Authentic assessment: a school's interpretation

Focus on Learning Problems in Mathematics, Wntr, 2002 by Roland G. Pourdavood, Lynn M. Cowen, Lawrence V. Svec

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The assessment process was recursive. In many instances teachers who thoughtfully implemented this process were impressed with evidence of students' cognitive growth from September to May in grades 14 and from January to May in kindergarten. For instance, a third grade teacher noticed much progress with a student who demonstrated very little understanding about time and money on the third grade performance task at the beginning of the school year (September, 1999) but showed exceptional gains by May, 2000.

TIME AND MONEY: (Performance Task)

Third grade: Ellen earned money baby-sitting. She wanted to save her money to buy a portable CD player that costs $128.00. Ellen charged $4.50 per hour to baby-sit during the day and $5.50 per hour after 8:00 p.m. Mr. Holmes hired Ellen to watch his two grandchildren every Saturday in May from 3:30 p.m. until 11:00 p.m. How much money does Ellen earn in one Saturday? (see figure 1).

Figure 1

Third grade student's solution to time and money performance Task in
September

TIME   MONEY

3:30   $4:50
4:30   $4:50
5:30   $4.50
6:30   $4:50
7:30   $4.50
8:00   $5:00

The answer is 87 I go the answers becuse I add

In September, a third grade "underachiever" developed a chart to show the solution. In the first attempt, the problem solution is incomplete. The student did not understand elapsed time. She calculated 3:30-7:30 as five hours. She also was unable to calculate the amount of money for 1/2 hour (7:30-8:00). Besides these errors, it appears that the solution, evidenced by its lack of completion, was beyond the student's skills and knowledge even though the problem was relevant. This conjecture is somewhat supported by her limited and inadequate written response, "The answers is 87 I go the answers because I add."

The same student responded to the same problem significantly differently in May. The student's solution showed increased understanding and a more sophisticated strategy for solving the problem (see Figure 2, Appendix I).

Figure 2

The same third grade student's solution to time and money Performance
Task in May.

       TIME          MONEY

     3:30-4:30       $4.50
     4:30-5:30       $4.50
     5:30-6:30       $4.50
     6:30-7:30       $4.50
     7:30-8:00       $2.25
     8:00-9:00       $5.50
    9:00-10:00       $5.50
    10:00-11:00      $5.50

TOTAL: 7 hr. 30 min  $36.75

Most impressive of all was how articulate the student was when she defended her thinking and explained how she solved the problem.

I made a table for the time and the money. After that I put down the hours until 8:00. Then I put the money until 8:00. 3:30-4:30 was $4.50. 4:30-5:30 was $4.50. Then 5:30-6:30 was $4.50. 6:30-7:30 was $4.50. 7:30-8:00 was $2.25 because 7:30-8:00 was not a whole hour. Then after 8:00, she gets $5.50. 8:00-9:00 was $5.50. 9:00-10:00 was $5.50. 10:00-11:00 was $5.50. Then I added all the money and got $36.75.

Also evident was "improvement" in the student's understanding of elapsed time and her ability to calculate money for 1/2 hour. It appears the student grew in her ability to calculate time and money accurately and in her confidence to communicate her thinking process. Apparently, the solution reflects the social norms within this mathematics classroom. It seems the teacher and students may value the importance of connecting communication, illustration, and reasoning to solve problems and justify solutions.