Entrance slip for our Sept 24 class

 The point that made me stop was the author’s idea that the garden can be a co-teacher. I have never thought about the importance of the learning environment before, maybe a more open and natural environment can help students feel more comfortable and less pressured. Perhaps this can make them more willing to participate in learning and more open to new ideas. I look forward to learn more about this in our class.

One difficulty I can foresee is that a garden is an open space. If there are many students, they may not be able to hear the teacher clearly. This can be especially difficult in mathematics, where students need to follow explanations carefully. One possible solution is to bring a speaker or a small portable microphone. I am looking forward to our class on September 24, because I hope it can show us more clearly how a garden can be used meaningfully in different subjects, including math.

Reflecting on Sketching and Teaching Sep 17th

 In the first half of the class, we did the sketching activity. I have never been good at drawing. Since I was young, I knew that I was not very good at controlling a pen, and even though I have practiced handwriting for years, the improvement has been limited. Because of this, I stopped trying to draw a long time ago. However, when I was asked to draw something for this activity, I actually started to discover some techniques through trial and error. At first, I started with the most remarkable object, but then I found it difficult to arrange the objects behind it. I realized that it might be better to start from the background and then move forward. I also found that simply drawing the outline of a tree did not really make it look like a tree. So I slowed down and observed it more carefully, I noticed that what made the tree recognizable was mainly its trunk and larger branches. So I lightly drew the general shape first, then added the trunk and major branches, and finally the leaves. The result was much better than my first attempt.

At first, I did not really understand how this activity could help us become better mathematics teachers. After doing it, however, I think the point may be that if we want to become better at something, we first need to be willing to try, then observe carefully, learn from failure, and keep adjusting what we are doing. This also connects to our discussion of Grant and Zeichner's ideas about reflective teachers. Open-mindedness is obviously important because teachers cannot be too stubborn about their previous experience or existing practices. Responsibility was especially meaningful to me because I have experienced its importance directly in my own teaching.

I mainly teach Grade 11 and 12 mathematics and physics, and I often meet students who lack even basic knowledge of some fundamental concepts—not deep understanding, but simply knowing what those concepts mean. For example, some students cannot clearly explain what a function is or how a function expression is related to its graph. This makes Grade 11 and 12 mathematics very difficult for them. Sometimes I complain in my mind that their previous teachers did not fully prepare them, but then I also ask myself: when my students graduate and go to university, will their professors complain about me in the same way? Will I become the last part of an ineffective education system?

Because of this concern, I went to the UBC Math Department website and downloaded past exams in calculus, linear algebra, probability, and complex analysis, and worked through them myself. I wanted to have a better idea of what students may actually face in university. Since then, when I teach calculus, I pay more attention to ideas such as the Mean Value Theorem, the physical meaning and applications of definite integrals. When I teach systems of linear equations, I emphasize their geometric meaning instead of only teaching students how to get the answer. I think this may also be part of what Grant and Zeichner mean by wholeheartedness: not only caring about whether students can pass the course in front of them, but continually learning and adjusting our own teaching because we care about what happens to them afterwards. 

Respect Before Reflection

 Grant and Zeichner discuss three important attitudes of a reflective teacher: open-mindedness, responsibility, and wholeheartedness. I agree that all three are important, but I also believe that they are deeply influenced by the teacher's own values. Even when we try to be open-minded, it is still us to decide what is worth questioning and what kind of development we value for our students in the end. For me, RESPECT should come before these three attitudes. We first need to understand students and respect their learning purposes and life goals before deciding what is “better” for them. For example, I once reflected on why many students do not want to take my AP Physics C course. After talking with them, however, I found that many of them do not plan to study engineering or physics, or they have not finished calculus yet. Should I then try to persuade them to choose engineering or take a more difficult physics course? I do not think I should. In this case, being open-minded also means questioning my own assumption about what students should want. I am still not sure how a teacher can balance respecting students' choices with helping them realize possibilities that they may not yet recognize, and I hope this course can give me more insight into this question.

I also strongly agree with the authors' idea of responsibility. Different expectations and teaching methods can have very different long-term consequences for students. Since I mostly teach Grade 11 and 12 mathematics and physics, I often meet students whose foundations are weaker than I expected. Some cannot clearly explain what a function is or the relationship between a function expression and its graph. When I ask them about their earlier learning, some tell me that these ideas were never emphasized as long as they could solve the questions. As a result, mathematics becomes much more difficult for them in later grades, and some begin to believe that they are simply “not good at math.” This has made me think more seriously about what knowledge students will need later, especially in university, instead of only asking what they need for the next test. For me, responsibility and wholeheartedness therefore mean more than teaching the required curriculum well. A good teacher should try to understand what each student wants, genuinely care about those goals, continually reflect on how to help the student reach them, and develop the ability to make a meaningful contribution along that path.

Exit slip for the first class

One idea from our discussion of Frank McCourt that stayed with me was how he responded to students when they resisted what they were learning. He did not always immediately tell them that their reaction was wrong. For example, if students disliked a book, he seemed interested in why they disliked it. This made me think about how I normally respond when students resist something in mathematics or physics, since this happens a lot.

In my own teaching, when a student says that a topic is too difficult, it is usually followed by a request to lower the difficulty of the exam or exclude this “difficult” part from it. My first reaction to this kind of negotiation is often to find a way to get the student back on task. After this class, I wonder whether I should sometimes treat that resistance as information. Maybe the student's reaction conveys more information about how I am teaching, how much the student understands, or whether the lesson feels engaging to them. I still don't have an answer that I'm satisfied with, and I'll keep looking for this answer in the coming classes.

Hello world EDUC450

 Hello world, this is my first post for EDUC 450.