Pro-D Day Reflection

    I learned a lot from the BCAMT conference. It was my first time attending a Pro-D event and meeting so many math educators. This year the theme is connecting. Thanks to the awesome guest speakers, I explored connections between different points of view, teachers and students, and math and cultural context etc. Also, I appreciate the insights and resources the participants shared in the chatbox. 

    My biggest takeaway is the recall of six areas of human activity embedded in mathematical thinking: counting, measuring, locating, designing, playing and explaining. Although the saying that math is a universal language is not true all the time, people could find universal commons of math thinking in these six areas. By being aware of the similarities and differences of math learning and teaching in different cultural contexts, teachers could be more helpful to students with different backgrounds. 

Reflection on Group Curriculum Micro-teaching

 

    It was great to work with Dion and Mike! 

    In general, we tried to cover too much in a 15-min micro-teaching. It would be better if we provide more basic knowledge on the topic and have time for students to try different methods instead of one. Also, giving clear pictures and rationale for learning the topic should be included at the beginning of the class, so students could know where they are and where to go. The good aspect is that the small group activity was very effective. In this way, students not only learned from teachers but their peers as well. If time allowed, we could hold a larger group discussion and perhaps a debate on which method is the best to use. Therefore, students can have a chance to explore the pros and cons of different approaches to solving quadratic equations. 

    Personally, I believe I should practice more on my teacher volume and use more body language in the teaching process. 

The Giant Soup Can Puzzle

    Given that the soup can has a diameter of 8cm and a height of 10cm and the height of the bike in the photo is 80cm. The diameter of the water tank is approximately three times the height of the bike, which is 240cm. Then use proportional reasoning to determine the height of the water tank: 240/8=x/10 and thus it is 300cm. As the water tank is a cylinder, the volume follows the formula: V=pi r^2 h. The radius for a circle is half of its diameter, so r=240/2=120cm. Therefore, the volume is pi*120^2*300 and the approximate result is 13571680 cm^3. The third part of the question requires research. According to a 15-year study in Scottsdale Report, 2935 gallons of water on average for firefighters to put out a house fire. To compare these two numbers, the same units for them are needed. Students could choose which unit to be used and personally, I decided to convert these two numbers into the unit of m^3 and keep two decimals. 13571680 cm^3 is around 13.57 m^3 and 2935 gallons is about 13.35 m^3. Thus, the answer is that yes it holds enough water! 

    I think there are three challenging points in this problem for students. The first one is how to make realistic assumptions. Then, they need to figure out which information is useful to them when determining the dimensions of the water tank. The last part is unifying the units. This kind of question is closely related to students' daily life so they could be more interested in and engaged in the problem-solving process. Also, the problem helps them to develop their mathematical thinking and gives them a sense that math is actually more useful than you think!

    An extension to this puzzle is asking the following question: due to weathering, the water tank is out of the right cylinder shape, does it affect the volume? Students need to come up with assumptions of the possible shapes after weathering. For example, it could turn to be an oblique cylinder. 

Group Curricular Micro-teaching

Solving Quadratic Equations with Different Approaches 

Dion, Mike and Yiwei

Group Lesson Plan

Slides

Worksheet-Graphing

Reflection on Eisner's Three Curricula

    The first stop for me was when Eisner argued the reasons for aspiring students’ preferences of universities. Since I did not fully experience the K-12 system in North America, this example was more clear to me to understand the explicit and implicit curriculum he discussed. It reminded me how I chose which Canadian universities to apply to from another side of the earth— I checked the world rankings. Similarly, there is a school ranking website named Fraser Institute for K-12 schools in BC. However, these rankings actually mislead parents or students who have no sense of implicit curriculum for the schools. Now, the new BC curriculum explicitly explains the hidden curriculum and sets standards with the three core competencies. The introduction of these core competencies not only reveals implicit information to parents and students but guides the direction of the development of schools and teachers as well. 

    The concept of the null curriculum was my second stop. I appreciated that Eisner brought this term into the discussion of the school curriculum. Other than simply neglect some knowledge and skills, it is important to know the reasons for ignoring them. Currently, many new subjects such as art designs are rapidly added to the new BC curriculum. Moreover, more new content is expanded under the same subject area. For instance, geometry, statistics and the history of math are attached to mathematics. These subject areas and content were selected to move from the null curriculum since educators saw the necessity of them and understood why other concepts could be neglected. Also, designers of the BC new curriculum changed the approaches of describing courses. The content and skill development section was replaced by two parts: content and curricular competency development. As a result, schools and teachers have a clear image of what to teach and what to put less weight and students understand the exceptions of learning.

Reflection on the Non-curricular Micro-teaching

I appreciate the feedback from my peers. Their comments encourage me a lot and provide valuable suggestions.

According to the feedback, I need to work more on clarity and timing in teaching. I chose my topic to be Mahjong since I am familiar with it. However, it could be a difficult game for people who are new to it, so it would be hard to follow for them. Also, it seemed that I tried to cover too much in a 10 mins lesson. Although I went through the lesson by myself several times before, the reality was very different from the plan. People need time to digest the new knowledge and reflect on them. 

For my future teaching practice, I will focus more on timing and pacing and plan more strategies for responding to different situations in advance. 

Reflections on Math Education Conflicts in North America

    First of all, I was surprised that the close relationship between global issues and change in math education in North America. Although the progressive reform seems to start with a spontaneous debate, it was driven by global factors such as WWI and international immigrants as well. Moreover, other countries’ achievements played an important part in the rest two math education movements. The new math is mainly caused by the competitions from the Soviet Union and the big concern and anxiety in the math wars came from the better math outcomes in other countries regarding the TIMSS ranking. 

    However, I think this kind of ranking is not accurate and all it does is creating stereotypes. This leads to my second stop which is my stand in the ongoing math wars — I believe that the assessment approach is the key. Different methods of assessment can describe the same student with very different performance results. In the current math teaching process, most teachers still mainly focus on submissive assessments, yet their teaching beliefs are actually progressive. It is impossible for a teacher to evaluate students’ development in mathematical thinkings based on the selection of multiple choices. Thus, I think applying more formative assessments could be more important than changing math curricula and teaching methods. 

    In addition, I noticed that parents’ role in math learning was mentioned several times in the article. I feel strongly related to this idea. As I talked about in my previous blog, my father is my favourite math teacher. However, when I got into higher grades, sometimes he could not assist me since the content was different from what he learned. At that time, I gained a lot of help from my peers. According to this personal experience, I think to encourage peer interactions in learning could be a good strategy in math teaching. 

Micro-teaching Lesson Plan

Topic: Mahjong 

Micro-teaching Lesson Plan

Worksheet for winning hands

My TPI result

 

    I was surprised that my score for social reform was low. I do value collaboration as the learning process, yet I have to admit that I show less care for social actions. Also, the apprenticeship factor was higher than my expectation. Many students dislike math since they do not see where math could be applied in their daily lives and future studies/careers. I believe that math teachers should address math in a more practical approach so that these students can rebuild their interests in math.

    One question raised regarding my TPI results is that why there are gaps between teaching beliefs and actual intentions. For instance, I have a low score in the teaching belief for the developmental factor, but the result also shows I try hard to accomplish it.