I found the contents of this article to be closely linked with the concept of which we discussed earlier in the term, about relational and instrumental learning. Except that these three categories of creativity, flexibility, and adaptivity are all very hard to teach directly, and they are not so much a teaching style that we have to adopt, but rather skills we as teachers are trying to cultivate in our students. Realizing this, I can’t but help to ask the question, can we teach students to be creative, flexible, and adaptive? Certainly, we can try, there is always hope of course. However, it is almost as if the students have to refine these three skills through active experience.
Creativity springs from inspiration, just like the example the author used in the being of the article, of how Ferit had this epiphany to add 100 and then subtract in order to complete the operation, but imaging the scenario of the teacher prompting the students to come up with the Ferit strategy, all that the teacher could possibly ask is, “Can anyone think of another way of completing this operation, other than the conventional way that we just used?” And at this point, the spot light is on the students and if they are actively thinking about it then someone (in this case Ferit) would be able to come up with the creative answer, there is no other way for the teacher to prompt the answer he/she would want. Or perhaps, we can also let the students get in groups and discuss how they would come up with a creative alternative approach. But ultimately, it is the students who have to actively think in order to reach the desired creative solution. Certainly, after obtaining the desired solution, it would be necessary for the teacher to encourage this type of thinking that Ferit used. I think it is rather difficult to teach these skills, but nonetheless, we can encourage these virtues.
It almost seems that students’ personality or characteristics are manifested when problem solving. Being flexible when solving problems for example is probably easier for someone who is flexible by nature, as a result they can appreciate and attempt other ways of solving a problem. On the other hand, someone who is stubborn or not flexible by nature might just stick to one way of doing a problem, and as a result not explore the other possible ways of solving a problem. This perhaps is also true for adaptivity. But this is not to say that someone who is stubborn can’t solve a problem in a flexible way. But I was thinking that personality does somehow affect how we attempt problems.
Anyway, these we my random thoughts for this article…
Hi Niyaz,
ReplyDeleteYou made me think on how flexibility might be a personality trait. Certainly, there are people who are more curious than others and therefore more adventurous, and are wiling to try out new strategies and find new solutions to problems. My exerience with children tells me that kids who are encouraged to experiment, to explore, and to try out new things from an early age will become more creative than kids who are always told what to do and how to do it. Creative kids are open to new things and are eager to other possible ways of solving a given problem. I wouldn't say that kids who are not flexible are stubborn, they might have never experienced the joy of discovering something on their own. They might just have a lack of confidence, or afraid to try out new things for the fear of failure.
Interesting comment about creativity coming from inspiration! Yes it's true, but at the same time, I think the more "perspiration" (ie, working hard to learning and exploring more examples) will lead to more "inspiration". As teachers, we can show more examples of creativity (and the joy that comes with creating something), and hence spark inspiration.
ReplyDeleteIt is also interesting that you mention flexibility relates to personality. I would argue also that it relates to how we have been brought up as students, ie, what were our own math teachers like? They model for us how to learn.
This is a scary thought, now that I am standing on the "teacher side" of the fence - what incredible influence and impact we can have!
I agree with you Niyaz when you say that creativity, flexibility, and adaptivity are things that we can't explicitly teach, but are rather characteristics we are trying to foster within our students.
ReplyDeleteAlso, to reiterate what Zsofia said about personalities that some are more curious and will be more adventurous and creative in their problem solving than others, but I don't feel that we need to worry about this necessarily. As long as the student understands what they are required to do and are able to make a good attempt, if not get the correct solution somewhat consistently, then I feel that we are doing our job.
You brought up some interesting issues there Niyaz.
ReplyDeleteI can agree with you on the fact that creativity springs from some sort of inspiration. Inspiration can come to us in many different ways of influence (self realization or some sort external influence via friends or classmates or something the student has read via in hardcopy or online).
In mathematics, I find that the most creative, flexible and adaptable students are those who are constantly entered into writing math contests. The contest questions always seem to force the students to think in several methods in order to get the right answer.
Although not every student is required to write math contests, I would always try to motivate (ex. giving them bonus marks) my class somehow to at least try some.
I like all of the comments about flexibility being a character trait. My question is, how as high school teachers can we encourage students who are inflexible to be more flexible? In my experience when you ask them to try something they are not comfortable with some of them, not all, but some of them shut down. How do we foster flexibility without having students shut down?
ReplyDeleteResponse to Nadine's question, to my opinion. when a student has a deep understanding about the subject that he/she studies than he/she will engage more into extra activities. That is when we can take one step further to inspire our students with flexibility, creativity and adaptivity in mathematics.
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