New Insights and Their Implications

New Insights and Their Implications - What did you learn from your peers, from the instructor, and/or the readings, about elementary school students, and/or about yourself, and the teaching and learning of math and what are their implications to teaching and learning mathematics?

During the past month in class I was amazed on the many different tools that can be used to help students learn fractions. I really enjoyed learning how to incorporate models into the classroom as well as experimenting with them myself. I thought the interactive sites on the web were outstanding and look forward to using them in the near future. I have always enjoyed fractions, but I do realize they may be difficult for some to understand so with the help of what we have learned in class as well as the models I believe I can now more effectively teach fractions. I look forward to learning more about math during the last month of class and can't wait to adapt this information to my own classroom.

Question and Answer

When we started the section on fractions I knew I was going to have problems understanding this topic because it has always been something that i have struggled with. As we went through the weeks about discussing fractions and learning more about them a lot of my questions were answered. The first question that i had was, how am I suppose to teach about a subject that I am not comfortable with. The solution I have come to is I will use my resources. Dr. Reins has pointed out a couple websites that I can use as resources to help my future students understand fractions. I will also use my book as a reference because they have many good ideas that I can use in my class room. The second question that I had was, what other models are our there that I can use to teach fractions to my students. This question was answered when as a class we were introduced to fraction bars, pattern blocks, dot paper, cuisenaire rods, and the cake pan method. I quickly caught on how to use each of the models and I will be using them in my classroom as well to help further my students understanding for adding/subtracting fractions and multiplying/dividing fractions. After the lessons on teaching fractions the only question that I still have is with all of the methods that we have been learning about is there one we should start with first or is it OK to start with any and then cover them all eventually? I feel that I would want to start with the one that know the best so I can give the students a foundation and then branch of in showing them all the other methods.

Summary

I enjoyed learning how to use all the manipulatives we used in class and the different ways that they can be used to teach. I liked learning why we do the steps we do to solve math solutions instead of a rote method of trying to memorize. I enjoyed watching the CGI video in class, it was good to see an example of how it is supposed to work in the classroom environment. I think the CGI method could be very beneficial for students as long as the teacher can guide the lesson and engage the students in the activity.

Summary and Synthesis

I actually liked this last unit on fractions. I liked that we were able to work with different manipulatives like the pie pieces and fraction bars. Most of what I know (with Math) is due to rote style learning. I like that this last unit gave us different ways to teach fractions. I agree that teachers need to start showing their students how to develop an understanding of "why" to do things, rather than just doing things without a reason and just off of memorization. I believe that students will have a better chance of understanding and remembering different mathematical rules and operations if they understand why they are doing what they are doing. I liked learning about the CGI program as well and it was nice to watch the video to see the classroom with that learning approach. I think that it is important to give students many options when solving problems and I thought this unit did a great job of showing us future teachers how to achieve that goal in our own classrooms!

Summary and Synthesis

We have been learning about addition and subtraction problem types. I have never heard of join, separate, part-part whole or compare.I think this is an interesting way to look at problems. It took me awhile to understand the differences of and what each one meant. These four are different structures of a problem and they describe the way a number sentence will be written. This is good for teachers because they know where to start when giving their students addition and subtraction problems. The teacher will also know what types of problems to give to the students and also what types of problems the student struggles with.