# Grades to Grades

I teach a couple classes of freshmen. Next year they’ll take the 10^{th} grade math MCAS (our state’s official test suite) which has an awful lot of questions about data and very basic stats – bar graphs, pie charts, etc. They won’t cover that in geometry next year, so we just did a little unit in the week before winter break.

I decided to use two main pieces of information: their grades on the last test, and their year-to-date grades. At first I was worried that this would mean we wouldn’t be able to speak as candidly about how the data was distributed. But I did appreciate how it made students realize they did have to be nice about all these numbers, and we couldn’t just have a scapegoat data point to make fun of. They were very good about it.

First I used the test scores. There were 62 points on the test, which obscured the actual grades a little bit. I printed and cut out little cards to give to each group so that they could easily manipulate the numbers.

The first thing I did was to very simply ask them to find the mean, median, and mode. They definitely took advantage of the fact that they could move the numbers around. It also forced them to work together in useful ways. This was especially awesome for my class that only has 6 students in it who typically don’t like to acknowledge one another’s presence.

It might be interesting, or it might not be, to consider why some students spread all the cards out into one line, while some snaked them along on one desk. Both arrangements seem to have merit.

The next thing that I did was to explain how to make box-and-whisker plots. They’re all over the MCAS. I think having little slips of paper helped with this, since they had to find not only the median, but also the first and third quartiles. I will never understand why this is so tricky for so many students.

The last thing that I did with the slips with test scores on them was something that I stole from a blog that Dan Meyer linked to, run by Nico Rowinsky. This teacher had a small group of students arrange index cards in different ways, periodically checking in and making different recommendations. His goal seemed to be for them to make something like a histogram, and specifically for them to understand why it would be useful to arrange data in that way. I decided to do the same thing with my students more or less, but with everyone in the class at the same time. I made comments requesting students to make their arrangements easier to read quickly. I think if I do this again, I need to ask my questions differently, as I felt like I was being a little bit leading. I really should have said, “why did you do such and such.”

Something they different on in a big way was how big to make the groups. Some students went by the number in the tens column, some found the percentage score and grouped by the letter grade, and some did things that I still don’t quite follow, but are probably purposeful, but maybe not filled out yet.

The next day, I wrapped up that activity by making a worksheet using pictures I took at the end of class of the ways that a few groups students had arranged their data. Then I had a couple of questions.

I was being observed by my department head that day, so I had extra reason to be fancy:

I wanted to focus on understanding that we arrange data to let us get a sense of data without working too much, which is why I asked about what was easy to figure out, and what took work.

Firstly, they did not get into the naming thing. This might have gone better after looking at ‘circle graphs’ and other things with cute names, I think.

Secondly, they did take these questions seriously, but I was a little disappointed by how little detail they seemed to pick out. Each kid pointed out an interesting thing or two, but not much more. This was a pretty typical paper:

a) Easy to get:

more people got 50’s

b) Work to figure out:

How many 49’s there are

c) What would you change?

I would spread out the 49’s

I think it would have been more useful if I had first asked them to explain how the displays had been created, or if they could take another group of data and arrange them according to the same structure. For example, very few students noticed that in the first display, the students didn’t put everything in numerical order, which seemed obvious to me.

If I had unlimited time, it might have been nice to wrap everything up by asking students to take a final stab at their ideal way of arranging the information, and then explain why that tells people the most about the data. I definitely should have added more in about giving a final summary about the distribution of grades in the class.

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