One day, many years ago now, when my wife was picking up my son from kindergarten, he was very excited to read to her a story posted in the front of the room. His rendering was true to the meaning of the passage, he did decode a couple of words incorrectly. My wife was not going to say anything, but several of the other kids chimed in to correct him. Unfortunately, having been taught a curious mixture of whole language and phonics in kindergarten, at that time he did not possess the tools to verify whether he was correct or whether the other students were, and he had to take them at their word (or not).
I have had similar experiences with several of my math tutoring students when I first met them. I would ask them how to do some calculation, and they would light up and say that they had done that in school and they would proceed to go on their merry way manipulating the numbers, confident that they were accurately replicating a procedure that they had practiced at some point earlier. The problem was that what they were doing made no sense at all. The manipulations were not based on genuine number sense, but were arbitrary and misremembered procedures. And like my kindergarten son, they did not possess the tools to verify whether their answer was correct, and indeed, they didn’t even have a sense that after they offered an answer it was their responsibility to review it to make sure that it was sensible.
These examples, I think, demonstrate a critical component of lessons that is generally not discussed very thoroughly and explicitly, a concept I refer to as “verification.” By verification I mean the ability of a person to prove that what he has done is correct without reference to authority.
Now, of course, there is a fair amount to learn that involves arbitrary and solely conventional associations and therefore cannot be verified without recourse to some expert. The shape we use for the letter “m” for instance, is just a matter of convention, as is the fact that we use it to represent the /m/ sound. The association between this letter and its sound can be confirmed only by someone who already has learned this association of letter and sound. (I will have quite a bit to say about how to learn such conventional material in future blogs.) But the pronunciation of a particular written word is another matter. For example, the word “mop,” is spelled the way it is because it has three individual speech sounds or phonemes, /m/, /o/, and /p/, articulated in that order, and the letters “m”, “o”, and “p” represent those sounds. If a person understands this spelling architecture, then she can confirm the association between the written and spoken word. The same type of confirmation is available in the domain of mathematics. For example, the fact that 8 x 7 is equal to 56 is something that can be proven in any number of ways, such as counting the value of eight 7’s.
Understanding when verification is possible allows the teacher to correct errors in a very sophisticated and powerful way. If a child reads the word “mop” as /map/, for instance, it is not especially helpful to say simply, “No, the word is /mop/.” It is much better to point out that the middle sound she said doesn’t match the middle letter of the word and have her try again now armed with this additional information. (Detailed directions for this kind of error correction, and many others, can be found in the ABeCeDarian Error Correction Guide.) This approach treats the error as a “bug” in her reading procedure that needs to be corrected. The teacher doesn’t give the student the correct answer, but rather points out explicitly what the problem was and has the student try again.
This approach yields several benefits. First of all, it makes the material easier to learn. Instead of having to use brute force memorization to remember hundreds or thousands of things, the student learns how to use a relatively small set of known material in a relatively straightforward procedure to produce a correct response, a procedure that can be applied to get a correct response in any similar situation.
What’s more, the material is not only easier to learn in the first place, but it is much more likely to be retained. As long as some learned response is isolated and disconnected from other knowledge, it is easily forgotten. But when something is embedded within a rich network of associations and relationships, it is anchored in a way that helps keep it from drifting into oblivion.
Another benefit of this approach is that it encourages self-monitoring. The student does not always need to rely on a teacher to know if she has provided a correct response. She can determine this for herself because she is capable of figuring the thing out for herself. And it keeps the responsibility for doing the task firmly with the student. The teacher serves as a coach, providing guidance and support, and when a student makes an error, it is not an occasion for her to give up and have the teacher do it for her, but to evaluate what the problem was and try again. It is difficult to overstate how dramatically this improves a student’s attitude, her ability to apply herself, and her active engagement in her lessons.
Let me leave you then with two important questions to ponder as you think about your own teaching: Are you aware of the parts of your lesson that allow for verification, that allow students to determine on their own whether they are right without relying on your authority? And, when your students are learning content that can be verified, are you correcting errors not simply by providing the correct answer, but by helping identifywhere the “bug” in a faulty procedure was and having them try again.