I began my first day of my probability course today by asking each student individually students to do the following:

Introduce yourself to the class, say your feelings about math using a scale from 1 – 10, and use the word “probability” in a sentence about yourself.

The probability question led to some pretty interesting answers, so I will list a couple of them here:

There’s a proabability that I’ll pass this class

There is a probability that I will struggle with this class

There is a probability I will that I’ll start college in the fall

Aside from noticing their lack of positivity, these quotes told me that my students don’t really have an understanding of the word probability. It seems that they are substituting the word “probability” with the word “possibility.” In all of these contexts the word “possibility” would make sense syntactically, and for 3 out of 18 students to make this mistake, it seems that this might be a misunderstanding, and not just a typo.

To say “there is a probability” is not really a phrase that one would hear normally, and it doesn’t make sense in that sentence, but substituting “probability” for “possibility” in math might be a misconception that many students might not have to challenge. Students who only see the phrases “find the possibility”, or “what’s the possibility” may immediately realize that they are quantifying the likelihood of possible events and decide to do the appropriate procedure. These same students maybe confused in later math classes when see phrases like “compound probability” or “highly probable” and find themselves struggling with their conception of the word.

I tried to make a clear connection between probability and possibility while clarifying the distinction by saying “Probability is similar to possibility, because both talk about something that could happen. We use probability to take possibility a step further, and actually come up with a number that allows us to say just how likely it is for an event to happen”.

In case you’re wondering about the kids’ feelings for math, the average was about 5.9, with some 1s along with some 10s. Students share their feelings about math on the first day of class because the students get to hear and see a range of values. Some kids always love math, and others always hate it. This prompts me to give the speech where I say “I want us all to recognize that some people in here don’t like math. It’s already an uncomfortable environment for some people when they walk in the door. Let’s not make it more uncomfortable by making fun of people, being disrespectful, and separating yourself from the class experience by getting on your phone.” I hope it makes the less comfortable kids feel supported, and prompts the strong kids to consider their role in the class.

7/30 (First week of blogging in the books!) #MTBoS