I believe we can all agree that perseverance and confidence play a significant role in success. No matter what example of success we come up with, we can safely say that confidence and perseverance played a key role. For instance, confidence is built with each win we achieve, no matter how small. However, we aren’t perfect, so we cannot count on perfect records and thus must persevere through the inevitable failures. Taken together, confidence and perseverance are essential to any subsequent success.
A few weeks ago, I read an article in the New York Times Sunday Review entitled, “Is Algebra Necessary?” The author, Andrew Hacker, suggested that the math requirements in our high schools and colleges are a leading contributor to high school and college drop out rates. According to Hacker, “making math mandatory prevents us from discovering and developing young talent.” He also goes on to suggest that new classes should emerge addressing what he terms “citizen statistics.” These courses would cover topics such as the Consumer Price Index, and help “familiarize students with the kind of numbers that describe and delineate our personal and public lives.”
I highly agree with his idea and believe there is a place for a course on citizen statistics, however, within a curriculum that covers Algebra, Geometry, Trigonometry, and other advanced courses. In fact, I believe Hacker’s heart is in the right place. He ultimately wants more students to succeed in school and subsequently in their lives. I too want the same thing as I am sure does every educator. The difference is that I believe there is still a place for a solid math education and we need to consider its benefits before we eliminate it.
In the next few paragraphs, I am going to address specific comments made by Mr. Hacker. I will then close by coming full circle on my original thesis that confidence and perseverance are critical to success.
Early in the article, when referring to foreign students, Hacker states “…it’s their perseverance, not their classroom Algebra, that fits them for demanding jobs.” To this I counter that perseverance is developed by courses like mathematics. Perseverance is a quality that like most others needs to be practiced. We may all have some level of it, but ultimately to improve upon it, we must practice it. The type of problems and challenges encountered in a class like mathematics positions students to develop stronger perseverance by challenging them to solve increasingly difficult problems. Each subsequent challenge pushes students past their comfort zone and presents an opportunity for growth. To simply state that it’s perseverance that fits foreign students for demanding jobs without discussing where it may have developed creates a serious gap in Hacker’s reasoning.
Having said that, I strongly believe there are opportunities to reposition the same Algebra courses to be more like a game environment where students are pushed to try and try again until they advance levels. Such changes would more precisely target the goal of developing perseverance in students. Nevertheless, Algebra is a very practical solution for developing perseverance and subsequently, confidence.
Later in the article, Hacker states that “What of the claim that mathematics sharpens our minds and makes us more intellectually adept as individuals and a citizen body? It’s true that mathematics requires exertion. But there’s no evidence that being able to prove (x^2+y^2)^2 = (x^2-y^2)^2 + (2xy)^2 leads to more credible political opinions or social analysis.”
Perhaps there is no evidence to support a direct relationship today, but that assumes that simply because we could not devise a study or test that isolates a particular variable there must be no relationship. However, that does not mean it was wrong. It simply meant it could not be proven at that time. This concept is very different from something that was in fact proven incorrect as supported by evidence. While Hacker is absolutely correct that there is no evidence to prove a relationship, there is also no evidence to support the contrary; that does not mean there is no relationship and we should eliminate Algebra as a requirement. I often use the following analogy: algebra is to our brain as pushups are to the athlete’s physique. While an athlete (i.e. football player) does not need to perform pushups on the field, he or she still performs them as a part of his or her training regimen. And while we may not be able to prove that there is a direct relationship between push-ups and throwing a better pass, we understand enough to know that pushups lead to a stronger body which positions the athlete for a better performance. The same goes for Algebra. The brain requires exercise in perseverance, resiliency, and problem solving and subjects like Algebra provide it with repetitive exercises to keep it sharp and primed.
Hacker goes on to suggest that his proposals “need not involve dumbing down [the curriculum]. Researching the reliability of numbers can be as demanding as geometry. More and more colleges are requiring courses in “quantitative reasoning. In fact, we should be starting that in kindergarten.”
The problem with this suggestion is that starting a child on “quantitative reasoning” at a young age is like asking someone that has never played football to play in a competitive game. In keeping with the analogy, the person hasn’t been explained the rules, taught the skills, nor the strategy and we expect him or her to perform and succeed. Taking this analogy one step further, not only is this person not prepared to play, he or she has not even been conditioned (perseverance) to endure a full game.
Going back to my original thoughts about confidence and perseverance. My high school math teacher once said that math is the great equalizer. I never forgot that. And as the years went by I gave that more and more thought. Growing up in north Jersey, my family was not of a high socio-economic status. In fact, my parents could never afford to send me to a private school or provide costly supplementary education. When I started my freshman year at Penn State, I felt I was a little behind despite having been a strong student in high school. However, the subject that helped boost my confidence was math. The skills, perseverance, and confidence I had gained in high school math positioned me right along side, if not ahead, most of my fellow students. These critical qualities positioned me to make up the difference in all of the other courses where I felt I lagged. Not only did I know what it took to succeed, I was fully equipped with the tools to achieve it – perseverance and confidence. In hindsight, math truly was the great equalizer.
We will probably debate the question of whether Algebra is necessary for years to come, but it is my firm believe that yes, Algebra is necessary. Let’s not back out of our pushups and sit-ups. Let’s put in the time at the gym to make sure we are tuned to perform well in life.
And in case you are wondering, I did not major in math. I majored in business. I later went back to school for an MBA and a Masters in Psychology. Perhaps one day I’ll formally pursue a math degree, but just for exercise 🙂