# Peer instruction solves the problem

FIU finds that, in some cases, students make the best math teachers

It’s the equivalent of “Give someone a fish, and they eat for a day. Teach someone to fish . . .”

But this one goes: Show students the steps to solving a high-level math equation, and they complete their assignments. Teach students to reason out problems on their own, and they ride that skill to careers in software development, engineering, medicine and more.

That’s how 2022 graduate Daniela Zamora Zuniga describes what FIU’s learning assistant program aims to accomplish: Get university students to go beyond the step-by-step process of working out an answer and instead teach them to think in a way that serves them for a lifetime. It’s an approach that gets to the heart of STEM education at FIU.

The university now teaches the bulk of its calculus courses with that intention, a once-notoriously difficult class that over the years saw many students finish in frustration – and failed grades – even as they moved on to courses in other disciplines that build upon the very foundation of calculus.

Zuniga took the revamped calculus course as a student – she passed with flying colors – and then in the next semester was hired as part of the learning assistant team that has been fundamental to a positive transformation on campus. The LAs, as the learning assistants are called, are undergraduates tasked with helping peers succeed in an “active learning” environment. Such a classroom typically divides 60 or more students into groups of four or five. Round tables and chairs on coasters contribute to the interactivity required of the participants.

“They get to the class and basically know nothing about what’s going to happen that day,” Zuniga explains of how students begin each one-hour, three-times weekly session, “and they leave knowing *everything*.

“We give them a packet with material that same day. They read it, discuss it, they work on some problems and then they ask us questions.” Sometimes, the instructor, who rarely gives prefatory remarks and generally circulates among the groups as do the LAs, will conclude by addressing all assembled about any general questions that came up, Zuniga adds, but much of the activity centers around self-education.

The seeming simplicity of the modality contrasts with the traditional way of teaching calculus.

"In a lecture-style class, usually a professor shows something on a board. They’ll write a couple of examples. They’ll tell you the steps: First you do this, the derivative. Then you do this, you substitute. Then you get the final answer,” Zuniga explains.

“That doesn’t really help you understand *why *you’re doing things and what those steps mean in the big picture. Learning the steps doesn’t really get you to reason mathematically,” she states. “Whereas when you get to math reasoning, you can do things without going through the steps because you understand the math so intrinsically that you don’t really need a guideline. You can get to the conclusions yourself.

“That’s something that I saw students learn during those classes.”

And the best part: a positive domino effect.

“I worked with a lot of pre-med students desperate to get an A,” Zuniga says. When in later semesters she saw some of those same students on campus – she bonded with many of them during her scheduled office hours – they told her, “’I took physics with calculus and it’s so easy because I know calculus so well that I just have to worry about the physics part.’ Or chemistry or any of those other math-adjacent subjects,” Zuniga continues, “they really had no problem with the math part, which is what I think trips up a lot of people who take those math-adjacent [science] courses. Their knowledge extends to other classes.”

Today Zuniga works as a content editor for a firm that produces K-12 math books. “I’m grateful I had the opportunity to be an LA because it allowed me to get a position that involves a lot of the things that I learned,” she says.

“I think it’s a great initiative,” she adds of the program, “and I've seen it help people first-hand.”