There are two things that stand out in these chapters:
My knowledge of mathematics and how students learn mathematics – these are essential tools I need to acquire to be an effective teacher of mathematics. As the teacher, I play an important role in shaping mathematics for my students. My beliefs about what it means to know and do mathematics and about how students make sense of mathematics will affect my instructional approach.
First and foremost, having a deeper understanding of what mathematic content should be taught at each grade level., my role in fostering math learning is to integrate experiences with math into children’s everyday play. To make it work, my excitement and interest in children’s inquiries will encourage them to talk through their discoveries. My acceptance of their math reasoning, even when it may seem ‘wrong or illogical, will give them the confidence to keep thinking, questioning, and sharing. Most often, the feelings stem from my childhood experiences with math that placed too much emphasis on getting correct answers, when the process of finding the answers was not fully understood. So how can I fight the feelings of math anxiety when working with children?
I must remember that I should never ‘teach’ children math. Children learn math by ‘doing’ Math. Children need time to explore and discover math concepts on their own in non-judgmental environment. What children need is an adult to foster interest in them, encourage them to test their ideas and to keep sharing their reasoning with confidence and assurance that it will be accepted, no matter what!
Secondly, I need to know how my students learn mathematics – the awareness of individual development in context; what my students know, are there any common misconceptions and need to learn, then to be able to challenge and support them to learn it well.
The daily classroom experience that teacher provides has great influence on how and what students learn about mathematics. It provides a repertoire of activities, selection of meaningful instructional tasks and the ability to promote curiosity, questions, develop students reasoning and sense-making skills. Children needs more concrete experiences. They discover relationships among objects. Each new discovery about the physical world, and the thinking that accompanies these discoveries, lays the foundation for later mathematical learning.
“Learning mathematics is maximized when teachers focus on mathematical thinking and reasoning”(NCTM, 2009, n.d.)