I found the story about Ferit's strategy to be very interesting, yet the ending result of Ferit's habit of continuously using his method for every question was also expected. Students often tend to follow this patterning when they have realized that they have come up with something useful and try to apply it to as many cases as possible, regardless of how inefficient as it may seem in certain cases. Although such habits are hard to break, it is up to the teacher to help correct such habits by helping the students expand their knowledge of mathematical methods of approaching and solving questions/problems.
The emphasis of the article are mainly focused on creativity, flexibility, and adaptivity. These three aspects are interlinked with each other when it comes to mathematics because for students who are capable of achieving all of these skills, they will be capable of dealing with math problems/questions easier due to their arsenal of mathematical knowledge.
Of course being capable of attaining and mastering all three of these aspects at the secondary school level is indeed a complicated task to achieve. Teachers should try to motivate their students to create their own opinions and thoughts on how to solve a problem and then guide them to formulate and eventually construct the actual formulas and equations. During my short practicum, I was glad to see many mathematics teachers avoiding the lecturing method of teaching and more of retrieving information out of students that led to the grand formula needed to solve all the questions in that section.
It is to be noted that it is human nature that people choose the path that works for them best, regardless of how inefficient it may seem to others. These habits of using certain methods for certain situations are also a way of how people have become accustomed to dealing with these problems. What works well for someone, may not be as useful for someone else, but there is no harm in suggesting other methods because people may gain some insight on either adapting to the newly learned method or gain some sort of self realization on how to improve their own methods.
I totally agree with your view of to show that there are different ways in solving the same problem gives students opportunity to learn a topic from different perspective. Consequently, every student can be getting something out of them. We also have to be aware that be created doesn’t always gives you’re the “right” answer; however, we need to show students that as math teachers we value the thoughts and the process.
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