Assignment 1 – Precourse reading – Chapters 1 and 2.
Chapter 1
I have learnt that before we start to teach Mathematics we should observe our children first, like how do they learn mathematics and how I can teach it so that they are able to understand the concept. I as a teacher should impart teaching of mathematics by concentrating on the thinking and reasoning (www.nctm.org). I realise that The Assessment Standard clearly shows the importance of including assessment with instruction and points to the importance of how assessment assists in implementing change. I learnt that there are six principles of Principles and Standards for School Mathematics – equity, curriculum, teaching, learning, assessment and technology.
The equity principle state that all students should be given equal opportunity to learn under high expectations.
The curriculum principle state that the importance of mathematics should be inculcated as a whole principle in the classroom instruction.
The Teaching principle state that teachers must understand how they teach, how the children learn and choose methods that children will be able to improve on their learning in Mathematics.
The learning principle state that Mathematics should be learnt with understanding and build the ability to think and reason.
The Assessment principle state there should be ongoing assessment which will ensure that children are able to interact which will encourage students learning.
The Technology principle states that technology strives to teach children to reason and solve problems which increase exploration and different ways of representing ideas.
I learnt that there are five content standards and number and operations is given the most importance from pre-K to grade 5. I learnt that there are five process standards which are problem solving, reasoning and proof, communication, connections and representation.
I realised that different countries have different standards and methods to teaching mathematics. We often forget that teaching is a cultural activity and should observe our children on how they learn and adjust the teaching for the children so that they understand and apply the concepts easily. Usually text based and drilling methods do not help as it does not assist or develop the children to think and apply the skills at higher order thinking. It is noted in this text that text books influence the way teachers teach and do not allow the flexibility of allowing the teacher to cater to the individual needs and understanding of the children.
What I basically understand from Chapter 1 is that there are standards and text to follow in teaching the Mathematics subject, but as a teacher we should inculcate a love to pass on to the students and be able to make a change to suit the learning abilities of the children we teach. As I feel that we as teachers should instill a love for the subject so that the child is able to problem solve and think and reflect rather than just focus on how to solve the text book problem as understanding and applying Mathematics is a life long skill.
Chapter 2
I understand that doing Mathematics does not only mean solving a problem but to see how this problem can be solved in different ways. I realised that even young children should be given the opportunity of exploring the sciences of Mathematics. The terms that we use in the classroom to teach Mathematics plays a part in our execution of our lesson, like understanding, making sense of a problem instead of listen, memorize and drill. It is very important as a teacher how we set the scene for teaching Mathematics.
We should teach Mathematics thorough inquiry, we should encourage, entice and inculcate a sense of curiosity and enthusiasm as they strive to solve the problems. Students should never be put down or told that they are doing it wrongly but given support so that they are able to problem solve and be encouraged to try again to use other techniques to solve problems. This will encourage the students to try again instead of shying away from trying and being ridiculed and saying that you are not smart enough to solve this problem.
How can we include technology to ease the task of solving problems? Some problems can be solved by the use of calculators.
I understood that there can be different methods that you can break up a problem sum to understand it better like drawing diagrams, using models or pictures to create a clearer picture for the student to understand the problem.
The theories come into play in Mathematics as well, like constructivist and sociocultural theory where we learn from each other and our need to observe the child so that we can scaffold the child to the next level (ZPD). There is a connection between theory and practice – the relational knowledge.
I personally thought that learning Mathematics was always learning how to solve the sums according to the text book. But from this textbook I realise that teaching and learning Mathematics is a social and interactive experience. The students should be given multiple opportunities to reflect, make mistakes take these as learning opportunities, not as failures and how they can work together as a team to solve these problems. How these problems can be simplified and broken down using models. And how it is utmost important for the teacher to create an environment for the students to explore and learn at their own developmental capabilities.
I like to share my personal classroom experience in relation to what I have read in Chapters 1 and 2. Recently we had our National Day Celebration. To create a social and math experience, as I was cutting the cake to give to the children to design our Singapore Flag I asked the one of children “how many pieces do I need to cut”? He started to count the number of peers and the teachers in the classroom; he was able to count the ten of us in the room. There was one child who was not present for that day and I asked him who are we missing and he was able to name the child that was absent. I asked him so we have ten of us, how many pieces of cake do I need to cut and he showed his ten fingers and said ten. He is three years old. He was able to display one to one correspondence as he was able to count the number of peers and teachers and relate it to the number of pieces of cake that is needed for each person to have one piece of cake. I find that as we inculcate such mathematical experiences through social experiences the children will be open to learning math as it will be a fun and practical way of learning math from young.
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