Depth Over Speed


Jo Boaler is a somewhat controversial figure in math education. The Stanford professor is in the ‘reform’ camp, arguing that new approaches to teaching math, that rely on a lot of group work, real-life examples and discovery should be emphasized over more traditional methods such as memorization, worked examples, repetition and the learning of key principles and facts. Back in 2012, she was accused by two academics (see here) of questionable research methods and inconsistent data in her Railside Report. For an excellent, in-depth post on the subject, see here. 

Despite the credibility storm that surrounded Boaler, she still has quite a large following. Her voice in math teaching is one of the loudest. Her opinions influence policy and make waves in education circles. When she suggested that memorizing times tables isn’t necessary for students to achieve success in math, it made headlines. It got people talking. It stirred the math pot. While many educators don’t agree with her philosophies, she continues to greatly influence the discussion on how to best teach math.

That said, like many things in education, it’s important to separate the politics and the egos from what works best. Education can sometimes suffer from too much self-righteousness. If Boaler can offer advice that will benefit math teachers, who really cares about the other noise. Leave the politics to the politicians. While you might not agree with everything Boaler says, she does offer valuable insights in her recent book Mathematical Mindsets. Sure, many are points that have been raised before, but they are worth repeating.

One of those ideas is depth over speed. The pressure to cover curriculum that many teachers feel leads to a rat race approach to math instruction. As a result, lessons are often a mile wide and an inch deep. Teachers get stressed out and students retain less as concepts are glossed over and enduring understanding is sacrificed. The train keeps moving down the track and if some get lost along the way, oh well.

This notion that mathematical skill is all about speed is just plain wrong. And yet, that’s the impression that most students have of math class. The best students are the fastest. Whoever can finish a problem the quickest must be the most capable. There is a beeline to the solution. We have been conditioned to look for easy answers, what Dan Meyer calls ‘impatience with irresolution’. To satisfy this dissonance, we rush through it to get it done. Maybe sitcoms are to blame, who knows. 

Boaler provides a telling example of her observation of a Chinese math class. With two of the top three PISA math scores, Shanghai and Hong Kong (along with Singapore) are the best in the world. It’s not even close. The assumption is that they use a lot of drill and kill instruction, where speed is valued, but the reality is much different. Students typically engage with no more than 3 questions per hour. Like mathematicians say, their work is done slowly and deeply. Justification and reasoning form the essence of math. And these take time.

We need to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn’t really relevant. 


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