My inspiration

The teacher, which I would like to mention, was my math’s teacher when I was in grade seven and I was not getting good marks in Mathematics. I was always scared of math. At that time, this new teacher joined our school. After a couple of days when she took, a test and I got terrible grades. She came to our class and gave us the result and when it was my turn she said “do not worry I know you can improve”. Her word strike to my mind .I worked harder and harder .As a result, I got good and then better grade than before and showed my improvement. She was very happy, encouraged me so much that I won third prize in national level Mathematics Olympiad, and got the first position in tenth class  maths. After that, I did masters in mathematics and bachelors of education in Math in India and started teaching in school. Once, I got a chance to check the Maths provincial exams in   different school. I was so excited because this was my first time.While I was checking those exams, I saw the same teacher sitting in front of my table. I never saw her for a long time. That was a most memorable moment for me. She hugged me and introduced me to all the teachers in that hall and said this is the student about whom I always talking. I was so surprised because as I did not forget her, so as she.  I want to be like her because she helped a dull student to become capable of doing teaching.

TPI Reflection

According to the TRP survey, what I think about myself is that my dominant prospective is apprehension and nurture. It means my concern as well as the support to my students are way more than the other three prospective. I believe I am too much worried about my students. Hence, I help them a lot. From my experience, I think the observations are true, as in India teachers helped the students a lot in their work, thinking they facilitate their learning but in reality, they are encouraging spoon-feeding.

   Over here in Canada, the learning environment is different. Therefore, I need to be more focused on this area, to help student be independent on their work, as well as providing help when needed. This would ultimately result in building their self-confidence. Social reform (29) prospective is recessive for me, where as developmental prospective is 33. From this score, I can conclude that my teaching does not expect any social change. Overall, my expectations from the students are a bit high, so I need to lower my prospect in comparison to the learner’s development. Moreover, my beliefs and intentions scored lower, as compared to my actions.

My inspiration

How many squares are there in 8*8 chess board ?



The answer which strikes in the mind at the first instance is 64, (8*8) . I spoke to my self and thought it is so easy, but after some time, I said no! there might be more . I tried to visualize them as shown in the picture below. 

Starting from 1 square unit  (from one corner A) 1*1,then counting the number of squares in 2*2 square unit (taking 2 squares in each direction horizontally and vertically) which is 4 and similarly number of squares in 3*3 square unit is 9 and so on.

 At the end, to find the total number of squares in 8*8 square unit  I added them as 1+4+9+16+25+36+49+64=204.So there are 204 squares in 8*8 chessboard.


To extend this puzzle ,i will ask them if they can apply the same method to find the number of squares in 9*9  square board.

How many squares are there in 8*8 chess board ?



The answer which strikes in the mind at the first instance is 64, (8*8) . I spoke to my self and thought it is so easy, but after some time, I said no! there might be more . I tried to visualize them as shown in the picture below. 

Starting from 1 square unit  (from one corner A) 1*1,then counting the number of squares in 2*2 square unit (taking 2 squares in each direction horizontally and vertically) which is 4 and similarly number of squares in 3*3 square unit is 9 and so on.

 At the end, to find the total number of squares in 8*8 square unit  I added them as 1+4+9+16+25+36+49+64=204.So there are 204 squares in 8*8 chessboard.


To extend this puzzle ,i will ask them if they can apply the same method to find the number of squares in 9*9  square board.

                               Instrumental Versus relational approach

   In Richard's article , the three claims  insisted  me to think about the the consequences of these two approaches.

  Firstly,his claim that relational mathematics "is easier to remember". It  reminds me the incidence when we were in elementary school and told by one of the  teachers to learn and memorize  the formula of total surface area of a cylinder.We did ,but forget occasionally.After a while another teacher showed us  an activity in which she cuts the cylinder length wise to make it a rectangle. Hence, we came to know that cylinder is made up of two circles and a rectangle and moreover, we understand why  cylinder's total surface area  is equal to the sum of the areas of two circles and a rectangle . Now i realized that  those two teachers have the different approaches to disseminate knowledge . The former had the illogical approach and the later teacher had the relational method of teaching . It is relational approach which i still remember rather the former.other adopted by the teachers which is different.

  The second point ,I strongly agree is that the "over-burdened syllabi" is also one of the reasons which does not allow students to use the relational strategies to understand.For instance, it is convenient for the students to memorize the formulas of  integration ,differentiation,trigonometry  etc. rather than finding out the origins of these formulas.Hence ,the students do not  want to get out of their comfort level and waste their time to explore these formulas.

  Finally ,the article mentions the"Difficulty of assessment of whether a person understands relationally or instrumentally. In my country, grades of  the students depend upon their performance in exams.The examiner who is checking the exams  never knows  about the approach of  the student  towards the subject matter whether the student uses his relational or an instrumental understanding . Some times  the students  use their rote memory and get the good marks .Consequently ,they do not use their relational  understanding . 

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