Weekly Report & Reflection Week #9

A Proof From Euclid's Elements. http://bit.ly/1MZhNfG. Public Domain.

       This week I will be talking about my presentation on calculating the circumferences of circles.  The intention of the presentation was to provide a mock lesson for teacher candidates in my class and to hone my own skills in regards to organizing and presenting lectures in mathematics.  This presentation was done collaboratively with a peer teacher candidate.

       Altogether I thought this experience was quite positive.  Normally, I am not the biggest fan of collaborating assignments.  However, in my opinion, this collaborative assignment worked quite effectively.  Naturally, it helped that I worked well with my presenting partner.  We got off to a good start and organized ourselves without too much difficulty.  Cooperatively, we decided on which area of the curriculum expectations for measurement we would cover in our presentation.  That is, we identified the overall and specific expectations from The Ontario Curriculum: Grades 1 - 8 Mathematics that we would lecture on for our presentation.  These were: "Measurement: developing circumference...for a circle" (p. 109) and "measure the circumference, radius, and diameter of circular objects, using concrete materials (Sample Problem: Use string to measure the circumferences of different circular objects.)" (p. 113).  With this in place our next step was deciding on how we wanted to do our presentation in order to meet these latter curriculum expectations.

       In my view, this next step is where the value of doing a collaborative assignment really came to fruition.  My partner and I were able to share some thoughts and ideas about how we go about presenting the assignment to the class.  It was very helpful to have someone that could provide a different insight to the assignment and also help criticize or reinforce my own ideas (I hope this was reciprocal for my assignment partner).  After working together and brainstorming some ideas we decided on splitting our presentation in to three parts.  First, we decided to present with a lecture explaining the formula for calculating the circumference of a circle (Circumference = π × diameter = 2 × π × radius) and its applications.  With this information in place, we decided our second component would involve group work using string.  

       This second part of the presentation was a key factor for demonstrating student learning.  My presenting partner and myself knew this assignment would work based on our own experience preparing the assignment before class.  We created a handout with various sized circles on it and provided string and rulers for the class to use.  The learning goal for the class was to measure the circumference of the circles and reveal how this measurement worked with the circle's radius/diameter to calculate Pi.  String was a good manipulative to use to help differentiated instruction.  It was also a useful device for showing the relationship between the circumference of a circle as measured by the string with both the circle's radius/diameter and Pi.  With the success of this assignment we decided there was room to try something a little more unorthodox and, hopefully, enjoyable.

      For the third part of our presentation my presenting partner and myself decided to try an experiment called "Pi and Buffon's Matches" (please see Blog Post #8 for more details on this experiment).  Unfortunately, this assignment, although engaging, was not a great success.  Only one out of the three of our groups were able to come up with a calculation reasonably close to Pi.  I think if I were to try and repeat this experiment again with a class I would have to practice it many times in advance to make sure I was using an adequate amount of toothpicks with an appropriate sized paper for distribution.  While this was part of the presentation was not a great success, I feel that it has alerted me to the need for extensive preparation when trying to something a little unorthodox with a class.

       All in all, I thought the presentation went quite while.  I felt that we provided a valuable example to our associate teachers as to what a good lecture on calculating the circumferences of circles might look like.  While there is a little bit of work that still needs to be done in some areas, I would feel confident employing this style of lecture and group work assignment with a class of grade eight students.