New Insights and Their Implications

So far, this course has given me some great insights as to the new way of teaching math. I have learned that we need to work towards giving our students more of a relational understanding instead of an instrumental understanding. It is imperative to make connections between what they are doing and why they are doing it. From the discussions from my peers and from Dr. Reins, as well as the research I have done through the LPU, I have learned that students learn math best when concrete experiences are worked into symbolic experiences. This can first be done by first working on concrete examples through manipulatives and visuals. Then once the students obtain and understanding of the concept, they can move into semi-concrete examples by still working with manipulatives but by adding number sentences, etc. Then finally, once the students have grasped the concept, they can learn the symbolic meanings of what they have already learned. By doing this step by step, the students can gather their own conclusions and meanings on that topic and develop their own understanding--rather than it just being given to them. All of this is going to be extremely helpful to when I teach in the future. Since I am used to more of a instrumental way of understanding, it is important for me to switch my ways and develop my own teaching into a relational way of understanding. By doing this, my students will become successful learners in mathematics.