The End of the Quest for Numerator Points (aka Let's Stop Using So Much Math)

[Scott Habeeb]

Math.  Some people love Math and some people hate it.  Some excel at it naturally while others struggle mightily.  Some see it as a clear universal language, but for others it is is the embodiment of the Tower of Babel.  Some see its usefulness, some do not.  Some are indifferent, some are passionate.  Some are scared of it, some are excited by it, and others plod along doing their best to understand it.

While Math usually elicits a variety of responses, there is one place in most schools where the thoughts about Math are almost universally homogeneous.  When it comes to the traditional manner of grading used in our schools, everybody - parents, teachers, and students - relies on Math like a lifeboat in a shipwreck.

How are grades typically determined in most classrooms in most schools?  Basically, in most classrooms they're determined the same way they've always been.  It doesn't matter if the class is Language Arts, Fine Arts, or Culinary Arts, when it comes to deciding what a student's grade should be a CALCULATION is done to determine an AVERAGE.  People who in the rest of their lives might be scared to death of Math, suddenly become Disciples of Math and swear by a grade book average.  In fact, the word "average" becomes synonymous with the word "grade," as in "What is your average in that class?"

We all know how this works, but let's recap quickly.  Typically, assignments are graded by the teacher and entered into a grade book.  The grade is a fraction - a number of points earned (numerator) divided by a number of points possible (denominator).  The grade book adds up the numerator points earned for all assignments and divides that by the collective number of denominator points.  The resulting average is the student's grade.

There are 3 major problems with this system:

1. It's inaccurate.  
   Who came up with the idea that an average of all work or all attempts at learning depicts actual learning?  Why would a student's earlier and lower attempts at learning be averaged in with his eventual outcome?  In other words, if a student finally "gets it" doesn't that "get it" grade reflect better what he knows than an average of all previous attempts?  The only way that a mathematical average of all assignments doesn't falsify a grade is if the student scores the same on all attempts.
2. It's not realistic.  
   Perhaps someone out there can think of something I'm missing, but I can't think of any meaningful real-world applications of the "average all your attempts" method of determining outcome.  Even in the world of sports, where things like Batting Average and Yards Per Catch are routinely used, if a player with a low average hits a home run or catches a 99-yard touchdown it counts for just that - a home run or a TD.  No one says, "I'm sorry that catch only raised your average to 8.2 yards per catch so we'll only count it for 8.2 yards."  We are not held to our average in real-life.  Why are we held to it in schools?  Shouldn't we be preparing students for the real world where your most recent attempt at something is what counts the most - or at all?
3. It minimizes education.  
   This is the one I care about the most.  We - educators - have turned our classrooms and schools into one giant Quest for Numerator Points.  What do we care about most?  Learning.  What do we wish our students and parents cared about most?  Learning.  Yet by over-relying on mathematical calculations we have created a culture that wants numerator points above all else.  May I have extra credit?  What can I do to earn more points?  How many points do I need for an A?  These are all questions we hear on a regular basis that demonstrate the fact that the focus is in the wrong place.  If we ever want to get the focus back to learning instead of on earning a grade, then we must have the boldness to think beyond the Math Box.

Are there benefits to using the mathematical average process for determining a grade?  Sure.  It's definitely efficient.  It's easy to figure out and to calculate.  It somehow seems "mathy" which makes people feel like it has a basis in something real and dependable.  It works well with the typical grade books issued by schools.  It can also take the blame of the teacher by providing a math-based excuse or reason for a grade.

But do any of these benefits outweigh the fact that it's inaccurate, that it's not realistic, and that it minimizes education?  Surely not.  Reason 3 alone - turning our classrooms into quests for numerator points - should be enough to drive us to look for a better method.  How can something as powerful as the education of a young person be allowed to devolve into a quest for points?  Learning is so much more than that and so much more important.  

So what's the answer?  This post wasn't written to provide a specific answer - sorry.  The purpose of this post is to help us recognize that the Quest for Numerator Points - or the over-reliance on Math - is a problem that has to stop.  We can't change until we first recognize the problem.

The answer in general, though, lies in using Assessment FOR Learning strategies (click here for tons of examples).  It lies Standards-Based Learning strategies (click here for more information) or documenting student progress toward mastering specific standards.  It lies in teachers having the boldness to think outside the box and to collaborate on how to efficiently communicate accurate and meaningful feedback.  It lies in fewer numerical scores and more descriptive feedback.  It lies in more flexible grade books that measure progress instead of just average attempts.  It lies in not being satisfied with the status quo but instead being on a continuous journey of professional growth for the purpose of increased learning.  It lies in using scores and grades as feedback tools that help students make learning decisions and teachers make instructional decisions instead of looking at them as numbers to plug into a comfortable formula.

The answer isn't simple since it goes against decades of institutional inertia.  But once we boldly find it, we can quit this Quest for Numerator Points and embark on the exciting and important Quest for Learning!