Author: David Wees (page 45 of 97)

Educators make mistakes when grading. It happens. Sometimes we mark a student’s work lower than we should, compared to their peers, and sometimes we mark it higher than we should. The question is, what effect does this have on a student’s overall mark?

Here are some sample grades. The sample column is the original grade, the low column is a mark 1 lower than the sample, the high column is a mark 1 higher than the sample.

The overall grade was calculated here by finding the averages of the three categories (quizzes, homework, and tests – standard categories in many classes) with quizzes worth 20%, homework worth 20%, and tests worth 60% of the overall grade. These aren’t particularly unusual grades. Note, however, how wide the possible error is in the final grade, which could potentially actually range from 55.9% to 82.5%, which is a 26.6%, or a HUGE amount in any grading system.

Of course, teachers aren’t likely to mark everything low, or everything high. One could make an assumption that both of these cases are equally likely, and then instead of using the likely minimum mark, and the likely maximum mark, we could try and aim for 2 standard deviations from the mean of the possible grading outcomes. In other words, what’s a likely range?

I created a script (warning: takes a while to run in some browsers) which randomly generates a sample of 10,000 overall grades, starting with the baseline above, and randomly adding errors in grading for each assignment, assuming that teachers were equally likely to assign a lower grade as a higher grade, and as getting the grade exactly correct (this assumption is probably false, but I had to start somewhere). For one sample of 10,000 grades, the minimum grade is 60.2, and the maximum grade is 77.5, suggesting that the distribution of grades isn’t symmetrical (teachers are more likely to assign a grade which is too low to students who are at above 50% overall, and too high for students who are at below 50% overall). The standard deviation of these scores is 2.32, which means that 95% of the time, the grade will fall between 64.6% and 73.9% (the mean of the data set was 69.2). This is a range of likely values of over 9%!

Note that this script doesn’t account for a host of other reasons that the grades for this individual student could be in error. It doesn’t account for lost assignments, misread names, addition errors, etc…

How many teachers know that there are error bars on the percentages they are expected to give to students? Maybe if we reported this student’s grades as 70.1% ± 4.6%, students and parents might recognize that grading is more subjective than they realize? Maybe we could stop the practice of assigning letter grades to students work based on strict boundaries?

I remember than in grade 12, I was assigned a grade of 84% overall in English 12, with an A being an 86% in my school. This meant that I missed out on a major award at university (it was my only B in grade 12) and that I had to write an entrance exam to get into my first year English course (I passed). I’ve obviously done fine despite this grade, but I remember it often, and it is a reminder to me of the often arbitrary nature of teacher assigned grades.

Rick Mercer is right, we need to do more.

This is not a problem that we can expect schools (and parents) to solve alone. We will never end bullying in our schools while we continue to accept it in our society.

I’ve normally started my classes with a description of what math we will be learning, and a class discussion about what the math means. 

When I first started teaching, I would lecture for 30 minutes, and students would work for 60 minutes (I started in with a double block of math) during double block math classes, and in a 45 minute lesson, I would still lecture for 30 minutes, and students would get 15 minutes to practice and do other activities.

I discovered early on in my teaching that the less time I talked, the more time students had to work on activities and exercises, and this led to improved understanding. I read research suggesting that adolescents could actively pay attention for about 10 – 15 minutes, so I focused on getting the lecture portion of my lesson down to this length, and on embedding more questions and subsequent discussion into my lecture.

Today I tried something new. I found questions (with an emphasis on real world application) related to exponential functions that students had never seen before, and started class by handing them out as a package, and asking students to work on these problems in groups. I then spent class circulating around the room, answering the occasional student question (but being very careful what types of questions I answered) and pushing students to try finding multiple solutions to the problems. When students were completely stuck, I offered support, but by asking them questions, rather than just giving them the solution.

Now, I’ve definitely had classes where I haven’t taught an idea to the entire class before, but this is the first time I’ve introduced a completely new topic without either presenting a lecture on the topic ahead of time or using some sort of guided instructional aid for the students (like a video prepared in advance of the lesson).

Here are some observations I had while I was circulating around the classroom.

• Not one student asked me "is this solution right?"
• Students were actively engaged in the problem solving process.
• The questions I overheard from students (to each other) were often about the nuances in the problems, rather than "how did you do this?"
• Every group of students found the most efficient standard solution to the problem, as well as 2 other ways of solving the problem.
• No one attempted to Google for the solutions, or even open their textbook to see what information it had.
• My students were thinking.

At the end of class, I asked students to continue working in groups and come up with notes to explain the topic. As the students will be taking an exam in about a year and half on all of the material they are writing, I recommended that they write the notes for their future self that might not remember having worked on these problems. Next class, I plan on having students form new groups, and collaborate to construct meaningful notes for the future, and then work on some more related problems.

I’ve flipped the classroom. Instead of me presenting the ideas, my students look for solutions, and I help them. Instead of me giving notes to students, they make their own notes. Instead of the classroom being about the content, it’s about the process.

There were no videos, no notes in advance, no computer assessed exercises; just a focus on changing who was doing the thinking.