Data Landmarks and Context

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One of my classes is working on a unit related to data displays and number systems. Around a week ago the class was putting together sets of numbers to match data landmarks.  This was a challenge as students had to think differently.  The class was also asked which data landmark better represents a student’s performance.   I was meaning to write a post then, but a number of things came up and it never happened.  Fast forward a week and here we are.   

Students were given two sets of scores from two different students. 

Jack’s scores:  85, 81, 78, 100, 84, 89 

Sonja’s scores:  55, 87, 91, 92, 68, 93 

Students were asked to find the median and mean for each student.  For the most part, students were able to identify both of these landmarks.  Here comes the kicker … now students needed to determine which landmark better represents each student’s performance, mean or median?  This was a challenging prompt for a couple reasons.   

  • Students weren’t accustomed to using the word represent in this context.  Students were taking the view that the students should get the higher grade and that would be the mean or median. They explained that the student should receive the higher grade because they (the person) is a hard worker and deserves to be rewarded with the highest score. 
  • Students thought of the word represents as the typical score.  When discussing the mean earlier in the year the word typical would often come up as a synonym. 
  • Students looked at the last score as the most recent and thought that should be the final representation.  My school is heading in the direction of standards-based grading so that’s maybe why students took that approach.  I don’t know. 
  • Students looked at the lowest and highest score of each set of data and reviewed the range to help them pick the median or mean 

 

After struggling a bit, the class came together and we discussed a few possible solutions.  The class agreed that the question allows a lot of room for interpretation and context certainly matters.  The fruitful conversation brought about a change in perspective for some as students started to see this type of math differently than just numbers sprawled across a page.  The numbers had meaning and the context drives the answer.   

A little later in the week students were asked the following prompt: 

If you were the teacher in Jack and Sonja’s class, would you use the median or the mean to calculate students’ grades?  Explain. 

This was a bit confusing at first, but students made progress in understanding the context and how it helped determine which landmark to use.  Again, I had answers related to the teacher wanting to give the higher score to help students with confidence.  Other students used the data landmarks to find the average.  I felt like students were more comfortable using the average as they could say that they used every data point, therefore making sure all assignments counted for something.   

I’m looking forward to next week as we dive into histograms.