Principles for Correcting Mistakes Children Make When Learning

A few weeks ago I created two new sections for the site, Your Living and Learning Moment and Learning in Real Life. I've been adding to each section regularly, but the topic of how to help a child who doesn't understand what you're trying to explain is always important and I want to highlight this piece for those who don't listen to the videos. The author, Dr. David Wheeler, is a professor of mathematics writing in an academic journal and what he says is useful and important beyond teaching math.

More from Professor David Wheeler’s good article “An Askance Look At Remediation in Mathematics” in Outlook, Winter 1980 (see GWS #20, page 17). As with much else we put into GWS, this article may be very useful to homeschoolers, not only as a guide in their own work with children, but also as something to quote from in their homeschooling proposals.—John Holt

… Are there any principles of remediation? Are there any techniques for implementing them? Remediation will not be achieved by giving the students once again a version of the teaching that failed to be effective the first time—not even, I suspect, if the second version goes at a much slower pace. Something different is required. Let us put the matter of remediation into perspective by distinguishing it from the correction of errors. Mistakes and uncertainties are proper to learning. Anyone learning a new skill—driving a vehicle, playing an instrument, speaking a language—is clumsy and tentative in the early stages. The feedback that the learner gets from his actions in the beginning, his mistakes, gives important information about the components of the skill that are not yet mastered; it tells what he still needs to work on. We should expect students who are learning to read, say, or to master some elementary mathematics (activities with substantial skill elements), to make mistakes, and for these to diminish as the skills are progressively brought under control. More than this, if students are not permitted to make mistakes and correct them by themselves they stand little chance of achieving autonomy in the skill since they are being denied evidence they need to know their progress from the inside. Mistakes are not, of course, the only source of feedback to the student, but their importance lies in the fact that this feedback emanates from the task itself. The student who knows he has made a mistake, that something is wrong, does not need the verdict of some adult authority—which, because it does not come directly from the task itself, can often appear arbitrary, unrelated to the skill being worked on. It is easy to see now that a student who has no idea whether what he or she has done is right or wrong is not in a position to receive the messages that the task is offering; the natural course of learning is blocked. Such a student needs remediation. The problem for the remediator is not primarily to cure the student’s mistake- that remains the responsibility of the student—but to endeavor to restore the natural course of learning so that the student can profit from mistakes as other learners do …

Some General Rules For the Remediator

1. Self-discipline. Teachers often use speech too much, too often and in too free a manner. They create noise for their students and for themselves. Remediation requires being alert, attentive, non-distractive; in a word, quiet. Listening and watching are the basis for effective intervention. And when intervention is necessary, it must be supplied in a disciplined way, not a word more said than is needed …
2. Get students active. Don’t waste precious time talking, explaining, emoting. Ask a question first off, or tell the student to do something at once. You’ll find out if it was a bad question or if the student can’t do what you suggest. If so, try another question or instruction, and so on. The remediator needs feedback from the student, just as the student needs feedback from the task. Don’t prejudge the student’s difficulty; wait until the feedback tells you more about what it is …
3. Focus on task. Take the particular problem that presents itself and get the student to work on that. Don’t distract the student by providing further input and information, bringing up other matters, etc. If you ask “Why are you doing that?” (or worse, “Why did you do that?”) you are asking the-student to stand back from the situation and give a reason for what he is doing. This is both difficult to do (probably much more difficult than the task itself) and disturbs the student’s focus. Don’t diminish the task by trying to do the student’s work, or by deliberately simplifying it so that the challenge is taken out of it …
4. Be businesslike. If the student is having real difficulties and knows it, there is already enough tension in the situation. Cool it. Don’t either blame or praise. Don’t waste time displaying that you care. Any such behavior makes the student’s task more difficult …
5. Elicit awareness. Use any device you can think of, short of telling, to draw the student’s attention to important aspects of the task. Sometimes it is enough to point at something, or to ask “What have you forgotten?” “Is this part right?” “How do you know this is right?” Get the student to talk (for example, “Tell me how you did this”) since speech can sometimes bring things into consciousness for the speaker.