Years ago, research with children revealed that many could be tricked into giving the wrong answer to an arithmetic story problem, problems like: “You are buying 6 pencils for 36 cents. How much did each pencil cost?” Researchers found that some students would subtract if the word “left” appeared anywhere in the story, even when the story began: “Mr. Left went to the store and bought 6 pencils for 36 cents.”

“They’re not thinking!” frustrated teachers complain. But let’s think about that for a moment. In first learning how to do word problems, children search for key words that will tell them whether they should add, subtract, multiple, or divide. Along the way, they realize that the word “left,” as in “How much money did John have left?” means you need to subtract. When they apply this rule to the “Mr. Left” problem they don’t stop and think about the meaning of the problem. They simply apply a rote rule in an automated sort of way.

But isn’t this what most of us do, most of the time, when we are first learning something new? Whether we are trying to learn the physical steps involved in improving our golf swing, or the steps our teacher is advising us to follow in subtraction when we are “borrowing,” or the series of questions we are supposed to pose when a customer comes to the counter with a complaint, we may well follow the “procedure” automatically, without much thought.

And why do we do this? Quite reasonably, when we are learning something new, we first notice and practice the most obvious aspects of what we must do. We skim the surface of understanding and follow the method or procedure mainly by rote. As we execute a task in this recipe-fashion, as we “practice” what to do, we become more experienced and more able to wonder about what we’re doing, and how and why it works. For most of us, there seems to be a natural progression from clumsily executing rather poorly understood rote actions as we learn something new to deepening our understanding with practice, experience, and exposure to the theory behind the action.

One college statistics professor told me how his students complained that the questions on the midterm and final exams were much more difficult than the questions that were part of the quizzes he gave on each chapter. He was sure that this wasn’t true, since he sometimes switched questions. He would take questions used some terms for chapter quizzes and use them on the final exam during other terms – and vice versa. No matter which questions appeared in which tests, the students always were sure that the chapter quizzes were easier

“What I realized,” he confided, “was that some students would apply the correct statistical test in problems on a chapter quiz not because they really understood why that was the right test to use but because they knew it was the test covered in that chapter. In the midterm and final exams, covering many different chapters, the students couldn’t figure out which test should be used for which problems.”

It’s very instructive for teachers to delve into their students’ confusion and mistakes. One English composition teacher told me about a student who had written this sentence: The trees, were turning brilliant red. “Why did you put a comma after “trees”? she asked. “Oh,” the student replied, “last year my teacher said you have to put a comma after trees.” The teacher speculated that at some time that student had written a sentence like: “The elms maples and oak trees filled the forest” and his teacher had written something like: “You have to put a comma after the trees.”

The point is that just following instructions in a rote fashion, we sometimes make foolish mistakes, like subtracting when Mr. Left appears in the problem. Rather than assuming that such mistakes mean someone is stupid, search for the reason behind the mistake. If you can uncover the blind spot that led to the blunder, you’ll become a more effective teacher, coach, or trainer because you’ll discover what needs to be done in order to fix the problem.