Is that convex or concave?

In my first week of student teaching, I started teaching mathematics. The first unit was geometry, and my first lesson introduced them to polygons and the difference between convex and concave polygons. I looked over the teacher’s manual and made some changes. In my math methods class, I remembered using many tools to help learn about geometry ideas. I substituted Geoboards for making polygon shapes. The book had the students using straws that were placed together by twist ties.

I started the lesson with math problem review on white boards. Then they completed a short quiz on the information from the day before. After this, we always correct the homework, which takes a good 20 minutes. Once we finally started talking about the new information, I taught the students in a large group, but we only had enough Geoboards to work in pairs. I had them make a convex polygon, and they would hold up the boards for me to see. Then we did the same thing with concave polygons. I felt I was rushing through the lesson because I wanted enough time for them to work on homework. We had changed the schedule that day from 75 minutes of math to 60, and I had plans for 75 minutes.

Since I was moving to quickly through the information, I cut things out, and I didn't go over the information as thoroughly as I could have. The students ended up having 15 minutes to do their homework, and the advanced students that finished didn't have anything to help occupy their time. I learned quickly that the students needed something to do when they finish their work.

The next day as the students entered the room they were given a quiz to see what they remembered from the day before. We didn't have time for math on this day because the schedule was full of other activities, so I brought the quizzes home to assess how they did on the new material. There was a question asking the students to circle the convex polygons, and there were six shapes to choose from. As I correct the quizzes, I found out that only two students understood the material. This was shocking because I thought I did a fairly good job. The comment I remember from my cooperating teaching is that the noise level got high at the end of the period. Of course it got high, the students were done with their work and had nothing to do besides talk with a neighbor.

I am glad I quizzed the students because I took that information and recreated the lesson for the next day. I took a large block of time to draw polygon shapes, and talk about the characteristics of a polygon. Then I drew shapes of convex and concave polygons. At the end, I had the students tell me the answers to the quiz questions. I felt like after the review they actually started to understand the concept.

Every new teacher has surprises when teaching new information for the first time. I was so stressed out about the time that I did an injustice when teaching the material. Sometimes a lesson may have to spew over to the next day, and that is ok. This last week I spent a lot of time reading over the student reference book, so I understand the material well enough to teach it. I was always decent with math, but until now, I couldn't tell you the definition of a polygon, quadrangle, or a parallelogram. Maybe I should have these terms filed away in my brain, but I don't. I am surprised at the amount of information I need to learn to be a successful teacher. After teaching lessons, Ms. R and myself go over the good things and the areas that could improve. My word choice and verbiage are always an area that needs some work. Ms. R has taught for many years, so she knows these terms like she knows her daughter's name. Is it common for new teachers to learn some or a lot of the information before they teach the ideas for the first time? I know if I ever teach a geometry unit again, I will know more of the content.

After teaching for a week, I am making adjustments to the way I prepare for the next week. I am implementing a daily schedule of when I spend time writing lesson plans, preparing for the day, and correcting papers. I also have mandatory personal time in the evening. I have been doing work constantly, and I will not be able to keep up at this pace unless I take some time to myself. As a professional teacher, I will have to find that healthy mix as well, so I better learn to pace myself now. I am also going to adjust my lesson plans, so I can find a way to spend less time creating them yet still have them be effective. As teachers we are always learning, which is probably why so many people love this career. Let's learn on!