Lesson That Bombed

Today, I tried a discovery activity with my 6th graders that required them to make a few connections with previous information they have learned about. Unfortunately, it failed miserably and I am concerned about how this will affect the students mentally. We were starting a lesson on the area of a circle and we had just discussed the area of a parallelogram.

I took a circle and cut it up into pie pieces, then placed them next to each other with opposite orientation (imagine the sides of two pie pieces running along each other, with the point from one piece touching the crust from another piece, then continuing that pattern, first piece points down, second piece points up, third piece points down, etc.).

By doing this, we form was resembles a parallelogram. The height is the radius of the circle and the base (or length) is half the circumference of the circle. From here, I tried to get them to see relationships and justify how we can derive the equation of a circle from this method. I even put all the equations they needed up on the board. But the students had a hard time seeing that if C=pi*r^2 in one equation, they could replace 'C' in another equation with pi*r^2. I tried and tried to get them to see it, but they just could not make the relationship.

I spent the whole class and all I got was a glazed look and many students saying they did not understand. There actually were a few students who said they understood what was happening, but most of them did not. However, most of the one's who did not understand were the weaker students and they often give me a confused look. I am beginning to think that it was to early for these students to see this type of activity. With the reactions to this activity, I feel they are not ready for understanding the reasoning behind where equations come from and how we develop them.

Now I am forced with a decision.

1. The activity is not something the students need for the lesson. Really all they need is to plug numbers into the equation and solve. So they really do not need to understand this activity to complete the homework. So if they were completely lost during this activity, which many of them were, it is not necessary for the completion of the lesson or quiz.

2. Part of the problem that these students had with making these connections is that they have not had to do that in the past. It has always been, "here's an equation, plug numbers into it and get a number back." If I accept this and move on without trying to clear up the activity, I am not helping them develop critical thinking and abstract thinking skills. However, I feel I could spend another two days on this activity and many of them would still not understand.

As of right now, my goal is to have the students come in tomorrow and make two circles with a compass, one to cut out and one to keep as a circle. Then I am going to have the students complete the same activity and hopefully they will be able to see relationships if they are actually engaged in the activity. If this doesn't work, then I guess it doesn't work and I will have to accept it.

At the end of the lesson, I was very discouraged. I wasn't sure if it was something I was doing or if 6th grade is too young, developmentally, to comprehend this activity. If its the case of development, then its still something they need to be introduced to because its going to show up later, so why not now.

As a side note, I have been extremely busy the last few weeks and feel that I need a break. I have spent the last 4 free Saturdays in the school working, prepping or grading for about 4 hours at a time. I feel that I am having a hard time keeping up and can't get ahead. I will say that I have also noticed that I am giving more time to working with the students, instead of presenting the lesson and then working on other things. I am presenting the lesson and then walking around and clarifying things with students. This is taking time from me working on class activities, but hopefully it will help the students in the long run.

Aaron