# What are our Goals in Class?

I have spent the past 25 years teaching at schools that go all the way from kindergarten through high school. I often tell my students that I have a crazy dream that it would be great experience to work with a group of them starting in kindergarten and move up together all the way to high school graduation. We’d REALLY get to know each other and be able to reference ideas/habits/experiences together. I am in no way equipped to teach younger children and I know this is a crazy mental exercise anyway but I do think often about habits and language that my students arrive at my classroom with that I wish they did not have. For example, when faced with the distributive property I always hear what I refer to as ‘that four letter F word’, when faced with a fraction on both sides of the equation I always reflexively hear ‘cross multiply’ [even when there are other factors in a problem] These are just two silly examples of fights that I am too often willing to wage in the classroom. A more interesting one, and one that has deeper implications, popped up in my class last week.

I often have a problem projected on the board when class starts. It is rarely a problem directly linked to the day’s tasks, I just want to get the brains moving and, hopefully, get some conversations started. This year in my Calculus Honors class I have noticed a discomfort with some of the classic word problems of the sort that pop up in Algebra II regularly. This is not a big surprise, these kind of word problems don’t get practiced regularly and there are all sorts of gut feelings that don’t always yield correct solutions. When I throw up a class opener problem I usually make a quick reminder of ‘Hey, look, there is an interesting question on the board!’ On the day I am thinking of, the question I posed was this one:

The first minute or two of each class involves a couple of gentle reminders to attend to the question that is posted and this day was no different. Another minute or so later I heard two remarks almost simultaneously that caught my attention. One student, a boy named Parker, said ‘I know the answer’. He did, by the way, know the answer correctly. Another student, a girl named Maya, said ‘I know how to do this.’ She did, in fact, know how to do the problem but had not arrived at the solution as quickly as Parker did. These remarks instantly caught my attention and I said to the class ‘Did you hear the difference between those two remarks?’ I repeated them both but did not follow down a conversation because I was not sure yet what I really wanted to say. This blog post is an attempt to unpack what I want to say.