New Insights and Their Implications

This last month I have gotten a better understanding of shapes and how they relate to each other. I have had past experiences using Tangrams but haven't really analyzed and classified shapes into groups by their properties. I am not good at identifying shapes by name but the class discussions have helped me understand why shapes fall in the category that they do. The book also talks about using Tangrams and other manipulatives for discovering shapes and their properties.
Usually when it comes to math if I don't understand a problem the first time I see it, I am never going to get it. In my College Algebra class I relied on a friend who is a math minor to explain things to me, so I definitely agree that peer tutoring is a great way for students to learn from each other. In this class it has been fairly easy for me to understand the concepts and even if I don't completely get it right away, after I see a few examples and work it on my own it becomes a lot clearer. I just have to have time to think about it and see why it makes sense.
I was unfamiliar with the van Heile levels but I can definitely see how the concepts that take place in the first two levels are essential for students in the elementary grades. The book also gave some great examples to demonstrate students' learning. Overall, I feel that I am getting a lot out of this class because although I am familiar with the concepts we discuss such as area and problem solving, it is being presented in a new way that really gives meaning to why I use certain strategies when solving problems.

Summary and Synthesis

Summarize and synthesize of the impact of recent experiences, ideas, and/or issues encountered on the Tuesdays and Thursdays in class thus far from your perspective.

Math in and of itself has never been extremely hard for me. I have always taken for granted that I had a formula that led me to an answer. This class has challenged my view of mathematics. I no longer just randomly apply a formula and spit out an answer. I think about the different things we have done in class. For instance when we found how the area of a triangle connects to the area of a rectangle or how we found different ways to find an area formula for different trapezoids and the algorithm to back it up. While these things were not necessarily difficult, they challenged me to look beyond what I have been taught and look how they connect in my own world. While this may be sad to say, I had never realize the connection between the area of a rectangle and triangle. I was never taught how to or expected to prove my algorithms or answers.

Today in class we were working on fractions. While we did not get far into the lesson, I am already doing things that I would never have thought to do before. While I am still somewhat confused with why we were doing some of things we were doing, I made a better connection with fractions that will hopefully help me understand what my students will have to go through to understand what they are doing. While I am still confused I already know more than just rote procedures!!!