Re: Geometric/Numerical Puzzle

Thirty equally spaced points on the circumference of a circle are labeled in order with the numbers 1 to 30. Which number is diametrically opposite to 7?

At first, I thought about using the circle as a clock to mark the numbers from 1-30, so 12 o'clock is 1/30 and 6 o'clock is 15. As the circle is divided into 30 equal parts, so number 7 should be 7 unit spaces away 1/30 and the opposite number should be 7 units away (clockwise) away from 15 which is 15+7=22. So the opposite number of 7 should be 22! 

The extension of the questions 

Think about another bigger number, assume the circle represents numbers from 1-100, and find the opposite number of 25, which turns out to be 75. The answer could be solved by both geometrically and algebraically. See the circle draft below. 25 is the 1/4 of 100 so the opposite of 25 on the circle should be 3/4 of 100 which is 75! 

What makes a puzzle truly geometric, rather than simply logical?

If there are no numbers representing each space on the circle or there are no particular patterns of the spacing then the puzzle becomes truly a geometric problem. 

Re: The new BC curriculum & secondary math course pathways structure

(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. 

a) Historical wrongs, which the newly designed curricular includes the history of the Asian and South Asian communities and their contributions to the development of our province—as well as the injustices they experienced. I was pretty shocked that the new curricular would talk about the problem that has been existing for a long time. As BC is such a multi-cultural province, it's important to address the issue in our educational system. 

b) Habits of mind, I quote, "habits of mind are characteristics of intelligence or sets of behaviors that people engage in when they are confronted with problems. Different disciplines may have different habits of mind, captured in the Curricular Competency learning standards." I'm happy to see the new curriculum focuses on developing students' thinking habits and their habits of solving problems instead of focusing solely on how to solve problems. Having a personalized thinking habit towards academic problems will be tremendously helpful in students' learning journey even in their post-secondary studies. Helping them to find out their own "habits of learning" is more sustainable than teaching them facts that are evolving constantly. 

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

Re:Homework for our next class (Wed. Oct. 14): Elliot Eisner on Three curricula all schools teach

    The first thing that stopped me while reading the article was the quote "One general goal of such an institution would be to enable children to become the mappers of their educational journey so that when they leave school they are in a position to pursue goals and interests that are important to them.", that is exactly my ideal philosophy of how education should be! As a soon-to-be educator, I want to give the initiative of learning to students as they will eventually become their own teacher in their lives. What an educator should be doing is to get them to be prepared when they start working in the real world. 

    Secondly, what made me think deeply is ironically on how the education system "prepares" our students. Rather than the ideal philosophy of mine, the students were rather trained/modified into how society wants them to become so that they can fit into the workforce like how society functions. As the author mentioned that "The school seeks to modify the child's behavior to comply with goals that the child had no hand in formulating and that might not have any intrinsic meaning.", I feel so torn about that statement. A part of me wants students to learn freely and be whoever they want to be, but the other part of me is afraid of the lack of real-life experience /prep they have if I don't give them enough prep for the real world. I think we should find the balance between the two, I don't want our future generation to become robots so that they think and act all alike, but I don't them to be so "unique" that they cannot fit into the real world. 

    One more point I want to mention is that we should stop using the rewarding system starting at such a young age as I think it's important for kids to know that some qualities like being kind, on-time, and polite, etc. should be a moral thing to do rather than an optional quality of someone. 

    I'm aligned with BC's curriculum in terms of the goals and rationale and it's also aligned with the author's vision. Thinking mathematically is more important to think about mathematics, thinking mathematically can be applied in other subjects and even in students' lives which is much more valuable in their lives and workplaces in the future! 

Re: Individual non-curricular microteaching and lesson planning for Wednesday October 14 in class!

People always want to have better skin or maintain their youthful skin as long as possible, also prevent aging! Skincare is much more than just the cosmetic products you put onto your face, it's about what you eat, your sleeping quality, and your general health condition. 

In this micro-class, students will learn how to have better skin based on their own skin type and prevent the first signs of aging as early as possible. Also providing some cosmetic dermatology treatments for mature skin/first signs of aging if the individual feels it's needed! 

Cannot wait to talk to you all about skin! 

Re:Battleground Schools

The first statement that surprised me was the statement "Mathematics education in North America since 1990 has oscillated between two poles, each of which is associated with a political stance, a conception of what mathematics is, and a set of assumptions of the place of mathematics in society." It turns out that there are "left" and "right" wings in the educational system. The conservative math teaching really resonated with the experience I had growing up. I think the stereotype actually started from here. The dry and boring materials led people to think math is hard, cold, distant, and inhuman. I think changing the way of how teachers educate really could make a difference in the long-run. 

The second part that surprised me was how there are three 20th century reform movements in mathematics education. From progressivist Reform to The New Math to Math Wars over the NCTM Standards. It seems like the math education has been going through a bumpy ride. People start realizing the importance of math and how math is the foundation of a lot of subjects! 

Lastly, what shocked me was how social media is filled in everywhere in our daily life. It's sad to see that social media is now controlling our life including how we view the mathematic education system. In another class, we talked about how education was a tool for the government to control how the masses think and behavior which we all know that media is controlled by the government as well. It's kind of scary to think deeper on issues like that. What are we really learning and why we are learning it? I think students need to firstly learn how to think independently and critically!

Re: The Dishes Problem

So the problem goes like this: 

2 guests for 1 rice 

3 guests for 1 broth 

4 guests for 1 meat 

there are a total of 65 dishes, and how many guests are there? 

Without using algebra, we know that the LCM (Least Common Multiple) is 12 (3*2*2)

Which means that 

12 guests need 6 rice, 4 broth, and 3 meat for a TOTAL of 13 dishes. 

We know that we have a total of 65 dishes and 13 dishes for a set of 12 guests, so how many sets (12 people) are there? 

65/13=5 sets of 12 guests, which gives us 12*5=60 guests in total! 

• Does it makes a difference to our students to offer examples, puzzles, and histories of mathematics from diverse cultures (or from 'their' cultures!)

Absolutely! Personally, I felt immediately "closer" to the question as an Asian student which helps in the sense that I'm more interested in this problem. It's also interesting to see the word choice of "broth" they used in the problem instead of "soup" because Chinese people don't usually eat the ingredients in the soup because they put a lot of Chinese herbs in the soup but they don't consume them, they are for the fragrant and medical purpose. For students with other backgrounds, it's also a great conversation starter and builds an interesting course plan for teachers! 

• Do the word problem or puzzle story and imagery matter? Do they make a difference to our enjoyment in solving it?

Yes! From a psychological perspective of how humans learn, it definitely helps when students can visualize the problem. As humans, we tend to be attracted to any object with colors, sounds, movements, and emotions. Providing students with images of problems will leave a bigger impact on their memory neurons, giving them more imagination freedom which I think will help them to understand word problems. Having word problems that are familiar in our life as it's easy to read our own experiences rather than thinking in someone else's shoes, so having an image that students can relate to will definitely help them in terms of their problem solving skills.