Well class is coming to a close and I am working hard to put the finishing touches on all of my final assignments and projects. It is hard to believe that the semester is already over. For this final post I am going to reflect back on some of the things that I have learned and some of the things that I am going to continue to work on before I get a job teaching math. As I have progressed through this class I have learned many teaching strategies for math, the different ways that students learn math, and some teaching aids.
One of the main concepts that I feel was emphasized during the class was to have the students explain their thinking. One reason for this is to see where students are getting things mixed up and then being able to help them figure out a way that will work for them. Another good reason for having students do this is to show that there may be more than one correct way to get to the same answer. So many students have this misunderstanding that there is only one way to do the problem, instead of them finding a way that works for them. Finally, students may know what they are doing, but are making simple error in their computation. Having them describe what they are doing will show if they understand the concept.
A couple of the teaching strategies that I thought would be very useful were the verbalizing and then algebrifying exercise and the complexifying exercise. The first one had students verbalize what they were finding in a problem and then having them write an algebraic formula based on what they were describing. Students struggle with the idea of variables and this exercise can help them find a way to clarify this concept. The other exercise has students take a very simple function and then add to it to make it more complex. Students then trade their work with someone else to see if they can then simplify it back down to the original function. By seeing how to make the problem more complex, it is easier to see how to work back wards to make it simpler.
During class we were able to work with a few different types of manipulatives. I had never had the chance to work with these while I was in High School or Middle School, but I have learned they have many benefits to students. For your students that learner more visually or with a more hands on approach, these will be great for them. Even for the students that are at the top of the class, they will see some benefits as well. I will be making sure I have some of these for my classroom and I will continue to look for resources on how to use them and what concepts can be taught using them.
Technology is a good resource to use today and the two programs that we worked with in class will be great tools. GeoGebra and Desmos are another great way for students to experiment with a new concept and to get more visual learning. I will continue to work with both of these programs to see what they are capable of and to see what concepts can benefit from being taught or introduced using one of these programs.
The final thing that I will need look at are the common core standards and the state standards. I want to have a better understanding of these standards. As I am learning about the various requirements for each grade level and class I want to start compiling resources that can be used with each one. I am thinking that I can organize all of the materials that I find into google docs. As I learn about a new standard or find something useful that I can use later I can easily add it to my list.
This class has been a great resource for me and I have learned so much about how to teach math. It has started my journey at looking at how I will teach math if and when I get a job. I am excited to continue to learn and to find new resources.
