1. Math. Everyone uses it, but how do you define it? I suppose it would be the attempt of man to form patterns from the numbers, structures and space that we use everyday. There are several forms of mathematics and they can be used for a variety of different purposes. Some may study pure mathematics while others choose to apply it as a science with physics and engineering. Whether we are counting money, building a house, or calculating the force that a spring gives off--we all use math.
2-3. I learn math best when I am given examples of specific problems that I will be dealing with. Once an explanation of the concepts are given, I need to work on problems on my own otherwise I won't understand them fully. I believe that my students would benefit from this method as well. Although working in groups can be helpful, I think it should only be done after each student has time to work out the problem in their own way. Every person works through things differently and I believe it is important to give them that opportunity before providing assistance. Once they have done this, then they can either discuss the problems with classmates or ask me questions that they have. I realize that every student learns in their own way and so questions can be answered specifically for different students' mindsets.
4. It is very helpful when math teachers show different approaches to solve problems and give the students helpful methods to remember the material. The math classes that I learned the most in were taught by teachers who were very interactive with the students and were always willing to work through any obstacle we came across.
5. I think the worst thing for math teachers to do is to give a broad description of the material and concepts and then leave the class alone. Although students should have time to work on the problems themselves, it is useless if the material provided wasn't helpful. My younger sister is in high school right now and constantly needs to call me for help because her teacher never teaches them properly. If an instructor doesn't get to know the students and how they learn things easiest, it can be very detrimental to their education.
Maybe instead of holding off in group work in class it would be better to encourage a different student every day to do a problem on the board in front of the class with the help of the class so that as the student is writing what the class tells them to they are understanding how to do the problem.
ReplyDeleteI definately agree with what you said about teachers showing different ways to reach a solution. All students learn differently and it is important to get to know each student and their learning styles to be able to successfully connect concepts with each student.
I was thinking about what you said about group work and I think I mostly agree. What often happens in groups is that one student will dominate the disscussion with their method, which the others may not necessarily understand. However, at the same time, group work can be a very valuable way for students to bounce ideas off each other. I know that sometimes when I'm trying to work something out for myself, I can get stuck completely on the wrong track, in whereas a group would keep me in check. I think it depends on the students - if they are perfectly willing to sit back and let others do the work, then group work is probably not the best idea!
ReplyDeleteI agree completely that students need the time to work out the problems on their own. It is helpful to hear how other students solve problems, but you will never learn the material well if you rely on others guiding you through every step. However, I disagree that giving broad descriptions is bad. Students need to understand the general concept and principle instead of memorizing how to solve a specific problem.
ReplyDeleteI really liked what you had to say about having students work individually and then go to a group. I think students need the time to think through the problems on their own and come up with their own ideas of how to solve it. Then when they go to a group they can learn better from each other and get new, slightly different ideas.
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