Circle Puzzle

 1. My approach to this puzzle: 

2. Extension of the puzzle:

Possible one: Assume there are 32 dots on the circle, what's the one that is directly opposite to dot 5?

Impossible one: Assume there are 31 dots on the circle, what's the one that is directly opposite to dot 5?

I do think it is meaningful to give an impossible puzzle because this can train students to think critically and skeptically. An impossible puzzle also raises another question: why this puzzle is impossible? Which can guide students to have a better and deeper understanding of the concept. 

3. A truly geometric puzzle can be something like a tangram, where logical analysis can be more difficult to conduct compared to hands-on trial and errors. 

Response to the New BC Curriculum

(1) Please write about two things that were new to you or surprised you from the curriculum orientation guide and/or glossary of new terms

In the Highlights of BC's Redesigned Curriculum, two aspects are mentioned: 1) Historical Wrongs (acknowledging the contribution from Asian and South Asian communities) and 2) Aboriginal Perspectives and Knowledge (integrating aboriginal culture through methods such as place-based learning). I am very glad to see that they are included in the new curriculum because in this way, Asian and Aboriginal communities are no longer marginalized through education. Schools used to treat these two groups as a part of history which has no impact on the future, and this does not help with the situations of Asians and Aboriginal people. The new curriculum shifts the perspectives on the development of our society from a Eurocentric point of view to a more holistic view. 

In the Glossary of Curriculum Terms, the term "habits of mind" is new to me. From my own experience, schooling always focuses our abilities in different subjects. The connection among subjects, and how we "think" when we are confronted with problems are rarely mentioned. However, I do recognize that I behave in a certain way when facing problems, whether it's a challenging math problem or a biology project. I tend to do an assessment on whether this task is within my ability first, and then I will try tying the task to something I have seen before. If educators are aware of this "habits of mind", we can guide students to develop scientific habits that will help them navigate through challenges. 

(2) Create your own schematic chart of possible pathways in the courses of the BC Math curriculum from Grade 8 - 12.

Response to Elliot Eisner on "Three curricula all schools teach"

The article talks about how schooling forester’s competitiveness (page 91), and I find it interesting because competitiveness seems to be both explicit and implicit in the current system. For example, programs such as IB (International Baccalaureate) or AP (Advanced Placement) advertise their program as helping students to become more competitive for college admissions. The society is used to the idea of "competitiveness" being embedded in the education curriculum. However, the hidden or implicit "competitiveness" that occurs in almost every aspect of schooling is not well recognized. Every assignment, exam, or even in-class discussion can be a competition for students. Due to its nature, there will be students who perform better and students who perform worse. How can we reduce such competitions that do not necessarily help learning is worth to think about. 

 Another point that caught my attention is on the arrangement of class schedules. Elliot Eisner mentions that most art classes are placed in afternoon blocks, implying that arts are not "real work" that requires higher levels of intelligence (page 92). Such subtle implication is certainty biased, and can shape students' minds in an unintended way. When designing curriculum, educators need to avoid bringing their own prejudice into schools. 

 The BC provincial curriculum is making efforts to reduce unwanted implicit messages to students. Cancelling provincial exam is one step towards the reduction of competitiveness. More emphasis is put on the core competencies instead of grades.

Micro-teaching Lesson Plan

Subject	Biology
Grade	9-12
Topic	What happens to our body when we starve/fast?
Duration	10 minutes
Required Tools	Computer, calculators
Assessment	None
Objectives	Introduce basic metabolism process of carbohydrates, lipids and proteins, under well-fed and starving conditions.

Lecture Summary	Duration
Introduction: Metabolism overview	2 min
How our body uses dietary energy	2 min
What happens when we stop eating	2 min
Fasting and starving	2 min
Activity: how long can we survive without food?	2 min

Reflection: 

Thank you for all your feedback! I was super excited about this topic so I tried to squeeze in too much content. If this was a longer lecture, I will definitely provide more explanation to some of the terminologies and allow time for listeners to ask questions. 

Response to "Battleground Schools"

The article talks about the prevalence of math phobic attitudes among many adults in North America, and I personally resonance a lot with this phenomenon. One of my motivations for becoming a math teacher is my numerous encounters with math phobia. Whenever I introduce myself as a math major student, I hear two things from people's reactions: 1) You must be really smart, and 2) I hate math/I suck at math. My experience is consistent with the social presumptions concluded in the article where "those who like mathematics are nerds" and "there is no shame, and lots of positive social valuation. for those who claim to be incapable of doing and understanding mathematics". The fact that such presumptions are still prevalent is concerning, and I hope to be a math teacher who can change people's attitude towards math instead of reinforcing them.

I am surprised to discover the close relationship between math education and politics. The fact that math curriculum is designed to fit political and social needs, whether it's the promotion of democratic thought processes or the need for rocket scientists, makes a lot of sense. This makes me question what is the purpose of math education today? Is the rise of computer technologies in the recent decade another period of "New Math"? Or, should we develop a curriculum that centres on students' understanding and their individual needs, instead of on society needs?   

The Dishes Problem

Solve this puzzle without algebra:

For a group of 12 people, 6 dishes of rice, 4 dishes of broth, and 3 dishes of meat is needed, which gives 13 dishes in total. Divide 65 by 13 gives 5, which means there are 5 groups of guests of 12. Thus the total number of guests is 5 multiplied by 12, which is 60. It is

The importance of offer examples, puzzles and histories of mathematics from diverse cultures:

There are a few benefits of demonstrating math using contents from different cultures.

Historically, different cultures use mathematics to solve real life problems that is specific to a region. Using examples under various culture contexts can engage students through introducing new information that is not limited to mathematics itself. 

In a Canadian classroom, chances are that students come from a number of different cultural backgrounds. To include examples from those backgrounds shows acknowledgement of their original culture, which can help students, especially new immigrants, feel more confident and relaxed when living in a society that is dominated by European culture.

Presenting the problem:

How a problem is phrased and presented can be very important in altering students' involvement. Math phobia is very common among students, and a problem that involves only pure math language can be intimidating. Starting the problem with a story can increase students' interest and provide insight to the practical use of the math concepts. More representations can be used to supplement a word problem, including pictures and videos, to further engage students.