Content & Processes in YMAT Ch. 3 & 4

Upon completing Chapters 2 and 3 of Young Mathematicians at Work, I can identify several content and process goals in place. First and foremost, like Carols classroom, Susan was focusing specifically on the content of developing fractions and reducing them to their lowest form. While the word problem she presented her students with did not necessarily constitute a context problem and provide opportunities for the students to engage in a plethora of strategies, they were still able to solve the problem using a few different tools. (After reading the chapter, I now know that the use of a variety of tools does not necessarily suggest multiple processes implemented. In the case of this classroom, tools vs. strategies was what ensued as a result of the provided problem) While some students chose to implement paper and pencil techniques, other were able to perform the necessary computations in their head, while still other implemented unifix cubes. However, this primarily represents a use of diverse tools rather than processes because all students approached the problem from the same angle knowing that it indeed required a fraction of 18/24 to be reduced. Perhaps had Susan framed the problem more similarly to Joel, who provided a context problem regarding the best buy of cat food, the students would have had a better opportunity to approach it from various angles. Looking at the problem that Joel presented to his class, we can certainly see that not only did his students use different tools, but used different processes and strategies in order to obtain the solution. Because he presented them with a context problem, one that had meaning to the students without an implied agenda, they were able to truly explore all of the options for solving. While some students began dividing 15 by 12 and 20 by 23, others began reducing the number of cans and price in half until they reached the number 1. Some students solved for 20 cans, figuring out how costly these would be at each store, while still others solved for one can in order to determine the difference and decide which store was the better buy. In addition, this problem lent itself to rich inquiry and truly engaged the students in the task at hand. Those these two teachers had the same general content goals in mind, the processes that each problem provide were drastically different. While Susan's word problem was primarily teacher-driven with more of a linear model of problem solving, Joel's was student driven and allow the students to explore a variety of feasible processes.