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.
grace
April 14th, 2010
Agreed. I designed a series of intro-to-probability lessons for my AP Statistics class based on finding the probability of drawing a red card, a red card and a black card, a red card and then a black card, etc., and was shocked when about a third of my class couldn’t tell me how many red or black cards were in a standard deck. Oops.
Teaching word problems (and writing good ones) was one of those big unanswered questions for me, especially since many of my students were struggling readers/writers. It was hugely helpful for my students to analyze word problems to identify the “tricks” in the wrong answers, as you did in this example, and I tried to be really conscious about finding the right balance between giving accessible problems and problems that were rigorous slash aligned to what students would see in the future (linguistically, not mathematically, although the latter wasn’t easy either).
Karl Fisch
April 27th, 2010
I’m currently reading What’s Math Got to Do with It? by Jo Boaler and she cites some research about math and reading scores correlating at about .93 on some California achievement testing (if I’m remembering correctly). She makes the case that our assessments should often be stripped of often confusing contexts for that reason (while arguing that the work we do together in class should be full of context).
Amy
June 6th, 2010
Agreed. I designed a series of intro-to-probability lessons for my AP Statistics class based on finding the probability of drawing a red card, a red card and a black card, a red card and then a black card, etc., and was shocked when about a third of my class couldn’t tell me how many red or black cards were in a standard deck. Oops.
Teaching word problems (and writing good ones) was one of those big unanswered questions for me, especially since many of my students were struggling readers/writers. It was hugely helpful for my students to analyze word problems to identify the “tricks” in the wrong answers, as you did in this example, and I tried to be really conscious about finding the right balance between giving accessible problems and problems that were rigorous slash aligned to what students would see in the future (linguistically, not mathematically, although the latter wasn’t easy either).
yuppers
October 31st, 2010
good read, post more!