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 .