Mary Johnson, an 81-year-old educator in the District, shows the beginnings of her flowchart that helps students logically solve math problems. (Jahi Chikwendiu/The Washington Post)

Mary Johnson is not a person you’d typically associate with the future. She is 81 and talks about teaching math in the District during the 1960s as if little time has passed.

But week after week, Johnson still drives from her Clinton home to the after-school program at the Washington Tennis and Education Foundation campus in Southeast and, according to officials at the program, consistently lifts underperforming math students to grade level and beyond. This month, she received a copyright for a diagnostic test that she says can assess specific gaps in students’ math knowledge in minutes.

She’s now working with the foundation to raise money to digitize the test, which includes eight to 10 math problems for each grade level, so that it can be used in schools throughout the country.

“I believe all students can learn math if they understand the laws,” Johnson said. “If a student masters a problem on my test, I don’t care what test they take, they master it.”

Johnson, who has a doctorate in math education from the University of Maryland, looks far younger than her 81 years. She’s petite, but she can still move around the classroom, from the white board to the students and back with ease, making eye contact with each student along the way.

Johnson demonstrates her mathematics diagnostic test with Mason Edmond, 10, and Ange Sery, 10, at the Washington Tennis and Education Foundation. (Jahi Chikwendiu/The Washington Post)

“Why?” she repeatedly asks 10-year-old Ange Sery as she sits with him and another student reviewing how to add fractions.

Johnson’s methods rely on drilling in the basic concepts of math — or, as she puts it, “the laws of math” — and ensuring that students understand why each step of solving a problem is necessary.

If a student doesn’t conceptually understand that they can’t add apples and oranges together, for example, how will they know what to do a few years later when they see different variables in an addition equation in algebra class.

When, after a few tries, Ange says the word “factors” to explain what he needs to do before he adds the two fractions, Johnson’s soft voice goes higher and her words spew out faster as she praises the boy’s correct answer. She keeps stuffed folders documenting the progress of each student, and after 60 years of teaching, still delights in a student figuring out a math problem.

“Her teaching is more unique,” said Ange, who has worked with Johnson for more than two years and says he now receives mostly A’s in his fifth-grade math class at Watkins Elementary School. “If you don’t know anything about math, she takes her time and teaches you.”

Johnson was raised in Norfolk and says her mom declared that Johnson would be a teacher even before she was born. In high school, she would finish her entire math textbook halfway through the year and then teach her classmates the work. They liked the way she clearly explained the concepts, and they requested that the teachers allow Johnson to lead the class instead.

“I always dreamed I would be a teacher, but I never dreamed I would teach thousands of children all over the world,” she said.

After graduating as valedictorian, she went on to attend Virginia State University, where she earned her degree in less than three years.

Her résumé in the decades since then hits on most facets of education: She has taught at traditional schools and colleges, participated in research projects, developed curriculums, and co-founded the Washington Math Science Technology Public Charter in the District in 1998, where she served as principal for a few years. Her husband, Eugene Williams — also a prominent educator in the area who previously served as an assistant principal at Paul Laurence Dunbar High School — works with students in the Washington Tennis and Education Foundation after-school program in reading.

Throughout her career, Johnson has encountered educators who have adopted her methods, which include flowcharts that students use to break down every step of the problem so that teachers can see where students are struggling.

“She’s non-threatening and builds students’ confidence,” said Arlene Maclin, a professor at Morgan State University who has worked with Johnson for decades. In 2003, Maclin had recruited a class of low-income African American students for an optical engineering program at Norfolk State University, but the students’ math skills weren’t up to college standards. She brought in Johnson to lead an intensive two-week math workshop and, according to Maclin, nearly all of the students were ready for calculus by the end.

“She doesn’t teach tests; she teaches them how to think logically,” Maclin said.

For now, Johnson is focused on teaching children at the after-school program and expanding her Success in Learning Math Approach, which she’s dubbed Silma. She has trained hundreds of teachers across the country in her methods, instructing them on how to employ her diagnostic tests and quickly compose a student profile from them.

The diagnostic tests are brief, she says, but students are required to show their work, and Johnson says each question is carefully designed to test a student’s grasp of multiple concepts.

“The turnaround she’s done with these students is stunning,” said Eleni A. Rossides, executive director of the Washington Tennis and Education Foundation, which serves low-income students throughout the District. “She understands how to deliver the information, how to teach it. People come away from working with her, like, ‘Wow, I get it.’ ”

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