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Hi Cindy, I do not think that high school students have to be checked at every step. However, in the discourse of your teaching, stop, write a problem on the board, take sufficient wait time and then call upon at least two or three students to answer the question. Quickly record their answers on the board. If they are all the same, do not repeat them. Ask if there is a different answer. Do this as if you were constructing a multiple choice question and its answers. Imagine that you are a student and give an answer with an error that is frequently made. Ask why this is wrong. An example of the above would be finding the hypotenuse of a right triangle using the Pythagorean Theorem. For a triangle with sides 8 and 15, give the answer 23. Point out the error that the hyp^2 does not equal the sqrt of 8^2 + the sqrt of 15^2, but rather the square root of the sums of the squares. Do you have your students work in groups? If you do, at the end of the lesson give a few problems to the group. Have all of the students in the group explain a problem: in presenting the answer of the question to the class the first student starts the process, the second student continues the process, and the third or fourth students ends it. This does not involve every student but if you choose your groups randomly everyone gets to speak over a few days. As a process in high school I am not certain that the signals that you indicated are all that valid. Many students can arrive at the correct answer and make errors in the process. This is more frequent in algebra than in geometry, but wrong logic in geometry can sometimes achieve the correct conclusion. Think of your lecture or teaching as the process of learning. Use assessments to check for understanding. That is where homework and group classwork should be directed.
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