What Is The Best Way To Group Students - Mathematically

 It had to be a couple of mathematicians who applied group theory to determine the best way to group students to produce the maximum amount of learning.  They looked at the question of dividing 30 students into two groups so they can practice skills while working with their coach with the end result of improving their ability to play soccer.  

There are two ways they can divide the students up.  One way is to group them by skill level with those who have the highest skill level in one group and those who are not as skilled are in the other group.  The second group is dividing the groups into mixed groups with each group having both those players who have a high skill level and those who are not as good.

We know that as far as sports and reading go, most places group students who have similar skills end up in the same groups whereas most math and social studies classes are divided more along the lines of placing students of differing abilities into groups unless you include the honors type classes.  

They evaluated both methods using mathematical principals and equations. This was really the first time, mathematics was applied to determine an answer to this age old question.  They did make certain assumptions including the fact that there would be multiple groups, the students would have different skill levels, the best teaching situation would be teaching students at a level that matches their skill level, and the groups would provide maximum benefit for the whole group. What they discovered is the students who were group according to similar skill levels received the maximum benefits from instruction.

This is because teachers when they teach the material to students of about the same ability level, they are not presenting material that is too advanced or too trivial for the group. Thus there is less chance of students being bored with the material or lost due to not having enough of a foundation.  This was predicted upon the idea of most collective benefit for all of the students.

The results of this study has applications to education, economics, music, sports, and medicine.  In addition, the authors suggest we rephrase the question of "how do we raise everyone's score" to "How do we set up a situation where all the students benefit the most?" This gives us a first step towards meeting the needs of all of our students.  

One last thing, the authors realize their conclusions may be considered controversial but on the other hand they were specifically looking at skill based groups versus mixed groups rather than random, flexible, or other grouping.  It is possible, this might be one way to help students regain ground they lost during the pandemic.  Let me know what you think, I'd love to hear.  Have a great day.