Today in EMTH we learned about Sense Making, or how a teacher knows when a student is making sense of what is being taught and how to encourage it.
We started by working on an activity that we had been eyeing at over the past few classes. It had to do with hand shaking, and what I understood from the question was, that if a party was only attended by couples and some people shook hands, how was it possible for everyone to have shaken a different number of hands?
So, my partner and I began to work on it. Firstly, because of the vague question, we established a couple of assumptions, such as a person may not shake hands with him/herself, and we also tentatively added that a person likely won’t shake hands with his/her spouse. As a class we had also decided to begin with a party of 10 people, to more easily find some answer after which we might move backwards towards an unknown number of people. We created a graph to find that with these stipulations, it was not possible for everyone in the group to have shaken a different number of hands (ex. for a group of 10 people to shake a different number of hands then one must use the numbers 0-9 considering that one cannot also shake their own hand, but it is not both possible for one to shake everyone else’s hand  and for one to shake no ones ). After that we removed the assumptions to create a possible answer, but decided that there should be something better (it might be awkward for one to try shaking his/her own hand). It was then that I realized that we had assumed a stipulation without writing it: each person was only shaking another person’s hand once. Well, after that my partner and I were able to create possible scenarios in which both the original criteria (don’t shake own or spouse’s hands) were met, and everyone shook a different number of hands in total.
The activity showed more than anything that students come in with presuppositions, and so when a teacher tries to teach something more figurative or abstract, then a student might have difficulty wrapping their head around the foreign concept. So, for a student to be able to make sense of a topic, one thing a teacher might do is put it in more familiar terms, like using a real life example. When math remains abstract, not only is it difficult for many people to understand it, but because of their lack of understanding it becomes increasingly irrelevant to their lives, and then what is the point of teaching math if students are not going to use it? There will always be some math that is not applicable to the everyday lives of a lot of students, but when a teacher explains math in a way that students understand, they will be able to apply it to their lives more, and maybe even increase their overall capacity for understanding.
That is the kind of teacher that I want to be.