Math education can be difficult-for students and teachers.
Those difficulties are often magnified when students have learning disabilities such as dyscalculia that can make it difficult to learn math facts or dyslexia that can make it hard to read word problems. Or maybe they are learning English and struggling to grasp math concepts in a new language.
In interviews with Education Week, experts-practitioners and researchers-offered perspectives on how to make mathematics instruction best serve those student populations. Their advice clustered around three themes:
Emilia Frias, who has taught English-learners and students with disabilities in special education and general education classrooms, has long understood the struggles her students face.
A former English-language learner who was also identified with learning disabilities as a child, the Magnolia, Calif., school system special education teacher did not learn to read until 6th grade-and her difficulty with reading often carried over to math class, where word problems left her frustrated and puzzled.
Now that she's on the other side of the equation, Frias uses carefully constructed lessons to meet the disparate needs of her 3rd and 4th grade students with moderate to severe learning disabilities. She is always looking for the individual strengths that will carry them further, and she doesn't shy away from making words central to her lessons.
During a recent live-video session, Frias used trays filled with home-baked cookies to deliver lessons on multiplication for some, addition and subtraction for others, and counting for those who are still working on one-to-one correspondence-the early math skill of counting each object in a set.
"I had questions for each of those levels: 'How many were in tray 1?' 'How many were in tray 2?' 'How many were altogether?'â" Frias explained. "Then I had questions like, 'Which one had more; which one had less?' And these are questions that I'm typing out for parents to be asking their kids."
Just like their peers, her students need to know how to use math in life, and that includes mastering math words and phrases, Frias said.
"I want to give them all the vocabulary and terminology, and I would do the same thing with my English-learners," Frias added. "If we don't, they're missing out on a lot of opportunity that their peers have exposure to."
Cathery Yeh, an assistant professor of teacher education at Chapman University in Orange, Calif., works alongside Frias and other teachers in the Magnolia schools, helping them develop lesson plans and strategies for teaching math to English-learners and students with disabilities.
To reach all their students, math instructors at all levels of K-12 education must shed the belief they only teach math, Yeh said.
"Math teachers-we often see ourselves as content-area teachers. Like our job is to be knowledgeable about math and not necessarily responsible for promoting language development," Yeh said. "But we have to support learning math through language and learning language through math."
Part of the challenge in supporting learning lies in being cautious about the overly broad labels attached to students who receive special education or English-learner services. The labels often fail to focus on the strengths or particular needs of students, experts say.
"These kids show up, they have labels" given to them by schools, said Judit Moschkovich, a professor in mathematics education at the University of California, Santa Cruz. "Then we make all kinds of assumptions."
U.S.-born English-learners could excel or struggle with math. Immigrant students sometimes come to U.S. schools with more math knowledge than their U.S. peers. Some refugee students have missed years of formal schooling.
But however much educators need to pay attention to such differences, they should drop the misconception that English-learner students need to be proficient in the language to learn math, Moschkovich said.
"It takes a long time to learn a second language, and we can't wait," she said. "Even as they're learning English, they are able to learn mathematics and even communicate mathematically."
Unwarranted assumptions are also made about students with disabilities. Brad Witzel, an education professor and special education program coordinator at Winthrop University in South Carolina, said educators who teach math should define expectations for students based on their skills, not their labels.
"We don't fully understand the cognitive power of children with disabilities," Witzel said. "We're so stuck on deficit skills we end up focusing on what they can't remember rather than what the concept to be learned is."
A problem that can compound such deficit thinking is that assessments and individualized education programs for students with disabilities often fail to provide a clear picture of whether students have difficulty with reading comprehension or number sense-or both, Witzel said.
A student identified with a learning disability in math could be a struggling reader or a fluent one. If the difficulty is with both math and reading, text-heavy math books make the problem worse, and explicit vocabulary in math class becomes even more critical, Witzel said.
"I worry about how we can tease [math and reading disabilities] apart," he said. "We need to be much more precise."
Melissa Brennan, the 2020 teacher of the year in Orange County, Calif., strives not to oversimplify lessons, she said, because her students-many of whom have autism spectrum disorder-deserve and can handle more.
Now that schools are shut, she's delivering distance-learning lessons on counting, place value, and estimation that parents can replicate with items they can find lying around the house.
With the help of Yeh, Brennan, who teaches in the Magnolia schools, began to shift her thinking about a decade ago from what her students could not do to how math could help sharpen the focus on what strengths they have.
"Society has to change our notions around who can and cannot do math," Yeh explained. "The goal isn't for our children to memorize procedures, but to develop ways of knowing and thinking mathematically that can help support them in problem solving and reasoning for life."
While visiting Brennan's class when school was still in session, Yeh watched her teach a lesson to her students, who have mild to moderate learning disabilities, on evenly dividing a group of items like pretzels or toys. Educators call this a "fair share" lesson, and it introduced her nonverbal students to the mathematical concepts of division and fractions.
The everyday activity of sharing familiar objects put those concepts within reach for students with IEPs that mandate their math instruction focus on counting, Yeh said. Students can often do more, but to make that happen, educators must be sure the learning connects to their daily lives.
With her strengths perspective, Brennan has even discovered a bright side to the school closures that have forced her and her students into distance learning. As she works with parents at home, she finds many begin to really understand what their children are capable of.
"They could be good at pattern recognition or really understand the principles of the lesson even if they haven't memorized math facts yet," the teacher said.
Frias, Brennan's colleague, learned long ago what she was capable of, and sometimes that understanding is her most valuable lesson to students. In her first special education teaching job, Frias taught in a juvenile-justice facility, where many of her students had learning disabilities. When she explained to them that she also has visual- and auditory- processing disorders, many of them dismissed her claims.
Frias had her mother dig through boxes with her school papers to find a copy of an old IEP. She brought it to class as proof and to deliver a message to her students with disabilities.
"Yes, it is harder for us," Frias said, "but it doesn't mean we can't do it."