The Myth of the Careless Error

Having studied student error patterns on standardized tests for a decade, it has become increasingly apparent that careless errors on the SAT/ACT are typically not as “careless” as they seem. In fact, clear patterns emerge when you sit down to study students grappling with inherent “carelessness.”

In a recent tutoring session, one of my students was shocked to see that the exact same "careless" errors she made at home she repeated with great consistency in our session. In one geometry problem she "carelessly" solved for the diameter rather than the radius of a circle, both at home and in the tutoring office. In another problem dealing with the coordinate plane, she "carelessly" flipped the X for the Y value of a point, both at home and again in our session. Later she mistakenly solved for the 7th rather the 8th value in a sequence problem, at home and in session. All in all, my student repeated the exact same “careless” errors on five distinct problems on a single practice test, leading to a loss of 60 points on the SAT.

My student was stunned to discover something that many tenured tutors know: at the core, most careless errors are not random. There is no internal dice that rolls, leading to a random moment of carelessness, at least, not for the majority of students. Typically these errors are systematic errors or “processing” errors: the same mental processes which lead to "careless" errors at home remain active in our sessions. The gaps in my student’s process were fairly consistent. Only through repeating the same problems in multiple contexts and seeing the same errors repeat, did she become aware of the pattern.

The key to solving for "carelessness" is actually to identify the gaps in the mental processes of the student. If we fix her mental procedures/protocols for handling certain types of problems, we would solve for the recurring “carelessness.” We achieve this by giving the student fixed rules to bring to novel problems. We must help them embed these rules and strategies into long-term memory through repetition and variation. We call her attention to these rules again and again, using brief mantras that are stickier in long-term memory. By locking these rules into the memory of the student, and forcing her to recall the rules through practice, we make carelessness much less likely.

I gave my math student some simple math rules to help her solve for her “carelessness”:

• Write everything down.
• Label everything: every term, every element of a graph or chart, every X,Y value.
• Break things down one piece at a time and immediately translate every mathematical term into your own work before reading further. This was a major relearning for my student to stop reading mid-sentence and write the math down, before returning to the rest of the sentence.
• Always circle what you are solving for.
• Never carry things mentally from the SAT problem over to the scratch area. That's too far! So many errors occur as you are holding the math in your working memory before you get to the scratch area. The key is no mental carrying! Put everything down and work immediately below the phrases you've written down. When it's all written cleanly, in an organized fashion, you don't have to hold anything in your head: it's all on the page.
• Use your calculator every chance you get.
• Transfer your answers to the Scantron one page at a time

Any students who are struggling with “carelessness” would benefit from becoming more curious about the instances in which carelessness occurs for them. If you study your errors enough, a pattern will usually emerge: either a deficit in a particular content area or a deficit in a mental process leading to systematic errors. We can solve for the content area deficits by focused review and study; we can solve for the processing errors by teaching the student to attend more closely to their problem solving process, to watch their mind at work, and learn strategies for structuring their own thinking. Students who study their minds at work and learn better problem solving processes will ultimately do better on high stakes tests as well as perform more effectively in numerous academic domains.