Teaching Students with Autism to Solve Mathematical Word Problems
Pictured above: Peggy Schaefer Whitby helps a student develop strategies for learning. | Photo by Russell Cothren
Behavior analysts working in public schools in the 1990s did not hear as much about autism as they do today. They would enter classrooms to work with children who usually were experiencing difficulty with behavior, but also demonstrated limited academic achievement. The analysts needed to figure out the best approach to educating these children.
Peggy Schaefer Whitby was one of those behavior analysts. She worked with children in the public school system who had significant behavioral challenges. She found that it worked to implement the principles of Applied Behavior Analysis to address the behavioral and communication skills of the children. Over the years, she applied them to more and more children, most of whom had been diagnosed with autism spectrum disorder.
“I loved teaching this group of kids because the strategies that I used worked so well,” she explained. “Then I realized there were no academic interventions out there.”
In early elementary school, children with high-functioning autism may be high performers. Once they arrive in middle school, though, they often hit a wall. In middle school, teachers expect more self-direction from students. The course work becomes more applied and abstract, particularly in mathematics. Children with austism often struggle in these modes of learning.
“We have an ‘I do, we do, you do’ approach.”
Schaefer Whitby is one of the few researchers investigating evidence-based strategies for teaching mathematics to children with austism. Most other research focuses on communication and social skills.
“There is a myth that children with autism are savants in mathematics,” Schaefer Whitby said. “Certainly there are people with autism who have savant-type skills, but these kids also struggle with mathematical learning. We have children who can count and memorize math facts, but struggle with application. Problem-solving also involves reading comprehension issues.”
Children can learn techniques for solving math problems. Some children experience minimal difficulty organizing the information in their minds and creating a strategy for a particular problem.
“We know that people with autism develop strategies,” Schaefer Whitby said. “They may not always develop the most effective strategies.”
Many teachers have used Solve It! to develop effective strategies for adolescent students with learning disabilities. Solve It! is a set of cognitive strategies for word-problem solving based on methods used by the best problem solvers. Schaefer Whitby applied it to students with autism.
Solve It! uses seven cognitive strategies, combined with metacognitive strategies, that essentially place the learner in the right mindset, or schema, to solve a problem. The seven cognitive strategies are: read, paraphrase, visualize, hypothesize, estimate, compute and check. Students memorize these steps using the pneumonic R.P.V.H.E.C.C. At each step the student uses metacognitive strategies of self-management, self-checking and self-evaluation.
To teach students with austism how to develop a useful approach to solving word problems, Schaefer Whitby had them watch how she solved a problem. As they “caught on” to her approach, they would solve a problem with her and, eventually, solve a problem independently.
“I embedded a rule — because kids with autism tend to like rules and will follow them — that they had to do each step,” Schaefer Whitby said.
Soon they solved problems using the new strategies without someone telling them how. After 10 days they consistently solved the problems correctly. In three weeks they applied the strategies to the general education setting. “I could see on their classroom papers where they wrote R.P.V.H.E.C.C. and checked off as they went along,” she said.
“We look at how these kids visualize and use schema.”
Students with high-functioning autism tend to read — and see the world — in a very literal and concrete manner. One of the word problems in Schaefer Whitby’s study described a person baking cookies. In this example, a student with good schema may visualize the cookies ordered on a pan, whereas a person without a good schema may draw a picture of Mom baking the cookies.
“There’s a lot of extraneous information in a word problem,” Schaefer Whitby said. “Our children have difficulty focusing on the relevant pieces.”
Solve It! requires paraphrasing to help the students identify the important facts in a word problem.
“We taught them to underline the important part of the questions, and they were able to do that,” Schaefer Whitby
said. “However, many of them struggled with putting the word problem into their own words. They wanted to repeat it exactly
as it was read.”
Children with austism may have poor schema that prevents them from visualizing what they need to solve the problem. This can occur in a simple multiplication problem. A student with good schema represents two times three as two sets of three. A student who does not have good schema may visualize two objects in one set and three in the other.
All of the study’s participants assumed, no matter the type of problem, that the order in which they entered numbers into a calculator did not matter. They followed rules and used strategies they were taught in elementary school that did not apply to higher-level mathematics.
“It is important for teachers to understand that we teach kids strategies when they are young that don’t really hold true as they get into more advanced mathematics,” Schaefer Whitby said. “We have to be careful telling kids with autism these rules because they will hold onto them and continue to use them.”
Schaefer Whitby, other researchers and autism specialists do not necessarily need to instruct students directly or continue instruction to ensure students maintain the strategies. There is another method that enables students to excel academically, even students who do not participate in research projects.
“If the child does not maintain the strategies, we look at procedural facilitation,” Schaefer Whitby explained. “I use a video model to teach the kids how to use the strategy and have it in the classroom so a teacher does not have to be there. You can use it as a video model in priming where the students watch it before they solve the problem. You can also use it as a video prompt where the students stop at each step to see how they solve the problem. My next research studies will be looking at that.”
“The research has implications for teachers and practitioners.”
More and more children are diagnosed with autism. Of all such children, around 30 percent are considered high functioning. They can attend school with the general populace, but many need cognitive strategy intervention like other students with learning disabilities.
“One of the young men that I worked with was brilliant,” Schaefer Whitby said. “He loved computers, but he only loved non-proprietary software because he can go in and change the code. So I had a 13-year-old who could do his own programming on non-proprietary software but who could not pass mathematics. What is the future for this child? If he cannot pass mathematics, he can’t get a regular high school diploma. Yet he could be the next Bill Gates.”