You just can’t hurry some things. They take time. In middle school, grasping the big ideas of proportional relationships seems to be one of those things. Students need to build an understanding of a constant rate of change and how it presents in tables, graphs, equations, and verbal representations. They need to build an understanding of what it means to have no “start-up” value in each of these representations as well. They need to explore these ideas in a little of different ways in order to make sense of it.
Because there are so many pieces to this idea, there are a lot of different places that understanding can break down. In order to know where that breakdown is happening for each student, I like to take anecdotal records. At the end of the day, I can go back and see who knows what and make decisions about what I need to do the next day to help each of them move forward. The thing is, I don’t have time to write a paragraph about each kid as I walk around the class looking at their work and listening to their discussion. I need something that just takes a second or two for each kid at any given time. To that end, I decided to create an anecdotal record form specific to proportional relationships.
I started with what I want to know my students can do.
- Recognize a proportional relationship in a table
- Recognize a proportional relationship in a graph
- Recognize a proportional relationship in an equation
- Recognize a proportional relationship in a verbal representation (word problem)
- Be able to connect proportional relationships represented in a table and a graph.
- Be able to connect proportional relationships represented in a table and equation.
- Be able to connect proportional relationships represented in a table and word problem
- Be able to connect proportional relationships represented in a graph and equation
- Be able to connect proportional relationships represented in a graph and a word problem
If students can’t identify a proportional relationship in a given representation, I also want to know if the break down is the rate of change or the y-intercept.
I came up with this Proportional Relationships Anecdotal Records form. I have one box for each student (I can use more than one page for a given period). I put the student’s initials in the box and then circle the place where a breakdown is happening. If the student is not recognizing a proportional relationship, I can write in k if the breakdown is the rate of change or the letter b if the breakdown is at the y-intercept.
I will probably use this to drive a brief review activity the following day. I will pair students to do a card sort or to use the cards to play rummy. Initially, I will pair them so that a student who has the idea down is working with a student who doesn’t. After working with the idea for several days, I may place them so that kids who are struggling with the same issue are working together. At that point, I can work with that small group to address whatever disconnect is still in place. You can get the card sort here.