As a middle school math teacher, the one question I hear more than any other question is "Why do we have to learn this?" I hear it from students and parents alike, and to be honest it can be a very valid question.
In some cases, I can come up with very concrete answers -- so you can tip correctly when you go out to eat, so you can make sure you get the correct change back when you buy something, so you can divide two pizzas evenly between three friends, so you can be sure you're making the best purchase for your hard-earned dollars, so you can double a recipe, so you can get a good job, graduate from school, etc.
Even with these clear-cut answers, many students still come up with very valid responses -- "I can just use a phone app for that", or "I'll just use a calculator." I can't really disagree with these statements. Middle school students are quickly developing the ability to create very valid counter arguments. And when a 13-year-old has visions of becoming a famous movie star, musician, or athlete, the "so you can get a good job" argument doesn't go very far.
And in some cases, the math we're learning in school will rarely be used in day-to-day life activities. Sure, we all need to know how much ground beef we can buy for $10 when we go the store, but who among us ever needs to convert .000067 to scientific notation, or write a linear equation for a line with a slope of -4 containing the point (0,-2)? Even the most enthusiastic of math professors would have to admit that a large percentage of people will not have to use those skills directly in day-to-day life.
So if we're not using these skills, or if we can just use a smart phone or computer, then why are we learning them? Why is math so important when it comes to scholastic achievement and education, and why is it such a focus for schools?
Well for starters, if we don't continue to develop math skills in our young students, we will soon find ourselves without computer programmers and engineers to develop these new technologies. All of those program designers were once middle school math students, working and struggling to complete lessons, and quite possibly asking the same "why do we have to learn this?" questions.
But its much more than just catering to the future engineers and scientists. Put quite simply, math is about solving problems. Period.
The word "problem" in mathematics is typically applied to equations: "Solve the problem 6x + 7 = 55". But problems in life can be much broader. "How do I reach the top shelf?" "How do I fit all these activities in my busy schedule?" "How do I convince my boss that this decision is unfair?" "The car's almost out of gas, how far can I go?" These and many more are the problems everybody faces on a day-to-day basis. And math prepares us for dealing with and solving these problems.
Successful problem solvers are able to understand what is expected of the problems they face. They know all of the details surrounding the problem at hand, perhaps the most important step to solving problems. Finding the solution requires attention to detail and patience. After examining the details, intelligent choices need to be made and a strategy developed. The plan must be carried out in an order that makes sense. Careful planning and often justifiable experimentation must take place. Once an actual solution is obtained, it must be tested to determine whether or not it is reasonable.
And that process -- evaluating, understanding, strategizing, planning, trying, experimenting, often failing, persevering, putting forth effort, testing, and ultimately succeeding -- is what math trains us to do. Just as a musician, athlete, or artist needs to practice to hone his/her craft, problem solvers need to practice too.
Mathematics also teaches us to think and communicate logically, to be precise in thoughts and words. We need to show our steps, and communicate just what we've done and how we justify our answers. Good mathematicians explain their processes and defend their answers. And even if a student goes on to a career that doesn't work with numbers on a day-to-day basis, they will need to communicate. The best lawyers, the most convincing of salespeople, the people who always win arguments -- they all use mathematical processes to construct their arguments. It's structure, it's explaining your point-of-view in an easy-to-follow, logical, step-by-step process, and paying attention to every small detail -- the same process we use to solve problems in the math classroom.
It is my sincere hope that many of our children will go on to become successful engineers and architects and accountants and computer programmers and scientists. But I also hope that many students will go on to become artists and musicians and soldiers and teachers and athletes and writers.
And no matter where their career paths take them, problems are inevitable. I face them, you face them, we all face problems. It's how we approach and handle those problems which will set apart the successful. Working through and solving problems is ultimately what mathematics is all about. That's why math matters, and to answer the popular question, that's why we have to learn this.