# To Accumulate a Rate — Integrate!

Teaching High School Mathematics

# How accurate is your stick?

The following is just a rambling list of thoughts as they came to me and has not been edited or revised:

A student definately learns a certain amount during the course of a semester in a course. Whether their learning is small or large it is something we as teachers must attempt to measure. We observe when we watch students work and when we ask students questions, but that information is difficult to quantify and we need to post a grade that reflects the amount of material the student has demonstrated they understand. So, we give points for homework, quizzes, and tests and record the percent students get correct. An A represents that a student has typically earned 90% or higher in the course, a B 80%-90%, and so on. However, if a student earns 89% and earns a B+ for the course, how accurate is that grade? Did I make a mistake? Should they really have earned a B or an A- or even an A?

How long is the hallway outside my classroom door? I give 5 students a yardstick at different times and ask them to measure the length of the hall. as they mark 1 yard and slide the stick to start measuring the 2nd yard it’s possible that they didn’t quite line it up correctly. By the time they get to the end of the hall they have moved and lined up the yardstick many times resulting in many little errors combining to a hallway measurement that is off. How far off? hmmm. Well, it depends on how good you are at lining up the stick.

When I grade a student’s test there are two things I think about. 1. How consistently do I grade all the problems across all my students. 2. How well does this test reflect the material that was to be learned.

For consistency I grade all the first pages at one time and then go on to the second page, etc.

I feel like I can control my consistency pretty well, but everyone is prone to errors. In my class an 89% is really 89% +/- some percent error. I wonder what my “some percent error” is. Let’s say my “some percent error” is 3%. 2 students who both have an 89% in my gradebook could really be 86% and 92% students. This makes me feel a little bit uncomfortable.

Inevitably at the end of the semester a student with an 89% comes in and asks me to change their grade. They’ll do “anything,” because their transcript can’t handle a B+. Let’s say I let them do something and this improved their grade to an A-. If this student is really an 86% student they are getting an A- when a B really describes what they know. However, if this student is really a 92% student then they are now getting an A- when their knowledge is an A and otherwise would have earned a B+. I’ve never once had a student ask for their B+ to be changed to a B.

This situation is only reflecting the grading in my classroom. Does the grade in my Calculus class reflect what my student knows compared to other students in Calculus across the state or country? This is a much harder question to solve. We can take the AP test and then they’ll be compared across the whole country. I’m not sure I like that solution because it is one test on one day and doesn’t score for understanding, but scores on the ability to do a certain type of questions quickly and learning the AP lingo. — Maybe the similarity in textbooks on a topic help keep the content consistent enough.??

When I give a grade, I’m telling the world what our school thinks a certain amount of knowledge in a course is worth. If I give a student an A in a course and they cannot perform in college, it tells that school that our A is not really worthy of an A.