Thursday, 18 August 2011

Reading Reflections on Chapter 1 & 2 : Teaching Mathematics in the Era of the NCTM Standards, Exploring What It Means to Know and Do Mathematics

Mathematics to me as a young child was a subject that I studied for and practiced doing problem sums because I was told to do so. I was told by my parents that it is a subject that I must concentrate on because it is important for me to do well in it. As time passed and I grew, I really did not like the subject very much mainly because I found it difficult, tricky and the most boring part of it was that there was always only one right answer to a question! That was how, I drifted away from liking Mathematics.

Of course, when I became a pre school teacher, I realized how fun and interesting Mathematics could be! After reading through Chapter 1 and digesting the National Council of Teachers of Mathematics (NCTM)'s Principles and Standard for School Mathematics, I feel so relieved. The six principles sums up a high quality mathematics education that is so promising. One particular quote from the NCTM that I totally support is:

"Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well". (NCTM, 2000, p.16)

I totally support this because I believe that every child has a different learning phase and technique and therefore, the teacher should be able to understand that before challenging them further. I do not believe that any child is not capable of doing Mathematics, it is just how a teacher changes the situaton for the child to learn. Teaching Mathematics in this era would involve learning through concepts and tapping on their capabilities and that is how the children are able to learn. Becoming a good mathematics teacher would also mean that one has to have a positive attitude, have persistence and she must be ready for changes. I believe that with a positive attitude, a teacher can bring her students to new heights of learning. Teachers should also be ready for changes as it makes the subject more "relaxed" and not too "structured". As there can only be one answer to a question in Mathematics, I do not believe that there can only be one method to go about solving it. When children are open to solutions to an answer, they are willing to try. If they are told to be rigid, they may withdraw.

Therefore I believe that loving Mathematics is not only about following the curriculum and teaching standards, it is also about the teacher and if she wants to make a change in her classroom.

How is Mathematics best learnt?
In Chapter 2, it is stated that there can be a setting for doing Mathematics. I believe that a productive classroom can benefit the children very well. As stated in the classic book Making Sense (Hiebert et al.,1997), the author described four features of a productive classroom from where children can learn from one another:

1. Ideas are the currency of classroom

2. Students have autonomy with respect to the methods used to solve problems

3. The classroom culture exhibits an appreciation for mistakes as an opportunity to learn

4. The authority for reasonability and correctness lies in the logic and structure of the subject, rather than in the social status of the participants.

These four features best describes my feelings towards a good classroom environment for Mathematics to take place.

What Does It Mean to Learn Mathematics?

Fig 2.8 on pg 20 shows a model that best describes how does one learn Mathematics. I totally agree that by using ideas that we already have to construct new ideas, we are acutually developing a connection between the ideas. The more we do so, the better we are understanding. This should be understood ny all teachers so that there is a common understanding ground that we are all standing on.

Conclusion of my understanding

Mathematics is a subject full of ideas and concepts. What we teachers can do is to ensure that we adopt some startegies that best fits into our classroom and implement it. We should ensure that all children learn something out of Mathematics and have a love for this subject because it is indeed a beautiful subject. I really hope to learn and share more in class.

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