Mistakes or Errors

The smartest student in my Trig class missed getting a 100 on the Regents exam because he multiplied 2 time 3 and got 5. He made what we infamously refer to as a stupid mistake. He knew how to solve the problem, but made a mistake. When it was pointed out that he had gotten the problem wrong, he looked at it and immediately was able to pin-point his mistake and correct it.

My son received a low grade on a Trig exam and was asked to correct the mistakes and return the test for a new grade. He protested that if he could do the problems right, he would have. He did not know how to do the work, could not correct it and the request was preposterous.

How often do we ask student to correct their work with no further input? They can correct the mistakes, the things they know, like the student in the first example, but when they do not know how to fix them, they are errors. The students cannot correct them on their own. If we grade their corrections, we are giving these students a double whammy.  In September's Educational Leadership's "Making Time for Feedback," Douglas Fisher and Nancy Frey point out this difference between mistakes, when you know the answer but were careless or tired and messed up, and errors, when you don't know how to do the problem. Asking students to correct mistakes does not improve achievement and students cannot independently correct errors so the task also results in no increase in learning.

Fisher and Frey point out that teachers often spend large amounts of time correcting student work. Unfortunately this is often a case of working hard, but not smart. If students are given the answers, they probably won't learn anything from the process. The further the assignment is from receiving the feedback, the less valuable it is. Students need teaching to respond to feedback and anyone who has seen students look the grade and then throw the papers away, knows that much of the effort teachers spend trying to give feedback is disregarded. We want teachers to spend time reviewing student work, but we want the time to be meaningful.

The authors of the article recommend completing an error analysis. This is something that special ed teachers are trained to do, but many general ed teachers are not. We need to look at the work, determine why the errors were made and then provide an intervention. Clearly not every error can be taught immediately, but we need to systematically address mislearning and non-learning. Daunting? It can be. Fisher and Frey, however, recommend an interesting way to evaluate student work to use it formatively. They propose selecting a few skills you want students to be able to perform. The authors' example is skills for understanding a primary source document: skimming and scanning to preview text, sourcing, and drawing conclusions (p 45). For a writing assignment it could be: using  the standards of written English correctly and meaningfully, organizing material to enhance meaning, using appropriate vocabulary, and demonstrating appropriate voice. For a math test on area it could be: knowing the formulas, applying the formulas correctly and multiplication. A science lab could be evaluated on: correct format, using the tools correctly, and drawing appropriate conclusions. For all of these examples additional or different criteria could be identified. A chart is created with the classes and errors are compared. Student initials or tallys are used to chart errors when grading. The chart is used to identify interventions to the whole class or groups that may be appropriate.

Targeting instruction to small  groups is something that elementary teachers do with reading groups, but often ends when students enter middle school. Curriculums are too dense to reteach or get stuck on something. Teachers are, after all, being graded on how their kids test. If the entire test content is not covered, it reflects badly on the teacher. Think of this paradigm instead. If we only cover 85% of the curriculum for 85% of the class (the 10 % at the top get enrichment to extend throughout the entire curriculum while the 5% at the bottom are pulled from class, experience absences or do not have the foundations to learn it at this time) and we teach it well, they learn it thoroughly. Students will do very well on the test AND retain the information for next year. Less review will be required at the next level and more time can be spent on new content. The common core has embraced the idea that we need to narrow the curriculum. (I will argue that their inch wide and mile deep is really a yard wide and a couple of fathoms deep, but that is a topic for another day.) We need to teach well so that students learn the material, not cover the material so that students experience surface learning so they can perform on the test and forget it the next day. Targeting instruction on the errors is one component of this idea.

We will not be able to teach the same thing to every class every year, but we will have more learning come out of the process. We will have the first student who experiences frustration because of his stupid mistake and focus it into an intention to be more careful, not my son who was turned off and became a behavior problem, missing the next lesson as well.