Getting to the right answer
Students in a typical classroom only focus on what the answer is and if it is right sometimes ignoring the steps they took to get to the answer. In math, it doesn't matter as much if they get the right answer but if they know the steps they are following. Students can get the right answer most of the time in many situations and still have no idea what they are doing. This is extremely detrimental to their math health. It is more important that students understand the steps they took to get an answer. There is not always just 1 right way to solve a problem. If a student can understand the steps they took, then they are more likely to develop logic and problem solving skills for future subjects. Students must be taught to look back at their work and understand why they got an answer. As students grow to do this more often, they will find that math becomes easier and easier because they understand the logic behind why each problem works. An example of this is as follows.
Solve for x:
3x + 2 = 11
Student A: Well, let me plug in guesses. 2 doesn't work but 3 does work. The answer must be 3!
Student B: Well, I need to solve for x. Let me undo the +2 by doing -2 from both sides. I have to do the same operation to both sides to keep the equation balanced. So, subtracting 2 from both sides gives me 3x = 9. Now, to undo the 3 in front of the x I need to divide by 3 on both sides. Doing this gives me x = 3. So the answer must be 3.
Student A got the answer quicker, but student B understood the process of why it worked. Who do you think would be able to solve the following equation?
.7x + 3x - 4 = -2x - 8
I don't think a simple guess and check will work here. Student B will know how to do this because that student understood the logic behind the question. As teachers, tutors, and parents we must do a better job of helping students understand why a problem works and not just how to get the answer as quickly as possible.