What makes a great teacher great? That's the question at the heart of 50 Great Teachers, from the NPR Ed Team.

Sarah Hagan has a passion for math, and the pi-shaped pendant to prove it.

The 25-year-old teaches at Drumright High School in Drumright, Okla. The faded oil town is easy to miss. Fewer than 3,000 people live there, and the highway humps right around it.

There are no stoplights, no movie theater and no bowling alley anymore. Just a clutch of small houses and hearty businesses: a funeral home, Family Dollar and a Dollar General.

That makes it hard enough to attract good teachers, says Judd Matthes, Hagan's principal. But it gets worse.

"We don't pay a lot in Oklahoma for beginning teachers," he says, laughing from behind his desk in the school's basement. "If you go next door to Arkansas, they're about a $10,000-a-year starting salary difference."

Which made Matthes wonder why a National Merit Scholar who had gotten a full ride to the top-notch University of Tulsa would want to start her teaching life in a place like Drumright, earning just over $30,000 a year.

Hagan gets to school early each morning, usually by 7 a.m.

Hagan gets to school early each morning, usually by 7 a.m.

Elissa Nadworny/NPR

Sarah Hagan's answer:

"It was April, and I hadn't graduated yet. And they said, 'Come work here.' "

Hagan, now in her third year at Drumright High, grew up outside of Tulsa. Home wasn't urban, but it wasn't Drumright, either. She hadn't planned on working in such a poor, rural district and got quite a shock when she arrived.

"The first time I saw my classroom," Hagan says, "it was the most depressing thing I'd ever seen. The walls weren't all painted one color. There was no dry-erase board. There were no bulletin boards."

And the floorboards squealed. They still do, but the rest of her room is now an unrecognizable riot of color.

Hagan's classroom is a riot of color and inspiration.

Hagan's classroom is a riot of color and inspiration.

Elissa Nadworny/NPR

Decorations hang wall-to-wall, floor-to-ceiling. A poster of Albert Einstein. Paper pompoms. A podium decorated with a sign in pink, purple and yellow reads: "Ms. Hagan, Teacher of Awesome (and by "Awesome" I mean "Math")." After each school year, she tears it all down and starts over.

This is the first key to understanding Sarah Hagan: She's a visual person.

Hagan is also remarkably self-assured. When she arrived at Drumright, her classroom wasn't the only challenge. The school had ordered new math textbooks, but Hagan had already decided — as a student-teacher — that she wasn't going to use textbooks.

"I don't want to be stifled by that. I mean, I teach a lot of things in a totally different order than a textbook would," she says.

To Hagan, the average math textbook was, itself, a problem to be solved.

"I decided we were gonna make our own textbooks."

She simply left the new books in their boxes. Instead, in a standard lesson, she uses everything in the classroom but a textbook: a flower pot, a garbage can, a roll of tape, loose spaghetti.

Yes, spaghetti. It's all part of Hagan's DIY approach to teaching and learning.

As for the textbooks they make, her students begin with blank composition notebooks. Each day, Hagan hands out a lesson she has written herself or open-sourced from other teachers across the country. It's usually printed on colored paper and requires some kind of hands-on work: drawing, coloring, cutting.

There's even some basic origami.

Notebook

Students then glue the results into their notebooks. Eventually, the books look like dog-eared, bulging relics from an Indiana Jones movie. Hagan argues that if students are allowed to be creative, they're more likely to remember what they've learned.

"The point is, we shouldn't have to be like, 'Oh, yeah, there's that chart on Page 763 that tells me how to classify something.' They should think, 'Oh, that's on that blue paper that we did a few days ago, and I doodled in the corner,' " she explains.

To help students learn the quadratic formula, Hagan made it a puzzle to be pieced together.

To help students learn the quadratic formula, Hagan made it a puzzle to be pieced together.

Elissa Nadworny/NPR

One morning, in Hagan's Algebra I class, the handout is orange, and the lesson is on naming polynomials — drudge work even for math enthusiasts.

So Hagan shakes things up. After walking the class through the differences between cubic and quintic, binomial and trinomial, she asks:

"So, you guys ever gone speed-dating?"

Math speed-dating.

Hagan hands the students slips of paper with a polynomial written on one side and its name on the other. She demonstrates with a confused football player. He holds up his card, and she names his polynomial. He then tries to do the same.

For many of these students, talk of polynomials elicited groans. Then Miss Hagan got them speed-dating.

For many of these students, talk of polynomials elicited groans. Then Miss Hagan got them speed-dating.

Elissa Nadworny/NPR

And it's important, Hagan tells them, not to let wrong answers linger:

"Because I don't want him thinking I'm someone I'm not."

And with that, the dating begins. At first, some of the students — especially the boys — seem a little reluctant. It's as if they don't want to be seen having fun in math class. But that lasts just a few minutes. Soon, everyone is bounding in and out of pairs, laughing and struggling and encouraging each other.

That afternoon, in Algebra II, Hagan comes up with a creative way to get her students to memorize the quadratic formula. She sings it to the tune of "Pop Goes the Weasel."

The polynomial speed-dating madness begins.

The polynomial speed-dating madness begins.

Elissa Nadworny/NPR

Their assignment: Sing the formula — from memory — to a teacher, a family member and a third person of their choosing. And witnesses have to sign a form proving it happened.

"She really tricks us into learning," says sophomore Jake Williams. "There's so much fun involved in the classroom and the learning part that we actually understand it and grasp it."

"You do puzzles and all kinds of stuff," says senior Krissy Hitch. "So it doesn't even really seem like you're learning. But then, when you take the test, you realize: 'Wait, when did I even learn all this stuff? Where did that even come from?' "

Junior Taylor Russell came to Hagan's class a skeptic:

"I have never, ever liked math. But this year, I really love math."

Making it fun matters. Algebra is high-stakes. A student who can't pass the state test can't graduate. Hagan even changed her grading system to make sure students know the math.

"You either get an A, a B, or a Not Yet," explains junior Ainsley Flewellen. "It's impossible to fail. She makes it where you can't not pass her class."

Hagan's no pushover. If a student bombs a quiz or an assignment, he has to do it again. And again. Until he gets an A or a B. But he's not struggling alone. Hagan is always there to help.

"She'll stay after school really, really late with you and help you with it. I've had to do that multiple times," Russell says.

That explains why, at lunch, students come to Hagan's empty classroom just to hang out or ask her for help with an assignment — even if it's for another teacher's class.

"She wants her students to be successful," says fellow teacher Melinda Parker, who can't say enough about Hagan. "Oh, we love Sarah. She works so hard. And we got her in Drumright. We got her in Drumright, Oklahoma!"

Sarah Hagan in a rare moment at home.

Sarah Hagan in a rare moment at home.

Elissa Nadworny/NPR

Parker does worry that the young math teacher could burn out. Hagan admits — sometimes — the work wears her down.

"Yeah, there's days where I complain. And the people I complain to think I'm insane because I haven't left this place. But these kids deserve better."

And so she stays, at least for now. Even in her scant free time, Sarah Hagan doesn't really leave the classroom. She writes a blog about teaching.

She calls it: "Math Equals Love."

Copyright 2015 NPR. To see more, visit http://www.npr.org/.

Transcript

MELISSA BLOCK, HOST:

Sarah Hagan teaches math without books and with color and things you can hold. She gets the kids in her classes out of their seats. This is just a part of what makes her one of the NPR Ed team's 50 great teachers. The team is profiling innovative teachers from all over the country. Sarah Hagan is just 25 years old, a high school teacher in Oklahoma. NPR's Cory Turner went to meet her and see her passion for math in action.

CORY TURNER, BYLINE: It's easy to miss Drumright, Okla. Less than 3,000 people now live in the faded oil town, and the highway humps right around it. There are no stop lights, no movie theater or bowling alley anymore, just a clutch of small houses and hearty businesses. There's a funeral home and a Family Dollar and a Dollar General. That makes it hard enough to attract good teachers, says Judd Matthes, the principal at Drumright High School. But it gets worse.

JUDD MATTHES: We don't pay a lot (laughter) for our beginning teachers. If you go next-door to Arkansas, they're about $10,000-a-year starting salary difference.

TURNER: Which made him wonder why a National Merit Scholar, who'd gotten a full ride to the top-notch University of Tulsa, would want to start her teaching life in a place like Drumright, earning just over $30,000 a year. Sarah Hagan's answer...

SARAH HAGAN: Well, they offered me a job, and it was April and I hadn't graduated yet. And they said come work here.

TURNER: That was three years ago.

HAGAN: The first time I saw my classroom, it was the most depressing thing I'd ever seen. The walls weren't all painted one color. There was no dry-erase board. There were no bulletin boards.

TURNER: And the floorboards did this.

(SOUNDBITE OF FLOOR CREAKING)

TURNER: They still do that, but the rest of the room is now a riot of color. Decorations hang wall-to-wall, floor-to-ceiling, and after each school year, Hagan tears them all down and starts over. Again, Principal Matthes.

MATTHES: It's real bright (laughter). When I walked in this summer, I said, whoa, you went and decorated, didn't you? She'd spent all summer decorating her room.

TURNER: To Hagan, visuals matter. She has a math jewelry collection, including a necklace with a pi-shaped pendant - as in 3.14. More importantly, she's remarkably self-assured. When she arrived at Drumright, the school had ordered new textbooks, but Hagan had already decided as a student teacher that she wasn't going to use textbooks.

HAGAN: I don't want to be stifled by that. I mean, I teach a lot of things in totally different order than a textbook would.

TURNER: To her, the average math book was itself a problem to be solved.

HAGAN: So I decided we were going to make our own textbooks.

TURNER: She didn't tell anyone that. She just left the new books in their boxes. Instead, in a trigonometry lesson, she uses stuff like this...

HAGAN: My flowerpot over there's a circle.

TURNER: And this...

HAGAN: I have a roll of tape that's a circle.

TURNER: And my personal favorite...

HAGAN: OK. So is our spaghetti going to be able to be the length of the radius of our hula hoop?

TURNER: Yeah, spaghetti - it's all part of Hagan's DIY approach to learning. As for the textbooks they make, they start as blank composition notebooks. Each day, Hagan hands out a lesson she's written herself or open-sourced from other teachers. It's usually printed on colored paper and requires some kind of hands-on work - drawing, coloring, cutting out a puzzle in algebra.

HAGAN: OK. So let's cut as much as we talk.

TURNER: There's even some basic origami. Students then glue the results into their notebooks. Eventually, the books look like some dog-eared, bulging relics from an Indiana Jones movie. Hagan argues, if students are allowed to be creative, they're more likely to remember what they've learned.

HAGAN: The point is that we shouldn't have to be like, oh, yeah, there's that chart on page 763 that tells me how to, you know, classify something. They should think, oh, that's on that blue paper that we did a few days ago and I doodled in the corner or whatever.

TURNER: When I visit Hagan's morning Algebra I class, the handout is orange.

HAGAN: So you need to put a four in the circle where it says unit. And our title of our unit is "Polynomials."

TURNER: After walking the class through the differences between cubic and quintic, binomial and trinomial, Hagan shakes things up.

HAGAN: So you guys ever gone speed-dating?

UNIDENTIFIED STUDENT #1: No.

UNIDENTIFIED STUDENT #2: Of course, it's how we met.

TURNER: Math speed-dating - she hands the students slips of paper with a polynomial written on one side and its name on the other. She demos with a football player.

HAGAN: He has a card that says negative six. So I would go up to Colton (ph) and I would say constant monomial. And you're going to check my answer.

TURNER: And it's important, Hagan tells them, not to let wrong answers linger.

HAGAN: Because I don't want him thinking I'm someone I'm not.

TURNER: And with that, the dating begins.

UNIDENTIFIED STUDENT #3: Are you a (laughter) sixth degree trinomial?

UNIDENTIFIED STUDENT #4: I don't know how to say the first part, but I know the last.

UNIDENTIFIED STUDENT #3: Sixth degree trinomial.

UNIDENTIFIED STUDENT #4: Yeah, trinomial. OK.

TURNER: Clearly not everyone got everything right, but everyone did have fun. That afternoon in Algebra II, Hagan came with a creative way to get her students to memorize the quadratic formula.

HAGAN: (Singing) X equals negative B plus or minus the square root of B-squared minus 4AC all over 2A.

UNIDENTIFIED STUDENT #5: That was good.

(APPLAUSE)

HAGAN: Thank you.

(APPLAUSE)

TURNER: The assignment - sing the formula from memory to a teacher, a family member and a third person of their choosing. And witnesses had to sign a form proving it happened. See, fun is Hagan's secret weapon.

JAKE WILLIAMS: She really tricks us into learning.

TURNER: Sophomore Jake Williams.

JAKE: There's so much fun involved in the classroom and, actually, the learning part that we actually understand it and grasp it.

KRISSY HITCH: You do, like, puzzles and, like, all kinds of stuff. So it doesn't even really seem like you're learning. But then when you take the test, you realize - you're like, wait, when did I even learn all of this stuff? Like, where did that even come from?

TURNER: That's senior Krissy Hitch. And junior Taylor Russell came in a skeptic.

TAYLOR RUSSELL: I have never, ever liked math, but this year, I really love math.

TURNER: Making it fun matters. In Oklahoma, algebra is high-stakes. If you can't pass the state test, you can't graduate. Hagan even changed her grading system to make sure students know the math. Here's junior Ainsley Flewellen.

AINSLEY FLEWELLEN: So you either get an A, a B or not yet. So you kind of - it's impossible to fail pretty much. Like, she makes it where you can't not pass her class.

TURNER: Hagan's no pushover. If you bomb a quiz or an assignment, you do it again and again until you get an A or a B. The key, says Taylor Russell, is you're not struggling alone. Miss Hagan's there.

TAYLOR: She'll, like, stay after school, like, really, really, late with you and help you with it. I've had to do that multiple times.

TURNER: Which explains why, at lunch, students come to Hagan's empty classroom just to hang out or ask her for help with an assignment, even if it's for another teacher's class.

MELINDA PARKER: She wants her students to be successful.

TURNER: Fellow teacher, Melinda Parker.

PARKER: Oh, we love Sarah. She works so hard, and we got her in Drumright. We got her in Drumright, Okla. (laughter).

TURNER: But Parker worries that the young math teacher could burn out. Hagan admits, sometimes, the work does wear her down.

HAGAN: And, yeah, there's days where I complain (laughter). And the people I complain to think I'm insane because I haven't left this place. But these kids deserve better.

TURNER: And so she stays, at least for now. Even in her scant free time, Sarah Hagan writes a blog about her experiences in the classroom. She calls it Math Equals Love. Cory Turner, NPR News, Drumright, Okla. Transcript provided by NPR, Copyright NPR.

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