After reading this article, I felt that I had already read this article. The ideas in this article were not new. This article talks about importance of creativity, adaptivity, flexibility and strategy use in mathematics. "Thinking Mathematically", by John mason gives us the same ideas but in terms of Phases, namely - The Entry Phase, The Attack Phase, and The Review Phase. The entry phase is comparable to creativity, attack phase is comparable to flexibility and adaptivity, the third phase is comparable to strategy use in mathematics.
To solve math problems accurately and efficiently, students need to develop flexibility—they need to learn multiple strategies, and how to choose among them in tackling a particular problem. But what is the best way to help students acquire this knowledge and skill? If we want our students to achieve these skills, we should not tell them which method is to be chosen to deal with the problem. Otherwise it will act as resistor in the student’s minds and they will not be able to invent strategies. But at the same time, this does not mean that we should leave the students on their own. We should act as a guide who instead of telling the answers, asks questions in way that students should think what they are doing and why. This will help all students especially those who are struggling in mathematics. This is a big leap from just solving the problems, without understanding the logic behind it. Making students creative is not a single day process. It will take time, but once they adapt it, they will be able to use appropriate strategies that are creatively developed for flexibly selected.
It is true Paramjeet that acting as a guide is really crucial in a classroom. As teacher we should train ourselves to step back, take the role of the guide most of the time and give the chance for students to learn and discover on their own. It is really easy to fall in the role of a lecturer.
ReplyDeleteParamjeet, you give us an explanation on how to to go about helping students develop flexibility, adaptivity and creativity. You mention that we should provide our students with a variety of strategies and then step back and let them adapt techniques that suit them best. I like the connection you made between these strategy uses and relational understanding.
ReplyDeleteI totally agree with you, Paramjeet. Developing creativity, flexibility and adaptability doesn’t happen over night. It takes a lot of time, effort, and practice for students to acquire these skills and strategies. One of many techniques that I have learned from my short practicum is to use open ended questions to motivate students to think critically and to develop their logical explanation to their own choices in solving problems. Of course, most of the time, we won’t be able to see the astonishing result right away; however, we need to keep emphasizing the importance of creativity, flexibility and adaptability in mathematics to students.
ReplyDeleteI appreciate your ideas of connecting the creativity, flexibility and adaptivity, with different phases of tackling a problem through problem solving approach. The whole idea is to guide students' mental processes to achieve a certain target, but in a creative way, that has the ability to provide better solutions. I also feel that your ideas are revolving around relational understanding of Mathematics which implies conceptual understanding, crucial for the skills of adaptivity and creativity.
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