Young Mathematicians at Work

Upon reading the assigned chapters of Young Mathematicians at Work I have made a few discoveries. First, I realized that the ways that students' problem solve may be drastically different from the approach we may personally choose to implement. For instance, when presented with the "submarine sandwich" question in class, my immediate instinct was to whip out my calculator and begin computing division problems in order to obtain percentages. The student's within Carol's 4th/5th grade class, however, used a plethora of strategies such as manipulatives (unifix cubes) and visual representations (drawings, charts, etc.). Because these strategies are not ones that I, myself, was naturally inclined to implement, it was extremely difficult for me to make sense of their thought processes. I struggled while reading, and re-reading, the passages describing the various steps the children took in their solution strategies. As teachers, it is so important that we wrestle with mathematical problems ourselves and find multiple ways of solving it before introducing it to our students. In doing this, we are able to discover a variety approaches that can be taken to problem solve and anticipate responses and methods that students may offer. In addition, I also learned that though this story problem is directly related to fractions, decimals, and percentages, it is not necessarily appropriate or warranted to force these equations and ideas upon students. As Fosnot states, "Asking children to adopt multiplication and division shortcuts too soon may actually impede genuine learning. When introduced at the wrong place or time, good logic may be the worst enemy of good teaching" (5). This serves to say that though developing these concrete ideals is the focus and goal of the lesson, it is best to let children discover these processes on their own through the formation of connections and constant exploration. If this knowledge does not arise naturally, or out of genuine curiosity, then it may not be thoroughly understood or retained. Finally, the text stressed the importance of developing mathematical equations that are both relevant and meaningful to the student's lives. By introducing the "submarine sandwich" problem, the teacher was able to present a real-life dilemma that she encountered with a previous class and sincerely enlisted the help of her students in solving it. Fosnot states, "When children are given trivial word problems, they often just ask themselves what operation is called for; the context becomes irrelevant as they manipulate numbers, applying what they know" (2). In essence, through the development of problems that students can relate to, they will be more willing to invest the time and energy that it takes to truly explore the possible solutions rather than robotically computing meaningless information.