What is Symmetry?

The second week of the program was both exciting and crazy. Our after school program now has twenty students. There are mostly fourth graders but there is now one fifth grader and two sixth graders. With twenty students and three RPI student teachers it was quite a challenge to get them to pay attention when they were so eager to get started. While the students were eating their pizza we had a discussion about four-fold symmetry and Native American beading. The students were broken up into three groups and each group was given a picture of a Native American beaded pattern and were asked to fold the picture one so that it is the same on both sides. Once they completed that I asked them to fold it again so that it had the same image in all four boxes. This was also very easy for them. After this we broke them into three groups to teach them basic graph skills and plotting points. There were three stations, one just exploring the software on the computer, one making a four fold design and then finding the points that make up the design and finally one that the students had to direct other students to find an object on a grid. I was assigned the task to lead the last station and it was more rewarding than I could have ever imagined.

I placed an object in a square on the grid and asked one student to stand at a corner of the grid and assigned them a partner to give them directions to the object. The student at the corner was only allowed to move according to the directions the other student gave. At first the students just kept giving directions such as left, right, up and down. For instance, a typical dialog was left, left, up, up, up, right, right,up. Then I told the students to use numbers in their directions and I got four left, up five and right 2. Finally, I had the students try to use negative numbers when they were going left or down. This was hard for the students that have never seen negative numbers and without the help of X and Y axises, but eventually it was starting to come more naturally. After each student got the opportunity to be both the person giving directions and the person moving we switched to another activity. I gave students a bag of shapes and each shape had four copies of it. I then asked the students to work together to create a four-fold symmetry design. They started in one of the corners and made a design then the took a copy of each of the shapes and physically flipped them to make the other three corners. After doing this activity they really seemed to understand the the idea of four fold symmetry.

During both of these activities I struggled with the balance with telling them how to do something and letting them figure it out on their own. I found that the best practice is to just have them start and see where they go and tailor your lesson to that. This is because they start with what they know and understand and you can build from that. This removes the problem of teaching above them and then having to backtrack. I also understand that this is not ideal but I feel that it is an excellent practice if time allows.