Home work- Take TPI Test and Reflect on the Result

The result of my TPI test is showing above. The graph seems pretty flat. My dominant perspective is Apprenticeship, and my Recessive one is Social Reform. The second dominant is Transmission, and the second Recessive is Development. 

I am not so surprised that Apprenticeship is my dominant perspective. I think it is related to the years of manufacturing background and experience that form my teaching beliefs in practice and mathematics application. For the Recessive in social reform, I guess it related to my own education style in the past that does not empathize with social reform. I am surprised that my beliefs and actions are 3 scores higher than the intention in both my first and second recessive, which seems not very consistent.

The interesting question raised is how the results will be different because of teaching the different subjects. I probably will try this test again to teach other subjects, such as Chinese. I wonder how my dominant and recessive perspective will change after years of experience in real-world teaching.

 

Homework Nov 22nd-Thinking about math textbooks

Most of my mathematics education as a student have treated math as a tool for solving problems.  Thus for me, the examples shown in the article by authors Herbel-Eisenmann and Wagner does not invoke some particular thoughts and feelings.  To me, the diagrams are simply illustration intended as a visual aid to a problem to be solve.  I think this is in part influenced by my math education in China where my K-12 math textbooks are very condensed and abstract, focusing on the concepts and theories, and diagrams are often limited to geometric problems or graphs of equations.  The text are also often in 3^rd person or simply statements without references to the reader or anyone else. However, if textbooks are trying to connect to the readers through use of language and diagrams, and with children being more aware of things around them than before, I do see the need to be more careful with presentation.  Reading the author’s examples reminded of a short video that floated around Chinese social media a few years back where the mom expressed shock at her grade 1 child’s answer to the question asking how many people do you see in a picture of major protagonists in Journey to the West novel?

Her child answered 2 while she and likely the expected answer is 4.  The child reasoned that as two of the characters are deities originating from animal forms they don’t count as people.

I think textbook serves an important purpose as it is a central repository of what the student is expected to know for the course.  Yes, the authors are correct that textbooks make many assumptions about their readers like what they already know and familiar with.  I don’t think it is a valid criticism.  The reason is that textbooks are created with a set of assumptions and requirements, often based on feedbacks from its intended end users like school districts.  Thus, a grade nine textbook adopted by BC will either be written with BC grade nine curriculum in mind, and/or BC will have adapted its curriculum in part based on the textbooks for various grades by the publisher.  As well, traditionally, students in grade 9 math as only there if they have passed grade 8 math, implying they have required knowledge and skills needed for grade 9. However, as we move towards a system where each student progresses through at their own rate that is not tied to the specific grade they are in then textbooks becomes of limited use.  For example, if the students in grade 9 math class are there because they are simply in grade 9 while their actual math knowledge and skill level might be grade 8 or grade 10 then standardized textbooks would be inappropriate as they are not designed for such learning environment.  Instead alternative sources like Khan Academy that can more easily tailored to each student’s individual level would be more useful and appropriate.

Math puzzle- Scale and reflection

I have thought about this question for a while,  I think the numbers should be spread between 1 and 40 and they should be added up to 40, so I can cover all the numbers from 1 to 40. and I decide the weight 1 and 3 are needed, so I can weigh 1, 2( with 1 on the other side), 3, and 4. Now I need to decide my 3rd number which is can not be too close to 3 but cannot over 17 since it will be over 40 if we add the fourth number. I couldn’t see the pattern right away, but I was sure that there must be a pattern for this problem.  I did lots of trial-and-error methods and I decide to try the third number as 9 and the fourth number is 27 since the first two numbers have a ratio of 3. luckily, they add up to  40. Then I start to test if the four weights are 1, 3, 9, and 27 works for this puzzle.

use 1- measure 1

use 1,3- measure 2 ( with 1 on the herb side)

use 3-measure 3 

use 3 and 1- measure 4

use1,3,9 -measure 5(1,3 on herb side)

use 3,9- measure 6 ( 3 on herb side)

use 1,9-measure 10

use 1,3,9-measure 11 ( 1 on the herb side)

use 3,9- measure 12, I will use arithmetic to illustrate for the rest.

1+3+9=13, 27-(1+3+9)=14, 27-(3+9)=15, 27+1-(9+3)=16, 27-(9+1)=17

27-9=18, 27+1-9=19, 27+3-(9+1)=20, 27+3-9=21, 27+1+3-9=22, 27-(1+3)=23

27-3=24, 27+1-3=25, 27-1=26, 27, 27+1=28, 27+3-1=29, 27+3=30, 27+3+1=31

27+9-(1+3)=32, 27+9-3=33, 27+9+1-3=34, 27+9-1=35, 27+9=36, 27+9+1=37,

27+9+3-1=38, 27+9+3=39, 27+9+3+1=40, here we go!

I don't think there has more combinations at least I don't find another one.

I can extend this puzzle to ask students to discuss why these combinations work.

what is the mathematical reason.

Micro-teaching reflection

 Overall I think our microteaching is good but there are a few areas that need to improve. I think peer feedback and evaluations are so valuable. We could improve by adding the definition of Volume and the importance of learning it in the introduction. For the involvement of learners, if we are teaching in the classrooms, I would invite students to calculate the cylinder volume by using what they just learned. For the time and pacing, we could organize the contents more carefully, so we can save more time for students' final activity and discussions.

Micro teaching-Volume

 

Presentation link:

https://docs.google.com/presentation/d/1Nwq4E_Lp5Bd5jigYc7hqQI73SM0su0TzL2UEsAklTh0/edit?usp=sharing

Math Puzzle: The Giant Soup Can of Hornby Island

I measured the can ratio height: diameter= 3.5cm : 2.4cm( approximately)

the length of the tank is about 2.5 times as long as the bike. The regular bike is about 180cm long. 

So, the tank length will 180*2.5=450cm.

Then the length: diameter ratio of the tank will be (450/diameter)=(3.5/2.4)

the diameter of the tank=308cm.

Therefore,

the volume= pi *(308/2)^2*450=33510708cm^3=33510L(approximately)

my student bird just wants to get everything a precise number. My teacher bird just wants to get good reasoning if it makes sense.

Then I did research about the fire tank: 

On this pumper/tanker fire engine, the primary water tank is inside the vehicle, it holds 1,000 gallons (3,785 liters) of water, and it runs down the center in the rear of the truck. A drop tank is like a big aboveground pool that can hold about 2,000 gallons of water.

So my conclusion is this water tank about 10 times of the primary water tank and about 5 times of drop tank, so it can hold enough water on an average house fire.

I want to extend this puzzle by asking: how much paint we need to use to cover the tank in one color?

The surface area of the tank is SA=pi*3.08*4.50=43.5204m^2 since both ends don't need to be painted.

If we get the Dulux from retail, you need about 1 can of paint, including waste

“Flow”, engagement and the Thinking Classroom

                                               

By watching this video, I am interested in the psychologist's famous investigations of "optimal experience" that revealed that what makes an experience genuinely satisfying is a state of consciousness: flow. During flow, people typically experience deep enjoyment, creativity, and a total involvement with life. The ways this positive state can be controlled, not just left to chance. I would like to read the book Flow: The Psychology of Optimal Experience, which will teach how, by ordering the information that enters our consciousness, we can discover true happiness and greatly improve our lives' quality. Regarding the engagement and the thinking classroom, I feel some students were not very engaging in the classroom while I was in my short practicum. I feel I need to be more creative to help students stay connected to the class learning topic and school life and help students connect with peer classmates over shared interests. Engagement refers to the degree of attention, curiosity, interest, optimism, and passion that students show when they are learning or being taught, which extends to the level of motivation they have to learn and progress in their education.