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.