihood they would by then have forgotten the formula anyway.
If it is not necessary for our students to learn the Quadratic Formula because they will never need it, then what about the math that leads up to it? — the carefully-crafted sequence developed over centuries to prepare students to learn it? Do they have to learn to factor quadratic equations or even solve linear equations? Graph those too! We need hardly stretch our imaginations past the present to know that spreadsheets and other web tools make it unnecessary for our kids to master these processes. Understand functions, of course! But to know and be facile with the algorithms for solving equations, never!
The Quadratic Formula is a paper algorithm, designed and used to solve quadratic equations on paper. It is no longer of value in this digital age. Like other, similar paper processes we insist in teaching our students, it is obsolete. Why do students have to learn a paper-based “long division” algorithm, a process for adding fractions with unlike denominators, or even subtraction of whole numbers by regrouping? They will never need to use these paper algorithms in their work life. And even if they did, they would use them so infrequently that they would not remember them. Those myriads of homework problems that they practice to mastery, like 3 digit multiplication on paper, worthless!
So is it now time for us to jettison the obsolete and to ask, “What math should our students learn to prepare them for the digital world they will inherit?” The answer is straightforward. Students should learn to use the computational tool used in business and industry, the spreadsheet, to solve not only the traditional math problems they are taught to solve today in our schools, but the kinds of interdisciplinary, data modeling problems they will need to learn to solve to do their jobs. That means they will not need to learn to calculate on paper, they will need to compute on screens. They will need to learn to creatively solve real world problems, to analyze data, to build models, to work collaboratively, and to reason quantitatively as part of a cross disciplinary team. To know what they should learn in our schools we need only look to the real world around us and the problems people now face in the 21st century workplace.
Imagine giving students the opportunity to creatively find a new way to solve any quadratic equation, not memorizing an obsolete paper formula but using a fundamental powerful general coding tool, recursion, to build a simple spreadsheet. Imagine embedding this in a problem solving context that relates it to real world activities like throwing a ball. Imagine making sharing central to this student experience so that they can share their learning. Imagine employing these tools and this logic to deep and substantial projects and inquiry across the disciplines, and applying them to the urgent issues facing our planet. This is the future of learning. Therefore, this should be our mission — to prepare our students for their future and not our past.