Next steps

You have to start and also continue.

Our tutoring consultant covers several subjects, including the Spanish language.  Last week he had one student for the first time in that subject.  Although she had a reasonable level of understanding, she was extremely reluctant to speak Spanish.  She was afraid of making mistakes.  And with good cause: although her meaning came through clearly most of the time, her errors in gender, number, verb tense and other details were numerous.  With a great deal of patience and encouragement, she was coaxed to at least attempt to say what she wanted to say in Spanish, rather than giving up and complaining in English.

You have to make mistakes to make progress.  That’s a self-help truism; “if you don’t make mistakes, you don’t make anything,” and similar sayings abound.  It’s not confined to learning foreign languages (or business).  Our tutor has one mathematics student who is very reluctant to do anything to a problem if she hasn’t seen one exactly like it before.  Y. will ask, “how do I do this one?” even if there’s only a minor difference from one on the previous page.  In contrast, S. will plunge in and cover half a page with algebra, until our tutor asks, “S., what are you doing?” and he answers, looking ruefully at his work, “I don’t know.”  S. is much the easier student to work with, because it takes only a bit of redirection to get him to the goal.  Y., on the other hand, must often be given the answer, which means there’s no guarantee she can do it on her own next time.  It’s the difference between steering something with its own motive power, and pushing a heavy cardboard box across the floor.

But trying something is only the first step.  Mistakes have to be corrected.  Many mathematics students get very frustrated because they make a small mistake in a long problem, which means they get the wrong answer even though they’ve done a lot of work and most of it is right.  We have no magical answer for that.  Our tutor advises students to work in a clear, organized way and put in all the steps; then the probability of making mistakes goes down, and if one does happen it’s easier to find.  Practice, too, helps reduce mistakes.  In languages it helps to hear and say sentences with the proper grammar and syntax, so that the table of conjugations is replaced by remembered usage.  This all takes time.

And students often resist taking time.  One recent student complained that actually working out a sample problem for a standardized test had taken far more time than was available in the test itself, so in the real thing he’d have to guess.  Well, as much as we dislike standardized tests, they have to be dealt with.  And though the student would not believe it, with practice he would get to the point where he could polish off that sort of problem in short order.

You have to try, and sometimes make mistakes.  But you can’t stop there: you have to correct the mistakes, which can take much time and practice.  After that, if you need to, you can work on speed.