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  • Writer's pictureJoanne Jacobs

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.

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6 Comments


Malcolm Kirkpatrick
Malcolm Kirkpatrick
Sep 24, 2023

We have known since 1977 that direct instruction outperforms "discovery" methods of Math instruction.

Search "Project Follow Through".

"Evaluation of the project occurred in 1977, nine years after the project began. The results were strong and clear. Students who received Direct Instruction had significantly higher academic achievement than students in any of the other programs. They also had higher self-esteem and self-confidence. No other program had results that approached the positive impact of Direct Instruction. Subsequent research found that the DI students continued to outperform their peers and were more likely to finish high school and pursue higher education."

As with the Phonics versus Whole Language dispute, proponents of demonstrably failed methods sail on, completely indifferent to evidence.

Subsidized school…

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Miller Smith
Miller Smith
Sep 21, 2023

Baltimore City, Maryland has been in the news lately for 18 high schools having not a single student test proficient in math. Blaming the teachers seems to be the mode of the media.


The teachers have to follow the policies that are given to them by the school system's educational leadership. Here are those policies:


All students have the right to an unlimited number of unlawful absences. At no time can a student be failed for not showing up to school.


All classwork must be given 100% if it is turned in on time, complete, and a "good faith effort" as has been exerted by the student. Good Faith Effort is evidenced by time on task, effort to find or…


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Guest
Sep 21, 2023

Like I said in another comment in another post: the ed world is run by English majors. How many "math education professors" can pass a math test themselves? "Math education professors", like Jo Boaler don't have degrees in math (hers are in psychology). This is where journalists need to step up. When you're interviewing a "math education professor" ask the f***** what the highest level of math they've taken, and put it in your article. I've heard Boaler claim "I use maths every day", making it sound like she's some engineer. But the interviewer doesn't call her out.

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Guest
Sep 25, 2023
Replying to

One eye-opening summer I taught an upper-division statistics course to a batch of math ed majors. None of whom understood how to use calculus to optimize continuous functions. Don't even ask what happened when I showed them ordinary least squares using matrices.

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Guest
Sep 20, 2023

Wait a second -- you mean that you can use the Pythagorean theorem for problems other than making boxes? Why didn't anyone tell me this??

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buy
Sep 20, 2023

Apparently, water is wet.


Ann in L.A.

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