National Assessment of Educational Progress (NAEP), 2007

SourceNational Assessment of Educational Progress (NAEP), Grade 8, Block M9, 2007

Question (calculators are allowed):

7.  Tammy scored 52 out of 57 possible points on a quiz.  Which of the following is closest to the percent of the total number of points that Tammy scored?

A.  0.91%                               
B.  1.10%
C.  52%
D.  91%
E.  95%

Answer:  D

What Are The Flaws in This Question?

  1. The calculator, not the student, solves the question.  Calculators can determine the solution to various percent problems:  the percent of a number, the percent increase from one number to another, etc.  Basic calculators even have a percent (%) key.  So if a student gets the right answer, we don't know if it was actually the calculator that got the answer instead of the student.
  2. There is inconsistent terminology, specifically, the word "total."  The question refers to "the total number of points that Tammy scored."  But the first sentence does not use the same language ("total number of points") to mean the same thing, which may be confusing to some students. 
  3. The wording in the question is unclear and awkward.
  4. Only two of the choices involve the same number, namely, "91."  The students may conclude that the correct answer must be one of those choices.  They may reason that 52 out of 57 is obviously not .91%, so the answer must be 91%.  In this case, the options are helping to give away the answer.

How to Fix This Question:

  1. Calculators should not be allowed, since the calculator, not the student, can determine percent.  But if we take away the calculator, the numbers need to be changed to be more "friendly," i.e., easier to use in calculations, since the question isn't testing how to do extensive calculations.  In fact, numbers should be chosen so that the decimals are not repeating, thus making the words "closest to" unnecessary.
  2. Since this question has multiple steps and multiple concepts, it would be a good idea to rewrite it as an open-response question instead of a multiple-choice question;  i.e., break it up into multiple parts, have students show their work, and give partial credit for correct work shown.  One part would ask students to write the appropriate fraction.  A second part would ask students to convert the fraction into a decimal.  A third part would ask for the percent.