Summary and Synthesis

Sitting in the first day of K-8 Math Methods, I felt somewhat apprehensive. Math makes me nervous. I have never felt confident in math. When we received our first math assignment, I was nothing but nervous. To be honest, I was not accustomed to this type of problem solving. I was expecting the formula and process method of learning. However, I soon began to open up to this new form of mathematical teaching. The experience of different activities within our class periods have helped me to gain an understanding for the hands on approach to solving mathematics we have been learning about. One specific learning activity that has stood out in my mind deals with finding the areas of a polygon. Experimenting with different methods of finding an area of a polygon helped to open my mind to a more constructivist approach to learning mathematics. I realized the importance of exploration in mathematics, and the impact is has on students learning. Another learning experience that has impacted my understanding for exploration in mathematics would be the combing of formulas to find the areas of a trapezoid or a parallelogram. These experiences have also helped me to understand the concepts behind the processes of mathematical inquiry. My understanding for these mathematical problems stand out for one reason, because I now understand the relational concept behind the process. Overall, I have realized the importance behind helping to students to develop conceptual understanding in regards to problem solving. Many of the discussions that have taken place within our class periods have helped me to become more confident in providing a more hands on learning experience for my future students.

Summary & Synthesis

Math Methods has been an eye opening experience for me. Learning math was a hard concept and subject to learn. I have always had a somewhat negative attitude towards math, because it has been a trying subject. Since taking Math Methods I have learned a different way to approach a problem and learned the strategies to solving a problem. I have also learned that the way I was taught was more less repitition and learning the information for a test and less learning on how to discover strategies and patterns to problems. In Math Methods I have learned that students need to be able to have a solving strategy that they can justify and have multiple routes to explore for an answer. I like the alignment process. This alignment component provides a continious loop of modifications and improvement of learning and teaching.

New Insights and Their Implications

It was interesting learning about the different steps you have to teach in order for students to be able to learn fractions. There are some things that we talked about in class that I never really thought about when working with fractions. Fractions was one concept that I thought was very difficult to learn when I was in the younger elementary grades, so that is why I found this to be so insightful. Talking about this in class gave me a new perspective on how to teach fractions and also made me realize the different new terms that you need to introduce to students when learning about fractions. I also thought that looking through the magazines was very helpful to get some ideas on some hands on activities that you could use in your classroom. Learning about this was very helpful for my future teaching of fractions and ratios.

Summary and Synthesis

Before thursdays' discussion on fractional concepts I thought of a fraction as a number over a number, the top being the numerator and the bottom number the denominator. A fraction simply tells us what part of a whole. After discussing fractional concepts in class, I see now why I, and many students sturggle with fractions; its because we lack the foundational understanding of fractions. There is so much more to fractions that I was never taught. I just learned the basics. Thrusdays discussion on fractional concepts gave me a whole new perspective and knolwedge of fractions, for my own persoanl understanding, but also what I need to do as a teacher to help students understand concepts of fractions. I am now aware of the 6 steps that need to be followed/taught for the development of fraction concepts. In class we discussed the first 3 steps. Step 1: Introduce Sharing and The concept of Fractional Parts and Understanding of the Unit, we discussed students notion of fair sharing and the teacher's job to break students away from using a halving strategy. I learned the best way to do this is to change the number of things being shared and the number of sharers (odd division) to force students to confront their halving strategies. Students must also understand a "unit" of a fraction before they can compare parts of a fraction to a whole. Step 2: Introduce Models for Teaching Fraction. During class we looked through two different magazines that had a wide variety of different models/manipulatives for students to use to help them understand fractional concepts. Choosing what manipulatives to use is very important for teachers to consider. It was brought to my attention, that what we see isnt always what the student sees. Therefore, we must choose manipulatives properly, introduce them to the students and ensure they will enhance and assist students learning. I also learned from class discussion that the lables on the models can sometimes take away from students true understanding by dening them the oppprtuinity to reflect on the size of the peice relative to the whol and decide for themselves what the fraction is. Lables on pieces also remove flexibility in the materials. Teachers need to consider these factors when using manipulatives. Step 3: Intrdocue Fractional Symbols. Here we discussed the importance of building ideas and notions first and then introducing symbols. In class we also determined the difference between fractions and ratios; which sadly none of us could explain the difference when asked during class. After comparing and discussing the two, we arrived at the notion that a fraction is a realtionsip between a part and a whole and a ratio is a comparision of two distinct sets. After thursdays class discussion, I have a better understanding of fractional concepts as far as the first three steps go. The topics discussed in class have helped me understand the way students learn and what specific concepts and ideas I need to teach them about fractional concepts prior to teaching them fractional computation.

Summary and Synthesis

Looking at the different magazines with all of the manipulatives really showed me how important it is to be well informed on what is needed in the classroom. There are SO MANY options to choose from that I imagine it can be quite overwhelming. Additionally, before class I would have thought that having the labels on each model would have been helpful. However, now I see that the models can be more versatile when they do not have specific labels on them. Furthermore, it has been brought to my attention that students need to be slowly introduced to certain concepts. Simply showing them the full blow concept of fractions, for example, will prevent them from actually learning about fractions. Teaching a concept slowly over a large period of time is significantly different than what I grew up with and what I had previously thought. Overall, I feel that the steps that we have learned and continue to learn about regarding developing concepts will help me to better understand how students learn and how to approach teaching a wide range of concepts.