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.