YMaW Ch. 5-7

First and foremost I just want to say that this week's readings were very tough for me to comprehend and understand. Not only is the material extremely heavy in content and intricate processes but it also founded upon one's basic knowledge and understanding of fractions. Because I have not taken a math class in 2 years it has been a struggle for me to understand the strategies students within the text are implementing and the rationale behind them. That being said, I did take away some very knowledgeable ideas and resources that could be used when teaching in the future. Primarily, I learned how important it is to develop a plethora of ways to model mathematical problems and situations so that students can mathematize effectively. Page 73 states, "Mathematizing-the human activity of organizing and itnerpreting reality mathematically-rather than a closed system of content to be transmitted or even discovered, mathematical models become very important." The book then goes on to provide a variety of direct modeling strategies that can be utilized to directly represent equations concerning fractions. I found the Ratio Table to be an extremely efficient way both organize fractions and rations and determine how to adjust those ratios by either making them bigger or smaller. The number line and double number line models, however, proved to be rather confusing to me and I am not sure I thoroughly grasp the concept. Another way to represent the multiplication or division of fractions is through use of an array. Arrays assist students in visually representing the direct action taking place in the equation and allow them to obtain appropriate answers through these means. On page 125 it states, "When children are given the chance to compute in their own ways, to play with relationships and operations, they see themselves as mathematicians and their understanding deepens." I found this quote to exceptionally summarizing of the preceding chapters in that its focus and emphasis remains on allowing children to explore mathematics in order to find what models and/or methods are most appropriate and conducive to their own, specific learning. As future teachers, this is one of the primary goals we should strive for.