The Teaching of Math

This week’s article summary is Speed Drills Teach Kids to Hate Math.

The article relies heavily on the research and work of Stanford professor Jo Boaler—a number of Trinity students and faculty have taken her online course on how to better approach and study math.

To Boaler, the danger of speed/memorization tests is they often lead to math anxiety and loss of confidence in math.

It’s important to note that Boaler is not against the eventual automaticity of math facts; it’s that she opposes our traditional manner of getting there.

Boaler contrasts how we have traditionally taught math with how we teach children how to read and write--through application and often with no time limit: in fact, the longer you take to write, the better.

My guess is that Boaler would say that schools need to--as Trinity is doing—give as much attention to the pedagogy of math as the content of math.

Joe

--

Timed math drills and rote memorization won’t make kids better at math. Students learn math best when they approach the subject as something they enjoy.

“There is a common and damaging misconception in mathematics—the idea that strong math students are fast math students,” says Jo Boaler, a Stanford University professor of mathematics education. Fortunately, adds Boaler, the new national curriculum standards known as the Common Core Standards for K-12 schools de-emphasize the rote memorization of math facts. Still, the expectation of rote memorization continues in classrooms and households across the United States.

Number sense: While research shows that knowledge of math facts is important, Boaler says the best way for students to know math facts is by using them regularly and developing understanding of numerical relations. Memorization, speed, and test pressure can be damaging, she says. On the other hand, people with “number sense” are those who can use numbers flexibly. For example, when asked to solve the problem of 7 x 8, someone with number sense may have memorized 56, but they would also be able to use a strategy such as working out 10 x 7 and subtracting two 7s (70-14). In fact, in one research project found that high-achieving students use number sense, rather than rote memory, and low-achieving students do not. The conclusion was that the low achievers are often low achievers not because they know less but because they don’t use numbers flexibly. “They have been set on the wrong path, often from an early age, of trying to memorize methods instead of interacting with numbers flexibly,” she writes. Number sense is the foundation for all higher-level mathematics, she noted.

Math anxiety: Boaler says that some students will be slower when memorizing, but still possess exceptional mathematics potential. “Math facts are a very small part of mathematics, but unfortunately students who don’t memorize math facts well often come to believe that they can never be successful with math and turn away from the subject.” Prior research found that students who memorized more easily were not higher achieving. Using an MRI scanner, the only brain differences researchers have found are in a brain region called the hippocampus, which is the area in the brain responsible for memorizing facts—the working memory section. According to Boaler, when students are stressed—such as when they are solving math questions under time pressure—the working memory becomes blocked and the students cannot as easily recall the math facts they had previously studied. Some estimates suggest that at least a third of students experience extreme stress or “math anxiety” when they take a timed test, no matter their level of achievement. “When we put students through this anxiety-provoking experience, we lose students from mathematics.” Boaler contrasts the common approach to teaching math with that of teaching English. In English, a student reads and understands novels or poetry, without needing to memorize the meanings of words through testing. They learn words by using them in many different situations—talking, reading, and writing. “No English student would say or think that learning about English is about the fast memorization and fast recall of words,” she adds.

Strategies, activities: In her paper, “Fluency without Fear,” Boaler provides activities for teachers and parents that help students learn math facts at the same time as developing number sense. These include number talks, addition and multiplication activities, and math cards. Importantly, she says, these activities include a focus on the visual representation of number facts. When students connect visual and symbolic representations of numbers, they are using different pathways in the brain, which deepens their learning, as shown by recent brain research. “Math fluency” is often misinterpreted, with an over-emphasis on speed and memorization, she says.