One challenge while working with scatter plots and bivariate data is the gulf between analyzing data in graph form, and putting it in graph form to analyze. It’s not explicitly in the standards, but I it has revealed many of my students’ skill deficits.

One big one is figuring out the scale to use on a scatter plot. Many of my students can find an appropriate scale intuitively, and most of the rest can do it with a bit of reasoning and trial and error–and that’s how I would love for all of them to do it. But a number of students cannot find an appropriate scale, and freeze up when asked to try. So I reluctantly gave them a rule — divide the maximum by the number of lines on the coordinate plane you want to use, and round up. For instance, if you need to represent data from 0 to 217 on 18 lines, divde 217 by 18. Get 12.something, and round up — 15 or 20 will both work well.

Anyway, I had students working with a data set that ranged from 900 to 10,500, and the grid on the page had 13 lines. One kid was totally frozen. I prompted her through finding the maximum and the amount of space she had before realizing she had already done that work and divided. When I told her what she already knew — that a scale of 1,000 would work well — she said, “but what about 900?”.

It took me a moment to realize that she had gone through all of the reasoning I was directing her through, and she had a misconception I hadn’t even considered. Much of the data we work with is in the range of 1-20, and we don’t see many valuesÂ *below* the scale of the axes. It’s not a misconception that a student with strong number sense would be likely to have, but it makes a ton of sense from the perspective of a student trying hard to reason about something she doesn’t have intuition for. But she found a scale, and looked back at the data–and how could she graph a point at an x-value of 900 when her scale was 1,000? Where would it go?

Anyway, I told her that her reasoning for the scale was great, and that she should fill out the scale, and then try graphing the point. That was all she needed, and she was off and running.

I was pretty humbled by my inability to predict student misconceptions from students who have the most trouble with math. As I have been throughout this year. That is the skill that, as a new teacher, I didn’t have at the beginning of the year, and I’m still just developing. But I did an injustice to this student today. My first reflex was to dumb down pieces of the question that my student had already comprehended — doing her a disservice in the process, sending the message that I didn’t think she could do what she had already done, and done faithfully given my instruction.

This really makes me nervous about my ability to instruct in what I used to think of as basic skills — I think this student would be better served by struggling and figuring this question out on her own. What if she would learn better by getting less direction from me, failing at first, but eventually owning her own understanding, in a way that she clearly didn’t given what she showed in class today? I don’t know. And I don’t know how to facilitate that kind of understanding. Things I have left to learn…