Creating Misconceptions in Math by Teaching Concepts Too Soon

Teaching math concepts too early can create mathematical misconceptions that

are difficult for students to overcome. That's because often times, when concepts are taught too early, they are taught rotely, where students are shown a set of steps to follow to solve a problem. When a teacher attempts to correct the misconception by building understanding of why the rote way works, students often respond that they already know how to do it. With this kind of mindset, new learning is difficult if not impossible.

I see this very often with the standard algorithm for addition and subtraction. Students are taught early on to carry a one for addition For subtraction they're taught to cross out the number in the place to the left, put a one next to the number to the right and over the crossed out number write the number that's one less. Where's the math? Where's the understanding of place value that makes these steps work? Yet this is what many textbooks have our first graders doing.

Math is a sense making activity, just as reading is. We need to make a commitment to our students that we will help them understand math, not just be able to do math.