 Hello, my amazing math minds, and welcome to this week's Math Tip Monday. My name is Heidi Rathmeyer at ESU 8, and today we are going to have another installment of 13 rules that expire. This is an article by Dr. Karen Karp, which addresses how teachers can perhaps lead students to some misunderstanding of math concepts by using imprecise vocabulary or relying just on shortcuts and tips or tricks and not really promoting the conceptual understanding of math. So today, the phrase or the phrases that we're going to talk about have to do with the equal sign, which students sometimes are led to believe is an operation, like find the answer or write the answer or it makes something. The problem with this is, well, it expires pretty early, and I think a lot of teachers use it even past first grade. So let's see where some of this confusion may come from. So on my iPad, we can see we have some simple problems. The first one we would encounter certainly early on in the primary grades, where we would have seven plus two, and the mistake comes in when teachers might say makes something, which gives the impression that the equal sign is the operation as opposed to the plus sign. So obviously what we want here is nine. Now, really, the equal sign is a relational symbol. We are just showing that what's on this side of the equal sign as the same amount as what's on this side of the equal sign. And here's when you know your kids are using the equal sign as an operation as opposed to a relation when you come to this bottom problem, where we have seven plus two equals a blank plus five. Now if you have a kiddo that is treating the equal sign like an operation, they're going to put a nine in there. So if you see that, you know that's the problem. They're treating it as an operation as opposed to a relational symbol. So obviously the answer we want here is four so that the amount on this side is the same as the amount on this side. So this is a very good example where you can understand a student's misconception based on the way the problem is set up and their understanding of how this equal sign is used. So I think that's really important because I know when I get into the algebra that I might teach with eighth graders is often we see equations set up like this where kids think everything needs to be done on the left hand side and they forget that this is a relational symbol because then when they are given this set up they get really confused and they don't know what to do because they think all the doing needs to happen on this left hand side. So I encourage you with the younger kids to not only write problems like seven plus two equals something, but to write it as seven plus two equals something over here so that they understand that the equal sign is not about an operation. It's about a relationship between what's on one side and what's on the other. So when we get to algebra they don't run into this issue here with this scenario where they just don't even understand what to do when it's exactly the same thing as they would have done on this top one. So those are just some examples of some misconceptions that students can obtain based on some of the vocabulary we might use in the classroom or even just how some problems are set up and how we solve some problems. So as you're working with equations in your classroom just be very careful with the vocabulary that you're using be precise with the vocabulary and make sure we're emphasizing the conceptual understanding of just what an equal sign really represents. So until next time, stay well, be kind.