Mathematics major Emma Bowmer, a senior at Middle Tennessee State University, isn’t shy about her passion for math.
“I like the shock factor when I tell certain people that I’m a female interested in mathematics!” she says with a laugh. “And I like the thought of helping somebody else give people that shock factor.”
The urge to inspire others with a love of mathematics — particularly other female students — drove Bowmer to minor in secondary education, pursuing her teaching license through MTSU’s MTeach program, which works to increase the number and abilities of mathematics and science teachers across Tennessee and the nation.
This summer, Bowmer and several of her MTeach classmates had a unique opportunity to conduct research and classroom observation in an area of rising popularity: integrating technology into the classroom.
“I want to help another generation of students in a whole new way,” Bowmer says, noting that technology was often absent from her own middle- and high school classrooms. “I don’t blame anyone for not wanting to use technology, because it’s intimidating. But this is the everyday life of the student at home; [technology] is something that’s going to be in everyone’s life, so if you don’t use it, you’re missing out on a great learning resource.”
The MTeach students observed local teachers integrating a few specific technology-based programs into their classrooms and recorded the younger students’ responses, thought processes and problem-solving skills.
“My students got to witness the lesson taught by the classroom teachers as well as interact with the students and help collect the data,” says MTSU’s Jennifer Lovett, an assistant professor in the Department of Mathematical Sciences.
To review the kids’ step-by-step thought processes, the MTeach students made live recordings of their classroom activities and analyzed how they reacted to each program.
“We had consent forms signed so that we could videotape the students while they did the activities and record their responses,” Bowmer explains.
The project focused on computer programs designed to engage students in defining mathematical concepts. One program allowed students to choose different colors of drinks from two virtual “vending machines.” One “machine” produced randomized results, and the other’s results represented a function. Each student had to identify the “function,” then define it based on the patterns they noticed.
The second program featured different carnival activities, including watching a character launch from a cannon and descend by parachute. Students had to draw his ascent and descent on a graph as accurately as possible, creating a slope representing the speed and height of his journey. The man then launched a second time, following the curve of each student’s graph. Students then evaluated how closely they had represented his rise and fall.
The activities highlighted the differences between passive learning, where students simply receive and repeat information, and active learning, where students take the initiative in discovering and defining new concepts.
“With ‘Vending Machine’ and the carnival activities, we were shooting for our students to be ‘hands-on, minds-on,’ ” Bowmer says. “One of the things that I and other MTeach students are learning is that there’s a right way and a wrong way to integrate technology in the classroom.
“A lot of activities, including technology use, are ‘hands-on, minds-off.’ Sometimes giving students technology is like giving them the answers without realizing it. We’re learning to use technology as a ‘hands-on, minds-on’ lesson, where they’re truly engaged.”
Programs like these examples, which allow students to explore scenarios and create their own definitions, are particularly useful in keeping young learners engaged in the task, Bowmer says.
“The majority of the students were very interested,” she adds. “They were thinking on their own, and hardly any of them needed a teacher’s guidance for the activity.”
After recording the kids’ methods and thought processes and taking note of their feedback, Lovett and her MTSU students sat down to discuss their results.
“We focused on examining student thinking and the different approaches students use to tackle a problem, as well as how to incorporate those approaches into lessons that [our students] will teach,” Lovett explains.
Empowering students to teach themselves new concepts had a noticeable effect on their self-confidence, Bowmer notes.
“During our research, we observed a lot of changes in understanding through the videos of the students. They came in with smiles on their faces, high-fiving each other, a sense of pride and confidence. I like to call it pure enjoyment of the task,” she says. “Even though they’re in school and they have to be doing it, it’s great to see them enjoy it!”
Are students are more likely to retain information that they learn on their own? Bowmer’s response is enthusiastic.
“I 100% believe that they do,” she says. “All we did was tell them, ‘Give us a definition that would make sense in this activity.’ And we let them know that this isn’t just about ‘Vending Machine’ or this specific activity. They actually identified, for themselves, one of the trickiest concepts in mathematics. It gives them a ‘eureka!’ moment, a little bit of confidence in their own ability.”
Observing the learning processes of younger students also has taught Bowmer to reevaluate her expectations for herself as a student.
“It’s definitely taught me to be a lot more patient with myself,” she says. “I’ve learned that I need to pace myself and that it’s OK not to understand something immediately.”
Implementing the idea of “hands-on, minds-on” also has shifted Bowmer’s own learning goals. “I needed to change my perspective and value the ‘why,’ rather than just how to do something. Now I can look at myself as a learner and as someone who values the information itself,” she adds.
Bowmer says she hopes to convey to younger students the thought processes behind certain mathematical concepts, much as her own teachers did.
“I remember that one of my high school teachers had a whole lesson to teach us about parabolas, but instead of just showing us a graph, she showed us a paved road. She said, ‘Did you know that every road has a specific curvature to it, so that water doesn’t puddle on the road?’” Bowmer recalls. “It’s little real-world connections like those that are so interesting to me. I still think about that lesson when I’m driving!”
Lovett adds that technology in the classroom is a fun and effective way to make such abstract mathematical concepts tangible for students.
“Technology allows students to explore mathematics deeper and open windows that would not be accessible without it,” she says. “I’m always excited to share with others the power of technology to explore mathematics.”
— Freya Cartwright (firstname.lastname@example.org)