Elgin High School senior Guadalupe Barragan works on lessons from her Advanced Placement calculus course. She says she never expected to be taking a college-level course after starting high school at a sixth-grade math level. (Melissa Jenco/TribLocal photo).

Entering high school with the math scores of a sixth-grader typically isn’t part of the equation for seniors who land a spot in Advanced Placement calculus.

But for Elgin High School senior Guadalupe Barragan, hard work and a teacher who saw her potential added up to just that. And now she’s inspired other students to make the same climb.

“I wanted to do good in high school, but I never thought I was going to do this,” Barragan said. “This was nothing I had in mind.”

She has always liked math, but struggled with it. In middle school, she said, math teachers were some of her toughest.

“Sometimes they didn’t explain things enough or you get behind, they say something you don’t understand, and they get on other (topics) and they don’t wait for you,” she said. “That was the hardest part.”

That changed when she entered Brian Karsbaek’s algebra class during her freshman year at Elgin High School and was three grade levels behind.

“I started with Mr. K in his class and he was a really good teacher,” Barragan said. “He was always pushing us, so he inspired me in a lot of ways. I wanted to keep going.”

After a couple months, Karsbaek could tell Barragan had potential and recalls her being “hungry for knowledge.”

“I could see she was very motivated, always had her work done,” he said. “From that respect I could tell she would make it out of that track and on to other tracks. On to AP calculus? That was a dream at that point.”

By the end of freshman year she had moved up from a sixth-grade math level to 10th grade where she belonged.  But just catching up wasn’t good enough. She enrolled in geometry during summer school and went on to take honors algebra as a sophomore, pre-calculus as a junior and now is steamrolling through tangents and derivatives in Karsbaek’s Advanced Placement calculus class.

Along the way, she spent summer days and lots of hours after school and at home, finding a new confidence from Karsbaek to ask for help when she needed it and not letting frustrations deter her.

“I couldn’t do it,” she said of quitting. “I’ve been through all these things so to let it go, no.”

Her perseverance even inspired the class behind her to make the same leap. The year after she took the summer geometry class, 20 other students signed up to do the same, including Marlene Escobar and Olivia Sirichandeng, who are now juniors taking pre-calculus.

The girls said they heard Barragan’s story as freshmen and were impressed that she proved herself when some doubted her.

“I didn’t even think it was possible … but it was, so now I think we can make it,” Escobar said.

“We’re pretty proud of ourselves,” Sirichandeng added.

Barragan hopes her math prowess will help in her future career as an obstetrician — or maybe a math teacher.

“I love kids, the way they’re born,” she said. “I love how the body works to do that. I think it’s amazing.”

She also is considering becoming a teacher to try and be as inspiring to struggling students as Karsbaek was to her.

“It makes me feel really happy. I never thought I was going to do this,” she said. “It’s something I’m going to remember my whole life.”