First, do Harm

Hippocrates’s quote, “First, do no harm” is the tenet of the practice of medicine.

When it comes to teaching math, sometimes, it’s more effective to “First, do harm”.

Before I teach a child a new concept, I probe to see where the child’s understanding is. Sometimes, I learn a child has had a deep-seated misconception about the topic, I need to first shake her confidence. I need to first, do harm. Until I can shake the child’s confidence that her deep-seated (and wrong) understanding of a topic, the child is not likely to pay attention to the proper way to do something. You get this right? When we are confident the way we do something works, we are not as open to new ways of doing it.

Many 4th/5th graders think that 1/2 + 1/3 = 2/5. They’ll give you a convincing explanation that that’s how they have been adding since first grade. 1 + 1 = 2 and the denominators 2 + 3 = 5. It’s a mistake to bush off their deep-seated conviction and ask them to replace it with the proper way to add fractions. You surely could try, and feel good that you’re doing a great job explaining things, oblivious to the child’s clinging to her belief and letting your words roll down her back like water down a duck’s back.

It’s more effective to first, do harm. I ask the student to shade half of a circle, and 1/3 of another circle. Then I ask them to shade 2/5 of a circle. Then I ask them to look at what they drew and ask them, “If you add this piece (1/3) to this piece (1/2), should you get more than a half, or less than a Hil?” Student: More. Me: Is 2/5 less than a half or more? Student: Less. Me: Does it make sense that you added to a half, and you end up with less than a half?”

That should shake the student’s confidence that her initial thinking has a problem. I love confounding children like this. I love rattling them. You know why? When they are rattled, unsure, they are more open to new ideas.