I remember either seeing or hearing about studies that show a high correlation between verbal and math standardized test scores. (Alas, the only data I could find was in a table on page 18 of a paper about correlation between ACT and SAT scores which gives a correlation of about .7 or a common variance of about 50%. If you find a better study, please point me at it.) This doesn’t surprise me given some of the word problems I’ve seen.
“Express this sample space as ordered pairs.” My student today had this problem and immediately tried to graph the sample space on graph paper. I pointed out that wasn’t what the question was asking, but I could see how he thought that, and after that clarification, he easily solved the problem. This isn’t the first time this student has started down a wrong path because he didn’t understand what the question was asking.
“You draw two cards from a standard 52-card deck.” This is a common beginning of probability questions, and initially seemed reasonable to me. That is until probably the brightest student I’ve worked with, who happens to be Indian, was struggling with a question like this, and I came to realize she had never seen a standard deck of playing cards. I wound up scribbling a deck of cards on paper, but my impression of a reasonable thing to expect students to know changed.
“There were 90 employees in a company last year. This year the number of employees increased by 10 percent. How many employees are in the company this year? A)9, B)81, C)91, D)99, E)100″ I found this sample problem in the book Real Education by Charles Murray (which I don’t recommend. It has some good points, but mostly it made me angry.) Apparently, over half of eighth graders got this problem wrong, and Murray used this as an example of what below average math skills means. Unfortunately for his argument, the most likely reason to get this problem wrong is misreading it. Of the 4 incorrect answers, 3 of them can be obtained by changing/misreading a single word of the problem. Answer A)9 comes from adding “more” between “many” and “employees” in the question. Answer B comes from changing “increased” to “decreased”. Answer E comes from dropping the word “percent” after the number 10.
The take away point here, for those of us writing test questions, is make sure that we are testing the math and not the reading skills of our students.