Solving for x

I have always hated math. Being a perfectionist, that was kind of an inconvenience for me. I remember solving equations in middle school until I was red-faced and teary-eyed. Being naturally good at math had always appeared to me as an elusive, magical trait, like the Holy Grail or Fountain of Youth. My parents assured me that no one else in the family was a mathlete, and it was okay if I was not either.

With the help of a couple great teachers who showed me a different, more digestible side of math, I have shed my hatred for the subject. But not everyone gets the opportunity to study under exceptional teachers in one of the top schools in the state. If this is what it takes to get American students to tolerate math as a subject, what does that say about the state of the American public education system as a whole?

This is the question I want to explore.

___________________________________________________

According to a study conducted by Ogilvy Public Relations, 30 percent of Americans say they would rather clean a bathroom than solve a math problem. If splashing around in a toilet bowl seems more desirable than working through an equation, that is a problem.

In addition, a Google survey conducted on the thoughts of Hagerty students about math revealed that 55.4 percent of students said they are good at math, yet only 24.6 percent said they enjoy math. While students may put in enough effort to earn an acceptable grade in their math courses, this does not translate to a genuine interest in the subject.

Every student knows their best and worst subjects, but it seems that a great number of American students bears a hatred for mathematics. The only exception is a handful of students who devour the math courses offered at their schools like potato chips. It is disturbing that the enjoyment of a subject that is so integral to everyday transactions is generally reserved for the most elite.

So, why do we hate math? Where did this distaste originate? And most importantly, how do we solve it?

STARTING CLOSE TO HOME

To understand where students go sideways in math education, it makes sense to start with them. Students undergoing credit remediation by taking online PLATO courses in an on-campus lab do not like math, and they list a number of reasons for why they were unsuccessful in the past.

“Teachers have not accommodated my learning style,” junior Christine Shanks said. “I want teachers to get to know their students and how they learn. I could learn completely different from the kid sitting across the class.”

Shanks has sought other sources of help outside of school. Peer assistance sites like OpenStudy or Brainly, Khan Academy courses and Mathnasium tutoring are what many students turn to for math help.

For other students, the problem is a lot more psychological.

“A lot of teachers make fun of us for asking questions or just make us feel stupid if we don’t understand,” junior Kayla Pashley said.

The same Google survey from before collected more data on students’ thoughts about math, and gave them an open platform to express themselves. Here are some of the free responses:

4 item(s)

The general theme seems to be that students take issue with their instructor’s teaching style or the teacher’s reactions to those students with a lack of understanding.

It is hard to believe that all teachers ignore or humiliate their students knowingly. There is a disconnect between student learning styles and teaching methods, and one problem is finding out where it is.

SECOND OPINIONS

Calculus teacher Carolyn Guzman’s first response to this issue was “I don’t have an answer. I’ll tell you that now.”

Coming from a woman who nearly landed a gig traveling to the moon for a living, that is not exactly a good sign.

“[Math is] one of the few subjects that is extremely dependent on prior knowledge to keep going deeper. Our educational system allows you to learn something for a week or two, take a test on it and then you’re off to something else,” Guzman said. “The learning should be valued, not the grade. But what do you do when kids start taking advantage of it?”

It is easy to point the finger at individual teachers for teaching to a certain skillset, but the current grading system is not doing any favors for teachers when it comes to breaking this cycle, as much as they may want to.

“To make it easy on math teachers, we teach you shortcuts, not why the shortcuts work. We teach rules, rules, rules, and you can’t remember all of them,” Guzman said.

Guzman’s only parent-teacher conference to date was with her son’s elementary school math teacher because he was performing poorly on timed multiplication tests. At school, he was learning to memorize his times tables and rattle them off as quickly as possible. At home, he was learning to see the pattern and the thought process behind multiplication, since Guzman knew what mindset she would expect from him when he hit high school. Needless to say, their two teaching styles conflicted.

“What’s he majoring in now? Mathematics,” she added.

As funny as this story is in retrospect, it is a prime example of how teachers are locked into teaching material a certain way because of grading standards.

“I think math teachers, as a whole, are not the best PR. Sometimes we suck the creativity and the challenge out of understanding,” Guzman said. “At some point, you stop viewing it as a challenge and start viewing it as jumping through hoops.”

Teachers of lower level math courses face the same issues with student motivation.

“The biggest problem that kids have today is confidence,” Math for College Readiness and SAT Prep teacher Brittany Campbell said. “With math, you have to get it wrong in order to learn how to do it right, but we don’t like to be wrong. That’s the struggle.”

Students can be their own worst enemies when it comes to learning new things, but finding a way to make this easier on students has a lot more to do with psychology and politics than simple teaching method adjustments.

“What we need to do is take out [testing] standards. It’s not allowing kids time to understand,” she said. “The whole thing needs to be restructured, but teachers having an open dialogue with their students is important to figuring out where they’re at and whether you’re going too fast or too slow.”

CONSULTING THE EXPERTS

If psychology and politics have a hand in this issue, people with expert opinions might be able to lend the most insight. University of Central Florida professors Dean Pamela Carroll of the College of Education of Human Performance, Dr. Michele Gill from the same department and Pegasus Professor Dr. Peter Hancock from Psychology offered their opinions.

Carroll praised Seminole County’s shift toward hiring elementary school teachers with specialization in certain subjects, as opposed to hiring one teacher to teach everything. Superintendent Walt Griffin is leaning toward hiring a teacher who specializes in math and science and a teacher who specializes in reading and social studies and having them work together. This then eases elementary students into middle school and high school teaching models.

Despite this shift for the better, she still cites standardized testing as a roadblock to student success, like Campbell and many other teachers. She drew a tiny box on her notebook, shaded it in and pointed to it.

“You’ve probably taken a standardized test that might test on this much of the universe that you’ve learned, and you probably get this much right, but everything else is unaccounted for. It doesn’t matter that it’s unaccounted for, unless you happen to miss this,” Carroll said, gesturing to the box. “Then they say, ‘Poor thing, she’s either not going to graduate, or she’s going to be in a different kind of class or she’s going to feel bad about herself.’ Students are tracked according to where they perform in this little box, when they really know a world of information.”

But in the end, it all circles back to teaching methods, even coming from the dean of a university college of education.

“For all of us, regardless of the subject matter, if we have a reason to learn, we dive in better. Even when I was in algebra class, I’d raise my hand to ask why I needed to learn this. [My teacher] never really had a good answer, so I never felt like I had a reason to learn what she was teaching. If she said, ‘Let’s learn how to make a robot do what you want it to do,’ I would have been all over that,” Carroll said. For Carroll, math’s fascination was a well-kept secret during her grade school years, and she was not the only one. 

“The interesting thing is, we tend to teach math in a vacuum, where people don’t actually teach math as they teach something else [in the real world],” Hancock said. “When I was young, I had to sit in a row of desks with 20 other students counting their times tables. What is 12 × 8? It’s 96. It’s still embedded in me. If someone asked me, ‘If there are 12 people on a jury and eight juries might have to decide [on a case], how many people have you got to recruit?’ I might have done better.”

For people like Carroll, the “cool” factor of math would have motivated her. For Hancock, practicality would have motivated him. Shanks’ comment about teachers getting to know their students’ learning styles is becoming a lot clearer.

Hancock points to a society where prominent mathematicians are glorified as opposed to pop stars (as much as he loves Lady Gaga) as a possible catalyst for change in students’ perceptions of math. The only reason many Americans know about Alan Turing, English mathematician and cryptanalyst, is because of “The Imitation Game,” a Hollywood movie about his life.

“I would propose to go about education beyond the notion of disciplines. The most important thing you can teach anyone is critical thinking, and you can’t do effective critical thinking without mathematical skills,” Hancock said.

Gill prefaced by saying that she has never done any research on the topic and only speaks from personal experience, yet she went on to introduce perhaps the most relevant piece of this puzzle: psychologist Albert Bandura’s self-efficacy theory.

Self-efficacy is defined as one’s belief that they are capable of doing something. This is influenced by four key components, the strongest being mastery experiences. If a student has positive mastery experiences, they will feel more empowered to continue performing in that area. A lack of mastery experiences, conversely, negatively colors one’s future desire to do that activity.

Second to this are modeling experiences. Seeing someone else similar to oneself succeeding in a subject can be encouraging for students because, hey, if they can do it, maybe I can do it, too.

The third influence of self-efficacy involves social persuasion. If one is encouraged to do something by the people around them, they will be more inclined to enjoy doing it than if they are discouraged or left to their own devices.

Here’s where American societal expectations come into play. What if mathematicians were the new pop stars, like Hancock said? Sure, Albert Einstein’s face with his tongue sticking out is plastered on various posters and t-shirts, but is that because of a societal respect for his work or the popularity of the image? Gill has her doubts.

“For whatever reason in our country, it’s ok to be not good [at math], especially if you’re a girl,” Gill said. “During the Space Race, math became cool again. Today, digital coding or gaming is cool, but students don’t see it as math, so there’s not a ton of societal support for it.”

Gill’s observation about society’s expectations of girls and their math performance should not go unnoticed. According to Ogilvy PR, women are significantly more likely than men to say that they are not good at math (37 percent versus 21 percent). In addition, 36 percent of Americans admit to saying that they can’t do math, yet women agree with this statement more than men (43 percent versus 29 percent). The issue of women’s participation in STEM fields is a different subject entirely (more on this here), but it is representative of social persuasion’s influence on human performance in mathematics.

The last element of self-efficacy refers to the physiology of doing something. This makes sense, since someone probably won’t want to do math if they characterize the feeling of doing it as butterflies, nausea or stress. If you feel bad, you do bad.

In the end, however, it all depends on the teacher’s ability to help the student navigate through these feelings of self-efficacy.

When Gill was in college, she taught a student who was a bit of a hippie and had always wanted to do math, but never knew how. Gill’s calculus professor let her do a project to teach the student a whole semester of calculus in six months as part of her independent study. They worked six hours a day, three days a week, and the student finally took an exam the professor would give his regular students. She passed with an A, something she never thought she would accomplish in a math subject.

Like many students, senior Kim Ariza’s perceptions of math are influenced by her belief in her own ability. She was diagnosed with ulcerative colitis (read about her experience here) sophomore year and missed a lot of school as she was undergoing chemotherapy. She is currently making up Geometry via PLATO.

“A big part of [my dislike] of math has to do with the environment it’s taught in; I don’t think the classroom environment suits each student’s needs,” Ariza said. “If I had learned it a different way, maybe I wouldn’t have had it in my head my entire life that I wasn’t good at it.”

BALANCING THE EQUATION

Senior Jessica Vasquez has always hated math. She remembers solving equations in middle school until she was red-faced and teary-eyed. Being naturally good at math had always appeared to her as an elusive, magical trait, like the Holy Grail or Fountain of Youth. Since middle school, she has played musical chairs in an attempt to settle into math courses that suited her learning style, switching from honors to standard to virtual to dual enrollment.

“My brain works more with letters than numbers, and definitely does not do well when the two are mixed,” Vasquez said. “I’m more of an abstract thinker than a systematic thinker, and [math] never really clicked.”

Last semester, she took dual enrollment statistics, her last high school math course. After years of struggle, she can relax, knowing her math credit requirements are fulfilled. She finally made it, but it was not easy.

When it comes to helping students like Vasquez enjoy math, there are multiple problems in the system contributing to one ultimate problem, and education reformers are in the middle of a national debate about which one to go after first.

As hard as the American public education system has tried to standardize math courses, there are too many variables when considering the national situation: state legislation, schools, teachers and, finally, individual students.

This is not solving for x any longer. This is the most difficult math problem educators have encountered, and there are an infinite number of variables.