Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning (Corwin Mathematics Series)

by Peter Liljedahl

Are there still measurement errors? Yes. Measurement errors also occur through our own inconsistencies. We know, for example, that test papers graded early on are often graded differently than ones that are graded near the end. For some teachers the grades improve over time; for others they get worse. We also know that if we take a break in the middle of our grading, the papers that are graded prior to the break are graded differently than the ones that are graded after the break. If that break is extended and involves sleep, a meal, and some positive or negative social events, this may exaggerate the difference. And this doesn’t even take into account the variance introduced by the students and the complexity of their lives. We know, for example, that some students perform better in the morning than in the afternoon, or on Mondays better than Fridays, et cetera. Taken together, it is safe to say that there can be a measurement error on any given student’s test paper at any time. Let’s conservatively say that this error is only 1%. What this means is that the grade they received on the test is an accurate reflection of what that student knows to within ±1%. This is a pretty good margin of error—much less than reality. But this is on a single test. The thing about measurement errors is that, over multiple measurements, it compounds. So, if over the year, this student will take 10 tests for you, at the end of the year her grade will be accurate to within ±10%. Depending on y...