What are we testing

[George Sheridan <learn@jps.net>]

During the California Mathematics Standards Test (part of STAR), my 
tiniest second grader raised her hand.

To avoid having mathematics test scores influenced by reading 
ability, students are given some visual cues plus an oral direction 
like, "Tell how much money this is." They work in 8.5" by 11" test 
booklets, with as few as one or two of this kind of problem on the 
page. So there's plenty of room to show full-size images of dollar 
bills and coins. But for some reason, each year the state gives us 
pictures of dollar bills that are about one fourth the size of 
Monopoly money, and dimes about one centimeter in diameter.

My little angel asked me what coin was pictured on the page. Of 
course I was forbidden to tell her. She elaborated on her dilemma: 
the coin looked something like a quarter, so she had reached in her 
pocket and pulled out a quarter to compare. She rotated the real coin 
so that the head of George Washington was tipped at the exact angle 
of the head illustrated in her test booklet. She noticed a difference 
between the coins, however. Above Washington's head on her real 
quarter were the words, "United States of America." The one pictured 
on the test had the word "Liberty." That difference, plus the 
discrepancy  in size, led her to believe that the coin pictured could 
not be a quarter.

Following test protocol, I said something like "Just do the best you 
can," and walked away. Pretty soon, her hand was up again. On a 
subsequent problem, she had noted that the picture of a nickel was 
even smaller than the picture of a quarter. She wanted me to know she 
had figured out that the coin she had been puzzling over must have 
been a quarter.

I think she got both problems right. But how many other students were 
thrown off by the size difference, or the fact that the quarter 
pictured was an old style no longer being minted? The testing 
contractor would report that they do not meet the second grade 
content standard 5.1 for mathematics: "Solve problems using 
combinations of coins and bills." In reality, some of these students 
have no difficulty with coins and bills, but have a problem with 
smaller-than-life-size pictures.

Every year, the STAR test includes this same stumbling block in all 
the problems where students are required to know the value of coins. Why?


George Sheridan