Blog Post Due Nov 29^th

TPI Survey Reflection

My survey result shows that my dominate perspectives are nurturing and apprenticeship. My back-up perspective is developmental, and my two recessive perspectives are social reform and transmission.  The difference among sub-scores B, I and I categories are within 3 points under each category except the developmental perspective.

To interpret the difference under the developmental perspective, I see my intention for developmental is the highest, and there isn’t a big gap compare to action.  However, there is a 4 points difference between the belief category and the intention category.  This internal inconsistency can be explained by the fact that I don’t have enough teaching experience.  Although I have certain beliefs in teaching, I didn’t have chances to put them into actions.  As a result, the beliefs I have haven’t been solidified to form a concrete teaching philosophy.  It is surprising to me that one of my dominate perspectives is apprenticeship.  Is that an indication that I want my students to be more practical in applying knowledge into workforce (more employable)?

One of the interesting questions is that “effective teacher must first be experts in their own subject areas”.  I recall my answer to this question was strongly agree.  However, when I think more about it, I feel I am not sure if I really agree with this statement.   I have different people expressed different opinions on this matter.  I remember my Financial Accounting instructor is a very successful chief accountant in a big firm.  He once advised me that one has to be good at what you are doing.  For example, if I want to be a successful accountant I need to be an expert in accounting knowledge (I was studying accounting at the time).  I deeply believed in his thinking until I started working in the fields of education.  My supervisor has a very different view.  He believes knowledge can be obtained through learning.  For example, being a math teacher doesn’t mean that one has to hold superior mathematical knowledge in order to teach.   What one really needs to have is the ability to accept, adapt and learn any knowledge at any given time.  I guess is this type of thinking endeavours me to pursue a profession as a math teacher.

 

Blog Post Due 22nd 

The Ever-Changing Role of Mathematics Textbooks 

In respond to how might a text position students in relation to their experience of the world, the authors gives an example of when to use words with high or low modality. They explained that the TMM textbook authors choose to use high modality words (e.g. must) when referring reader’s past mathematics experiences and use low modality words (e.g. probably or might) when referring reader’s’ real-life experiences. They then posed question whether the model reader would think that his real-life experience mattes less that their mathematical experience. If I understand the point correctly, I would disagree with the article. If I were the textbook author, I would actually write the same way. When I structure my chapters and sections, I would make assumptions that one mathematical concept should be the prerequisite of another. When introducing anything new, I would also expect that the reader knows the pervious knowledge by following along with my textbook chapters. To make analogy, this is similar to the situation where students have to finish grade 10 math in order to enroll in grade 11 math class. Studying math is a continuous learning process where one thing builds upon another. However, I do resonate with the article that math textbooks depersonalized with their readers. I guess that is part of the reason why the majority of society agrees that math is a dry and boring subject. When I think back to the courses I have taken in university, I won’t give credits to the textbooks. By year three, I stopped buying textbooks unless it was necessary. If the authors can connect the readers by using first person pronoun and also second person pronoun, it will be like that the author and the reader is having a conversation about mathematics. I would prefer a textbook as such. I would say that textbook is playing a limited role in our schools in recent years. The learning is directed to a digital world where all resources are available, not only textbooks but also tons of worksheets, tutorial videos etc. Even without a textbook, one can still ace the course. Maybe it is convenient for some math teachers still use certain textbooks because they are familiar to the textbook structure, the way the content is delivered, and the questions at the back of each chapter.

The Scales Problem I found two tricky part of this puzzle. First, when I thought about this puzzle, I didn't think that to balance the scale with the only four weights I have, I could actually put weights on both sides. The second tricky part is that it should start from the biggest number and going backwards to find the 4 weights. I started from number 1 and I knew 1 must be one of the 4 weights. When I realized that there is no way by putting all the weights on one side and the herbs on the other, I started to try to herbs and weights on both sides. Soon I discovered that it is not possible to weigh bigger grams of herbs. I still need 1 as one of the weighs because it will be needed to weigh 1 gram. Then go back and started my trial and error from the biggest number 40. Here is a picture of the combinations, the 4 weighs are 1,3,9, and 27. To extend this puzzle, I could probably choose other numerbs such as 121. However the combinations will be too large that may be too difficult using trial and error method since there so many number to try. Maybe give a smaller number set say 1,3,9 first and let students work on it first. Once they have figure out the pattern, then I can extend the large set say 1, 3, 9, 81 and let them find the generality of this puzzle.

Reflection on Microteaching For the Monday mircoteaching, I have the follwoing comment about my performance: 1. I have read my classmates' comment. Most of them felt the acitivity was good but they wanted to have a clearer instruction. I actually have thought the feasiblity of this proof activity. I couldn't think a better activity for Pythagorean theorem but obviously there are constraints for doing it online. I was imaging how would I set up this one in a real classroom evnironment. I would still not giving out answers before the students start to cut the squares and try to figure it out themselves. However, I would give out papers with the 3 squared drawed for the students to save time and maintain accuracy. I will also walk around in the classroom and help students out or give some hints. Since yesterday's lesson was online, I couldn't prepare the papers and scissors for my classmates, and in addition, time is another constraint for this activity becuase just cut the 3 squares will take a very long time. 2. Good part about the microteaching was I wasn't very nervous. Maybe it was becuase the classmates were very active during yesterday's class teaching and we were talking and chatting in between each group. I felt very relaxed and didn't feel nervous at all. 3. I need to remind myself next time I need to repeat myself and make sure instructions are clear and concise to avoid confustion.

 Micro-Teaching Lesson Plan | Pythagorean Theorem 

Subject:  Mathematics       Grade:  8 Date: Nov. 16th       

Presenters: Ivy, May &  Sarah                                                   

 

Lesson Overview	Introduction to the Pythagorean Theorem:  a^2 + b^2 = c^2.
Big Idea	Discrete linear relationships can be represented in many connected ways and used to identify and make generalizations.
Curricular Competencies	Thinking - Through applications, students will need to critically think about where they could apply the pythagorean theorem in their own lives. Extension activities can also allow students to engage in Communication and Personal & Social connections.  Modeling the Pythagorean Theorem  Finding a missing side of a right triangle  Deriving the Pythagorean Theorem  First Peoples constellations
Content Objectives	Model the Pythagorean Theorem Finding any given side of the right triangle Derive the Pythagorean Theorem  Applications of the Pythagorean theorem
Materials and Equipment needed	Paper, scissors

 

Lesson Stages	Learning Activities	Time Allotted
Part I Part II Part III	Short history (May) Explain Pythagorean Theorem (May)  Applications of Pythagorean Theorem -First Nations Problem (Sarah)  Explain the canoe problem  Demonstrate how they could use the pythagorean theorem in order to solve the problem Interactive Activity : Proof Pythagorean Theorem using paper and scissors (Ivy)	5 minutes 5 minutes  5 minutes

 

 

The Giant Soup Can Puzzle

Due on Nov 13^th

To sovle this puzzle, I printed out the photo which has the bicycle and the water tank. I measured the length and height of the bike and the length of the water tank with ruler (I am not sure if this is the right way). I wasn’t comfortable using the ratio between the height of the bike and the width of the tank in the picture because the way the bike was positioned.   I found two ratios: the height of the bike over the length of the bike (3/5) and the length of the bike over the length of the water tank (2/5) approximately.  I manipulated the ratio equations so that the dimensions and the volume of tank can be represented by the height of the bike (since it was given). 

First, I found the length of the tank by substitution.  Then, after doing some research, I knew that the actual size of a Campbells’ soup can has dimensions of 41 cm and 51cm. This ratio can be used to find the width of the tank.  Once the width and length of the water tank were identified, the volume of it was easily found by using cylinder volume formula. The final answer was quite award (I might misunderstand the question) because the fractions looked really large, but it was an interesting experience.   As for now, I still don’t know whether my approach was right or wrong.  In the end, I found from the website that an average size of a bike has a length of 68 inches (about 170 cm).   Using my previous formula, I fou nd that the volume of the tank was about 40.12 cubic meters.  Then I researched on how much water needed to put out a single-family house fire.  The result showed that to effectively control a house fire with 100% involvement, it required about 400gpm water.  I did the conversion once again and it seemed that the tank contained enough water to put out the house fire. 

From a student’s perspective, one would like to have concrete numbers given in the questions.  However, taking from a teacher’s perspective, by not showing any numbers, the students have to research on the information needed to solve this puzzle and have to make logic conclusion whether the water tank will contain enough water to put out a house fire.  This approach will provide students opportunities to take initiatives in their learning and find out reasonable solutions by doing research.

To extend this puzzle, I could choose triangle or semicircle as the base shapes. I can link them to the real-life architectures such as pyramid or temples and use pyramid and semicircle shaped trees as comparison.  Since tress have the length of the truck which don’t belong to the shape to be compared with, it may add another layer of difficulty but also more interesting.

 

 

 

 

 

 

 

Blog Post   Due 8^th

Flow Experience – A Completely Engaged Life with Happiness

The notion of “flow”, as described by Mihaly Csikszentmihalyi, is a state of heightened focus and immersion in activities that one truly loves and enjoys.  When one is fully engaged in something that one is doing, one’s mind is completely concentrated and hardly being distracted.  The state of flow should happen when one has a genuine love and enthusiasm and is willing to devote his/her time and energy towards something.  As Csikszentmihalyi explains, to have a “flow experience”, one should not only completely be involved in what he/she is doing, but should have a sense of ecstasy, great inner clarity, a sense of serenity, timelessness and intrinsic motivation.  When one is experiencing “flow”, one is no longer feel his/her own existence and time is no longer sensitive anymore.

Relating to my short-practicum experience, I do recognize the importance of this “flow experience”.  At the beginning of my first teaching, I felt nervous and tried to deliver whatever I prepared for the lesson. However, as everything went on the right track, my nervousness has disappeared and I started engaging in interacting with my students. While helping my students during seated practice time, I didn’t think about my lesson plan anymore. I just fully immersed myself in a state of “flow” which I could only think of how to explain to my students the mathematical concept so that they can truly understand it.  I believe that was the moment where I found happiness in math through teaching.