## Same But Different is a powerful routine for use in math classrooms. The activity of same but different is an activity where two things are compared, calling attention to both how they are the same and how they are different.

### This apparent paradox is the beauty of the activity. I would like to highlight the precise language of same BUT different. In this analysis, instead of making a choice – am I going to prove that these are the same or am I going to prove that they are different – students are considering how two items can be both. This is a critically important distinction.

I learned about the idea of same but different years ago when working with a speech and language pathologist who specializes in executive functioning disorders for teaching children grayscale thinking. Grayscale thinking is the ability to see the world as having some middle ground versus being a world of black and white. For example, there is something between happy and sad, or in between short and long, etc. People who have trouble with grayscale thinking tend to be rigid and get stressed when life doesn’t fall into one category or another. “The problem with black and white thinking is that it usually does battle in a world that is nuanced and gray,” says Byron Williams in his article on the subject. The routine of same but different helps call attention to the features of things – and how we can connect something new to something we are already familiar with, thus helping to develop flexible gray scale thinking.

For example, think of a young child who only likes to play with HIS truck. We can compare his trucks to someone else’s truck and notice all of the ways the two trucks are the same. We can hone in on what it means to be a truck – 4 wheels, big, an overall conversation about “truckness.” With this in mind, we can say to an anxious child, “So these are both trucks. This is your truck, and this is your friends truck. They are different, but also the same. They are trucks.”

We all know someone who struggles with this type of thinking. For me, this was my son. Such conversations became the norm always pointing out how things were the same but different, such as, “We are at the beach! You know all about beaches. There’s sand, and water. We swim. But THIS beach is different. There’s a dock we could swim out to!” We were calling our son’s attention to the common features of things, making things comfortable while helping him form a connection to something new. The amazing thing was that through using this language explicitly and practicing this repeatedly, he began to do the same. He began to attend to categorical thinking and the features of things and learned to make links and connections. His world became less black and white.

### I believe having  this insight from the point of view of speech and language pathology we could profoundly impact mathematical reasoning with the routine of same but different.

One of the reasons students struggle in math is that they fail to make any connections. For some children (those lacking grayscale thinking) every concept they learn is its own entity without any connection to the larger network of mathematical ideas. Just like the young child who only likes his trucks, someone who has poorly developed number sense might see each number as its own thing, and not part of the larger number system. Ask a young child where they can find 8 on a number line to 10. If they don’t race towards the end of that number line knowing it’s near ten, but instead start at one and make their way up the number line, that could be an indication that they are lacking a systematic understanding of the counting system. They can only locate 8, for example, by considering each consecutive number starting at 1.  A mathematical conversation using the language same but different that calls attention to how a new concept in math is the same as that other familiar and comfortable concept but different in a specific way could be a tremendously useful conversation in growing that network of connections. I believe this could also reduce anxiety as children become the sense makers in the conversation.