Marie Lewis Student Work Blog

The other day I was working with a small group on finding the mean of a certain set of numbers.  Before the students completed this task they were given two steps to solve for the mean.  They were instructed to first add the values to find the sum, and the divide the sum by the number of values in the set of data.  When the student went to solve the problem, he added the numbers, and then added them again.  He proceeded to divide by the correct number of values, only to arrive at the incorrect answer.  I was confused by his method of problem solving, seeing as we went through the “how to” of solving the problem. 

            As I thought about his thinking I first arrived at the conclusion that maybe he just had absolutely no understanding of what an average is, causing him to mindlessly add and then add again.  It was also brought to my attention that maybe he was looking for a number that was easily divisible by the sum of the number set.  Lastly, the idea arose that he was looking for two number sets to divide by, just as the average is between a high and low number. 

            One way to advance the student’s thinking would be to ask him to explain his thinking when performing the task.  I think it would be beneficial to hear his reasoning, which could potentially trigger him to realize where his own misconceptions lie.  I could advance his thinking by having him explain what an average is or talk about where the word average is seen in everyday living.  This might help spark his understanding of what an average is and lead him to a better goal of finding the correct answer.  This student would benefit from using manipulatives to see how the sum is divided into equal groups.  He would also benefit from a real life application of averages, such as batting averages or temperatures for the week.