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Changing Beliefs
Following six weeks of student teaching I have made many realizations and solidified many of my beliefs about teaching mathematics. I feel that only a few of my views about teaching have changed, but those slight variations have shown a significant difference in my students' success. In general, I continue to believe that students need to see how what they are learning relates to the real world, especially for students who may not attend college. On the other hand, one of my changes in view deals with ensuring that every student has a complete understanding of every subject. I first believed that I could help every student understand every concept even if it took extra time. The past six weeks have shown me that this is not always possible. With a class of twenty-five students there are going to be a few students who will not try and there are not enough hours in a day to spend with them. I have learned to do what I can and hope for the best. I feel that the view that has solidified the most is about varying activities and still ensuring that the students learn the basics of the subject.
When I first began student teaching I believed that students needed some variation in the types of activities that were done in the classroom, but in general the routine should be pretty consistent so that the students knew what to expect. I felt that the main structure of the class should be lecture and practice with some extra, fun activities interjected to give the students some flexibility. I have always felt that students need to practice the material either using textbook exercises or worksheets so that they can get a firm grasp on the concepts. During my student teaching both of my courses followed this format for the first chapter I taught, but after that things changed. I saw both extremes, one in my technical geometry classes and one in my college geometry classes and I realized that my views were actually the happy median.
Both the technical and college geometry classes started off really well by having a lecture on a topic and then working on the concepts using worksheets for a second day. After two-three topics were covered there was a quiz that followed from wh at they had learned. The majority of the students were understanding what was going on, despite the topic being very difficult (i.e. 30-60-90 triangles in technical and numerous theorems on polygons in college), and did very well on the quizzes and tests because they had the opportunity to ask questions and work on several problems that were exactly the same.
There were fun, math related activities to change the structure of the class. For example, one day in technical geometry we did an activity where each student was in charge of doing one problem on a worksheet about the short and long leg formulas for 30-60-90 triangles and then presenting it to the class. They could ask for help and worked really hard because they did not want to make a fool of themselves in front of everyone. They seemed to enjoy it and most students were catching on as to how to do the problems. In the college geometry classes we spent one day working in groups on writing proofs about parallelograms. The students worked well together and were able to help each other through parts that were difficult. The majority of the students understood the properties of parallelograms and proof writing much more following the activity and it showed on their tests and quizzes.
When we started the next chapter on polygons in the technical geometry classes my teacher suggested moving quickly through the chapter since it was pretty easy and we needed to move on. Therefore, I changed my format and would lecture and do practice pro blems with them on the board. After two or three topics (2-3 days) they would take a quiz and we would move on. There was very little variation. The only fun activity we did was the dollar bill folding activity and we even squeezed that in at the end of a day of class. I noticed a big difference in the students' understanding of this chapter. Some of the students had almost given up completely because they had gotten lost earlier in the chapter and could not catch up, while others just did not voice their questions and therefore never learned the information. The test and quiz scores dropped dramatically and there are students who still complain that they do not understand some things. Therefore, I feel that more time needs to be spent on practice and fun learning activities so the students will continue to be interested and want to learn the material.
The college geometry classes took a swing in the opposite direction and incorporated more fun learning activities and less practice and lecture during the next chapter on transformations. On the first day I briefly discussed rigid transformations and isometries before introducing an activity on creating tessellations. As I would find out later the students quickly forgot what rigid meant and what an isometry was. They did not have enough practice with the terms and were so involved with the tessellations that they did not pay much attention to what was covered. This continued throughout the chapter as we did activities with Miras for reflections and kaleidoscopes for rotations. When it came time to review for the test there were many questions and a lot of things that the students did not understand. They will be taking their test on April 3 and we will see if they were able to understand the material. If they do well then I feel that it was more because they studied a lot over the weekend and not because of what we did in class. Based on this experience I feel that more practice and lecture are needed, despite it being boring, to ensure that a full understanding is achieved.
Based on these two experiences I have solidified my belief that there needs to be an emphasis placed on lecture and practice while still included some fun, student-centered activities for a change in pace. I have tried both lecturing more and including more activities, but with terrible results. I think that there is balance that works for every class and the same thing may not work for everyone. While this view has been solidified the most, all of my experiences student teaching have helped mold my overall beliefs about teaching mathematics and how I want to run my classroom. It is an experience that I would not trade for anything and it is making me look forward to my first teaching position.