The last group of 97 recipients were given $10,000 each from the National Science Foundation and invited to Washington, D.C., for the award ceremony.
Initially, the applicants are screened at the state level. Elder said she was surprised to be named a finalist.
"I was shocked; I didn't think I would get it," she said.
Elder started teaching 15 years ago at Hillcrest Junior High, where she stayed for two years. When the position at McMillan opened, she decided to try it out.
"It was just the right thing to do," she said. "I felt like I needed to be here."
Her approach is hands-on.
"I'll give [students] a situation, and they use drawings to show the situation," she said. "The students have to be creative and come up with different ways to show me their answers."
She said she wants the students to appreciate and be able to use what they learn.
"I always try to … give them an understanding of math, not just an algorithm, but where it comes from and how it works, not just to memorize a set of rules," she said.
As part of the award process, each nominee had to videotape a 15-minute lesson for the panel to review. Elder chose a lesson that was true to her curriculum and showed application of the subject to real-life situation.
"They had miniature-sized doors in front of them to rotate, fold and see about symmetry," she said. "Then they had to create their own doors, with tons of different shapes and designs."
She said this method effectively engages the kids in learning.
"It's very student-oriented," Elder said. "The students are doing the thinking, and the kids had to justify to me."
Elder went into teaching because she wanted to inspire kids, she said, and she chose math not just because she loves the subject but also because she wants to change perceptions aboutit.
"In our society we have this idea that it's OK to not be good at math," Elder said. "I wanted to inspire especially girls and tell the students that it's not just the elite few, but we all could be good at math."
Fun is also a key factor in her curriculum.
"They can be creative," she said. "Most of the time they don't even realize they're doing math."
She sometimes missed being able to focus on just math as she could as a junior high teacher, but teaching multiple subjects allows her to instill a passion for learning in all things.
"My No. 1 goal in teaching is that every one of my students feel like they can succeed," Elder said. "I want them to be lifelong learners, to love learning."
Some years since she graduated with a master's degree in teaching and learning from the University of Utah, she's going back there with her husband to take a Spanish class.
"I always want to improve myself," she said. "I don't want to be a teacher that feels like I know everything."
Principal Jennifer Kranz of McMillan was one of the people who nominated Elder for the award.
"She's a phenomenal teacher," Kranz said. "When you are in her classroom, all those best practices we read about you see, particularly in the area of math."
Kranz described Elder as a caring person with a sense of humor.
"She is able to energize the students and to explain math in such a way that they come to love it," Kranz said. "With the children, she's able to act the fool at times, which is wonderful."
Fellow McMillan teacher Karen Emery, who teaches third grade, has known Elder for 15 years.
"I respect Rebecca very highly," Emery said. "She is constantly looking at the students' works and figuring out what each child needs."
She admires Elder's enthusiasm for math.
"She does calculus for fun," Emery said. "When she's bored, she pulls out her calculus book."
For Elder, the reward is the interaction with the students and seeing them succeed.
"I love the 'Aha!' moments when something clicks, when they can prove to me how they can do things," she said. "They're not just robots spitting out correct answers."
Outside the classroom, she enjoys reading and photography. She's also a "Star Trek" and "Star Wars" fan and is a member of the National Council of Teachers of Mathematics.
She said it would be an honor to win the presidential award.
"It's just nice that I've been a finalist, honestly," Elder said.
She said she appreciates that the awards distinguish a group of people who are dedicated to their professions.
"I just love that they're recognizing teachers," Elder said. "We're not just coming in here for a paycheck. We love our students. We love our job, and we put our hearts and souls into teaching."
Presidential Awards for Excellence in Mathematics and Science Teaching
For the recipients:
A certificate signed by the president of the United States
$10,000 from the National Science Foundation
Award ceremony in Washington, D.C.
Participation in professional development programs
Meetings with policymakers to discuss how to improve math and science education