Topic of Microteaching

I would like to teach some Chinese vocabulary, such as "找 朋友， 你是我的好朋友” which means "Looking for a friend, you are my good friend" through children's song "找 朋友".

Dish problem

 Every people needs to use 1/2 dish rice, 1/3 dish broth, and 1/4 dish meat. So,  the minimal possible number is 13/12 dishes for each, and the number of all customer must be the multiple of 12 (LCM of 2, 3 and 4). So we got 65/ (13/12)= 60, and 60 is also a multiple of 12.
Check the answer, 60 customers, need 30 dishes rice, 20 dishes broth, and 15 dishes of meat. Therefore, the final answer is the max of the 60 customers.

Refelction: Math Art Project

The Mart Art project my group has chosen is a permutation arts model, which created by a high school math teacher, Chris Nho from Chicago, Illinois, U.S. Permutations explores questions about how many ways you can arrange several different objects. The print used four simple colour patters to attract the audience to wonder about patterns and structures. We choose it because it is easy to operate in school and meet with the high school curriculum, Permutation. We notice all stages children are playing with patterns and structures. Therefore, we chose the playful designs, such as colourful hearts, animal cartoons to represents the different objects. We hope the colour hearts pattern might increase the younger students’ interest while the cartoon pictures might meet the higher-grade students’ attention.

We invited young kids, teenagers and young adult to play with the art projects. The youngest kid needs more support to figure out the heart patterns while the 19-years boy could deal with more complicated requirement. Two teenager students performed in the middle; they spent a long time, and made few mistakes during the process, but could figure out the result more independent than the younger boy. All three groups of students actively involved in playing with the patterns. During our presentation in class, four different groups showed different solutions to solve the problem. The first group is more abstract, they used numbers to represent the different cartoon shapes. The second group used the name of the animals on the tree diagram. The first two groups only showed a simplified (part of the whole tree) to show their ideas. However, the third group drew the complete five layers tree diagram. The fourth group developed their strategy is based on the ancient practice that they count the five objects solution based on the result of the four objects, so they conclude that like 5 X24 =120. The whole process of the project showed that the diverse in math thinking.

The art project changed my mind. First, although the permutation is listed in grade 12 high school curriculum, all ages kids have the potential to explore the problem by hand-on exercise. Second, using the hand-on practice to help students with a relational understanding of concepts might much better than using instrumental formula. Students might be much easier to recall the concept of counting principle and permutation from the colourful hand-on memory. Finally, the project helped me to develop a growth mindset. I had a fixed mindset that I could not do arts, but this project showed me hope. Even I have weak hand skill in painting, I still can create an art project by using computer tools.

The man's father is my father's son

The question:
"Brothers and sisters I have none. That man's father is my father's son"
 who is the man? and who is "I"?


logical reasoning:
  "I" have no brother and sister, so I am the only child of my father, therefore, my father's son should be "I", the speaker.
 Then the man's father should be I.
So the man is the speaker's son, and I is the speaker.

Locker Problem

Two letters from Students

Hi Brenda:
     How are you? I missed you.
      Tell you a piece of good news, I am graduated from college and started to work as an AI engineer at Apple.
     I really appreciate your encouragement and caring. You helped me to be confident in learning math. Now, those skills I learned in your class might not directly help me in my career, but the confidence to conquer the difficulties helped me in dealing with issues. I still remembered you guided me to play with math games and I even won you twice. Thanks for spending time to understanding my needs and help me to go through the hard part.
   Now, I am looking forward to my future with confidence. I will get you informed.
   Keep in touch!

Wish you the best!

Your student. Bob

Hi, Brenda,
    You might be surprised to get my letter. Yes, I am Brain. One always gets a good grade in your class. However, I dislike you. You have never called my name right You are the person made me so embarrassed in front of my peers. They were calling my name after you. You never have known how much pain I got from it.
  Do you work better, to remember their name!

Brain.

Mathmatics and Me

The person really helped to connect me with mathematics was Mr.Huang, my math teacher in elementary school in China. Yes, in China, we had different teachers for each subject. Mr.  Huang was my 4th-grade teacher when I moved from another town. I had been a difficult student how often called out of the classroom, but Mr. Huang changed me. "Math is amazing, and you will love it", he told me that on the first day we met. Actually, I could understand the math concepts quick, but could not sit still in the classroom. So, he allowed me to go to his office when I finished my homework and helped him to mark other's papers. I was proud to have this special treatment and worked even harder on math, then, I found of math now.
One young lady who was struggled on math material gave me the encouragement to be a math teacher. I was her private math tutor. Working with her told me the importance of the self-confidence on learning math. She had a good sense of logical, so after we tried a few logical puzzles, and she successfully managed it, I saw her happy face. She started to try more. I believe,  the succeed on the logical puzzles formed her safe base on exploring more areas. She started to build up the confidence, and slowly but steadily build up her math skills. The more she gained, the happier she gets, and the more confidence in her mind, and the harder math concepts she was willing to try. So, this experience encouraged me to think about supporting the new generation to learn math.

Representations in mathmatical teaching

The idea of both inner and external representations in delivering mathematics teaching practice echoes with my own beliefs about math teaching. When we teaching math to children, it is easier for them to absorb the concept is to connect the abstract math signal concept with other external representations, include the external representation related with social life, or the other scientific phenomena. Through these activities, students can create the cognitive connection between the abstracted mathematics concept, like the signal formulas, with the phenomenon which they could see, touch, and feel.  

The connections between inner and external representations are important to recall abstract concepts and apply them to solve problems. For example, if the students connect the rectangle with their own bedroom setting, link the width and length with the room measurements, they are easier to understand and recall the concept of the area of the rectangle. Later, if the students can connect rectangle with other staff in their life, such as books, windows, etc. The more external representations they could collect and connect with the rectangle concept, the easier for them to recall the inner representations of the rectangle properties. Similarly, the more inner representations of the rectangle properties the students could learn, the more they could apply on external representations of real life, such as do a design to rearrange their rooms.

Group discussion of Skemp article

1) What 'should' come first in learning math: instrumental or relational understanding? Why? In what

contexts?

When we teach students,  it’s always good to have a relational understanding. So we start with relational teaching to let students connect the concept with their foundation knowledge. If the student has difficulty to understand, then they can memorize it as instrumental understanding, and digest it later to build the relational understanding.  Class size and the diverse level of the students influence the teaching style.

2) When is a general view of a topic appropriate? When to get really specific?

When we start a unit, we start with a general view and build up the connection with the former knowledge. Then we move to specific applications. By the end of the unit, we go a general view of the topic, to create the mind map of the chapter, and build up the relational connection.

3) How can we, as mathematics teachers, work to improve the negative attitudes of math anxiety in our communities? Are these attitudes the same in all cultures, or could Canadian society learn more positive approaches to mathematics from other cultures?

The society needs more support on math learning, and also emphasize the advantage of math skills and knowledge. The whole society needs to agree on the importance of math and encourage the young generation to learn it. This kind of environment might be found in the Asia culture, include china. 

Brenda, Carla, Roya

Reflection on Skemp’s article “Relational Understanding and Instrumental Understanding”

       While I am reading the article, few times I stopped and reread. The first time, I stopped at the mismatching “football” between two teams. This example recalled my experience on the term before and after immigrant to Canada. The second time, I stopped when the pupil responds “because area is always in square centimetres”. This example reminds me of my students when they were not fully understanding the meaning of units and area. They just instrumentally copy the examples in class without identifying the different meaning. The third time, I stopped after Skemp discussed the ground of instrumental teaching, because I believe there should be more reasons than he listed, such as the limited pupil’s foundation skill and knowledge level. I also stopped a few more times for the rest article, his opinion raised my interesting and encouraged me to relate with my experience.

       Overall, I agree with him on the part of the discussion about advantages on both sides. Relational mathematics is the desired way to teach students; however, the reality of educational environment might limit the teacher’s choice. As secondary math teachers, there should be various level students in our classroom. The most capable students can easily get the relational expression within the limited class time and move forward. The average student might struggle on it and can only make minimal amount of connection with the relational understanding. Some students might have limited foundation knowledge which brought from their elementary education and tries to avoid to learning math. For the weakest student, if they could understand and support with the easier instrumental understanding, they can cumulatively build up their confidence, and motivation to work more on math. Based on student centre education, I would like to stand on that, no one method can math all student’s needs. Math teacher has to be more adoptive on choosing the right way to facilitate student’s learning.

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Sorry, if you see the Chinese Characters on the website. I am working on it.

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Brenda