Wanyi’s EDCP 342A Math Blog

Doolittle (2018) Off the grid. In S.Gerofsky (Ed.)  Geometries of liberation.  New York: Palgrave, pp. 101-121. Please read this very interesting piece and write a blog post on it by Sunday, December 8 at 8:00 PM. Suggested prompts: Talk about 2 or 3 'stops' you had in reading this: things that stopped you, surprised you, etc. Think about how this paper might offer new approaches to Indigenizing mathematics curriculum and teaching. Does it challenge or stretch any of your ideas around this? The author questions the grid concept "We know well the benefits of using the grid, but what are the  dangers? What are the preconditions for the grid which may not be satisfied in real-world applications? What are the extremes at which the grid can  fail? What are the consequences of failure? And what are the alternatives?" This questioning process makes me think of the development of Non-Euclidean geometry which also starts from questioning the truth of Euclid's 5...

Solution: We can use the following Binary number system to solve this puzzle. First, number the bottles from 1 - 1000. Convert the bottle number to binary. Number the rats D1, D1, D2, ...., D9 representing the binary digits. Then, rats will drink wine in the following rule: Binary number of bottle 1 is 0000000001. Rat D1 will drink wine from bottle 1 Binary number of bottle 5 is 0000000101. Rats D1 and D3 will drink wine from bottle 6. Binary number of bottle 12 is 0000001100. Rats D3 and D4 will drink wine from bottle 12. ..... Hence, by seeing which rats have died, we can figure out which bottle is poisoned. For example: If rats D3 and D4 die, then we know the bottle 12 is poisoned. 1000 bottles can be represented with 10 binary digits (binary number of bottle 1000 is 1111101000) , and we have 10 rats (each rat represents 1 digit), so we are able to use 10 rats to test 1000 bottles of wine.

Unit plan: https://drive.google.com/file/d/1dEA-K0NxATPNhRoQvEhQ9RBmYYXjUbVC/view?usp=sharing Lesson Plans: Lesson Plan 1 Lesson Plan 2 Lesson Plan 3

Unit plan: https://drive.google.com/file/d/1kwqfNnzoaGwlhGIeDGthOhWikcvFCD67/view?usp=sharing Lesson Plans: https://drive.google.com/file/d/1BuMyxkr9X7D-G-IN_RR4fiBqsP6bOy95/view?usp=sharing https://drive.google.com/file/d/1clL_FGBXZ5MJ0-7ZqO_2g7cWX6VX8mqa/view?usp=sharing https://drive.google.com/file/d/1RoZh1UWJTGV4a56NaXunW8yUH1NTzq0o/view?usp=sharing

Here is an interesting critical-thinking take on the ways that math textbooks may 'speak to' their readers (assuming that people actually do read and listen to math textbooks...) Wagner & Herbel-Eisenmann on math textbooks and the ways they may position their readers Please read this thought-provoking article and blog on: •How you respond to the examples given here -- as a teacher and as a former student •What are your thoughts about the reasons for using/ not using textbooks, and the changing role of math textbooks in schools? The author gave an example that TMM's initial "investigation" whose instruction included much more exclusive imperatives (or "scribbler" imperatives such as "write", "calculate" and "copy" ) than inclusive imperatives ("thinker" imperatives like "describe", "explain", "prove"). I agree that it is appropriate to scribble before thi...

My first though is to figure out 4 numbers from 1 to 40 that can be added together to obtain any whole numbers from 1 to 40. So, one of the 4 weights must be 1g, which is the smallest weight. Should the next be 2g? There is only one whole number can be obtained by combining 1g and 2g, which is 3g. What about 3g? The combinations of 1g and 3g give us 2 whole numbers, which are 2g (3g-1g) and 4g (1g+3g). What about 4g? But any combination of 1g and 4g won't give me 2g. Now, 1g and 3g are the two of the 4 weights in my mind. And using a similar pattern, I figure out 9g is one of the 4 weights: Combination of 1, 3, 5: 3-1=2 3+1=4 5-1=4 5-3=2 Obviously, 5g is not a choice since numbers obtained by combining 1,3 and 5 can be obtained by combinations of 1 and 3 as well. New numbers produced by combining 1, 3 and 6 6-1=5 6+1=7 6+3+1=10 Now we have 1,2,3,4,5,6,7 and 10 New numbers produced by combining 1, 3 and 7 7+3=10 7-1=6 7+1=8 7+3+1=11 7+3-1 7+1-3 Now we have 1...

Sorry for missing this art project reflection.  The image shown above is the our replica of Mergerate’ art work which is the work we investigate in this project. I would like to thank my group member Kyle for setting up the project on LaTeX. Then we finished coding as a group. In this work, the triangular grids are numbered sequentially beginning with 1 at the centre and continuing outward along a spiral path to 486 at the far left. A triangle is coloured cyan if it is prime, magenta if it is a happy number, and yellow if it is a triangular numbers. The Fibonacci number is represented as a transparent white triangles layered on top. A blended colour is used for integers belonging to more than one sequence.  Following is our extended art work. After group discussion, we decided to include perfect squares and lucky numbers in our extended art work.  We found that the perfect squares produced an interesting "spiral galaxy" pattern with 5 arms that was sim...

"....the use of extrinsic rewards can create a set of expectations on the children's part that dampens their future interest in activities if extrinsic rewards are not provided. It reminds me of my experience of teaching 10th grade mathematics in Shanghai. 10th Grade has 4 homeroom, and students have all the classes in their homeroom. I was a math teacher of two homerooms and my colleague was teaching the other two. In my colleague's class, students would get a token every time they answer a question, and students were told that there would be a reward for students who gained the most amount of tokens. In the middle of the semester, one of her student transferred to my classroom for some reasons. And my new student was disappointed after he knew I was not doing this reward activity. After knowing this kind of extrinsic rewards was happening in the other two homerooms, my students wish I could do this as well. I appreciated the effort that my colleague had put to encoura...

We revised our lesson plan several times. Our drafted lesson plan had a video at the beginning  introducing the laws of exponents, then there was a recap on each exponent laws and practice problems at the end of the lesson. Thanks Susan for remaining us to think about the use of the video. We had a debate on whether we shall keep the video or not. We finally decided to play the video at the very end of the lesson after the practice problems, as a review, and added one related simple problem after each law was introduced. My big take away from the the process of creating a lesson plan is that we have to be clear about the purpose of everything including the activities and use of media, that we plan to do in our lesson, and make sure it efficiently serve our student's learning. Also, creating a lesson collaboratively as a group can be challenging when we have different thoughts. I learned from my partners that we should not hesitate to share our different thoughts in a respectful wa...

The Table M.1-Dichotomies Underling Different Stances in Mathematic Education remains me of a conversation about the difference of mathematics education between China and Canada with an instructor of teacher education college from China. He said educators in China have been aware that students could be benefit from inquiry-based learning, however, because university entrance exam was very competitive and challenging, teacher focused much on teaching in a "traditional" way to help students success in the exams, and had no time spending on teaching through inquiry. I quite understand the situation since I was born and raised in China. Chinese education system and policy have a big impact on teacher's teaching method. But I also came up with a question that if the situation will not be changed in a short period, how can educators in China help student success in the university entrance exam, in the meanwhile efficiently integrating inquiry into their teaching? The article ...

Here is the link for the  lesson plan :  https://docs.google.com/ document/d/1etGrGcqE- e4oPHBfrTyiv0mbyIDHRFBaLWJ8ner _2lE/edit?usp=sharing Here is the link for the  presentation slides :  https://docs.google. com/presentation/d/ 1P4FjxiBigrhkAtP5T1KoncAuyrga6 YD-SvBxiCvTQN8/edit?usp= sharing

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? (From the UK Association of Teachers of Mathematics book,  Eight Days A Week ) My thoughts: 7 and it's opposite number form half of a circle. 30/2=15  So there are 7's opposite number is 15 (including it self) numbers away from 7.  7+15=22 Therefore, 22 is the the number diametrically opposite to 7. • What process did you use to work on and solve this puzzle? First I started form a small number which are 4 equally spaced points on the circumference. the number diametrically opposite to 1 is 3, which is 1+4/2. From that I found a pattern that a number and it's opposite number form half of a circle, and the opposite number = number + number of points/2. • Could you create other extended puzzles related to this one -- some possible, some impossible?  (Is there any value to giving your students imposs...

"How many guests are there?" said the official. "I don't know.", said the cook, "but every 2 used a dish of rice, every 3 used a dish of broth, and every 4 used a dish of meat between them".  There were 65 dishes in all.  How many guests were there? Taken from A puzzle from 4th century CE, China from the Sunzi Suan Jing 孙子算经 Please consider: • Whether it makes a difference to our students to offer examples, puzzles and histories of mathematics from diverse cultures (or from 'their' cultures!) • Whether the word problem/ puzzle story matters or makes a difference to our enjoyment of solving it. Solution: Let x be the number of guests, then we know that there are x/2 dishes of rices ( "every 2 used a dish of rice") , x/3 dishes of broth ( "every 3 used a dish of broth") , and x/4 dishes of meat. Then  we can have the following equation: x/2 + x/3 + x/4 = 65. 13x/12 = 65 x = 60 After solving the equation above, we have x...

The common suggestions I got from my peers are that the clarity of presentation and activity, timing and pacing should be improved. And the learning objectives should be better addressed and met. I agree with that. The paper cutting activity involved approximately drawing 6 rectangles in same size and have even space between them. By observation, Brenda and Hugo spent the most of time to use ruler to try to draw these rectangles accurately. This is an excellent strategy, but it is hard to finish in 6 minutes. And Danielle had no problem with the "approximately" and successfully finish the paper cutting. The takeaways from this micro-teaching are that if the instruction is unclear, people in the same group will have different way to implement the activity, then the outcomes will be diverse. And 10 mins is a very very short time for teaching one skill to beginners, especially for cutting 囍 whose instruction can be complicated. For the next micro-teaching, I should carefully c...

Lesson Name : Micro-teaching Lesson: Chinese Paper Cutting Instructor ’s Name:   Wanyi  Li                               Date:   Oct. 2 , 2019 Instructional Objective(s): Be familiar with Chinese paper cutting including its history and properties, and know how to make a paper cutting about a Chinese character, 囍. Lesson Activities: Teacher Activities Student Activities Time Introduction: 1.   Asking warn up questions to check prior knowledge/experience of Chinese paper cutting. 2.   Sharing My personal experience with paper cutting. Body: 1.   Introducing the origin/history/use of Chinese paper cutting. 2.   Exploring the properties of Chinese paper cutting including elements and their meanings/geometric property   and its meaning. 3.   Furthe...

I plan to introduce Chinese Paper Cutting in my micro-teaching lesson.

From the first sentence we knows that "my father's son" is the speaker. So, "that man's father is my father's son" can be converted to that man's father is me who is the speaker. So, that man is speaker's son. The way the speaker used to illustrate their relationship is not straight forward, which makes this problem difficult and interesting.

Letters from two of your (future) students in 2029 One loved your class! The other, not so much Then a couple of students on what you hope for and worry about as you embark on your teaching career Letter from a student who love my class: Dear Miss Li, I really enjoyed your class. The connections between math topics and real life that you brought to the class have shifted my point of view about mathematics and made me appreciated mathematic as a powerful subject in our life. I still remember the relational understanding and instrumental understanding that you were introduced to us. The process of relational learning was painful sometimes at the beginning but it is very helpful in my further mathematics study. The way you integrated history and art into math class has engaged me in mathematics learning. You are such a caring teacher who always created a supportive, positive and kind learning environment to us.   Letter from a student who did not love my ...

“The locker problem”: A school has 1,000 students and 1,000 locker. On the first day, all the lockers are open.   student #1 closes each locker student #2 opens each 2nd locker student #3 changes each 3rd locker student #4 changes each 4th locker student #5 ……………….5th locker After all 1,000 are done, which lockers are open/closed?why? Answer: Every door with a square number within 1000 (2^2 th, 3^2 th ....... 31^2 th, except 1^2) is closed, and others are open.

1. It makes me feel good when I finally figure out the answer to a challenging math problem. 2. The smiles on my students' faces when they find the solution makes me feel good. 3. I think the logic behind math is very charming and I am attracted to it. Math is organized and in order.  4. I met a very enthusiastic math professor at UBC who is a real model of teacher for me. 

Read the article written by Richard R. Skemp: Relational Understanding and Instrumental Understanding three things that made you "stop" as you read this piece, and why where you stand on the issue Skemp raises, and why. 1st stop: While reading the article, the example of instrumental understanding made me “stop”. The student asked why the area of rectangle is given by A = L x B. The teacher “explained” that the formula told to multiply the length by the breadth to get the area of rectangle. Then the student believed that he understood it because he always got the right answer. It remains me of my teaching experience as a 10th grade math teacher. The class I taught was an honour class. Students and parents very cared about the marks. So, at the beginning of my teaching, in order to make my class “efficient”, I presented the ideas straight forward, addressed the formulas, clearly showed them the procedures of problem solving, and then done some practice to maste...