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.

Micro teaching reflection.( Factoring trinomials)

Planning: We ( Me and Karmdeep) decided to micro-teach factoring polynomials from Foundation Math 10 and Precalculus. I looked into Foundation Math 10 textbook and found that Factoring polynomial is quite a big unit so decided to teach only factoring trinomials by using the visual method. In addition to this, we tried to think from a student's perspective and reflected on how can the student relate polynomials in real life. Therefore, we used PHET simulations to demonstrate the trajectory of parabola( trinomial). Moreover, we used virtual algebraic tiles to show the factoring of the trinomials on the projector. I should add that Karm deep did a very good job of making the algebraic tiles with colorful card paper which we used for our activity.

What worked well: I feel that our microteaching went okay and the learning objectives of the lesson were met. I am glad that all our students during the microteaching lesson were very engaged. They really liked the idea of using real-life examples of polynomials and exploring the mathematical representation of their path. The PHET simulation further enhanced the understanding of the trinomials. When it came to teaching, I suddenly got passionate, energized and felt as if I am actually teaching a grade 10 students. The activity at the end was very hand-on and we helped our students wherever they needed help and addressed their inquiries.

Areas of improvement: The major area of improvement for me is timing and pacing. In the last microteaching lesson, I finished a bit early but this time we had to drop the example demonstrating the use of zero pairs in making the factors using algebraic tiles. Some of the students were able to identify the use of zero pairs in the activity and took it as a challenging question but some of the students wanted the concept to be discussed before which I think we should have. The reason behind this is that I made the introduction longer, therefore less time was left for the rest of the lesson. The key take away is that I should be mindful of the time and teach accordingly and focus on the learning objectives for the particular lesson. My tendency is to give whatever knowledge I have about that topic to my students to make the explanation more meaningful but I should understand that they will learn the concepts gradually and eventually with time.

Geometric puzzle

It was a little hard for me to draw 30 equally spaced points. So, I thought of visualizing a clock that has 12 equally spaced points and matched the numbers diametrically and found that 1 is opposite to 7, which means 1 matches with ((half of 12) +1)= 7. Similarly, Considering 30 equally spaced point on clock, then matching the numbers which are diametrically opposite to each other, I found that 1 is diametrically opposed to (half of 30) + 1= 16, hence drawing and generalizing , I found that 7 is opposite to (( half of 30) + 7) = 22.
Therefore, the formula becomes, A number diametrically opposite to x in evenly spaced points on circle= (half of evenly spaced points) + x.


This problem can be extended to figure out what if the number of evenly spaced points is odd, how would the formula change.
The value of giving an impossible puzzle is that while solving the puzzle they might get introduced to new insights of math, which did not think before. But on the contrary, it can be sometimes a bit time consuming and frustrating as well for some kids who just want to focus on the curriculum.

I believe if the puzzle has some kind of geometric figures attached, I tend to solve it by actually drawing it out and then inferring the logic behind it and then generalizing it if possible.

Micro teaching factoring trinomials ( Jashan and karmdeep)

https://docs.google.com/document/d/1fJ1WK1Lve0qjCyyguCis01WwdubvuL90VQhQBS4FbwY/edit

Reflection on "Battle ground schools"

The whole contrast between conservative and progressive was interesting to reflect. It was shocking to see that according to conservatives the only reason to study math was just knowing “minimal math survival skills” and the “abstract technical skills” were only for a very small proportion of people whereas the progressive approach of math is to develop the problem-solving skills in all the students without any discrimination. Although I believe that fluency (supported by conservatives) is important in math, during my past school visits, and in my Canadian experience, I have seen the dependency of students on the calculators for simple calculations. Therefore, I think students should be taught in such a way that they understand the logic and then building on the logic they become fluent as well. (For instance, multiplication tables can be understood by thinking in groups, 12× 9 can be explained as 12 groups of 10 take away one group of 12)

I found that it is important for the math teacher to have a good grasp of the math concepts. I can understand how elementary school teachers have to teach everything including math even if they are not comfortable teaching math. But it is important to realize that the young students tend to develop the same attitudes which their teachers have, so it is essential to be always on the progress of learning and overcoming the “math phobia” and the other challenges for the enrichment in both students and teachers learning.

Dewey ‘s thoughtful remarks made me stop and digest them. I found it interesting how the two entirely different approaches (conservative and progressive) can lead to entirely different human beings. The Ones who are “obedient rule followers” and the other ones are reflective” scientific and democratic thinkers”. Students can greatly benefit and develop their mental inquiries by doing things and exploring its corollaries rather than just following the facts. Although I believe, doing practice, following the algorithms and knowing the reasons behind it, plays an important part in understanding math concepts in depth.

The rise and fall of the new math war is another evidence that the conservatives approach focusses on educating certain group of students who can understand abstract mathematics and have the potential to become future scientists, but we know that everyone has different  capabilities, so it is important to recognize those potentials of the students and design the pedagogies to help them explore their talents. In addition to this, I insist that we should also explore modern mathematics topics such as set theory, linear algebra, abstract algebra in addition to calculus to give the wide exposure to the students who want to extend their knowledge in math.

The dishes problem

Let the total number of guests be x

Number of dishes of rice used by the guests= x/2

Number of dishes of broth used by guests= x/3

Number of dishes of meat used by guests=x/4 

Since we know that the total number of dishes are 65
Therefore, there are many ways to find x, out of which two are discussed below :   
   

First method:                                                 Second Method:

x/2+ x/3  +x/4 = 65 (i) Hence, finding the lowest common multiple of 2,3,4 It comes out to be 12 On solving, We get, 6x + 4x + 3x = 780 13x = 780 x= 60, No. of guests = 60

We know that the Right-hand side is a whole number, therefore 2,3,4 must divide x  evenly, which is possible only if x is common multiple of 2,3, and 4. And, the lowest common multiple of 2,3,4  is 12. I found that on substituting 12 instead of x in the equation (i)  does not equal 65 Let’s try 24, 36, 48, 60, 72( multiples of 12) and substitute them to figure out which one satisfies the equation and gives us 65. On solving, I found that. x =60 satisfies x/2 + x/3 + x/4 = 65

Follow up questions:
I believe that it definitely matters if the students are offered examples, puzzles and told the history of mathematics from different cultures. In this way, they can learn cultures of their classmates as well. Nowadays the classrooms are very diverse and children from widely different backgrounds and cultures are at the same platform in the class. Hence, making them aware of each other's cultures along with cognitive math learning is an intelligent step towards creating an inclusive environment. Moreover, teaching math history of different cultures through puzzles or examples is an excellent way of acknowledging the great contributions of the mathematicians from different civilizations and this effort will certainly make the students realize that the math they are studying now is not the works of only one civilization or community, people all over the world have put efforts in to make it more meaningful.

I believe that word problems/ puzzles are really effective to break the monotonicity of solving regular math problems. I have seen some kids getting very excited to solve a puzzle introduced in the classroom. It adds the fun and the spark element in the student's routine. and I can relate that one feels immense happiness and a sense of accomplishment after solving the puzzle. In addition to this, I also believe that too many word problems and puzzles in the classroom can sometimes disinterest some students. The simple reasons for the disinterest can be an unwillingness to put in extra effort to solve the puzzle or think outside the box.

Micro teaching Reflection

Microteaching was really a good exposure towards teaching and then reflecting on what went well and what could have been done better . My topic for microteaching was making of paper bags. I felt that my classmates were well engaged throughout the task of making paper bags. I saw the happiness on their faces after holding their own hand made colorful bags. But what I realized is that although all of them were able to make the bags along with me, we finished the task bit early. I should have made some backup plans.  Although I taught them a way to make handles of their bags, I should have also brought some scissors to actually have them make the handles. I  anticipated that making bags will take a longer time but we finished early. It was due to the fact that somewhere at the back of mind I felt that it will take more than 10 min and I should speed up. Hence, I made the introduction smaller and started making bags. Therefore, in order to cover up the time, I had to extend my closure time more than planned. Overall, I really enjoyed teaching , learned the basic structure of the lesson plan for future lesson plans and also learned to manage the time and the content efficiently. Moreover, feedbacks received from my colleagues are very helpful and appreciable for my future teaching. Moreover, this activity gave me opportunities to learn some very interesting games and strategies that added spark and fun to my beautiful life.

Lesson Plan: Making paper bags

Lesson: Making paper bags

Time Duration: 10 min

Grade: Any

Big Ideas	Ø  Making the best possible use of the things around us.
Objectives	Ø  Students will be able to make shopping paper bags. Ø  Students will be able to realize the variety of different uses of paper bags and its ecofriendly benefits.
Core competencies	Ø  Working collaboratively, communicating with each other and ensuring everyone gets the desired result builds up their relationships and gives them a sense of togetherness. Ø  Thinking critically and making inquiries that how can a plain paper be given a desired shape

Materials Used

Printed colored paper, glue sticks

Lesson Components:	Learning activity	Time allotted
Introduction	Ø  Asking them how useful is the paper bags they think and what if they learn how to make paper bags it would be of great use for them such as storing accessories, gift wraps, etc.	1-2 min
Lesson development	Ø  Everyone is given a paper and glue stick. Ø  Steps are followed by students as led by the teacher to make the paper bag. Ø  It is ensured that everyone is at the same pace such that no one lags behind.	7-8 min
Closure	Ø  What additional can be done to make the paper bags better. Ø  Reflecting on their own art.	1 min