104 assignment #2

The concept of understanding is really a deep one. I liked that one page 82 the author talks about if you understand it then you can teach it, use it, prove it, connect it, explain it, defend it, defend it, and read between the lines. Understanding is not just knowledge but a deeper meaning that can be broken down into 6 facets. When we truly understand something we can do these six things which the authors call the six facets of understanding. When a person undestands he or she can explain, interpret, apply, have persective, empathize, and have self-knowledge. So far with my students I think I focus a lot on explanation. I am always asking my students to explain or to prove their answers. I tell them that mathematicians can always prove and explain their answers. I tell them that they just don't give the answers, but they go a step further and prove or explain them. In math it is so easy just to accept an answer... a one word answer, but I try to stay out of accepting those type of answers from them. Facet 2 talks about interpretation. In math I ask the questions why do we have to learn this? How can we use this in the real world? For example in learning about money, this concept with directly apply to them when they spend money at a store or make money. Students definately have to know how it applies to them personally. Facet 3 is all about application. How can they use this knowledge in new situations. How and where can I use this knowledge. As my students learn to count by fives and tens, how is this concept applied to other areas of math? If they truly understand then they can apply it to counting money using the nickels and dimes and when they have to count tally marks and grouping things by fives or tens is easier than counting one by one. If they truly understand then they can apply that knowledge of counting by fives and tens to other useful areas in math. Facet four is about perspective. Here the student would be able to ask from whose point of view? Is it reasonable or what is the evidence? Does this mean that understanding something in one way doesn't prevent understanding in other ways? In terms of facet five this is where they are able to get inside another person's feelings and worldview. I can see how this is applied in terms of our school culture; however, when I take this to the level of math, I am not sure at this moment while I am writing this how empathy is applied in the area of math concepts. Help me out here. Facet six is self- knowledge. This is the ability to understand who you are as a learner. It is knowing your strengths and what your weaknesses and what you need to help yourself with understanding. Some of us are visual learners others need objects to manipulate. Some of us do well with lectures and others learn in different ways. WHen I first read this chapter back in August, I thought it was interesting, but it definately caught my attention more now that I can use this to track what I am doing currently with my students and where I need to go with my teaching to make sure that my students can explain, interpret, apply, give perspective, give empathy, and gain self-knowledge about who they are as learners. I tend to think about this not only for my students but for myself as a lifetime learner.