Depth, Not Speed

Jan 14, 2018 | Newton

I've always been dismayed at how much anxiety school classroom Speed math facts tests cause my tutoring students.  Today, I met a 2nd grade student, Jeremy  (not real name), who impressed me with his problem-solving skills.  He was able to see that Half of 61 is Half of 60 plus Half of 1.  He was able to tell me that if 2 lemons are needed to make a glass of lemonade, how many glasses of lemonade 10 lemons will make.  He also figured out 45 + ___ = 103 by methodically stepping up to 50, to 100, then adding 3 more.  YET, this student is flunking Speed math facts at school.  That was the reason his parents brought him to Mathnasium.  I was just so saddened that this child, who has exhibited above-grade-level mathematical thinking skills and logic is being labeled slow and "below-average" in class.

Here's what 2 famous math educators have to say about Depth vs, Speed.

Depth Not Speed
Jo Boaler (Stanford University):  "Many people incorrectly believe that being good at mathematics means being fast at mathematics. It doesn’t and we need to dissociate mathematics from speed. When we value fast computation (as many classrooms do) we encourage a subset of learners who compute quickly and discourage many others, including deep slow thinkers who are very important to mathematics. We no longer need students to compute fast (we have computers for this) we need them to think deeply, connect methods, reason, and justify. Here are some suggestions for dissociating maths from speed and encouraging a broader range of students."

David Vaillencourt, Math Teacher:  "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. "

Watch this video as well: