My Weekly Report and Reflection 5 (Week 7)

Week 7’s content was very interesting and incited some terrific discussion amongst the class! The reading was specifically interesting, and I found it difficult to comprehend. Nonetheless, after meticulously reviewing the chapter as a class, I was able to better understand it and it aided my knowledge regarding to the types of understandings that occur in education. Furthermore, reading this segment allows me to facilitate these mathematical understandings for my future students.

The “Dot Problem” allowed us to practice our problem-solving skills in multiple ways. This was also the goal of our problem-solving assignment, which is due next week. We must be able to solve problems in many different ways as a mathematics teacher, since our students will all think differently and come up with different solutions. This also demonstrates, mainly, how even the simplest questions can have several methods for answering. When we grade our students’ answers, then, it is crucial that we consider the various mathematical processes and strategies that they may use. For instance, my two group members and I compared our answers afterward and noticed that we all had something different from one another. When Joyce came over to view my answer, she asked me to explain it further by showing my thinking, instead of just discussing it. Once I started to show it to her, she told me that she had something entirely different in mind. She then illustrated what she had been thinking. This was a great learning experience; Joyce as I acknowledged the fact that students have many different learning styles and strategies, and I will need to be aware of this in my own classroom.

Furthermore, I found it fascinating to see how much “cleaner” some solutions looked compared to others. My answer, in particular, was very messy with a lot of correcting and crossing out. My sheet would, thus, be difficult for many people to read and to understand my thinking. Conversely, Gabriela’s solution looked much “nicer”, since it had no apparent mistakes and was colour-coded with neat diagrams. Although both Gabriela and I came to the same conclusion, some teachers may grade my solution less due to the fact that it is harder to follow. This is an issue that I must address when I evaluate and assess children’s answer. In other words, I cannot be bias to those students who think like I do or to those who come up with “neater” solutions.

As we progressed through the lesson and reached the “gallery walk” segment, Joyce introduced us to new part of the “gallery walk”. Once we all had time to post our solutions and walk around and observe the others’, we grouped the answers based on similarities. We “stacked” answers which appeared to follow the same – or similar – processes. This is advantageous because it is helpful for individuals to see each other’s answers, without being overwhelmed and confused with duplicates.

One challenge that I perceive as a future mathematics teacher is that it is sometimes difficult to respect other people’s views, especially when those people may not be as advanced as you are. Educating youth is one of the most challenging fields of work, since you must consider all perspectives, not just your own. In objective subjects like mathematics, therefore, teachers are forced to think about all of the potential solutions that their students may come up with, rather than just solving a question with one single solution that the teacher came up with. This unbiased thinking and assessment is a difficult skill to develop, but it is one that is mandatory in the profession of teaching mathematics.