To me, mathematics is not just manipulating numbers or using a correct formula to plug a whole bunch of things into. Mathematics includes understanding, exploring, and discovering. It includes looking outside of the box, and creating new ideas that can be tested.

How do I learn Mathematics best?

I learn mathematics best when the teacher has a very structured way of teaching the basic material, then gives examples, and then allows the students to make discoveries about what they have just been taught on their own. Then, as students try to do an assignment, the teacher allows for questions to be asked, and then helps the student when they get stuck.

How will my students learn mathematics best?

Students have many different ways that they learn. I would try very hard to use many different methods to teach students. These would include visual learning, such as writing on the board, hands-on activities that illustrate the principle I am teaching, examples that we would work through in class together, and then time for the students to try it on their own. This would hopefully work by using different styles of teaching to reach the different styles that people learn math the best.

What are some of the current practices in school mathematics classrooms that promote students learning of mathematics?

Many mathematics classrooms these days are doing exactly what I suggested I would do with my students, which is to use a variety of teaching methods to try and reach the different ways that the students would learn. I thoroughly enjoyed my Statistics class where we did many hands on activities that illustrated and demonstrated the principles we were trying to learn. The result was shown at the end of the year when we took the AP Statistics test, and all who took it either got a 4 or a 5 because we understood the concepts so well. As teachers continue to be creative in the way that they teach the material, more students will grasp the concepts that sometimes seem difficult in mathematics.

What are some of the current practices in school mathematics classrooms that do not promote students learning of mathematics?

This, I believe, occurs when teachers fall in to one of two categories. The first are the teachers who simply get up in front of the class, talk for the whole class period, and then give an assignment to the class as the class is leaving. The second are the teachers who do not have a solidified structure. Teachers need to be flexible, but if there is no structure to the class at all, the teacher can lose track of what he or she needs to teach the students, and can also teach things out of order of the best way to teach them. These two practices in school mathematics classrooms make it very difficult for students to learn math, because it does not allow the student to discover or learn for themselves, and doesn't allow them to try the concepts on their own.

I loved what you said on the 3rd question about how you would try several different methods because everyone learns differently. I also liked how you said teachers should have an underlining solid structure of teaching so that things are organized. Though they should definitely be flexible enough and care enough about their students to change their structure immediately if it is not suiting the needs of the students, which I'm sure any of us math ed students would recognize and do.

ReplyDeleteGreat job!

I liked when you explained what helps you learn math. Examples plus allowing the students to discover something really helps students become engaged and involved in what they are learning. Trying different methods to help teach other students is great! I believe that every student learns differently so by using different methods hopefully all of the students can learn better. I also liked the last answer about how you think teachers should be flexible but also structured. There needs to be organization to promote learning but if students ask questions a teacher needs to work around that as best as possible.

ReplyDeleteKevin, I really liked your idea on how to teach. Mostly, I like how you said that you would reserve time for students to do problems and then be able to ask questions. Often times I will sit through a lecture and feel completely confident, then get out and attempt the problems, and wish I had more time to ask the teacher questions!

ReplyDeletePerhaps however, in your two categories of teachers that could use improvement, you could reconsider the type that lectures the whole class through. Mostly, I would agree with this, however there are a few styles of math that contain so much information that I appreciate when a teacher fits in as much as they can, so I don't leave without anything. But that is only on rare occasions.

Good job though, you really nailed everything!

I also really like how you are planning on using several teaching methods AND gave us examples of those methods. I know in high school, sometimes I needed a visual before I actually understood and sometimes I needed to just try it by myself.

ReplyDeleteAnd I agree with Ali on this one, as students it's hard when a teacher just lectures but sometimes you need all the information you can get. Luckily for us, middle school or high school is the goal and information can be spread out over the week or the chapter and as teachers we'll have more control over that.

I appreciate the way that you want to use a variety of methods to address your students' preferred learning styles. Do you think that some activities are good for all students, regardless of what their preferred learning style is? Another way of thinking about this issue is to ask whether or not the things students would learn when the content is presented, say, visually might be different from the things students would learn if they just heard the words. Can all things be taught in each of the preferred learning styles?

ReplyDelete