Wednesday, July 9, 2014

Common Core Math: Is it wrong to want to know which way is right?

The latest New York Times article on the Common Core State Standards begins with a refreshing acknowledgment of the frustrations that the Common Core has been causing among those most directly affected by it. The article opens with a description of a mother who, because of "the methods that are being used for teaching math under the Common Core,” plans to home-school her four children:

Ms. Nelams said she did not recognize the approaches her children, ages 7 to 10, were being asked to use on math work sheets. They were frustrated by the pictures, dots and sheer number of steps needed to solve some problems. Her husband, who is a pipe designer for petroleum products at an engineering firm, once had to watch a YouTube video before he could help their fifth-grade son with his division homework.
“They say this is rigorous because it teaches them higher thinking,” Ms. Nelams said. “But it just looks tedious.”
The article also mentions
viral postings online that ridicule math homework in which students are asked to critique a phantom child’s thinking or engage in numerous steps, along with mockery from comedians including Louis C. K. and Stephen Colbert.
But then the Times proceeds to regurgitate the Common Core's tired rationale:
The new instructional approach in math seeks to help children understand and use it as a problem-solving tool instead of teaching them merely to repeat formulas over and over. They are also being asked to apply concepts to real-life situations and explain their reasoning.
When did math students ever repeat formulas over and over again? And when did students ever not apply concepts to real-life situations? And when did “explain your reasoning,” ubiquitous to American Reform math and rare everywhere else, become the one, one-size-fits all path towards, and the one, one-size-fits measure of, conceptual understanding?

The Times also cites employers, who “are increasingly asking for workers who can think critically”:
Employers “want a generation of people who can think and reason and can construct an argument,” said Steven Leinwand, a researcher for the American Institutes of Research.
But if there’s even one employer out there who (a) is looking for mathematically competent employees and (b) has taking a close look at a representative sample of Common Core-inspired math assignments (as compared with traditional math assignments), I have never seen him or her cited anywhere.

Citing global tests like the TIMSS and PISA, in which American children lag behind those in other developed countries, the Times also claims that “traditional ways of teaching math have yielded lackluster results.” The Times does not mention that many of America’s current students grew up, not with traditional math, but with Reform Math, and that the countries that outperform us in math have eschewed our types of reforms in favor of more traditional ways of teaching math.

Having carefully omitted these facts, the Times proceeds on to argument by authority:
The [Common Core] guidelines are based on research that shows that students taught conceptually retain the math they learn. And many longtime math teachers, including those in organizations like the National Council of Teachers of Mathematics and the National Council of Supervisors of Mathematics, have championed the standards. …
Math experts say learning different approaches helps students develop problem-solving skills beyond math.
Do these math experts include (a) any actual mathematicians who have looked at representative samples of Common Core-inspired math assignments or (b) anyone who has conducted or reviewed studies that actually address this question empirically?

As for the not-at-all-surprising claim that “students taught conceptually retain the math they learn,” this does not support Common Core-inspired math in particular. Traditional math also teaches conceptually.

The Times cites one authority in particular, Linda M. Gojak, the former president of the National Council of Teachers of Math:
“I taught math very much like the Common Core for many years.When parents would question it, my response was ‘Just hang in there with me,’ and at the end of the year they would come and say this was the best year their kids had in math.”
For what it’s worth, I’ve never met a single parent who has said that. But given how much Reform Math has watered down the actual math, it’s easy to imagine that some of the least mathematically inclined children experience their first year in Reform Math as their “best year in math.”

The Times ends up suggesting that most of the frustrations amount to growing pains—the pains of a transition to a whole new curriculum, or as one superintendent puts it, “a shift for an entire society.”

The article notes that, besides the issues of winning over skeptical parents,
textbooks and other materials have not yet caught up with the new standards, and educators unaccustomed to learning or teaching more conceptually are sometimes getting tongue-tied when explaining new methodologies.
Frederick Hess, directory of education policy studies for the American Enterprise Institute, puts it better:
“It is incredibly easy for these new instructional approaches to look good on paper or to work well in pilot classrooms in the hands of highly skilled experts and then to turn into mushy, lazy confusing goop as it spreads out to classrooms and textbooks.”
To its credit, the Times article, besides including Hess among its authorities, acknowledges that certain subpopulations may have particular problems with Common Core-inspired math:
Some educators said that with the Common Core’s focus on questioning lines of reasoning and explaining answers, the new methods were particularly challenging for students with learning disabilities, or those who struggle orally or with writing.
“To make a student feel like they’re not good at math because they can’t explain something that to them seems incredibly obvious clearly isn’t good for the student,” said W. Stephen Wilson, a math professor at Johns Hopkins University.
(It's refreshing to see an actual math professor cited here.)

Besides the language impaired, there are the mathematically gifted:
Some parents of children who have typically excelled at math find the curriculum laboriously slow.
In Slidell, an affluent suburb of New Orleans, Jane Stenstrom is concerned that her daughter, who was assigned to a class for gifted students as a third grader last year, did not progress quickly enough.
“For the advanced classes, it’s restricting them from being able to move forward,” Ms. Stenstrom said one recent afternoon.
Her daughter, Anna Grace, 9, said she grew frustrated “having to draw all those little tiny dots.”
“Sometimes I had to draw 42 or 32 little dots, sometimes more,” she said, adding that being asked to provide multiple solutions to a problem could be confusing. “I wanted to know which way was right and which way was wrong.”
Surely some people will see this child, however gifted, as overly rigid in her mathematical reasoning and problem solving skills. But here's my take: when it comes to mathematics, (or, for that matter, engineering, accounting, pharmaceuticals, surgery, piloting airplanes, operating machinery, or, dare I even say it, educating our children), "wanting to know which way is right" is a pretty reasonable desire--especially when it comes to one of the Common Core's main obsessions: all those "real-life situations."

9 comments:

Jaime H said...

This is my favorite quote from Professor W. Stephen Wilson

“There will always be people who believe that you do not understand mathematics if you cannot write a coherent essay about how you solved a problem, thus driving future STEM students away from mathematics at an early age. A fairness doctrine would require English language arts (ELA) students to write essays about the standard algorithms, thus also driving students away from ELA at an early age. The ability to communicate is NOT essential to understanding mathematics. There will always be people who think that you must be able to solve problems in multiple ways. This is probably similar to thinking that it is important to teach creativity in mathematics in elementary school, as if such a thing were possible. Forget creativity; the truly rare student is the one who can solve straightforward problems in a straightforward way.”

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Katharine Beals said...

Anonymous,
I was going to ask you how your comment is relevant to this post (i.e., are learning disabilities bogus?), until I looked around and noticed that you've cut and pasted it all over the Internet. However, I've decided to leave it up as a curiosity.

Katharine Beals said...

Jaime H,

Thanks for sharing. I love the idea of ELA students writing essays about the standard algorithms!

Deirdre Mundy said...

When I was young, teachers always said that math was a universal language--- you could sit down with someone from another country and do math together, even if you didn't speak each other's language.

How is math a universal language if you have to write an essay on every concept?

gasstationwithoutpumps said...

I agree and disagree with your final comment 'Surely some people will see this child, however gifted, as overly rigid in her mathematical reasoning and problem solving skills. But here's my take: when it comes to mathematics, (or, for that matter, engineering, accounting, pharmaceuticals, surgery, piloting airplanes, operating machinery, or, dare I even say it, educating our children), "wanting to know which way is right" is a pretty reasonable desire--especially when it comes to one of the Common Core's main obsessions: all those "real-life situations." '

In engineering,it is important to recognize when a method is correct, but it is also very important to realize that there is not just one way that is right. Indeed, engineering is all about finding right ways to solve problems, and there are few design problems that have only one solution. Students who are locked into "finding the answer" make poor designers and engineers.

And engineers do need to learn how to write up their designs and their mathematics in a way that makes it clear that they have done it correctly. So the goals of Common Core are good at heart.

But…

There is little to write about mathematics in a meaningful way at the level of elementary school students, and even few high school teachers can tell what is important to write about and what is just drivel from a practical standpoint. So mandating that those who are clueless about what is important to write teach students to write something is unlikely to have a positive outcome.

Barry Garelick said...

The Common Core goals may be good at heart but teaching expert behavior to novices is a waste of time. Period.

See quote from Steve WIlson posted by Jaime H above.

lgm said...

Sounds like the 9 yr old girl is asking for the grading rubric, not a single 'right' method. Unfortunately students that are advanced are being asked to provide explanations appropriate for students who are developmentally delayed, rather than atbtheir instructional level. That this gal has an advanced class available is an accomplishment, my district got rid of advanced sections in the elementary when nclb started.

Jim said...

Regarding the comparison of US student's PISA results with other countries -

US white students have scores pretty comparable to scores of generally white countries. US Asian Americans (who are not all East Asian) compare well to East Asian countries. US Hispanics outscore nearly all Latin American counties.

Aggregate comparisons between countries with very different demographics are not very useful. Taking US demographics into consideration the PISA results indicate that the US has an excellent public educational system.