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• Joanne Jacobs

# Discovering math: How do you know 75% is more than 50%?

I remember when "the new math" was new. It was supposed to teach kids to understand math, not just go through the motions. I'd just missed it, but my brother learned about Venn diagrams and a more laborious way of "carrying" and "borrowing" numbers. They had to call it something else too.

My fourth-grade teacher showed us a more laborious "new math" way to do long division. We weren't impressed.

As it turned out, "new math" did not changed the old reality: Lots of students don't understand why math works, even if they can make it work. (On the other hand, our commie competitor, "Ivan," didn't know what he was doing either.)

On Mind/Shift, Kara Newhouse talks to Staci Durnin, a sixth-grade teacher in New York, who's using a strategy that promises to get students thinking about math rather than "mimicking" how to get the right answer. The increasingly popular model was developed by Peter Liljedahl, a Canadian professor, in his book, Building Thinking Classrooms in Mathematics.

Durnin started class with a quick launch question: “You have 75% battery life on your phone or your iPad, and somebody else has one half of their battery life left. Who has more battery life? And how do you know?”

Teachers are supposed to explain for only three to five minutes -- students were new to percentages -- before students break into groups to discuss the problem, using vertical whiteboards. "Each group copied a table with three columns onto the whiteboard," writes Newhouse. "They needed to convert fractions and decimals into percentages, and vice versa. Some rows in the chart were already filled out, giving them examples."

Students began to notice patterns in the answers that were filled out.

Durnin and a co-teacher circulated from group to group, asking questions and providing information.

At the end of class, known as "consolidation," Durnin explained one group's correct answers, corrected mistakes and connected key ideas that students had "discovered themselves," writes Newhouse. Then students practiced individually, choosing between “mild,” “medium” or “spicy" problems.

Expecting students to teach each other with minimal guidance "defies the research and common sense, writes math teacher Ryan Hooper in Education Next. What's backed by evidence is direct instruction: "Teachers explicitly and systematically instruct students through tasks such as step-by-step procedures, modeling, teacher-guided practice, emphasizing foundational skills and fluency, and deliberately crafted lessons.

## 6 comentários

Darren Miller
30 de ago.

We adults are supposed to teach the children, expecting children to teach each other is malpractice.

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Bruce Smith
01 de set.
Respondendo a

Sorry, folks, but the mathematical pedagogy described in this post is exactly that used in Japan since before I read "The Teaching Gap" 25 years ago, after the Third International Mathematics and Science Study of 1995: this isn't new, and is well established, as are other, different pedagogies that also get high results; but one thing that hasn't changed is that "Students will understand percentages" has been a fifth-grade learning objective around the world for a long time now, which implies that the entire scope-and-sequence exercise of the Common Core was mishandled, and needs to be revised so as to be genuinely benchmarked to global best practices.

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rob
30 de ago.

Say whatever ugly things you want about "drill and kill", but repetition not only makes it easier to follow algorithms, but it aslo gives a person a "math sense". That math sense allows you to grasp math at a deeper level by making your grasp at the superficial level ironclad. At some point, you can "feel" the numbers.

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Darren Miller
30 de ago.
Respondendo a

It's not "drill and kill", it's "drill and SKILL".

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Andrew Grichting
29 de ago.

You have to wonder about the unceasing attempts to NOT TEACH MATHEMATICS that are always coming down from "on high". They have the evidence of repeated prior trials of this model - all have resulted in ongoing and documented poorer outcomes. The persistence in inventing new strategies that displace functional techniques without understanding why the existing models work is one of the clearest examples of Chesterton's Fence in educational research. Just to respond to this example, the assumption of pre-requisite knowledge built into this scenario will mean students with deficits will be unable to access the content. All teachers are familiar with the results of this - disengagement, masking, misbehaviour, etc.

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29 de ago.

I'm in a masters program and have a class that just started in statistics.

One professor actually spent significant time going through why A/B = 1.25 means that A is 25% bigger than B; and that if A/B = 0.8, then it is 20% less. He said he hoped by the end of the term, that would become second nature to all of us.

I turned my camera off and banged my head on the desk. (Metaphorically speaking.) The class is mostly composed of physicians and medical researchers, who should already have gotten a hang of that....back in 5th grade.

Ann in L.A.

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