Wednesday, April 28, 2010

My Lucky Score

Students and teachers are as interested in what the next test score will be as in the latest test score. Will it be at or above an expected score? What can be expected from luck? [YouTube]

The portion of the time each student will be lucky can be obtained from charts in the previous blog. These charts show the number of lucky scores obtained when the answer sheets were marked without looking at the test. 

The number of lucky scores becomes the expected frequency of lucky scores for each student. The bar graph becomes an uncluttered line graph.                                            

On 4-option questions, a student can expect to receive a lucky test score of 15 out of 60, about 1/8th of the time (0.12), by just marking the answer sheet without looking at the test.

Half of the time, the lucky test score is expected to be 15 or less, and half of the time 15 or more. Students can increase their luck by deleting one or more answer options. The average lucky score becomes 20 when one option is deleted on each question. 

Students can turn luck on and off by the decisions they make and the chances they take. The Arkansas Algebra I (AAI) test contains sixty 4-option multiple-choice questions. How students take the test determines how difficult it will be. If students think of options not on the test, they make the test more difficult, a 4-option question becomes a 5-option question or more. They are going in the wrong direction. 

Rather than picking a right answer, delete wrong answers and then guess. At the other extreme, if students can discard all but two options, on average, they can expect a lucky score of 30 out of the 60 questions, or 50%. [The higher order thinking skills needed to do this are promoted in the classroom by Knowledge and Judgment Scoring (KJS) and Confidence Based Learning (CBL). Students do not need to know “the right answers” to beat standardized tests. They need a practiced self-judgment.]

The expected average score is a stable value between 15 and 20. Where each student’s (my) lucky score will fall under that average is not. There is no way to predict each student’s lucky score. That is what makes luck enticing. We can predict the average lucky score and the range in which the lucky score will occur very well. Students can always pass the test with proper preparation.

The inability to predict individual student lucky scores is of little consequence with Confidence Based Learning (CBL), or the ACT and SAT, as chance has little effect at the mastery level of learning and performing. It has a devastating effect on students with similar abilities being selected to pass or fail a test with raw scores below 50%. Using an average score protects teachers and schools. It has taken forced disaggregation of NCLB test scores to prevent hiding low performance by groups smaller than about 30 students from being masked by the high performance of other students.

Fair means chance will distribute scores in a “bell shaped curve” or under the “normal curve of error.” (If there are enough questions on the test. The AAI, with 60 questions, has enough.) The curve has the name “normal” because this is what happens when you know nothing on the test, or mark the test without looking at the test booklet. It could be called the “know nothing curve”.

On a multiple-choice test scored only by counting right marks, Right Mark Scoring (RMS), there are no qualification runs to put the best or the worst at the head of the pack. Instead, chance assigns each student a secret handicap; luck, on test day. The student with the least ability in your class may draw 20 points and the next student may only draw 10. This is fair with RMS rules as both students have an equal opportunity to draw. [YouTube]

Some people believe that tests, especially high-stakes tests, should not be games of chance. They let examinees report what they know, based on their own judgment. Both knowledge and judgment are scored, just as on projects, essays, job assignments, and reports.

Knowledge and Judgment Scored (KJS) tests and Confidence Based Learning (CBL) tests give you a quantity, quality and test score. This form of testing and learning, in the classroom, promotes the student development needed for your students to be winners on any test based on high quality work.

Next, the three games played on a multiple-choice playing field, from traditional RMS (guess testing) to obtaining accurate, honest and fair scores.

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