One prompt from teacher Andy Kotko, and his 24 first-graders at Mather Heights Elementary School jump into action.
Arms shoot skyward. Voices rise in a chorus of answers. And later, at Kotko’s behest, little hands pat their own backs.
It’s math time, a period in which Kotko guides students in developing intuitive math skills through positive reinforcement, visualization and patience.
Last month, Kotko, 38, became one of two elementary teachers in California to receive this year’s Presidential Award for Excellence in Mathematics and Science Teaching, part of a broader national bid to improve math and science education. He had been an award finalist twice before.
The award comes amid a national shortage in teachers, especially in math and science. Earlier this year, the Palo Alto Learning Policy Institute report issued a report, “Addressing California’s Emerging Teacher Shortage,” showing that the college pipeline for math and science teachers fell by nearly a third during the four years ended in mid-2015.
This week, Kotko heads to Washington, D.C., for an awards ceremony and a visit to the White House.
Mather Heights Elementary serves 460 students in a middle-class subdivision southeast of the former Mather Air Force Base. Of those, 130 are enrolled in the Academy for Advanced Learning. Students qualify for the magnet program based on testing, evaluations and teacher input, according to Principal Sara Parenzin.
Kotko, who has a bachelor’s degree in physics from California State University, Sacramento, said he starts math instruction with simple fundamentals to ensure that each student is grounded in concepts before he adds difficulty.
“Before you know it, they’re doing challenging math, but it feels very comfortable,” he said.
He said he typically uses math vocabulary with his students that he would use for a college class because, within reason, his young students will rise to the level that is taught. “Before long, they adopt it and start using it as well.”
Kotko started one lesson this week with a review of previous work.
What’s the difference between a value and an expression? He answers his own question: “An expression has one value,” he told students Thursday. “But it breaks the value into different parts.”
A value of 5 broken into two parts, for example, can be expressed as 1 and 4, or 2 and 3, or 5 and 0.
Before you know it, they’re doing challenging math, but it feels very comfortable.
First-grade math teacher Andy Kotko
He directs the next question to students. If you know two parts of a three-part expression, say 2 plus 2, but you don’t have the third, “is that an open or a closed problem?”
A smattering of first-graders offer their answer: “Closed,” the students said, stretching the word in a unifying chorus.
“It’s closed, because there is only one answer,” he said in agreement.
After the class review, Kotko added a bit of complexity, introducing students to “open problems,” in which more than one right answer exists.
If the value is 5, and it is expressed in three parts, and one of the parts is the number 2, what are your choices for the other two parts? “You need to make a decision,” he said. “Do you want 1 and 2? Zero and 3? Two and 1?”
Students paired with classmates and rearranged plastic cubes to help visualize possible answers.
Noelle Long, 6, was eager to share her math skills.
“Ten minus 10 equals zero. Nine minus 1 equals 8,” she said.
While Noelle called math her favorite subject, her future remains something of an open problem: “I want to be a scientist, or a baby sitter or a mom, or a ton of things.”
Erik Kennedy, who lives in the neighborhood, said two of his daughters had Kotko as their teacher. One is now in second grade, he said, and the other is in sixth grade at a middle school. Kotko, he said, imparts an infectious desire to learn and never appears to be overwhelmed.
“It seems like he has every minute available to take care of almost every student individually,” Kennedy said.