A new set of guidelines in the US have turned children into “little mathematicians” who don’t know how to do actual math

November 26, 2012
November 26, 2012

A few weeks ago, I wrote an article for TheAtlantic.com describing some of the problems with how math is currently being taught. Specifically, some math programs strive to teach students to think like “little mathematicians” before giving them the analytic tools they need to actually solve problems.



The second email came from a teacher in another state:



To read newspaper coverage of the new standards, you’d think they were raising the bar for math proficiency, not lowering it. “More is expected of the students,” one article declares. “While they still have to memorize or have fluency in key math functions and do the math with speed and accuracy, they will have to demonstrate a deeper understanding of key concepts before moving on.”

But what does this mean in practice? Another recent article explains, “This curriculum puts an emphasis on critical thinking, rather than memorization, and collaborative learning.” In other words, instead of simply teaching multiplication tables, schools are adopting “an ‘inquiry method’ of learning, in which children are supposed to discover the knowledge for themselves.” An educator quoted in the article admits that this approach could be frustrating for students: “Yes. Solving a problem is not easy. Learning is not easy.”

With 100 pages of explicit instruction about what should be taught and when, one would expect the Common Core Standards to make problem-solving easier. Instead, one father quoted in the aforementioned article complains, “For the first time, I have three children who are struggling in math.” Why?




This brings us now to the final three pages of the 100-page document, called “Standards for Mathematical Practice.” While this discussion is short, the points it includes are often the focus of webinars and seminars on the new Common Core methods:

    1. Make sense of problem solving and persevere in solving them
    2. Reason abstractly and quantitatively
    3. Construct viable arguments and critique the reasoning of others
    4. Model with mathematics
    5. Use appropriate tools strategically
    6. Attend to precision
    7. Look for and make use of structure
    8. Look for and express regularity in repeated reasoning

These guidelines seem reasonable enough. But on closer inspection, these things are essentially habits of mind that ought to develop naturally as a student learns to do actual math. For example, there’s nothing wrong with the first point: “Make sense of problem solving and persevering in solving them.” But these standards are being interpreted to mean that students “make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution.”

This is a rather high expectation for students in K- 6. True habits of mind develop with time and maturity. An algebra student, for instance, can take a theoretical scenario such as “John is 2 times as old as Jill will be in 3 years” and express it in mathematical symbols. In lower grades, this kind of connection between numbers and ideas is very hard to make. The Common Core standards seem to presume that even very young students can, and should, learn to make sophisticated leaps in reasoning, like little children dressing in their parents’ clothes.




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