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Q&A #5103

Teachers' Lounge Discussion: Grading policy

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From: RON <rselby@cinci.rr.com>
To: Teacher2Teacher Public Discussion
Date: 2003072913:15:54
Subject: Re: Re: Re: Math Teacher responds

On 2003072912:16:40, Loyd wrote:
>Taken from a previous post:
>
><<<<<<<<<Your method:  60/100  + 17/20  + 8/10  = 85/130  = 65%>>>>
>
>the three terms are not averages.  What you have is unlike fractions
>and you can not add like that.  It is dead wrong.
>
>100 is the Least common denominator so the fractions convert to:
>
>60/100
>85/100
>80/100.  Now you can add the numerators and divide by the common
>denominator.  Divide by three and you will get the average.  
>
>T "your method" method should never be used by anyone teaching
>mathematics.  
>
>To call 60/100 an average is wrong.  It is a score represented as a
>ratio of right to wrong.  
>

With regard to the use of the word "average" , you are correct. With
regard to the method used to calculate the student's final average for
more than one assignment or test , the method of adding fractions with
unlike denominators is not the same as the problem at hand. Using the
usual correct method for adding unlike fractions gives equal weight to
each assignment or test , and that begs the question which needs to be
answered. 

Look at any individual score for an assignment. Choosing the third
score of 8/10, let's say there were two sections on the assignment.
The first section was worth 6 points and the second worth 4 points. If
student #1 gets 5 points on the first section and 3 points on the
second section his score is 8/10. If student #2 gets 4 points on the
first section and 4 points on the second section his score is also
8/10. But , using the method of adding unlike fractions , their scores
differ.

student #1  (5/6 + 3/4)/2 = (10/12 + 9/12)/2 = 19/24 = .7916666...
student #2  (4/6 + 4/4)/2 = (8/12 + 12/12)/2 = 20/24 = .8333333...

My suspicion is that almost all math teachers realize that the
differing answers are due to the differing weights. I also suspect
that almost all math teachers would assign both students the same
score of 8/10 on the assignment. 

The calculation is not of adding fractions , but of adding points
scored and points possible. The notation used which resembles
fractions is the confusing factor. The same is true of computing the
student's final average for more than one assignment.

RON

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