Instructional Experiences

EQAO and Presentations

       The following section of my portfolio will discuss my instructional experiences with EQAO and two presentations I delivered.  I will identify and explain how the artefacts I have chosen for these instructional experiences contributed to my ongoing development as a mathematics instructor.

EQAO

EQAO test question 1 - Grade six mathematics

EQAO test question 2 - Grade six mathematics

       One of my first assignments involving instructional experience was the "Problem Solving Activity."  This assignment required me to test and observe two students solving two different Education Quality and Accountability Office (EQAO) questions. This assignment was a good first step for me.  In the past I have had experience administering test questions for students, but until that point I had no experience doing so with questions based on mathematics.  Significantly, I have never closely observed students actually attempting to solve a mathematical problem.  In terms of assessing tests I would normally look at the final product as oppose to actually observing the student in the process of demonstrating their solution.  This latter point was particularly interesting to me as it provided me with more detail as to a student's strategy and method for finding their solution.  I found this to be quite informative, especially in relation to helping me better understand the root cause of their calculation and proof checking errors.  I think I would implement this strategy with students that I judge to be struggling with a particular mathematical concept or problem.  I believe this would be an effective method for applying a diagnostic assessment of student's particular strengths and weaknesses.  Along with my close observations of student work I found the comparative assessment aspect of the assignment to be quite useful.

       I believe that taking the time to compare and assess student work meticulously can teach you many things about common student practice and error.  Comparing the solutions of my two EQAO assignments revealed to me that many mistakes are easily avoidable with a little more care, patience, and due diligence.  That is, I found that the errors in my students' solutions tended to emerge from things such as measuring inaccurately or failing to review their work properly.  This helped me to understand that student work habits have an important role to play in terms of supporting the task of producing quality work products.  Therefore, these subtle, yet, important details that I learned from the problem solving activity provided me with valuable experience as to both instructional approaches and assessment strategies.

Presentations

Work Sheet Handout for First Presentation on Decimals

       For 8P29 all students were required to deliver two presentations to the class on two different mathematical units.  My first presentation was done individually and focused on decimals.  My second presentation was done collaboratively on the subject of measurement.  I will now briefly explain the significance of the two presentation in relation to my teaching experience.

       My individual presentation on decimals was a challenging experience for me.  I have given lectures before, but never on the subject of mathematics.  Lack of experience is often an impediment to effectiveness and quality.  Unfortunately, I think this was all too apparent in my presentation.  While I devoted a considerable amount of time preparing for my presentation it was difficult to anticipate some of the issues that would arise during its actual exposition.  For example, my presentation was too long.  Having never delivered a lecture on mathematics before I did not realize or expect the procedure to take as long as it actually did.  This was especially true in terms of writing out solutions to problems on a white board and providing students with sufficient time to solve the solutions that I had provided for them.  In other words, understanding the intricacies of time management in relation to delivering lectures and allotting room for student work was something I needed to consider more closely for future endeavours.  One possibility for improving this latter situation was to incorporate technology with my lectures.  Not only would this have helped me to differentiate instruction, it would have also save me some time writing out solutions that are prepared on a white board.  While my first presentation on mathematics was not an astounding success, it nevertheless taught me a great deal regarding the areas I needed to improve on.

Power Point for Second Presentation

Definitions, Curriculum Expectations, and Assessment Guidelines Handout from Second Presentation 

       My second mathematics presentation for 8P29 was a cooperative assignment.  This presentation came much later in the course so I felt much more prepared and confident compared to my first presentation.  I appreciated the cooperative nature of this presentation as allowed for opportunity for to improve some of my previous shortcomings.  More precisely, my partner in this assignment was particularly apt at incorporating technology with presentations on mathematics.  Working together, he was able to instruct me on some of his techniques and strategies for using computer programs for both presenting a lecture and addressing solutions to problems.  This was a positive experience for me as this interaction was able to instruct me on some useful skills that I would have found difficult to master if I was working independently. Furthermore, the use of technology, as anticipated, provided more time for student engagement in the projects that we provided.

       The cooperative presentation we were assigned required a focus on measurement.  My partner and I decided that rather than focus on measurement in general we would focus on a until of measurement in particular.  For this we chose the measurement of circle circumferences.  We studied a variety of potential student projects and decided on two different student assignments.  For these assignments we deliberately chose a project that we knew would have a high probably of success and, contrary to this, we chose a project that we anticipated would have far riskier chance of success.  The former project involved calculating for pi and calculating the circumference of a circle using string and ruler.  The latter project involved spreading toothpicks on a appropriately spaced line paper.  The second project was intended to be more fun than informative.  The goal of the second project was to demonstrate that the number of toothpicks that intersect with lines on the paper should, if divided by the number of the sample size, provide a calculation that is close to or equivalent with the number Pi.  Without going in to too much detail here, the reason the number Pi should emerge has to do with 180 degree rotation of the toothpick, which, if traced around in its rotation will create a circle.  Unfortunately the second assignment was not a success.  To me this demonstrated that creative, yet, risky assignments such as this one require meticulous trials before being implemented in class with students.

       In conclusion, I found that both my EQAO testing and two presentations made a significant contribution to my instructional experience with mathematics.  While my experience is still limited, I believe that I have learned useful lessons and strategies that will assist me in my further development as an instructor.  These projects have been useful as they provided me with opportunity to apply novel strategies of assessment (EQAO) and refine my skills and understanding of lecturing.  As the say goes: "there is no substitute for experience", and I believe these instructional opportunities provide me with experience I require to further my development as a competent mathematics instructor.