I think it’s fair to say that most people aren’t too fond of algebra, to put it mildly. Why do so many students, and adults for that matter, react to algebra the way Superman might react to Kryptonite? Perhaps part of the reason why so many people think that algebra is boring, or confusing, or just plain incomprehensible, stems from the way they were taught (or, as the case may be, “taught”). Often, algebra is presented as “Rules That Must Be Followed Unthinkingly and Without Question”; what’s commonly missing from this approach is the why behind the rules. Without that “why”, it can be difficult to understand and apply those rules, let alone remember all of them. Imparting that “why” effectively is an art form, and a topic that is deep and important, deep enough that we wouldn’t dare try to address it in a quick blog post. Here, we are interested in a different kind of “why”: why should we teach algebra at all?
Students are typically told that algebra will at some point be useful to them in their daily lives as adults, and that SO many people use algebra on the job, weekly if not daily! If you google “jobs that use algebra”, you will see websites galore listing all the many professions that use algebra. You will be told that nurses, plumbers, managers, and chefs all apply algebra in the workplace. Many people will tell you that algebra is used in almost every job there is! However, this is very, very far from the truth. Most people will never use algebra on the job, or in their daily lives off the job. That’s right, nurses, plumbers, managers, and chefs generally do not use algebra to do anything job-related or otherwise. And no, you will not use algebra when you go shopping. You might use arithmetic, but you won’t use algebra.
That’s not to say that algebra isn’t important to our lives. It is incredibly important. Algebra is one of the essential foundations of elementary mathematics, which in turn serves as the foundation for advanced mathematics, which serves as the bedrock upon which the sciences, technology, and engineering are built. But it is incredibly unlikely that students will ever use algebra, for any reason, in their future careers. And even the people who you think might use algebra all the time, like engineers and scientists, use software to do whatever algebra is necessary for them. They are generally not writing out the quadratic formula and solving supposedly “applied” problems about speeding trains about to collide.
So why do we kid ourselves about why we learn algebra? Why do we, well, lie to our students about how algebra will be a fixture in their future jobs? Just to give them a reason to foist it upon them, it seems! I think we should be honest with our kids. We learn about algebra for the same reason we learn about Shakespeare: to enrich our intellectual lives. And certainly that’s what Shakespeare does, for many people, for many different reasons. But algebra is a different beast entirely. Algebra can teach something that Shakespeare has a much more difficult time getting across: algebra teaches us how to think logically.
Algebra, and mathematics more generally, is the training ground for logical thought. It’s about understanding procedure and process, and where these come from and why. It’s about applying methods and algorithms in a deliberate and thoughtful manner. It’s about being consistent, and yes, following rules unquestioningly, but only after you have questioned them thoroughly. These are skills that our students need to practice and master for their future jobs: how to understand a problem, break it down into its constituent parts, and find a solution using those parts in a logical and step-by-step fashion. Algebra helps to train your brain, and once you have that training, you can apply these ideas to problems that are not algebra. And that’s the really important part.
Our kids don’t need to know a lick of algebra to excel as an architect, businesswoman, or doctor. But they do need to know how to apply the habits of mind and critical thinking techniques that a thorough study of algebra can provide. And not only is that incredibly practical, but even better, it’s the truth.
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