1. What is mathematics?
It is a tool used to measure and give meaning to things in this world.
2. How do I learn mathematics best? Explain why you believe this.
I learn best if we go through and solve an example together while the teacher explains the meaning and reason for what we are doing; explaining any of the equations that would be used to solve it. By doing this I am able to put action with reason. After we have gone through a few examples, I need one or two more, so that I can go through in class on my own before we go over it together. Most importantly, when I’m given enough time, I am able to comprehend it and solve it myself. Then I am able to better solidify what I have learned.
3. How will my students learn mathematics best? Explain why you think this is true.
They will learn best when they understand what they are learning. Giving them a formula to use does not necessarily mean they understand why the formula works or exactly how to use it. When they understand the underlying concepts better, then the will be able to learn.
4. What are some of the current practices in school mathematics classrooms that promote students' learning of mathematics? Justify your reasoning.
Some teachers choose to lecture mathematics, others use a method of discussion, some use scaffolding to help them, and there are a few who use discovery learning. Lecture is when a teacher simply explains and instructs the class on the concepts to be learned. A discussion consists of an examination of the concepts. Scaffolding is when a teacher helps the students a lot in the beginning and then slowly removes his/her help to where the student does not rely on the teacher. Finally, discovery learning is one of the hardest methods to use. It requires a good amount of time to be given to the students to explore ideas about the concepts being presented, but it allows for the students to discover mathematics for themselves.
5. What are some of the current practices in school mathematics classrooms that are detrimental to students' learning of mathematics? Justify your reasoning.
Well, I know lecturing is one of them. Lecturing gets the information out there, but it does not allow for student feedback. I does not ensure in any way students are actually understanding what they are supposedly being taught. I also think that when there is no instruction from the teacher at all that some students will lose hope in learning and they will give up on it. Students do need a certain amount of guidance. As a teacher, you need balance. Not everyone learns in the same way, so you have to use different methods of teaching to compensate for this.
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I agree with you that understanding is crucial to learning mathematics. I was wondering if the understanding you were talking about in your response to the third question was the same thing as the knowledge you talked about developing in your response to the second question. In other words, I guess I was wondering what you meant by understanding. Some people think that understanding means being able to do a mathematical procedure correctly. Do you agree with that.
ReplyDeleteI also share you skepticism about lectures. When I have to lecture, I always try to incorporate some form of informal assessment into my lecture, such as asking questions or having students complete a short activity. Even then, I am always suspicious that many of my students may not really understand what I'm saying and doing. For me, lecturing is pretty risky teaching activity if my goal is to have my students develop a rich understanding of the material.
I really liked the points you made in #3 and #5. It is so important that teachers teach beyond writing a formula on the board and telling you to punch numbers in. There is a reason that formula works, and most students don't feel comfortable using it until they understand it.
ReplyDeleteAlso, what you said about over-lecturing teachers is very true. No one likes a class where the teacher stands up and talks the whole time. The only thing I have to add to that is sometimes the teacher steers too far from lecturing and they really just leave the classroom to work in groups the whole time to figure things out together. That is almost as much detriment to students learning as is over lecturing.
Great Answers!
I also think that students can understand the principles behind formulas and equations because that's when you can really figure out how they can apply to several different things. I wonder how a discovery method is used in things like calculus, I'm not sure I've ever had a teacher teach that way or not.
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