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  • Writer's pictureJoanne Jacobs

How to teach math well: There are wrong answers

Engineering, computer science, accounting, finance and medicine will not be options for people who couldn't find the lowest common denominator in fourth grade (or understand why they were looking for it), warns Education Trust in an analysis of the 2022 math scores from the National Assessment of Educational Progress.


Overall, 26 percent of eighth-graders are "proficient" in math, 35 percent are in the "basic" range and 40 percent are "below basic."


A majority of black, Latino and low-income students score "below basic." Only among Asian-American students are a majority (56 percent) in the "proficient" range.


Credit: National Assessment of Educational Progress

Students need "evidence-based" instruction to have a shot at advanced math classes and the STEM pipeline to high-paying careers, concludes Education Trust.


There's a good chance they're not getting it, writes Holly Korbey in Putting the 'M' in STEM. Many school leaders and teachers aren't aware of the "evidence base for helping students learn math," she writes on her new Bell Ringer site. Furthermore, many popular teaching methods are not backed by evidence they increase math learning.


For example, “productive struggle” -- giving students an unfamiliar problem to tackle with minimal teacher guidance -- is popular. In theory, students will "figure out an answer on their own, leading to a deeper or perhaps more creative understanding than if the teacher had shown them how to solve it," writes Korbey. But no significant evidence supports its efficacy.


A growing body of scientific evidence points in the opposite direction, she writes. Students learn more when "the teacher explicitly shows students how to work a new kind of problem, then carefully guides them through examples where they can catch and correct mistakes."


Teachers often use productive struggle or inquiry learning "too soon, before students have acquired a base level of skill," says researcher Kati Maki. Students don't know enough to struggle productively or inquire intelligently. They get confused and frustrated.


A new study in Australia found "explicit, step-by-step teaching with consistent feedback" led to stronger outcomes in math and reading for high school students. Explicit teaching was linked to higher test scores and higher levels of "confidence and perseverance."

15 Comments


Heresolong
Heresolong
Mar 05

"the "false starts" involved in struggling with challenging tasks without adequate support or guidance lead to lost instructional time and inefficiency." Emphasis mine.


Even the studies that are cited state "provide modified inquiry learning with built-in scaffolds and support for student success." Were the authors actually able to find schools or teachers who were using a "productive struggle" strategy without support or guidance? They talk mostly in generalities.


I agree with the general thought but to compare "productive struggle", defined as "without adequate support or guidance" to "direct teaching" is a bit disingenuous because it isn't necessarily comparing two methods of teaching as used by good teachers.


Here's my general strategy for developing Law of Sines using an example from a…


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humphrey
Mar 05

Least common multiple (LCM), or greatest common divisor/factor (GCD/GCF)? Probably doesn't matter, as the kids probably don't know the difference between a factor and a multiple.

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Bill Parker
Bill Parker
Mar 05

I was learning LCD, GCD, and fractions, percentages, place value and exponential notation in elementary school (grades 4-6), and we had math drills all the way through 7th grade as I recall...(this was from 1972-1976 mind you)


We used rote memorization for basic facts, grouped students by ability and yes, some students actually flunked and went to summer school in my day...

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rob
Mar 04

I'm no professional educator, but it seems to me that "productive struggle" sounds an awful lot like "you see if you can figure it out while I sit over here and play with my phone".

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Heresolong
Heresolong
Mar 06
Replying to

If you were a terrible teacher that might be what it is. If you are any sort of good or caring teacher, not even close. Read my example above.

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Malcolm Kirkpatrick
Malcolm Kirkpatrick
Mar 04

Search "Project follow through".

Discovery learning is to Math instruction what Whole Language is to Reading instruction.

Colleges of Education should be demolished and the ground sown with salt.

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