Chapter 1 Reflection

In chapter 1, the author high-lighted different types of principles and standards for school mathematics.

It mentioned the learning principle for learning mathematics. The first learning principle is the importance of understanding the concept and to have the ability to think and to reason the mathematical logic to solve new problems. The second principle is that student can learn mathematics with understanding as as learning is enhanced in classrooms where students are required to reflect on their learning through evaluation to develop their mathematical understanding and reasoning skills. This is what we have always been taught in school, to understand the concept and not to memorize the sum. On the other hand, we are taught to learn and practice our mathematical concepts and skills through endless practice on 10-years series. So, how do we really understand the concepts if we are just mainly doing the same types of sums over and over again? From numbers to algebras to geometry to measurements and etc... It puzzles me how I have passed my math just by memorizing formulates and sums.

Thus, as an early childhood educator, I believe the importance of learning the concepts through hands on activities and not just through worksheets. Through manipulative materials, children are free to make mistakes and correct it when they get it wrong. This also allows children to self-assess and self-correct when the completed the activity given. Unifix cubes, counting bears and 2-coloured beans are good manipulative materials. These are materials which I constantly used it in teaching mathematical concept to young children.

As mentioned by Walle, Karp and Williams (2010) the five process standards through which students acquire and use mathematical knowledge:

Problem solving learn mathematical knowledge through solving sums.

Reasoning and Proof emphasizes the logical thinking on what makes sense and what not.


Communication is important in mathematical as one needs to know how to talk about, write about, describe and explain mathematical ideas.

Connections made within and among mathematical ideas and mathematical should be connected to others disciplines and to real situations.


Representations uses graphics to present the mathematical ideas and relationships as a form of communicating mathematical ideas to others.

Through the principles and standards, it allow us to understand how to become a teacher of mathematics which was mentioned in the textbook. It mentioned the importance of teacher to have knowledge of mathematics in order to teach mathematics to young children. I agree with this as teacher we must first have fear the subject that we are teaching because the children will feel it. Just like me, I love math because of my favourite math teacher in Primary School, if without her, I will not have survive math. Persistence and positive attitude are other characteristics mentioned in guiding children in solving mathematical sums which they are not able to understand over and over again. Thurs, persistence is needed to demonstrate to students that it is alright to make mistake and re-trying it again. Teachers should always be ready for change in their teaching approach to cater for different learning styles and needs. One approach may not work for all. Lastly, teachers should always be reflective in their teaching approach. Research and reading are important for teachers to constantly be more informed of other teaching methodology, to be a better Teacher of Mathematics.