Feb. Journal Article MTMS

Cramer, K., Monson, D., Whitney S., Leavitt, S., and Wyberg, T. (2010). Dividing fractions and problem

solving. Mathematics Teaching in the Middle School 15(5), 339-346.

Many students learn symbolic meaning for concepts without actually learning what the concept actually means. This article show how fraction division learning can be accomplished through the use of problem solving and use of pictures and reasoning. Students learned the basics of fractions at the sixth grade level before moving onto complex fraction problem solving. The students in this article completed an activity with the use of different colored paper circles--- all were the same size. Each of the different colored unit circles were folded into different amounts of pieces to show representation to students that different fractions are still in relation to the one complete unit. Students were able to see visual representations of the fraction parts to the whole unit which made the concept easier to apply to problem solving questions. Once students were able to investigate problem solving questions through pictorial representations, they were able to work on describing their process through language. As the students learned how to describe their picture representations through words and eventually symbols, they were able to understand the use of rational numbers. Students built upon this knowledge and eventually were able to learn more complex ideas such as dividing fractions. Through problem solving groups, class discussions, and reflections, students were able to understand the flexibility of a unit. These sixth grade students showed the capacity to learn complex ideas on which more abstract concepts could be built.

I believe that having students investigate the different ways to represent fractions is crucial to their understanding of the basic concept. As a student, I learned to jump right into symbolic work and never learned the basis for my concepts. Upon reading this article and seeing different student representations of their use of fractions and fraction divisions, I was able to visualize and understand the part-whole concept. Having the students take the different colored circles--all the same size--and fold them into different fraction representations really shows the importance of understanding a unit and how different fractions make up a unit. As a future teacher, it is crucial that we let our students learn the importance behind the symbolic work that they eventually do. I liked the way that the teachers let the students learn through discussions and reflections. Learning how to problem solve through picture representations of fractions before learning symbolic work was something that I really admired. We should not underestimate our students and should give them the opportunity to figure out the concepts so that they can build upon that knowledge in order to use symbols as representations.