Indigenous aspect of thinking

I was struck by the connection between the geometry and the clothing. I was amazed to realize that that linearity corresponds to the tension in the fiber. Therefore, the math is everywhere, it just requires our awareness and keen observation. It is important to notice how beautifully the grid is used as a metaphor to describe the control and ownership. My second stop was at anything that is real is independent of the grid system. As no grid system can explain the underlying geometry of the shape. Hence I really liked the idea of shifting the focus to understanding the geometry rather than focussing on using the grid system according to our convenience.

The idea of starting off with the simpler knots and then extending to the 3-D knots gives the students an opportunity to go beyond the rectilinear thought and also open their minds towards how the indigenous people get connected with their culture and looking for the mathematics behind the different geometries.

Math fair by MacNair Secondary students

The  Math fair by the MacNair Secondary  School students was amazing. There were such new ideas of representing the things I never thought, such as representing the integers ( their multiplication, division of negative, positive numbers) in the fun and interesting ways like " Did the turtle eat the cookie". I was really impressed by their ideas. I believe that students have a lot of potentials, emerging thoughts, and innovative ideas and they look at things through a different lens which is more meaningful to them. In addition to this, It was pleasing to see how the stories they made led them to solve the linear equations and made more sense to them which was much more effective than simplifying solving for the variable. " Fire and the water metaphors for positive and negative integers were interesting to see. I wish the best for those students and their teacher who is successful to build the student's faith in him. I wish for their success and hope that they would make a difference in the traditional ways of thinking about math and My big thanks to them and to their teacher for imparting new ideas to me and to my fellow mates.

Rat and wine puzzel

I will start with the small number of bootles and rats and then extend.
Let's consider rat 1 and only 2 bottles out of which one of them contains poison.
If the rat 1 drinks bottle 1 and die then bottle 1 contains the poison, but if not them the bottle 2 contains the poison.
Therefore 1 rat is required to test 2 bottles.
If we have 2 rats, then let's figure out how many bottles can be checked.
Rat 1 is given a mixture of 1 and 2
Rat 2 is given a mixture of 2 and 3
If rat 1 and 2 die then the bottle 2 is poisoned.
If rat 1 dies and rat 2 survives then bottle 1 is poisoned.
If rat 1 survives and rat 2 dies then the bottle 2 is poisoned.
If both the rats survive then the bottle 4 is poisoned.
Therefore, with 2 rats I am able to check 4 bottles.

Now let's start with 3 rats.
Rat 1 is given a mixture of 1,2,3,4
Rat 2 is given a mixture of 3,4,5,6
Rat 3 is given a mixture of 1,3,5,7

If rat 1 dies, number 2 contains the poison
If  rat 2 dies, number 6 contains the poison
If rat 3 dies, the number  7 contains the poison
If  all the 3 rats die, then number 3 contains poison
If  only 1 and 2 die the number 4 contains poison
If none dies number 8 contains the poison

Hence till now with 3 rats, I can check 8 bottles.
I can notice the pattern,
If there is 1 rat then the number of bottles check is 2
If there are 2 rats then the number of the bottles checked is 4
If there are 3 rats then the number of the bottles checked is 8

Therefore 2^n( 2 to the power n) where n is the number of rats.
hence 10 rats are enough to check 1000 bottles as 2^10= 1024
but for 9 rats I am not able to figure out as only 512( 2^9) bottles can be checked.

Revised Unit Plan

https://drive.google.com/drive/u/0/folders/1n2fVteD8uOyTbUEGe31iuwwA07Tpkv18

Textbooks and Mathematics

The modality of the linguistics is really important for the textbooks to be useful for the readers. It is interesting to notice that the use of the first-person pronouns( I and We) in the math textbooks helps the readers to get involved in the textbooks and make better connections. The absence of the first-person pronouns makes the textbook really dull and it also distances the reader from what the author wants to explain.  Moreover, the use of second-person pronouns( you) connects the reader directly to mathematics. I remember, during my high school days, I use to connect more to the questions which involved first and second-person pronouns. It helped me to imagine the experience what the authors want to interpret. In addition to this, the use of the graphics and the photographs also make a huge difference in the student's understanding. Although I agree with the author of the article that graphics are more helpful as it generalizes the domain whereas the photograph talks about that particular person. For instance, the example of the hand doing mathematics in the article, lets the readers imagine their own hand doing mathematics and helps them to have a better understanding and experience. I remember my mathematics textbooks in my high school and college was all about numbers and variables which would not make sense to any layman reading the textbook. There were no pictures for the reader to make connections to the real world. Therefore, only the students who loved numbers or were interested in math would excel in math, and the textbooks were not good enough to develop anyone's interest.

According to me, the use of textbooks should not be ruled out completely, some good points can be incorporated by the teachers from textbooks for making their teaching and learning better. Especially, the textbook questions can be used to do more practice. I believe a teacher can play an important role in the interpretation of the information written in the textbook, even if the textbook is not good enough for the student readers. As per my recent experience, while making the unit plan for science, I found BC connection 9 textbook really helpful and I was amazed to see how beautifully the author made connections between the science concepts and the outer world.

Scales Problem

The first weight which I think the vendor should have is 1 g weight. Then I was in a dilemma should I opt for 3 g or 2 g. Initially, I chose 2g and I was able to get a maximum of 3 g but if I chose 3g then 3-1 will give me 2 and 3+ 1 will give 4g. So, till now I thought 1g and 3g should be fine to weigh the herbs till 4g. Now in order to weigh 5 g next highest weigh should be 9 g since, 9-3-1 = 5 g, I tried with 8g but  Using 1, 3 and 8. I was able to get to the maximum at 12 g in comparison to 9,1,3 which leads to 13. For instance, I chose 1,3,8 then the highest weight I figured out was 25g since 25-8-3-1= 13g, But using 1,3,8,25 the maximum I was able to reach was 37g( 1+3+8+25). Therefore, I figured out I should choose 9 instead of 8. Since 1, 3, 9 covered all the weighs from 5g to 13g.
9-3-1=5
9-3=6
9-3+1=7
9-1=8
9+1=10
9+3-1=11
9+3=12
9+3+1=13
The weight should be 27g since 1+3+9+x= 40, so x=27g.
Moreover, using 1,3,9,27 we can have the weighs after 13g.
27-9-3-1=14                        27-9+3=21              27+3-1=29               27+9=36
27-9-3=15                           27-9+3+1=22          27+3=30                   27+9+1=37
27-9-3+1=16                       27-3-1=23               27+3+1=31               27+9+3-1=38
27-9-1=17                           27-3=24                   27+9-3-1=32             27+9+3=39
27-9=18                              27-3+1=25               27+9-3=33                27+9+1+3=40
27-9+1=19                          27-1=26                   27+9-3+1=34
27-9+3-1=20                       27+1=28                  27+9-1=35

Eisner on "Three curricula" taught by all schools.

While reading the article, my first stop was that giving rewards to the students can foster the willingness to perform better in their schools but on the other hand students, those who work for getting the reward don't perform well when they don't see any appreciation.  I have first-hand experience with this ideology. When I came to Canada in 2017, I started working as a math instructor at the Mathnasium of South Surrey( Math learning Centre), where students were getting punches in their rewards card for completing every page. I saw that the rewards acted as the driving force for them to complete more and more math pages and buy some big rewards from the rewards cabinet by redeeming their completed punched cards. On the other hand, there were some students who were not allured by these rewards and worked at their own pace. Therefore, I believe that giving rewards have their own pros and cons. Sometimes rewards can be beneficial to trigger someone towards taking the first initiative. On the other hand, rewards should not be the sole motivation to do something. The students should enjoy the process of accomplishing their goals.

Another thing that really speaks to me is the use of location and time. I remember in school time, subjects like Physical education, drawing, Fine Arts, Dance used to be the last periods of the school time table which subconsciously reinforced that the arts subjects were not as important as science and math. I truly feel that I am a deficit of those talents which I think I could have explored more if enough was devoted to those subjects. Therefore, I believe that enough time should be allotted to all the subjects so that students can explore their interests.

In addition to this, I was happy to realize that how one can even learn from the school time table. The time table teaches the students to cognitively flexible and be able to adapt to the new demands on the schedule. It helps them to understand the importance of punctuality.  Moreover, we as teachers should acknowledge the importance of the implicit curriculum which teaches the student about the social and moral values which will help to become a good human being which I believe is above all the explicit curricula.