There must be something deeply attractive about the idea that children’s math success can simply be forced upon them. On Aug 7, yet one more opinion piece promoting drill and memorization in children’s math education was published in the New York Times. By the morning of Aug 8th is was trending in the #1 spot. In “Make Your Daughter Practice Math, She’ll Thank You Later,” Barbara Oakley argues for the importance of math in the lives of children. Unfortunately, she does so in a way that is fundamentally misinformed about both the landscape of K-12 mathematics education in the United States and the research-based consensus on learning theory and cognitive development. Also unfortunately, when an opinion piece is written by a professor, even though it is an opinion piece, the assumption is that it is based in research. People take it as truth. The stakes of this misconception are extremely high when talking about the education and futures of of our children.
Dr. Oakley makes two points that are valid:
- Having a solid foundation in math can be fundamental to a child’s future, especially in the world of STEM. Mathematics is powerful as both gatekeeper and gateway when it comes to higher education, and employment. [I would add also, democratic participation in civil society as well as many creative endeavors.]
- Research shows that all children, regardless of gender (or race, ethnicity, or class, or anything else) have essentially equivalent innate potential in mathematics such that outcomes are shaped by societal inputs and expectations, not by any biological or innate differences between groups.
She makes a third point that is also correct, but not in the way she intended it. She says that the way we teach math in the United States is harmful to all students and especially girls. It is true that traditional ways of teaching mathematics have been shown to be harmful for all students, and even more harmful for non-dominant populations, including girls. This phenomenon has been widely documented by professors of mathematics education such as Rochelle Gutierrez, Jo Boaler, and others. However, Oakley’s characterization of “the way we teach math in the America” is backwards. Whereas she says we have foregone drill and practice for conceptual understanding, our problem in the United States is understood by learning scientists to be precisely the opposite. The United States is behind other countries on international measures of mathematics performance (including PISA and others) because of an overemphasis on procedural, drill-based approaches to math at the expense of conceptual understanding. It is conceptual understanding that is the basis for complex problem-solving, a critical component of 21st Century STEM literacy. Yes, mathematics educators and education policy-makers have been working to shift the way we teach math in the United States toward practices that emphasize conceptual understanding in tandem with procedural fluency. Unfortunately, as a country, the United States K-12 education system is still a far stretch from a system that “downplays practice in favor of emphasizing conceptual understanding.”
Yes, children should have opportunities to mathematize the world around them through conversations with teachers, parents, other adults, and each other on a consistent basis. But these conversations should be based in creative and flexible work with numbers that will build number sense, pattern recognition and fluency in composing and decomposing numbers. This is distinctly not achieved through drill or rote memorization. Number theory is not introduced through recitation of the multiplication tables. Furthermore, research shows that it is precisely these drill-type tasks that teach children that math is a dull, meaningless activity, and turn many away from math at an early age, including and especially girls.
Finally, the attitude that “foundational patterns must be ingrained before you can begin to be creative” is the root of inequitable mathematics education throughout the United States. The belief that children cannot engage in meaningful and creative problem-solving tasks until they have learned how to be compliant calculators leads to education that is training for menial labor, labor that was long ago replaced by calculator technology. “More drilling,” teaching your daughter that “all learning isn’t – and shouldn’t be – fun,” and that, as a girl, there are certain things she should simply suffer through “even if she finds it painful,” will not set her up for success. Anyone who teaches children that they need to silently comply through painful experiences before they will be allowed to let their brilliance shine has no intention of ever allowing that brilliance to shine, and will not be able to see it when it does.
EDIT: A number of people have been wondering about the “research-based consensus” that I refer to above. I am in particular referencing the extensive bodies of research that came out of the research program of Cognitively Guided Instruction as well as the research produced through the QUASAR Classrooms project. I have linked each to a relevant “sample chapter” or Google Book since many of the academic articles are behind paywalls. For people who have access to academic journals, either search term should produce dozens of relevant peer reviewed articles.
*Thank you to everyone who has commented, including the comments that I have not posted. I am closing comments at this point (8.30.18).