Authentic assessment: a school's interpretation

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

CHANCE (Performance Task)

Kindergarten: Ms. Grieshop's kindergarten class decorated special shirts. Each child had to glue a red, blue, and yellow button straight down the front of each shirt. Ms. Grieshop did not want all the shirts to look exactly the same. How many different ways can the three buttons be arranged so that all the shirts are different?

Figure 3 in appendix 1 contains two solutions to the above performance task. These solutions are from one student who attempted the performance task in January and May of 1998. There was no prescribed procedure for solving this non-routine problem. The problem was relevant and reflective of the students' classroom experiences. In January, the student successfully solved the problem. Each shirt's colored buttons were displayed in six different orders. The order appears to be random and may indicate that the child used process of elimination to find all possible combinations. What also emerged was reflective writing which showed the student's pride in his/her creative solution ("I LIK MI PR"-translation: "I like my picture"). In May the student did not use process of elimination, but instead attempted to organize how she/he manipulated the buttons. For example, the yellow button (y) was used twice at the top, in the middle, and at the bottom of the order, indicating a degree of sophisticated thought about arra ngements. This level of thought might be construed as cognitive growth in mathematics. Words were used to solve the problem as well as pictures and numbers, ("R R 6 CHRS"-translation: "There are 6 shirts").

TIME AND MONEY (Performance Task)

Kindergarten: Robert saved $2.00 every day for six days. How much money did Robert save in six days? (January 1998). Robert saved $2.00 every day for six days. Does Robert have enough money to buy three fish that cost $3.00 each? (May 1998). (see Appendix 1, Figure 4).

In figure 4, the kindergarten solution demonstrates cognitive growth and emergence of student understanding about money and rate. In January, the student illustrated dollar-bills and grouped them together by two's. The student invented her/his own money system by labeling the bills to match the number of days. This invention was probably used to "keep track" of the passage of time. The solution is portrayed only through pictures of twelve-dollar bills-even though the invented denominations imply more than twelve. In May, the problem was modified to meet classroom learning needs. Students were asked to determine whether there was enough money to buy fish that cost $3.00 each. This modification demonstrates the interconnections between instruction and assessment. The teacher probably assumed that students could handle a more "difficult" problem since the problem went beyond the relationship of time and money to the relationship between money and the number of fish that could be purchased. Perhaps this modifica tion is attributed to the teacher's experience and recognition of students' understanding of time, money and how money is used.