Entrance slip (Sep 30)---Mathematics Education for Sustainability

The first thing in this article surprised me is that  "a diet of vegetables and herbivorous fish may provide a ready solution for eliminating over 65 % of the pollution caused by protein production" (Renert,P21). Imagine that how much tropical forest can be saved, how much fossil fuel consumption and carbon-dioxide emission can be reduced from the saved 65% of pollution. World famine will be much less of a problem to deal with if we could think in this way to make connections between mathematics and the world problems. Follow this way of thinking we could find out that Avocado is not a Eco-friendly food since it uses too much water, while algae might be the food of the future.   

Second thing surprised me is the implication of  "humans' inability to feel large Numbers" and its impact on the real world. The author explained if human can not feel the sense of quantity and lack the emotion from it, the decision-making and action will be negatively impacted. Most people might not be aware of this fact thus fall victim to the negligence and poor reasoning. 

I agree that teacher have the responsibility to not only teach students knowledge and skills, but also enlighten their social responsibility, reasoning and other democratic citizenship qualities. The awareness of ecological sustainability should not be neglected as well.

To address this situation, I recall an excellent example I experienced in a high school in Surrey. Math teacher asked Grade 9 students to do a group activity. The question is to estimate how much water used per day. In this activity, every member in each group needed to collect data, calculate numbers of gallons of water used at different time for various everyday activities, make line chart, compare results. Then, in a student-led discussion, students actively discussed about what behavior could cause waste of water and how to prevent it. Finally, teacher lead the discussion to a higher level which is about why. This activity is a good example of environmental education in mathematics classroom. It enhances my understanding of the article I read today, and this article make me realized that as a Math teacher we could do better to preserve environments and resources for now and future with our students. 

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August 8, 2021

"The binary right-or-wrong logic enacted repeatedly in school mathematical discourse presupposed absolute certainty." (p.24) 

I used to think that the answer to a math problem can only be either right or wrong. Now, I don't think so. Can there be an answer other than that? Yes, of course. For example, 'undefined' is one (joking). Comparing to English writing and Art, it seems that there is no space for math students' creativity. Each of them has to get a certain same answer for a given question. The side-effect of this is that we are always trying to find that unique right answer. This is not the purpose of learning mathematics. Can math be open-ended and have multiple solutions? 

For thousands of years, people have been trying to find patterns from the complex and chaotic natural environment so that we can make predictions for sidestepping the possible risks. Mathematics has been invented to benefit us. Now, it is time to use it in turn to approach issues of the environment. 

Reference:

https://drive.google.com/file/d/1ROYpuEjXt0D9VW5eim7JozKq7D58NoH1/view

Exit slip (Sep 24)---- Online Forum: speak with Dr. Robin Wall Kimmerer

Reflecting on online seminar and class discussion, some take away I had are: 

1. For non-indigenous teachers, we could become co-learners with our students. There are so many books, songs, videos and movies about indigenous culture, we could learn it together. We need to open ourselves to learn more, and to protect our indigenous knowledge. 

2. Teachers could teach students some Canadian history of colonialism and the residential school system , so students could recognize the root of problems from historical perspective. It can help students to identify the implicit bias and other issues that may be happening today. 

        3. Responsibility and knowledge should not be separated. Teachers, as the role model, need to show your students not just tell them the way approaching the world.   

Entrance slip Sep 24---Scientific Language and the Language of Animacy

Reading:

Kimmerer W. Robin. 2014. Braiding Sweetgrass: Indigenous Wisdom, Scientific Knowledge and the Teachings of Plants. Milkweed Editions. P. 48-59.

Terminology, by its definition in some dictionary, is the language used to describe a specific thing or the language used within a specific field. If teachers use many new Mathematics/scientific terminologies during the class, students will feel hard to understand and feel discouraged.  Like learning a new language, teachers could teach in both languages in order to help students gradually learn Math terminology. 

Language is far more than a tool of communication. It is a combination of the cultural and the mind. Citing the words from the article, "The language is the heart of our culture; it holds our thoughts, our way of seeing the world."(p.59) Potawatomi is a language that incorporates respect for nature and all living beings including mountains, trees, and rivers. This idea shows tolerance and human fraternity. If I don't read this article, I would never know the existence of this language and the thoughts behind it. I am grateful that I can read this article in this course. 

In a diverse society, as a teacher, we should show our students respect and empathy at all time. Respecting their culture, language and perspectives is the way to build a mutual trust relationship. In the future, I will allow my students to talk in a language other than English if they feel necessary and respect others. We could even hold some activities to introduce different languages and cultures, and communicate different thoughts and ideas. My ways to indigenize my own classroom and curriculum is to be a good listener and observer first, then involve all my students in a positive learning environment.

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August 3, 2021

I think it is necessary to learn Mathematical terminologies in the math classroom when learning math, especially those terminologies with logic. These terminologies can help students understand the concepts and staying on the same page when discussing a topic together. However, I suggest providing students opportunities to study and explore a concept or method first, then give them a reasonable name for that concept or method.   

In Kimmerer's article, she reveals an indigenous way of seeing things. She learned about this tradition from its language. I don't think there is any conflict between the European scientific way of knowing and indigenous ways of knowing. In math class, I encourage students to see things from multiple angles and to solve problems in different ways. Math is learning ways of thinking and seeing. As long as you can prove or explain an idea logically and ethically, we should show our respect to it. I appreciate that Kimmerer opens a door for us to see this world. It is lucky for me to have exposure to this indigenous tradition. I will try to find a proper way to offer my students access to indigenous cultures in the math classrooms. 

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Notes of Sep 17, 2020

One interesting topic discussed on that day is Planning vs. Improvisation. I agree with some groups that it is always necessary for teachers to plan and prepare each lesson. It would be better to have some options and ways so that we could change up the lesson plan if it is necessary. When we teach we can have some improvisation according to feedbacks from students. 

I want to be a teacher who can make students feel comfortable to be in the classroom and be willing to engage in the learning activities. 

Some useful resources:

 Making mathematics with needlework

Crafting by Concepts

Crocheting adventures with hyperbolic planes

Websites:

Bridges Math and Art archives

Arbitrary and Necessary, Part 1. For the learning of mathematics

This article tells us how and why teachers should help students learn by their own awareness rather than by memorizing. Reflecting on my own teaching, I found that I didn't do well on teaching the necessary. Showing and demonstrating couldn't educate awareness. Even though students can solve math problems, they still may not understand the rationale underneath. This causes that our students can only know how to solve the problems that have been solved by the teacher in the class.

To improve this, I should first know which content in the curriculum is arbitrary and which is necessary, then think deeply about how to teach them so that students could use their awareness to learn. 

For content that is necessary, I could design some activities to help students work out for themselves why a statement is true, and use questions to inspire my students to think critically and figure out by themselves why it is important and should be learned.

To engage my students in the classroom my goal is to provide them ample opportunities to participate in eclectic learning activities. On the other hand, for the arbitrary, I will encourage students to generate their own memory aids to understand what they should know.

  

Exit slip (Sep 17.)--- Multi Dimensional Math Teaching

In today's first group discussion on being a reflective teacher, we firstly talked about conformity and reflective teaching. We concluded that there is a balance between conformity and reflective teaching. Teachers need to meet their teaching goals and tasks, however, if there is only conformity, some teachers might gradually lose their passion of teaching. On the other hand, through reflection teacher could improve their teaching practice on many aspects such as teaching styles. Reflecting constantly while still getting along with the institutions of schooling was agreed by our group.  

Secondly, we all agreed that reflecting can save time.  For example, if some teaching method is not working well, through reflection, teachers could try to improve it to ensure a smoother teaching practice, rather than spending more time on old method which does not work or inefficiently . 

Then, on the topic of planning, one of the ideas was that it is important to have a basic plan to ensure the systematize of teaching. Improvisation and adjustment is also necessary and vital. 

As for the last point, I think to be a critical thinker and learner we firstly need to be a good listener. To carefully listen what they are talking about and what they want to express. 

Our second discussion was about Jo Boaler's  lecture. I totally agree with her that every children could excel in mathematics. Some parents  say that their child is not smart enough to be good on Math, I know it is not true. We should never assume why a student is not that good on Math. As for multi-dimensional teaching style, I shared my relevant experience. When the first time I sat in a Math classroom of a high school in Surrey, I was surprised by that teacher's teaching style. It was totally different from the traditional chalk-and-talk teaching style which I experienced when I was a pupil. During her Math class, students do not need to take a lot of notes, and most of time they do not take any notes. The format of teaching is diverse and interactive. Thus students have more time to concentrate on understanding, learning and digesting the knowledge and skills been taught. Students discuss mathematical problems with group remembers, and they are encouraged to think and raise questions independently. Sometimes they play math games, such as Kahoot which is a popular game in that school. From my observation, multi-dimensional teaching works and have huge potential.

https://www.youtube.com/watch?v=2OgKnrPNZiI

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July 30, 2021 Reflection 

Today, I watched Jo Boaler's another 1-hour video. In the video, Jo Boaler introduced multi-dimensional mathematics. The key idea is as below: 

I think one challenge is to ask good questions. We expect that a good question can evoke students' curiosity and also is connected to the method that will be learned. As we know, in the majority of cases, there are normally more than one ways to solve a problem. So, letting students try the problem by themselves before copying the teacher's method would expand their scope, foster critical thinking and collaboration. 

How to teach math in a more engaging way? From the video given by our professor, I found this.

We need to try to open up the Math. Let students see a concept from different angles, solve a problem by different methods, present an idea using different representations. 

Another important point mentioned by Jo is making speed a part of math would cause math anxiety. When she said a lot of mathematicians are actually slow math thinkers, I couldn't agree more. We have to change that mindset which believes only fast thinkers can be good at math.

We also need to let students know that making mistakes is a good thing for their brain growth. 

One last takeaway is providing students diagnostic critical feedback and telling them you believe in them.

Here is another short video about how to praise. The resource is given by our professor.

https://www.youtube.com/watch?v=t_uAh4IN-As

Entrance slip #2 (Sep 16)----- On Becoming a Reflective Teacher

This is an article written in 1984. I suddenly found that the answers to my questions were given by Grant and Zeichner 36 years ago. Although this article was aimed at teacher candidates, I think the concepts and ideas within are still valid today and could inspire many people even who are working in other areas. 

 When I read "Is It Possible To Take The Time To Reflect?" I know I will find the answer to my question. Nowadays, we are all working and living in an increasingly fast-paced world. "Too busy" and "don't have time" are my excuses to delay my reflection or even neglect it. I have been always looking for the answer to solve this problem. Now I know, reflection could actually improve efficiency, not just took your time. It is very important to take time for reflection. As Grant & Zeichner states, "reflection necessarily paralyzes one from action is to distort the true meaning of reflective teaching"(p.109). I think no matter how busy we are, reflection is the action that should not be replaced. 

 

In the article, Grant and Zeichner teaches us how to begin reflection step by step. In the second step, "It is important for you to seek actively to understand the beliefs of others (peers, instructors, friends)within your formal courses and, more generally, by reading, observing, and talking to others in both professional and nonprofessional settings"(p.111) reminds me of Frank McCourt, since McCourt also suggests teachers to have the sense of critical inquiry, and be open-minded. I agree that taking an inquiry stance could ensure the improvement of our teaching practices. They also mentioned reading, and I totally agree that reading could help us to expand our intellectual horizons, thus we could think from different angles. Ultimately we will develop our critical thinking skills.

Reference:

https://drive.google.com/file/d/0B00n89L6TX5gSHJCZXUwR0Zocm8/edit?resourcekey=0-O7BUyqEwys2LJl2b-56NwA

Exit Slip Entry # 1 (Sep 10)-----'Teacher Man' and teacher inquiry: Frank McCourt

 

Two videos about Frank McCourt contain so many valuable perspectives. They are inspiring and constructive. In the first video, one that struck me the most comes from his words as below.

 

" If you are teaching, and you're not learning, you will not teach it."  

" I learned an awful lot from the kids in 30 years".

                                                           ------------ Frank McCourt    

 

Teaching is also a process of learning, learning from your students, learning from other teachers, and learning from failures. McCourt reveals to us that sense of critical inquiry, open-minded and empathy are necessary features for a teacher who knows the importance of learning. Furthermore, McCourt maintained this manner for 30 years. He said humorously " 30 years it nearly killed me, but I survived". I can see from this that teaching is never a easy thing, and it should never be taken for granted. What is his core motivation for teaching in such a way for so long? I think the answer is given by him, which is the " sense of responsibility".

The second video is an interview with Frank McCourt. He highlights the importance of building a connection with students. His willingness to understand and tolerate the thoughts of his students inspires me. I always want to be a caring teacher, and today I learned how to do that from McCourt. I believe that a healthy and positive relationship between teacher and students is formed on the basis of understanding and trust from the teacher. 

Course notes:

These are some attitudes outlined by Borasi in her article. She objects to these ideas. I think that some of these ideas are only true in some circumstances. For example, I think that staying too much on a problem is not always a waste of time, and it depends on how you spent that time. If you spent a lot of time trying different ways to solve it, you at least proved these ways were not working. 

I don't agree that ambiguity does not exist in mathematics. "Zero to the power of zero" is an ambiguity. If your math teacher tells you zero to the power of zero is undefined, but you see it is equal to 1 in computer language, please do not blame your teacher confused you. 

Frank McCourt: The Journey of an Ordinary Teacher

https://www.youtube.com/watch?v=Hlq7OBCqCSc&ab_channel=NYUSteinhardt

Hello World, and Hello Everyone!

Today (July 2, 2021), I come back here again,

many thoughts in my mind,

sad, grateful, mixed together.

I still remember why I posted a sunflower,

because we all came here for sunshine,

because the sun here is big and bright.

Here we have never-ending conversations, 

an infinitely wide floor,  

and resources forever.

Thank you for asking us to build blogs,

they are like homes,

we want to come back sometimes. 

(Sorry, this is my first time writing a poem in English if it can be called a poem.)