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  • Writer's pictureJoanne Jacobs

Don't make math harder than it needs to be

Struggle is supposed to be good for math students, writes Greg Ashman on Filling the Pail. Telling them how to solve problems is supposed to be bad. He thinks that's silly.


The "latest excuse for bad maths teaching" is the "claim that explicit, procedural approaches to mathematics . . . will make students anxious" by requiring "right" answers, he writes.


Photo: Chris Liverani/Unsplash

But a new study shows that explicit instruction reduces anxiety, Ashman writes.


Fifth graders saw the same video of a math lesson, then were asked to solve a problem. One group were shown the worked example of a similar problem while the other group did not.


Math-anxious students who didn't see the example reported more "mind wandering" during the test, while anxious students who saw the example were able to focus, researchers reported. That lead to "improved learning as measured three days later."

In addition, "students who reviewed worked examples were less worried than controls on average, which was related to learning."


It makes sense that trying to solve problems without knowing how would cause anxiety, Ashman concludes.


Timed math drills -- the "mad minute"of addition or multiplication -- are controversial too, writes Hechinger's Jill Barshay on Proof Points.


The National Council of Teachers of Mathematics urges teachers to “avoid” timed tests that might cause math anxiety, she writes. "But advocates say speed drills help children memorize math facts, freeing up their brains to tackle more challenging math problems."


The U.S. Department of Education urges timed activities to help students build fluency in a 2021 guide for elementary teachers. The What Works Clearinghouse "found 27 studies to back timed practice," considered “strong” evidence.

In one 2013 study, struggling first graders received math tutoring three times a week and were split into two groups. One played untimed games to reinforce the lessons. The other was subjected to speed practice, where the children worked in groups to try to answer as many math flashcards correctly as possible within 60 seconds. Each time they were encouraged to “meet or beat” their previous score. After 16 weeks, the children in the speed practice group had much higher math achievement than the children who had played untimed games.

Children in the speed group got a lot more practice, which builds long-term memories, said Lynn Fuchs, a Vanderbilt education professor who led the study.


"While the causes of math anxiety are debated and mysterious," writes Barshay, "many in the pro-drill camp suspect that children might feel less math anxiety if they became more proficient in the subject, which is something that drills might help accomplish."


Ed Week's Sarah Schwartz talks to elementary teachers about the importance of building math fluency.

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11 Comments


Guest
Jun 01, 2023

Are you still opposed to the use of calculators in the classroom?

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Guest
May 31, 2023

Barbie was right -- math really is hard!


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Joanne Jacobs
Joanne Jacobs
Jun 01, 2023
Replying to

When I was an op-ed columnist, I wrote a column defending Barbie. Math is hard for many people. We can do hard things, if we're willing to put in the work.

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Guest
May 31, 2023

A very good math teacher would demonstrate more than one way to solve the problem. In addition, a good math teacher would take harder problems and show/encourage the students to reduce the problem to something they know how to solve.


One of the problems with teaching math now if the pointlessness of homework. Even calculus/differential equations can be solved using websites. Why assign homework when there is no guarantee that the student is actually going to do the work?

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Guest
May 31, 2023
Replying to

Depends on what you mean by "more than one way". Teaching different ways can be confusing or beneficial. It depends on how different, the purpose of learning the different methods, and when the different methods are introduced. Usually, you want mastery of one, proven method to predominate.


Sometimes, it's essential to introduce an alternate way. Doing derivatives using limits gives way to the simpler: pull the exponent down then reduce it by 1.


(Some years ago, without the slightest bit of thought behind it, I subtracted two multi-digit numbers by adding up, instead of subtracting down. I hadn't been taught that, but somehow my brain put it together when I wasn't looking. In the end, I think it's a cleaner…


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Malcolm Kirkpatrick
Malcolm Kirkpatrick
May 31, 2023

As ever:

  1. "What works?" is an empirical question to which an experiment will deliver more valid and reliable information than will Divine (bureaucratic) inspiration. In public policy, "experiment" means competitive markets in goods and services and/or federalism (subsidiarity, many local policy regimes).

  2. Search "Project Follow-through". Direct instruction (i.e., "teaching") outperforms discovery methods of Math instruction.

  3. Enrollment determines budgets. System administrators have a direct financial incentive to maximize residence time in the system (i.e., to waste students' time).

  4. Children are not standard. One size and style of shoe will not fit all feet. One curriculum and pace and method of instruction will not fit all brains. Competitive markets create an incentive to identify and serve niche markets that tax-subsidized, rule-bound State…

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Guest
Jun 01, 2023
Replying to

I love seeing Malcom Kirkpatrick's comments where ever they appear. Thanks, MK.


No school sports program would ignore the example, drills, practice, correction, and rewards processes that have afflicted our math programs. Can you imagine a football team where all the plays have to be figured out, during the game, by the players themselves?

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Guest
May 31, 2023

"... children might feel less math anxiety if they became more proficient in the subject". Maybe, just maybe, what we call "math anxiety" usually just means being crappy at math.

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Guest
Jun 02, 2023
Replying to

Once again, someone who believes that everyone can master calculus is they have the right instructor. Which means someone who has never tried to teach math to a large group of people.

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