Percentages fail us when we see that 80% of our students are proficient readers (Hey, a “B-” is pretty good!) and do not realize that means that 1 in every 5 students is not a proficient reader (We need to do much better!).
Percentages fail us when we see that a student is 96% accurate when reading text (Wow! That’s almost an A+!) and do not realize that this means making 1 reading error every 25 words (Yikes.).
Percentages fail us again when we do not realize that a student’s improvement from 96% accuracy to 98% accuracy in reading (Meh.) means that the error rate has been cut in half (Wow!).
I don’t mean to knock the mathematical usefulness of finding percentages. There is brilliance therein. But taking those percentages and finding their corresponding ratios can, in some scenarios, get to the heart of the matter, whereas sticking with percentages clouds the picture. Sometimes ratios clarify gains that are not otherwise so very visible. Sometimes ratios show that “good enough” or even “really good” . . . really isn’t quite so good after all.
I started looking at this issue when I was director of an afterschool reading clinic. Our struggling readers were making improvements in their reading accuracy. Students and parents “felt” it and the “percent accuracy” measure showed this, but the true significance of the gains was not always terribly clear… until I turned “percent accurate” into ratios of errors to total number of words. For example, an improvement from 90% accurate to 93% accurate meant the student had improved from making 1 error every 10 words to 1 error in every 15 words. The meaning of the numbers in the ratio provides a well-drawn picture in our heads. We see the 10 words on a page and the error on one of them. We see the 15 words on a page and see how much farther the student is getting before she makes an error. Perhaps we even picture the student herself reading, moving us from numbers to real live people.
As a proponent of helping students learn to read with a minimum of 98% accuracy, rather than the 96% accuracy that has been shown to be “adequate” for comprehension of the text, it became important to me to show that every percentage point increase was, in fact, a huge jump for the student. The closer we get to 100%, the more significant is each single point increase.
More recently, I have found that staff in school districts benefit from looking at their state assessment data in the same way. We can compare two districts in this way: District A has a 92% proficiency rate (1 in every 13 students is not proficient). District B has an 83% proficiency rate (1 in every 6 students is not proficient). District B has more than twice as many students who are not proficient readers compared to District A. The fact that District B, essentially, has double the problem of District A is simply not visible when using percentages. Have you perhaps already, in your mind’s eye, seen 6 students and 1 of them is looking utterly defeated by this thing called reading? That’s the power of the ratio.
Because our school children are not just numbers, let’s use numbers in a way that produces images in our mind of students, their struggles, and their gains.
Below is a sample “cheat sheet” showing the correspondences between percentages and ratios:
100% proficiency: YEA
99%: 1 in approx every 100 students is not proficient
98%: 1 in every 50 students
97%: 1 in every 35 students
96%: 1 in every 25 students
95%: 1 in every 20 students
94%: 1 in every 17 students
93%: 1 in every 15 students
92%: 1 in every 13 students
91%: 1 in every 11 students
90%: 1 in every 10 students
89%: 1 in every 9 students
88%: 1 in every 8 students
86%: 1 in every 7 students
83%: 1 in every 6 students
80%: 1 in every 5 students
75%: 1 in every 4 students