Blog Post

Clear Math Misconceptions to Make Room for New Knowledge

CORE’s Excellence in Education Blog post this month is on the importance of clearing out math misconceptions in order to make room for new knowledge. See what happened during one math professional learning session when students were certain about the wrong right answer.

You Can’t Park New Knowledge in a Space Already Occupied by a Misconception

How many times have you tried to explain something to someone and just can’t break through because he or she seems to be holding on viciously to some misinformation or misconception? Oddly enough this puts me in mind of a recent experience I had at a school while conducting math professional learning. The principal was late to our meeting and came to the meeting agitated because he could not park in his reserved spot. He had agreed to let a teacher at the school use the spot two days earlier while he was away all day at district meetings. Unfortunately, the teacher’s car broke down and could not be moved from the parking spot. Two days later the teacher still had not arranged a tow truck to remove the car. So often I find with students that a wrong idea is a lot like this broken down car. It occupies a space reserved for the right knowledge, and unfortunately the right knowledge cannot be parked in the spot until the wrong knowledge is towed away.

I remember reading a case study about a teacher’s experience re-teaching fraction multiplication to her class. The case study is in a great old book called, Fractions, Decimals, Ratios, and Percents, Hard to Teach and Hard to Learn? [i]. One student in this class thought that the way to multiply mixed numbers such as 6 34 x 5 13 was to multiply the whole numbers (6 x 5), then multiply the fractions (34 x 13), and then add the two together for the final answer. This procedure made sense to him because it followed a procedure similar to adding fractions. Using this student’s method, 6 34 x 5 13 = (6 x 5) + (34 x 13) = 30 + 312 = 30 14 rather than the correct answer of 36. The teacher went over again the right way to multiply mixed numbers and explained why the distributive property applies in this situation. The student understood the procedure and could repeat the correct procedure. However, in the end he said as he walked away, “I still don’t see why my way doesn’t work.”