Emily Columpsi

"The art of teaching is the art of assisting discovery" -Mark Van Doren

Entry #3 – Teacher Change

1) I see teacher change as inevitable. For instance, upon entering the Faculty of Education pre-service teachers, like myself, had a personalized view of what teaching should be or look like (based on our own experiences). However, each semester our beliefs and practices were challenged and/or questioned by colleagues, professors, cooperating teachers and/or students, resulting in a shift/change in our initial teaching approaches and beliefs. Even experienced teachers, as discussed in the article, encounter opportunities for change. Beliefs and there related tensions, as well as “a lack of intellectual challenge and satisfaction in dealing or engaging students with the mathematics” can promote or result in change (pg. 453) . I see change as healthy and realistic; however, “it requires not only a desire by the teacher to change but also the belief that alternatives that are more beneficial are possible” (pg. 456). Yes, “change is a challenging journey to a desired but undefined destination,” but teacher change can be a self-transforming journey (pg. 456).

My view of mathematics was very similar to Brea’s. When I was a student in high school math was made simple through formulas and steps; teachers would dominate the classroom simplifying math as best as they could “into little bits so the students could consume it and regurgitate it” (pg. 450). The focus/aim was to cover the curriculum. This was my experience; thus, I believed my job as a future teacher should be the same. Once I entered University this belief changed. I saw that math was no longer about steps and memorization, but rather it should be about and geared towards student-centered instruction and inquiry. At first, I had an inner struggle/tension with this concept as it was different and unfamiliar. However, through the various readings, class activities, lesson planning and lesson teaching exercises that I have undergone in my EMTH 350 class, I have become more open to this change. The first class activity that we did, which focused on understanding radian measure and circle trigonometric functions through a concrete representation, was my first ever experience with inquiry. After completing the activity, I realized how important it is for teachers to provide students with the opportunities to “…question, explore, notice, conjecture, prove/validate, and generalize” (pg. 455). Furthermore, the readings emphasized the importance of giving voice to, or recognizing “the voice of, students, thus empowering them” (pg. 455). I used to see teachers as being the expert voice in the classroom; however, my short experience with inquiry has made me realize that the “authenticity of student voices” are key to effective learning and understanding (both for teachers and students).

The article provides three different types of change: instrumental change, conceptual change and foundational change. I feel that as of right now I have only gone through, and continue to experience, conceptual change within my EMTH 350 class. Everyday I interact with my colleagues/peers in a way that enables me to view learning as collaboration with others. We question, explore, and conjecture together; facilitating each others understanding (of course with the guidance of our professors). In addition, as we build our inquiry lessons together we are furthering this type of change.

2) If you were to ask me this question two years ago I would have said that the ideas in the article definitely challenged, even contrasted, my beliefs about mathematics teaching and learning. However, now that I have had the experience to see and work with inquiry lessons, resulting in a change in both my attitude and approaches to teaching, I feel like I can say the ideas in the article affirm my beliefs about mathematics teaching and learning. In my pervious blog post I stated my mathematics creed: I believe math is a universal language, a discipline, a human endeavour, a science and a social activity.  These beliefs about math were definitely acknowledged within the article. For instance, Brea wanted to show her students that math “does exist in the world, that it is a ‘living discipline’, that it has bloodlines” (pg. 450). This connects to my belief of math as a discipline and human endeavour, as there are patterns, relationships, and quantities that connect to and are transferrable to the outside world enabling further understanding, learning and respect. My belief of math as a science is highlighted when the article states that “math presents itself as complicated, uncertain, and unfinished” (pg. 450). In my eyes the study of math and science are similar in the sense that both are a complicated, ongoing process, encapsulating comfort with uncertainty as well as teaching for understanding. My belief of math as a social activity was emphasized throughout the whole article. Inquiry-based teaching practices encourage discourse and conversations that are rich with questions, answers and insights; thus, enabling math to become a social activity among the students and teachers. Lastly, math as a universal language is highlighted and connected to all the above. All students have in some way or another a shared/collective understanding of mathematical ideas and concepts, which in the end is connected to and enriched by the social activity of the students.

In the end, I believe that my teaching practices and beliefs are going to continue to change as I progress in my profession. However, as of right now, as shown in the above examples and connections, my beliefs about mathematics teaching and learning hold true to the article. 

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