Old is new in math teaching: 'You have to explicitly teach content'
Johnny can't calculate -- or order enough pizza for a group of six who each want one-third of a pie. Math proficiency, already low, plunged during the pandemic. Some math teachers are returning to explicit, systematic teaching, reports Sharon Lurye.
"For much of her teaching career, Carrie Stark relied on math games to engage her students, assuming they would pick up concepts like multiplication by seeing them in action," she writes. It didn't work very well. Then Stark, who teaches in the Kansas City suburbs, read a "Science of Math" website, and began using more direct explanation. “You have to explicitly teach the content,” she says.
There's a lot less research on effective math instruction than there is for reading, which has been transformed by the move to explicit, systematic teaching in phonics, Lurye writes. But dozens of studies support some principles:
Math instruction must be systematic and explicit. Teachers need to give clear and precise instructions and introduce new concepts in small chunks while building on older concepts.
That guidance contrasts with exploratory or inquiry-based models of education, where students explore and discover concepts on their own, with the teacher nudging them along.
Skeptics say memorizing multiplication drills and memorizing step-by-step procedures to solve problems are "mind numbing," Lurye writes. Supporters say "mastering math facts unlocks creative problem-solving by freeing up working memory. Once students know the basics, they can explore and collaborate.
Jo Napolitano has more on the controversy on The 74.
Teachers must use direct instruction some of the time, but not all of the time, says Nick Wasserman, associate professor of mathematics education at Columbia University’s Teachers College. “But it’s also really important that students have times when they are the ones being asked to think and reason mathematically. Giving students tasks for them to work on on their own — without a teacher telling them how to think — is a vital component of that.”
Students “need to understand the underlying constructs of addition, subtraction, multiplication, and division and be able to do them accurately with ease," says Elizabeth M. Hughes, associate professor of special education at Penn State. Students also "need to be able to explore new ideas and have a solid plan to solve known problems.”
Greg Ashman, a teacher and researcher in Australia, writes in Filling the Pail that explicit teaching is more efficient and effective than "immersing students in real-world problem solving." Asking students to struggle with a problem they haven't been taught to solve is frustrating and confusing for all but the most advanced students, he writes.
I have to believe that most students respond by giving up. Guessing games without clues are not "engaging."
Explicit teaching can expose students to many examples, helping them apply concepts to many contexts, he writes. Students asked to build wooden boxes using the Pythagorean theorem may conclude the theorem is good for creating boxes, but nothing else.