In learning to read, beginning readers "sound out" what they are trying to read. In this way, they gain confidence that they can read any word that they come across but they also gain confidence in themselves. Similarly, in math, students need tools to help them solve problems as each problem is different from the next. Talking out loud or to oneself about what should be done first, second, and third helps in thinking the problem through gives the math student a starting point to get over the hump of "not-knowing." What I often find when working with students is that they do in fact know more than they realize or give themselves credit for and, with a little prompting, are able to verbalize what needs to be done. What I aim to do is give students the encouragement and the tools to convince themselves to begin the problem with confidence and to talk themselves through the steps. There is a saying, "to teach is to learn." This can be used to a students advantage by the student actually teaching another person how to solve a problem or even to pretend that they are explaining to someone how to solve a problem in every minute detail. This helps them to examine each step more closely, see which steps need clarification, and cements their understanding more deeply. Henry Ford's often quoted saying of, "Whether we think we can or we think we can't, we are right." is appropriate here because what I have learned through teaching is that often a large part of my tutoring is aimed at getting students to agree with me that they are good at math.
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