Math is not just about numbers! The language of math is critical to understanding. That is part of the reason why
students with language disabilities sometimes struggle with math as well, in spite of having superior number sense and understanding.
When teaching math, it is critically important to use consistent, strategically chosen language to describe concepts and operations. It is important to think ahead and know the “big picture” of math, to avoid inadvertently using language that will cause confusion in the future.
Let me give you a non-math illustration. When my daughter was 5 years old, she wanted to play soccer. There was a need for a coach. I agreed to volunteer, even though I knew very little about soccer. The commissioner coached me and I coached the girls, and it was working out great. Then, I had this idea that I thought was brilliant, and taught the girls a strategy I named “leap frog”. Girls alternately ran forward and passed the ball to each other down the field, and finally passed it to the player waiting in front of the goal. We were unstoppable! Then, my mentor took me aside and explained that coming soon, this rule called “off sides” was going to apply, and “leap frog” was setting my team up for future frustration. You see, by not understanding the big picture of soccer, I was teaching my team a strategy that would later get them into trouble.
It is the same in math. Sometimes, teachers figure out little tricks and strategies to help their students in a particular situation, but later, that strategy causes them confusion and frustration. It is so important to keep the language consistent and know that the same language and strategies will continue to apply all through math development.
Let me give you a math example, on the positive side. When I first start teaching fractions, I know and consider what is coming up. The first fraction concept taught is parts-of-a-whole. Since I know that the next concept coming up is parts-of-a-group, I strategically choose language that will lead to a seamless transition to the more difficult concept. By strategically choosing my language, the parts-of-a-group concept can be grounded on the understanding of the easier concept of parts-of-a whole, and the language continues seamlessly throughout all math involving fractions (which is a lot of math, especially in higher level classes!)
The same goes for the much longer view. It is important to know and consider what is coming up in advanced math classes so students are set up for seamless transitions with no un-learning of carelessly chosen language that won’t apply all the way through their math careers.