Recently, a common question has been repeatedly posed to me, one which makes me uncomfortable on several levels.
The first being that the answer seems so simple that it begs me to wonder why bother asking it. The second being that the answer, although simple, makes me wonder if we are doing the best we can, or if we are simply giving someone verbal justice.
Why do we continue to teach math that has little application to a “normal” person?
This question begs at the systemic problem of post Geometry mathematics: “Those who do not understand mathematics, feel it is unimportant.” Dispensing with the simplistic, selfish nature of the question, the lack of vision of the person posing the question, and the refusal to answer it with “because we always have”, on its surface, the answer seems simple.
The logic associated with the late secondary mathematics allows students to engage in careers they would not be able to engage in without it. Essentially, it opens doors. The technological advancements that have prompted this question are things such as Photomath and other internet sites, along with the theory that we need to prepare students for what they will be doing in their careers, not a general path of instruction.
Let’s tackle these one at a time. The first argument typically presented is that if apps such as Photomath or sites such as Google can solve the problem, why do I need to learn about it? (see a previous blog for more introduction). This argument is fraught with problems, the least being with the instructor who is allowing students to live in simple DOK 1 styles of questioning. Those are the only questions that these apps can handle. Anything related to an actual scenario to utilize the math is well beyond the capabilities of these programs.
Furthermore, if we isolate the problem to a DOK 1 situation, as shown below, it opens up an additional area of concern.
Using apps such as Photomath produces a solution like the one shown below.
The goal of a problem such as this is to see if students understand the conceptual nature of mathematics. We want students to understand the solution process so that they can open the door to higher levels of mathematics. However, if they understand number sense, they can quickly see that (x+1/2) must be equal to one because 1/3(1) = (1/3). Therefore, the only way (x+1/2) = 1 is if x = 1/2. What takes photomath 17 steps can be solved in less than three.
Knowing “math” is not only more efficient, it is more effective. When I teach math, I want students to understand the solving process, or what most people believe upper mathematics is about. That said, I want them to understand mathematics so much more than I even care about the process.
The second argument is more daunting and more bothersome. Adults who have struggled in math, or never truly understood mathematics, believe it is solving equations for the sake of solving equations. They believe it is completing proofs for things that have no meaning, so they can somehow be more fulfilled by the process of just doing the proof. They see math careers as teachers, professors, and engineers. The reality is so far from this perception. It is the equivalent of telling someone that they know how to make an automobile because they know how to drive one.
Kiplinger listed the top 10 college majors for 2015-16. Each of the top 10 has a major focus, if not entire focus on mathematics. In addition, CareerCast lists the top 10 professions to enter. Of those professions, seven are focused on mathematics.
This isn’t math for the sake of doing math. It is math for the purpose of what math is. It is about seeing a pattern, or a logical process, in a situation and either finding a solution or a pathway to improving that situation.
In the past few years, math has helped solve problems in heath care, computers, and safety. In the near future, math will help to solve efficient energy solutions, global warming, and many more issues of our time.
Some would argue that science will be responsible for solving these problems. But I would argue that science is a subset of mathematics. Math by itself doesn’t solve problems, which is why many school districts are implementing STEM initiatives. One of the most significant realizations among educators over the past several years is that there are really two core subjects in education — English and mathematics. Without a solid foundation in both of these, career opportunities become drastically limited.
Beyond these responses, what is the best way to respond to the question of, “why do we continue to teach courses like Algebra 2, Pre-Calculus, and so on?”
Is there a better way?
I thought about my answer to this question a lot for this blog post. I plan to split my response across three parts. In part two, I will convey how my staff feels about the question and some of their responses. And in the final post, I will cover some possible answers to the question.
Look for part two of this blog post soon!