Surveys indicate that most people support high academic standards and testing to ensure students are meeting those standards. However, when questioned further, support diminishes when a single test is used to determine promotion or graduation. Adding to this, when parents see the actual questions on these tests, questions about appropriateness are brought to the forefront and support for testing declines. In my opinion, Nevada's current test measures what students should know and be able to do upon graduation.
Last week, the test results for the high school proficiency exam were released. The subject of equating test scores has caught the public's attention. Students needed to get an 82 percent to have a passing scaled score of 71 in reading and a 69 percent for a passing scaled score of 64 in mathematics.
Equating tests is not something new, it's done all the time. Whether it be an ACT, SAT, PPST or high school proficiency exams, test-makers try to ensure all versions of a particular test are equally difficult. When, then, do students think one version of a test is easier than another? The problem is that while some questions measure the same standards, they may be written differently. That might cause the difficulty level to be changed.
The following examples all measure the same standards. 1A. Find the mean of the following data: 77, 73, 80, 83 and 82. 1B. Ted's bowling scores last week were 85, 89 and 101. What score would he have to make on his next game to have a mean of 105? 1C. In Ted's class of 30 students, the average on the math exam was 80. Andrew's class of 20 students had an average of 90. What was the mean of the two classes combined? 1D. One of your students was absent the day of the test. The class average for 24 students was 75 percent. After the other student took the test, the mean increased to 76 percent. What did the last student make on the test? All of these questions measure the same standard, finding measures of central tendency. In my opinion, students should be able to do all these. Do you think they are of equal difficulty? That's why tests are equated.
Distracters also cause students difficulty. Distracters are multiple choice answers that cause students to jump to wrong answers. One of the answers for 1C, for example, would be 85, a wrong answer based on students seeing the scores of 80 and 90.
An interesting aside. Question 1B, in Nevada, measures a student's knowledge of finding the mean. That same question, with different numbers, is used in Texas as an algebra standard.
I could also make up a number of percent problems that look alike but have varying degrees of difficulty too. 2A. A dress that is marked $68 goes on sale at 20 percent off on Friday. How much will Maria pay by buying the dress on Friday? 2B. Maria bought a dress for $68 that was marked down 20 percent. What was the original cost of the dress? These two questions measure the standards on percents.
In both these problem sets, mean and percents, the "A" problems are a lot easier than the others. Even arithmetic problems that look almost identical might not be of equal difficulty. For instance, 58,621 divided by 81 is easier to compute than 58,621 divided by 87. Most students would use a trial divisor of 80 for both of those problems. Eight works well for the first problem; not so well for the second. Simply stated, more students would miss the problem with 87 as the divisor than with 81. Good, experienced teachers should be able to identify problems that look similar to the public but have different difficulty levels.
The fact that a good percentage of the public does not understand the concept of equating is indicative of American educational standards that were described in the TIMSS report, America's curriculum is "a mile wide and an inch deep." It appears that state legislators are more concerned with covering more material than students mastering, understanding or being able to apply what they are learning in school.
I know you're curious, so here are the answers to the problems. 1A. 79, 1B. 145, 1C. 84, 1D. 100, 2A. 54, 40, 2B. 85.
Bill Hanlon, a Las Vegas educator, is a former member of the Nevada Board of Education. His e-mail address is email@example.com.