Mathematics is a way to solve problems. Math is the basic foundation for almost anything you need to do in life. Mathematics is essential knowledge in any sort of education. Many people use numbers, figures, and equations in their everyday life. This is mathematics.
I learn math the best by following examples. If I am taught the basic concept first, and then shown some examples to illustrate the particular concept I am able to apply that concept to many other problems even though those problems might be more intricate. I am a visual learning, so watching someone complete a similar problem helps me learn to solve problems.
I think most students are also visual learners. I think a lot of people learn by examples. When people see how to complete a problem, I think it helps them to see that the problems are just done step by step, and it gives them the confidence to know that they can also complete problems that deal with the same concepts.
One thing that helped me in my high school were the workbooks that we completed while the teacher was lecturing. I don’t know if these workbooks are still out there, but it was really helpful because we had to listen to the teacher while writing down the important concepts that were being taught. Also, there were many examples in these workbooks, so we could practice the concepts with the teacher’s help before attempting our actual homework. These workbooks really helped me to follow along with what the teacher was talking about, and they helped me understand what concepts I had a more difficult time with.
One thing that I had trouble with in high school is when the teacher would only do examples. This sounds contradicting to what I have previously said, but sometimes the teachers just get up do examples without explaining the concept behind it. I had a hard time in high school when my teachers would do this. I think it is important that the teacher explain the underlying concepts before delving into examples and letting the kids loose on the homework problems. It is important that the students understand why they are doing certain operations and steps when working their problems. They need to have that foundation, or else they won’t really learn the material, they will just get enough information to roughly complete the homework.
I liked a lot of what you had to say and I agree that concepts need to be explained as well as doing examples otherwise the students would just know the arithmetic and not understand what it all meant. I agree that examples are a lot of help I would only say that I think it is important to make sure to allow the students to try to learn for themselves sometimes rather than always giving everything to them through examples(make them work it out in there head before too much explanation). This will help them to learn and think for themselves. Of course it is important to know when to give them examples right off the bat and when to allow them to learn for themselves. Thanks for writing.
ReplyDeleteI had a similar experience as you with a teacher who just delved into examples. I agree that it is important to teach the concepts so that students know why they are doing what they are doing. Otherwise, math can become so tedious and pointless.
ReplyDeleteWhen you talk about students learning best visually, I know that I too learn best that way as well. However, I sometimes wonder if that is really true for everyone. It might be beneficial for the students to try it out right then after having shown them the example.
I appreciated your comment on the importance of teachers explaining each example. If they don't, it is kind of like a deaf person walking through life trying to understand just by watching - more communication is necessary. I would like to add that it is crucial for teachers to explain each step, make sure the class understands what just happened, and then move to the next step.
ReplyDeleteYes, I do remember those workbooks. However to me it sometimes seemed like sudents just filled them out to get the grade - they wanted to make sure they were all caught up, but did not really understand what was in them. I think workbooks could be a great asset to understanding for the student who wishes to use it properly, but for others it seems the workbooks are not always the best method to promote learning.
I really liked your idea of building on concepts and applying them to new situation. I think then math becomes easier to learn and remember because it all builds on each other. Do students always make mathematical connections like these? How can we help them to do so?
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