Homework: geometric/ numerical puzzle

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

Think of it analogical to a clock with numberd from 1 to 12. But in this example, we are looking at number 1-30. If 15 is opposite to 30, we can work our way down to find 7 is opposite to 22. 

Extensions to this puzzle:

Assume there are 28 points, which number is diametrically opposite to 8? 

Asumme there are 25 points, which number is diametrically opposite to 8?

Which question is possible/impossible to solve? Why is that?

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

The wording of a problem can make a puzzle geometric. In our question, the words "equally spaced" and "diametrically" make it geometric. Although it can be solved with logic, but we can see that it is a question relating to geometry. 

Blogging: 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

The redesigned curriculum includes the "Historical Wrongs" section which addresses the contributions and injustices that Asian and South Asians experienced historically. It is important for teachers and students to acknowledge and admit the historical events that actually happened. These historical events have contributed greatly to our modern society development. Therefore,  their efforts should be not neglected. 

Another point that surprised me is the emphasis on "digital literacy". I remember back in the days when I was in high school, we were not allowed to use electronic devices during class time. The society is moving forward with latest innovations and technologies, and the BC redesigned curriculum is in fact promoting the use of digital technology as communication tools to assist learning. With the inquiry-based approaches in learning, students would rely on the technology to research, analyze and evaluate knowledge, so it is crucial for our students to have the digital literacy abilities.  

 (2) Create your own schematic chart of possible pathways in the courses of the BC Math curriculum 

Oct 13 Reading Reponse to Elliot Eisner on Three curricula all schools teach

 Two or three 'stops' you have in this article

Eisner raised the question "Do schools teach children to compete, and do they encourage competitiveness? "(p.91) I personally don’t think schools are explicitly "teaching" students to be competitive, but the norm and structure of the school make it a miniature version of the society. In society, no one will "tell" you that you are in competition, and it is an assumption that we are all competing against one another. In high school,  courses are graded and scaled on given standards. In society, we are competing for different job positions and power. In general, competitiveness is not fostered by school, but schools provide a platform for students to experience the competitiveness in a smaller extent. As Eisner stated, perhaps it is better for students to have learn to cope with the competitiveness in school before they step in the real world.  

I also agree on the Eisner's affirmation on "schools teach far more than they advertise". Schools are places for learning to take place, but they don’t limit to knowledge needed to graduate. Schools also teach children how to become fitted members of the society. Most importantly, schools aim to help children develop the ability to solve problems and think critically.

Ways that this might expand our ideas about what is meant by 'curriculum'. How does the mandated BC Provincial Curriculum connect with Eisner's ideas?

Curriculum are academic contents that teachers have to teach in a specific course or program. Eisner referred to this definition as explicit curriculum. The explicit curriculum clearly states what knowledge has to be taught to the students in specific courses, and they are standards that teachers have to follow in teaching. However, there is also the implicit curriculum which "teach a host of intellectual and social virtues including punctuality, a willingness to work hard on tasks that are not immediately enjoyable, and the ability to defer immediate gratification in order to work for distant goals can legitimately be viewed as positive attributes of schooling" (p.95). The mandated BC Provincial curriculum connects to Eisner's ideas of explicit and implicit curriculum. Although the BC curriculum aims to prepare students for entrance into universities or society with the academic knowledge and skills required, there are limitations to what the curriculum and schools can offer simply because teachers don’t teach everything in life. It is up to students to incorporate and utilize their learnings from school and apply them in real life circumstances.

Microteaching Lesson Plan

 

Subject/Course:	Basic Cantonese 101
Topic:	Yum cha and Dim sum
Level:	Beginner level
Lesson Duration:	10 minutes
Class Profile:	Adult new comers to Hong Kong learning Cantonese

 

Lesson Objectives:

1.      Students will be learning about "yum cha" as part of the Cantonese culture. 2.      Students will learn how to say 10 popular dim sum dishes in Cantonese.             3.         Students will recognize some dim sum dishes by the end of lesson.

 

Summary of Tasks/Actions:

1.      Greetings and ask students what they had for breakfast/lunch. 2.      Lead into our topic for today "yum cha", explain the topic. 3.      Ask students if they have been to yum cha before. 4.      Introduce my top 10 recommendations and teach students how to say them in Cantonese. 5.      Go through vocabulary and get students to repeat after me 6.      Check students' understanding by showing photos of dim sum and ask them to answer the correct name. 7 .   show a short video clip and ask what words students pick up from it.             8.       Talk about useful words and dim sum cart tradition from video.             9.       Take home worksheet

 

Materials:

·        Powerpoint slide on Google hhttps://docs.google.com/presentation/d/1how8jYAzizMnMGikzJnktjZfvYNCjVdEWGjIwdS_7HU/edit#slide=id.g9b8fff3913_0_2692 ·       Short Youtube video clip https://www.youtube.com/watch?v=exnshNBjVkQ

 

Activities:

·       Repeat after me ·       Discussions

 

Assessment/Evaluation of Students’ Learning:

·       Check your understanding slides ·       Mix and match worksheet

 

Reflection:

I think my microteaching went well today. It was meant to be a beginner level class for students with little to no prior konwlege to Cantonese. However, I think I can improve on timing a little bit better next time, I went faster than I expected.

 

Microteaching lesson topic

My topic for this microteaching activity is " Talking about yum cha culture and teaching how to say some dim sums in Cantonese"

Blogging on Battleground Schools

 Three things that surprised me in this reading: 

1. Stereotypes on mathematicians 

I am surprised but also not too surprised on the stereotypes of mathematics illustrated by the article. People who dislike mathematics may say that it is hard and boring, and those who are good at mathematics are nerds. Also, many people may have the stereotypical thought that men are better than women at mathematics, but this is not true. I have seen many women who are good at math, and there were many women in our mathematics department back in undergrad!  

2 .Dewey's teaching techniques

Another point that surprised me was Dewey's teaching techniques that involved "programing the envrionment." It seems to be quite similar to what we are proposing in the concept based teaching methods. Getting students engaed in activities around the materials provided, and away from the traditional sitting still and watching the teachers present teaching style. I was surpseid that Dewey's recommendations were never taken seriously in schools at that time. 

3. War and math 

Lastly,  it iwas surprising to see how war has a direct relation to mathematics. The authorities finally see the importance in mathematics in the needs of elite education for scientific developments and innovations. People began to look at mathematics seriously, and finally realized the need of mathematics in fostering future scientists. 

The Dishes Problem

Solving without algebra:

Without algebra, it would be something like…

2 people share 1 dish of rice 

3 people share  1 dish or broth

4 people share 1 dish of meat 

(12 is the lowest common multiple)

So 12 people needs 6 dishes of rice, 4 dishes of broth, and 3 dishes of meat, that is 13 dishes in total. 

If every guests eats 13 dishes, then we have 65x12=780 dishes in total. 

Then we can use 780/13 =60 to find out there are 60 guests in the feast.

It does make a difference to our students to offer examples, puzzles, and histories of mathematics from diverse cultures because it adds more fun! Math is a universal language that is shared among different cultures. It would be interesting to learn how mathematics has evolved to become universal in today's world by looking at it from different cultural perspectives. 

In terms of presentation of the problem, I would be more focused if puzzle story and images are presented with the word problems. It allows students to imagine and picture the problem in their heads, and it tends to be more attractive than just having words.