Final Reflection

Education 3940: Mathematics in the Primary/Elementary Grades was the course I dreaded completing the most. Through primary school right up through the elementary grades, I struggled with understanding mathematics. During high school, I completed an advanced math course by efficiently remembering formula upon formula. By the time I completed two math courses in my first year of university, I still had not gained a conceptual understanding of the mathematics involved. Therefore, my own personal struggle with mathematics left me feeling incompetent. I dreaded taking the Mathematics 3940 course.

And now, as I write my final reflection for Education 3940, I feel as though I have grown as an individual and am one step closer to becoming an effective teacher. First and foremost, I have alleviated my own fear of mathematics. When on the first day of class, we placed ourselves accordingly to how we felt about math, I stood nearer the middle of the classroom. I knew at that moment that I wanted to be able to stand at the front of the classroom where I could proudly say that I loved math. Even as I write these words, I cringe a little. I cannot yet say that I love math but I am very proud with the progress I have made over alleviating my own personal fear of math. The key to alleviating my fear of math was to jump into the course with no hesitation and most importantly, to keep an open mind. I believe the math fair really opened my eyes to what I could accomplish in the area of my own mathematical learning. As I completed each new problem-solving question presented by my peers with enthusiasm and determination, I felt such a great sense of accomplishment. For one of my observation days, I had the opportunity to participate in a mathematics professional development day. I was given the opportunity to view firsthand how students respond to mathematical content by way of reasoning and communication. That experience showed me the significance of understanding the mathematics behind a given formula. Both experiences allowed me to overcome my own fear of math to truly learn how to make math more meaningful to and engaging for students.

Over the course of this semester, the most important thing I learned was knowing how to create a safe and comfortable environment in which students could effectively learn mathematics. All throughout school, I was expected to complete a mathematical problem or formula the exact same way the teacher had shown us. I never could understand why students could not use their own strategy to complete a problem. Needless to say, I recognize the significance of enabling students to apply a number of strategies to a problem. When a student is encouraged to develop and/or apply a particular strategy to a problem, he/she can more effectively determine if the solution is justifiable. This in turn, allows the student a more comprehensive understanding of the mathematics at hand. I learned that mathematics need not be completed in isolation but rather should be encouraged through group work. Students effectively grow into learning when interacting with peers.

Another important thing I learned this semester was that problem-solving should be an integral part of the mathematics program. Instead of setting one day aside for problem-solving, open-ended questions should be offered to students consistently. Problem-solving questions should reflect the mathemmatics which is to be learned, be encouraged as group or whole class initiatives and be meaningful in relation to the real world, again allowing for a more comprehensive understanding of the math involved.

The most important thing I have taken away from this course is that as effective mathematics teachers, it is our responsibility to ensure that students not only efficiently complete a mathematics problem but to also provide a justifiable response as to how the mathematics makes sense.

"Go down deep enough into anything and you will find mathematics"
                                                                         Dean Schlicter

Team Teaching Reflection

For our team teaching assignment, Vicky, Jen and I presented an open-ended problem designed for a grade six class. Initially, we believed that the problem focused on the mathematical concept of area. But, upon further reflection, we decided that the problem enabled students a deeper understanding of spatial reasoning. The title of the open-ended problem was "Arranging Your Bedroom." Students were given a bedroom template, whereby they were asked to fill the space with at least six different pieces of bedroom furniture such as a bed, dresser and toybox. Students were given the dimensions of each piece of furniture so that they could determine how much space was being taken up. Students were also provided with some basic points to keep in mind when arranging their bedroom such as that tall furniture could not be placed in front of windows and furniture could not be placed in front of heaters. Vicky, Jen and I believed "Arranging Your Bedroom" was an effective open-ended, problem-solving question for a number of reasons. First, the question did not have one set solution. As long as the students took into account the points to remember and included at least six pieces of furniture, the bedroom plan could be arranged in any way, shape or form. Because there were limited restrictions as to how the problem could be solved, diverse learners could potentially find success in solving the problem. Therefore, the "Arranging Your Bedroom" problem would effectively challenge all students alike. Secondly, students were able to apply a number of strategies to solve the problem. For example, students could strategically map out the dimensions on the grid first and then draw in the furniture, students could fit in the furniture as best as possible without mapping out the dimensions first or students could use one or more of the same type of furniture such as three dressers and one bed. During the teaching presentation, a student had brought it to our attention that the bedroom could be arranged differently according to the way that the actual template was looked at, either horizontally or vertically. The problem could therefore be solved effectively in a number of ways depending on how the student saw it. The problem allowed for students to work independently but to also share their strategies with their fellow classmates. Thus, students learned from one another to gain a better understanding of spatial reasoning. In the context of the practical classroom, the problem could be presented as a whole class initiative. The students could potentially map out an entire section of the classroom and use life size manipulatives to fill the dimensions of a particular area. Lastly, the problem was effective because extended questions were provided to further expand the student's knowledge of spatial reasoning. The questions were deemed as optional because in the context of the practical classroom, some students may or may not have the opportunity to move beyond the initial problem. The extended questions were intended to challenge the learner. That being said, upon further reflection Vicky, Jen and I realized that the initial problem would not have adequately challenged the grade six learner. In order to challenge the learner, Vicky, Jen and I could have provided a second bedroom template with given restrictions, such as a smaller bedroom with more pieces of furniture required. As well, manipulatives could have been made accessible for students who benefit from a more hands-on approach.

In regards to the actual presentation, I felt that Vicky, Jen and I were confident in presenting the "Arranging Your Bedroom" problem. Vicky, Jen and I briefly discussed the problem at hand and then allowed for adequate time for the problem to be solved. I believe the most effective part of our presentation was when we asked fellow classmates to show how they individually designed their bedroom plan. In doing so, students could see how fellow classmates made use of multiple strategies to solve the problem. As well, difficulties encountered when solving the problem were discussed which allowed for a deeper understanding of the mathematics at hand. Vicky, Jen and I demonstrated effective time management and use of technology. The one thing I would change about our presentation was our interaction with the students while they worked to solve the problem. Vicky, Jen and I had initially planned to tell our classmates to focus on solving the main problem and to simply look over the extended questions. Looking back, I realize that the whole class discussion could have been enriched if some of the students had completed the extended questions.

Overall, I believe the team teaching assignment provided me with a positive learning experience. Through my own presentation, I learned that there are multiple ways to engage a classroom of learners in a problem-solving question that allows for multiple entry points. The team teaching experience taught me that as students work and struggle together to find a justifiable solution to a problem, growth in learning occurs and knowledge of mathematical concepts are extended.