Real-Life Math
School psychologists work with children to pinpoint any learning or behavioral disorders they might have. They are trained to carefully assess each individual to see exactly what the problem is and what kind of help the student might need.
Different tests are available to assess different problems in individual students. Some of the tests are complex and can be quite time-consuming. Assessing the test results properly and accurately requires a lot of training on the school psychologist's part. It also requires some strong math skills.
You are a school psychologist who is in the process of assessing a student. The student is in Grade 5 and seems to be having some problems with his schoolwork.
After getting permission from the student's parents, you begin testing the student. You will give a variety of tests, including one to determine the student's IQ.
Once the student has finished all the required tests, you can begin computing the scores and assessing the results. That means you'll be using some math equations to determine the results.
"A lot of our testing requires math," says Penny Corkum. She is an assistant professor in a school psychology program. "You need to compute the scores and then transform them to ensure parents and teachers understand them."
The student's IQ test is the last test for you to review. After marking the test, you determine that the student's IQ is 87. Although the average IQ is 100, the student is not necessarily out of the normal range.
The standard deviation on this particular IQ test is 15. This means that most of the IQ scores fall between 85 and 115. This is called the gradient range (85 to 115). You can determine those numbers by using the following equation:
100 (average) - 15 (standard deviation) = 85
100 (average) + 15 (standard deviation) = 115
When you explain this to parents, you tell them that 67 percent of the population (based on 100,000 people) falls between 85 and 115.
The next gradient is 83 to 118. This is the range where an additional 12 percent of the population falls.
How many people will fall into the standard IQ range (gradient of 15)? How many additional people will fall into the second IQ range (gradient of 18)?