Creativity, flexibility and adaptability are all necessary attributes of problem solving. I think the aim of teaching mathematics should be creative problem solving, to encourage students to seek out solutions, exploring patterns, finding new strategies- not just memorizing procedures, formulas and doing exercises. In order to achieve creative thinking in the classroom, students should be encouraged to use different problem solving strategies.
This article ties in well with what we have explored earlier this term about relational and instrumental learning. Instrumental learning provides a narrow curriculum based on mastering facts and procedures which does not allow students to become creative thinkers. Relational understanding, on the other hand, trains students to think creatively and develops their problem solving ability. Mathematically powerful students are capable of interpreting large amount of data and this allows them the flexibility and adaptability to come up with new strategies or to choose the most appropriate strategy to solve a problem.
Ferit's compensation strategy, adding 100 first and then subtracting 1, worked for 127+99, but he did not get the right answer for numbers such 133. His creativity enabled him to come up with a strategy that was new to him or at least unfamiliar to him. The lack of a solid mathematical background prevented him to switch between different strategies, he used the compensation strategy for all of the addition problems he encountered getting the wrong answer most of the time.
Hi Sofia!
ReplyDeleteI was also thinking about how all the articles we read throughout the course ties in nicely together. I believe that encouraging creative thinking is a way of accommodating both the low and high performing students. Even if their starting level is different, each student has their own understanding of math to some degree. And by allowing them to build upon what they already know we can encourage relational learning in class. Ferit was very creative to come up with his own technique of doing addition- and by seeing for himself that although it is a wonderful technique but that it doesn’t work for all kinds of addition problems, he will learn valuable lesson from that.
Hi Zsofia,
ReplyDeleteI like your connections between the articles. I also do think that Ferit although displaying creativity with his initial approach, seemed to blindly apply it to all cases. I think as teachers we need to inspire creativity but also need encourage the students to try various approaches. Leads back to the saying ... of when you have a hammer, everything looks like a nail.
I agree Min, learning from your own mistakes is a great way to learn. Eventually Ferit is going to realise that his method is not applicable to all problems. His teacher should give him some time to discover that on his own or at least guide him towards that conclusion.
ReplyDeleteHi Zsophia,
ReplyDeleteIt is good to know that you also think that this article is just the reflection of what we already done in this course so far. The whole idea is to enable students with the ability to find their own or modify know strategies. But at the same time I agree with donna as well that we cannot leave the students on their own.
We shuold find the ways to guide the students without them realise that we are showing the them the path to follow.
I like Feda's comment that Ferit's teacher should give him some time to discover that his method, though good in some cases, does not apply to all of them. If he were to come to that conclusion on his own, how much more rewarding would his discovery be of a method that does work in other instances. I think as teachers we can be too quick to jump in and "rescue" our students rather than letting them rescue themselves.
ReplyDeleteI agree with Min's comment that encouraging creativity will reach all levels of math students. Creativity is something that is accessible to all students because they will just start off at different points. What is the best way to encourage creativity and discourage the fear of taking the wrong path and getting stuck? I feel that students believe they have 'wasted time' if they spent time solving a problem one way and it lead to no solution. How can we help them see that this is NOT a waste of time and they are actually learning a lot by this?
ReplyDelete