Do you remember learning your times tables as a child? And what about “Minute Math”? Timed math quizzes and drills are commonly used as classroom tools to reinforce basic concepts like addition, subtraction, multiplication, and division. But according to Stanford professor and education scholar Jo Boaler, these teaching methods can actually do more harm than good.
Boaler’s recent paper, Fluency Without Fear, turns a critical eye on the use of rote memorization in elementary math classrooms. She stresses the importance of number sense – the ability to conceptualize numbers and their relationship to one another – as the core mathematical skill which students need most. In Boaler’s view, the emphasis on memorization and quick recall robs students of opportunities to develop their number sense. A student who is trained to instantly know that 6 x 7 = 42, for instance, will not have to think it through and make the connection that 6 x 7 must be 7 greater than 5 x 7, so 35 + 7.
In other words, math should be about comprehension and “fluency” with numbers, not memorization.
As Boaler discusses in her paper, number sense is important because studies have shown that students who use it do better academically in math classes – which is due, in part, to the fact that conceptualizing numbers in this way makes them easier to work with, so students with poor number sense are at a disadvantage. Moreover, number sense is critical for higher-level mathematics concepts. A student who cannot apply flexible thinking to real numbers will have even more difficulty when it comes to variables.
Though Boaler makes excellent points, it is exceedingly unlikely that times tables memorization will be abolished anytime soon – it is a firmly entrenched component of most math curricula, and it does have certain undeniable advantages. But the use of memorization and drills in the classroom doesn’t necessarily mean that your child is doomed never to learn good number sense. Parents can play an important role in helping children learn how to think about numbers. When your child asks a basic mathematical question, rather than simply stating the answer, guide them through figuring it out for themselves. What’s 11 + 13? Why, it’s just the same as 10 + 10 + 1 + 3. And 12 x 12? That’s just 12 x 10 + 12 x 2. By taking every opportunity to encourage your child to work out their own answers, you can help them to develop the skills they’ll really need to understand and excel in mathematics.
If you want to take more comprehensive action to help your child develop number sense, Boaler includes a selection of useful exercises at the end of her paper. If your child seems to be actively struggling with number sense, you can also get more involved instruction and skill development from a tutor.
You can read more about Boaler’s position in her paper, linked above, and at the US News and World Report.