## Friday, November 2, 2012

This past week, as I graded the first chapter assessment in my pre-algebra classes, I had a realization.  The last page was filled with problems on mean, median, mode and the best measure of central tendency (I will remind you soon about these) using a set of "test scores" from a social science class.  Some form of these questions have been on the chapter test for the past 6 years and I am embarrassed to say that I failed to see the negative impacts of averaging grades that were explicitly pointed out on these assessment questions.  Part of my ignorance can be attributed to the fact that I have been using a 4, 3, 2, 1, 0 grading system that equalizes the A to F grading range.  I learned many years ago that a 100 point grading range can be devastating to a student's grade.  But it took my student teacher and her discussions with students to really hit the point home.

The test scores that were given in the data set were:

92, 82, 88, 90, 82, 0, 98, 100

mean: 79
median: 89 (the middle number after putting the data in order from smallest to largest)
mode: 82 (the number that occurs the most)
mean (without the outlier): 90.3
outlier: 0

The mean or average of this data is 79 which is a C+ in most grade book programs.  When you look at this data, do you think the mean is an accurate evaluation of this student?  If we look carefully, there are four scores 90 or above, three scores in the 80's and then that ZERO.  Wow, can you believe the impact that one little zero has on the other scores when using the mean to calculate the grade?  What about the other measures?   Now it is story time...

As we went over this assessment question in class, an amazing thing happened.  Before discussing this question, I asked students which measure of central tendency was the best for "grading".  Overwhelmingly my students voted for mean.  I asked them why and they stated that the mean had been used in every one of their classes from fourth grade until now.  After the informal poll and the discussion, I posted the last page of their chapters 1 and 2 assessment.   I asked the students to get their phones or a calculator out and find the mean of the data since on the test they only had to describe/define how to calculate the mean of a set of data.  As each student saw the result appear on the screen of whatever device they were using there was a collective sigh of disbelief.  They were absolutely shocked at the result.  When they saw that the mean was 79, they began formulating arguments and questions as did I.

My first question was: Do you still think the mean is the best measure of what this student knows?  My next question was: Is there a measure that you would rather have your teacher use?  My last question was what are you wondering?
Here are some of my student responses to the data and my questions:

First, overwhelmingly, the students felt that the mean was the worst measure to use with this data.  They argued that the student obviously understood the material and that he/she had one bad day which had a huge impact on his/her overall grade (something that could be proven by using standards based grading).   If they had to choose, they preferred that their teacher use the median to "calculate the grade.  The interesting part came when we discussed the things my students were wondering.

I shared this problem and the discussion with the teachers at my school.  I am the lone wolf of standards based grading and this was not about converting others.  It was about awareness and having my colleagues consider the effects of their grading system on student learning and motivation.  Unfortunately, the message fell upon deaf ears.  I shared this information with the teachers because I promised my students I would.  I am sharing on this blog because I know there are many folks out there that will think about this and consider it.

Needless to say, my students have a new appreciation of standards based grading.  I will be sharing more about all of this soon.  I ask that you pause and consider your grading and what it actually measures.  Then join the #sbar group on twitter to join the journey to make grading more meaningful to all!