We welcome a trend away from an era of anti-intellectualism where teachers “tell” students what they need to know or how they need to do something and then monitor their regurgitation or rote practice of the skill.
There is a push to require students to explore concepts and processes on their own: to figure it out for themselves. Some attribute this shift to the new Common Core State Standards and its associated assessments that require students to do “more thinking, evaluating and explaining of why they chose their answer.”
We say: Hallelujah! That’s because we believe that the foundational purpose of formal schooling should be intellectual growth and improved quality of thinking.
Sadly there is also a trend of backlash against what many are painting as “new math” or overly complicated ways of teaching math. The chief strategy used to lend credibility to the complaints is citing engineers, retired math teachers and confused parents as those who are against learning mathematics in a deeper way. They long for a return to students memorizing a teacher-explained single way to solve problems. Political pundits disguised as journalists are joining in the mud-slinging and some states such as Tennessee are postponing the adoption of the new assessments.
Our hope is that we use more research in this debate. The retired math teacher in this article says that, in his opinion, it is not age appropriate to ask a 9 year old to think about the “why” behind solving math. Here’s a researcher who might disagree: J. Paul Gibson experiments with teaching basic computer coding to young children and found that 5 and 6 year olds “grasped his lessons with surprising ease”.
Arguably the most definitive work on learning comes from the National Research Council’s series called How People Learn which can be downloaded for free. They cite the results of teaching more conceptually based mathematics to hundreds of elementary-aged children from several different countries. The test results (out of 100%) are below, with the treatment group having the same amount of mathematics instruction as the control group, just taught in a more conceptual way:
| Test | Control Group | Treatment Group |
| Number Knowledge | 25 | 87 |
| Balance Beam | 42 | 96 |
| Birthday Party | 42 | 96 |
| Distributive Justice | 37 | 87 |
| Time Telling | 21 | 83 |
| Money Knowledge | 17 | 43 |
They also name three common misconceptions about mathematics that could contribute to this debate:
Misconception #1) Mathematics is about learning to compute.
Misconception #2) Mathematics is about “following rules” to guarantee correct answers.
Misconception #3) Some people have the ability to “do math” and others don’t.
If you believe any of those things to be true, then we can see why you wouldn’t like teaching the “why” behind mathematical procedures.
Another important point to keep in mind is that the industrial era is over. The argument that today’s American adults learned it a certain way and are just fine seems ridiculous given 1) the results of international math comparison tests 2) the decline in American-made products and 3) the shift from an industrial economy to a knowledge economy.
It seems clear to us from both research and our changing world that students should explore new concepts and processes first and teachers patiently wait to explain second.