As a teacher, coach, and Math Specialist, I’ve spent considerable time throughout the years engaged in conversations with students, teachers, tutors, and parents about the importance of conceptual understanding; for example, why ratio reasoning is developed in 6th grade and should not be short-circuited by the procedural teaching of cross products. “But I got the right answer”, the students would say. “They get it when I teach them cross products”, the teachers and tutors would say. “It makes them feel good when they can get right answers”, the parents would say. Notwithstanding the facts that 1. the students had no idea why they were multiplying two numbers and dividing by the third, 2. They only managed to get right answers to the simplest problems 3. They consistently misapplied the method precisely because they didn’t understand it, many continued offering this procedure to their children while the students resisted building the understanding they would need to tackle the exploration of proportional relationships to come. This scenario has been repeated for all topics at all grade levels.
So when I ran across Ben Orlin’s series How to Avoid Thinking in Math Class, I saw it as a gift to all of us out there fighting the good fight. It should be required reading for every teacher, parent, and tutor. Be sure to read to the end of the six posts – the last is the best!