If you had to look up every word in a dictionary in order to finish reading a newspaper article, your brain might end up sacrificing the deeper meaning of the story. Could relying on a calculator to do math have a similar effect?
Ding’s research focuses on strategies that teachers can use to help children who are struggling with math. She makes the case that memorization of basic math facts, such as multiplication tables, is key because it allows children to store information in their long-term memory, and frees up their working memory to tackle more complex problems. For example, adults don’t have to actively remember their own names or birthdays because those facts are readily available in their long-term memory, which works on auto-retrieve.
“If you have to decode every word you are reading, what happens? You don’t have reading comprehension at all because your working memory is occupied by saying each letter. Your attention can’t go to the who, the how, the where, and the what,” she said.
“Math facts are the same. We have to memorize or automatically retrieve all this mathematical vocabulary so kids have this kind of fluency. Then their brain–their working memory–frees up to understand more complicated problems.”
She said that a lot of progress has been made treating the memories of children with special needs in the last 30 years, thanks to new pharmaceutical treatments and behavioral therapy, paired with changes in family and environment. Improving a child’s long-term memory allows them to use working memory to tackle more challenging tasks.
“Behavioral therapy early on can change the connectivity of the brain. So when we change the environmental stimulation and we change the way we approach the kids, many of them learn new skills.”
Ding has detailed her research in two upcoming papers: “Involvement of Working Memory in Mental Multiplication in Chinese Elementary Students,“ and “Working Memory Load and Automaticity in Relation to Mental Multiplication, under review for publication in the Journal of Educational Research. For the studies, she and her co-authors recruited fourth and fifth graders of differing academic levels to complete a series of arithmetic problems.
The study found that even if a problem involves more steps, if it comes with automatic retrieval to students, they do better. When asked to complete a two-step equations that they do not have automatic retrieval, like(25×3)×4, students stumble more frequently compared to when they tackled three-step problems that they have automatic retrieval, like 25×10+25×2.
A common critique of the American education system is “we try to dig three hundred miles wide and only half a mile deep,” she said. When Ding moved from Beijing to Iowa, she said she was taken aback by the thickness of children’s textbooks, coupled with the multiple topics teachers must cover in a short period.
“Teachers are running around like crazy trying to cover one topic to another. But then we don’t have enough time reserved for practice, for rehearsal, to give kids the time to make sure we have developed fluency in this most basic stuff. Your memory needs time to practice,” she said.
One way to address this is with drills. Ding remembers hating drills when she was a student but now appreciates them because they helped her develop a basic math vocabulary in her long-term memory.
Ding is working with engineering teachers to identify and aid low-performing students. She said it’s common for low-achieving engineering students to exhibit slow processing speeds, which leads them to struggle to complete exams in a timely fashion. Most of time, the automatic retrieval of math/engineering facts is very weak in these students.
To make matters worse, Ding’s evidence shows they tend to pick just one strategy to solve all problems, which results from a “very weak strategy flexibility.” They probably just simply do not have a wide range of effective strategies banked in their long-term memory and are not proficient with “which strategy fits what problem situation”.
“Even if they find the right strategy, when you ask them to calculate, they calculate it wrong. When the execution is problematic as well, it’s almost a double deficit,” she said.
“When you have lots of strategies that are well learned and banked in your long-term memory, then you free up your working memory. If a task has steps 1 through 10, and you can automatically retrieve steps 1 through 5 from memory, then you have what you need to do steps 6-10.”