Exploring What It Means to Know and Do Mathematics

               How do we learn Mathematics? Jean Piaget and Lev Vygostky have answered them with their theories through the constructivism and sociocultural theory. Piaget mentioned about reflective thought where people connect existing ideas to new information where learners  construct new knowledge and tools to build on their prior knowledge. Vygostky stated about internalizing information within an individual's ZPD in which children are learning from their peers and adults. I like the saying about the construction of ideas in which not only children but even us as adults connects existing ideas to new ideas and giving a new meaning to it.


            During my time when I was learning Mathematics, memorizing formulas, time tables and so on is what I do best. But when it comes to understanding, I am totally weak in that. Why? The teachers did not make use of relational understanding where we were supposed to be given tools an manipulative or multiple representations to further understand the mathematical concept. Especially in young children, it is best to provide them with visual tools for them to explore and be involved. And although there are manipulative provided like what this chapter mentioned, they are ineffectively used. 

              I totally agree that using technology allows young generation to count. However, it may not be good to young children. Somehow I see young children nowadays do not use the concept I actually went through of counting mentally r even doing workings. Yet, it calculators help children work faster but it doesn't help children in generating their brain cells. I believe there are others ways for children to use in answering questions. It's because of the teachers who kept on wanting the right answers to the problem sums which led children so dependent on the use of technology.

              I totally agree that using technology allows young generation to count. However, it may not be good to young children. Somehow I see young children nowadays do not use the concept I actually went through of counting mentally r even doing workings. Yet, it calculators help children work faster but it doesn't help children in generating their brain cells. I believe there are others ways for children to use in answering questions. It's because of the teachers who kept on wanting the right answers to the problem sums which led children so dependent on the use of technology.

             An effective classroom for young children to be engaged in doing Math is essential. it should encourage children in risk-taking, reasoning, problem solving and so on. In my own teaching, I engage my children in productive struggle too as I believe that it is not wise of me to keep spoon-feeding them with answers. They will not be able to learn in that way and I ensure children that it is okay for them to make mistakes then from there they will learn. Children in my class have different abilities. Therefore, I created a classroom where their ideas and every discussions made are put up in class.

Teaching Mathematics in the 21st Century

             I remembered being taught the 5 content standards like geometry and measurement and even till now as a preschool educator, I'm teaching the students the same thing again. We can see that these content standards will remain even till the future. Not to forget, they are being taught in every level we are in too. Measurement is indeed a very popular topic and is greatly integrated in topics like science and language in young children's learning. 

            As the NCTM provides us with the Principles and Standards for School Mathematics, I believe that all teachers are making use of these six principles given  in educating young children in learning Mathematics. With these standards, every child is always given the opportunity to explore with the various mathematical concepts. Learning mathematics is not simple. I remembered being a child and my teacher just explaining the concept without any visual cues, I was definitely lost at that point of time. I feel that teachers should make use of the learning principle where teachers provide lots of experiences in the classroom making sure children understood the concept. Understanding the mathematical concept taught is very crucial as we know that math is everywhere. From my past experiences, it has lead me to have the positive attitude , persistence, and being reflective. This chapter explains it all and I believe strongly that by doing so, we will educate these young children better in not only understanding Mathematics but loving and enjoying the subject.

             However, I find that our Singapore government should work closely with the preschool teachers and understand mathematics for younger children. They have been stressing the children in this era in knowing the mathematical concept which are beyond their capabilities. It stated in this chapter that NCTM has  developed related standards documents about teaching where teachers made use of these resources in creating a classroom that supports teaching. However, when I flashback to how I learnt Math, I'm basically just trying to remember the formula and trying to get the grades to pass the exams without actually understanding them. Then what's the point of the major components that are needed to develop mathematical understanding when I don't see that happening in Primary and Secondary school as well.