University of Southern Indiana

Why + How = Power to the Nth Degree

by C. L. Stambush

woman standing by passing train

For many people, train A and train B running toward the same destinations but at different speeds results in internal chaos, frustration and a life-long loathing of math. We have flashbacks of ourselves as eighth graders sitting at the kitchen table struggling to comprehend algebra, labeling ourselves as not math people. Yet in today’s data-driven world, an aversion to math is the surest way to be left standing on the platform.

The ability to do math impacts everyone’s life, from administrators with spreadsheets calculating data, to potters tallying the time and temperature necessary to produce colorful glazes, to engineers computing tangent functions when building bridges, to writers formulating the necessary story elements to tell it effectively and efficiently, and everyone in between.

“We know that math, and algebra in particular, is a big gate keeper for students in terms of being successful in a number of career fields,” said Dr. Rick Hudson ’02, chair of USI’s Mathematics Department. “If students don’t become proficient in algebra, it limits the majors they can pursue. That’s a huge problem.”

Math hasn’t changed since many of us were kids, but the approach to teaching it has. Gone are the days when learning math focused on how to solve a problem and involved rote memorization of times tables and algorithms designed to get the answer fast. (Calculators on cell phones extinguished this requisite much the way evolution abolished humans’ need for plicae semilunares—the fleshy bit in the corner of your eye that was once another eyelid; birds still have it.)

blur of train tracks

Today’s math scholarship requires Sherlockian prowess, such as developing new skills and applying them to unfamiliar situations; gathering, organizing, interpreting and communicating information; formulating questions, analyzing and conceptualizing problems; seeking out additional data; developing curiosity, confidence and open mindedness; and much more. “Knowing ‘why’ something is true in mathematics involves being able to justify it with a reason,” Hudson says. “It involves deductive reasoning.”

Math educators today understand that both how and why are key to successful comprehension of mathematics, and are incorporating them into course work through addition and subtraction: developing methods that engage students in learning and eliminating negative mathematical perceptions and fixed mindsets.

To ensure all USI students acquire the necessary mathematical skills, the Math Department has created an alternative to college algebra (intended for students pursuing math-centric careers) with a quantitative reasoning course when Core 39 was implemented in 2014. The new course includes a variety of topics that are application-based, such as probability and statistics, and math modeling. “College algebra prepares students for the calculus sequence, and Math 114 is meant to be a final course for most students,” says Hudson. “We look at topics as they're applied in the real world (home mortgages, car and education loans) from an advanced level.”

Educating math majors and minors, as well as providing in-service learning opportunities for area professionals is the “square root” of USI’s Math Department, since these are the folks who’ll be establishing mathematical foundations for students in elementary, middle and high school.

Students preparing for careers in teaching math, and those already in the profession, must possess the analytical insight that allows them not only to teach the content, but to do so in a way that connects with young minds. To facilitate this, education math majors and minors take upper-level courses designed to engage them with students, either in a classroom alongside a professional or through course components that connect them to students through service-learning projects, such as family math night and pen-pal program. (Family math night exposes USI students to working with children and their parents to learn math through engaging, handson activities, and the pen-pal program is a letter exchange in which elementary and middle school students solve problems sent by USI students, who in turn analyze the solutions and provide feedback.)

“I feel like we’ve embedded a lot in our program to help educate our students to become better teachers. It’s a different kind of course than it was 20 years ago, in terms of thinking about the knowledge teachers need as opposed to the kind of knowledge the general public needs,” says Hudson. “The type of problems we give students today have them think about it from their future students’ perspectives much more than in the past.”

Insight into the workings of the mind is positive, but the way we think about math, our cultural mindset, is a negative. “The way we think about math in the U.S. is quite different from other nations,” says Hudson, adding, “The U.S. doesn’t tend to fare strongly on international tests in mathematics.”

Why? “Japanese teachers aren’t afraid to let their students really struggle with big problems,” he says. “In the U.S., the word struggle has a negative connotation.”

Struggle and making mistakes, however, are crucial to all learning. Research shows “that the brain sparks and grows when we make a mistake, even if we are not aware of it, because it is a time of struggle; the brain is challenged and the challenge results in growth,” says Dr. Jo Boaler, one of the nation’s leading mathematics educators.

“I get comments from students who say, ‘If I’d been taught math this way I might have liked it more.” - Dr. Doris Mohr

But struggle devoid of structure won’t guide students to greater understanding or skills. “We engage our USI students in productive struggle, so they can feel what their [future] students will feel when they’re presented with concepts they don’t understand,” says Dr. Doris Mohr, associate professor of mathematics. “We don’t want elementary students to end up in tears, but we want them to struggle with an issue for a while so learning takes place.”

In the days when the teacher played the role of “sage on the stage” there was only one way to solve a math problem, but that notion went the way of the dodo bird. “In the traditional approach to math, if you didn’t understand the one method a teacher showed you, there were no options,” says Mohr. “Now there are multiple ways kids can solve a problem. The main message I try to get across to USI students is there should be multiple paths.”

Hating math might be an acceptable practice in our culture, but without it you’re limiting your choices in life. Math literacy is as vital as reading literacy. “We assume everyone will leave school being able to read, but many don’t see math as being at that same level of necessity,” Mohr says.

Fear, frustration and anxiety add up to "I hate math", but through new teaching approaches, those components can be eliminated. “So many kids have math anxiety. I don’t think that needs to be,” Mohr says. “I think if it’s taught in a way that makes sense to them, in a way where mistakes are valued and something that can be learned, then they won’t be afraid of math.”

colorful donuts on a tray

Math Challenge: You walk into a local convenience store and a sign on the wall states, “Donuts .79¢ each.” How much do you hand the cashier, and what change will you get back?

Answer: Because of the placement of the decimal, the cost of a donut is technically less than a penny.

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