Jana daSilva

Teaching Math and Technology

Professor Albert

Critical Analysis- Problem Solving

February 5, 2007

At the end of chapter six, Thornton writes, “problem solving is at the heart of what we mean by intelligence (126);” this statement epitomizes the influence of social interactions on the child’s perceived ability to solve problems. Throughout the two chapters Thornton continually stresses the importance of actively supporting the learner through positive encouragement and interaction. The child absorbs the instructor’s energy whether it is positive or negative and uses this feedback to generate his or her own sense of achievement and ability: roughly translated this means that a child’s opinion about his or her own intelligence level can be greatly influenced by the social environment that he or she is exposed to. Opportunity to engage in meaningful problem solving enables the child to cultivate a more developed set of problem solving tools. In order to become a successful problem solver, according to Thornton, one must be assisted by an instructor using a technique called scaffolding, in which the learner is supported in stages by his or her instructor. As the learner passes through the various academic stages of problem solving the scaffolding is reduced until the learner is able to complete the task confidently without any additional support. In much the same was construction workers use scaffolding to help support an edifice during the building stages, the teacher must use techniques “responsive to the child’s immediate situation (102)” in order to demonstrate to that child that he or she possesses the tools to succeed and master the problem.

“Sensitivity to the child’s need [combined] with support and nurturance with a firm, demanding style of communicating and enforcing rules (100)” states Thornton, have a direct impact on the child’s ability to learn and grasp the conceptual material. Unfortunately, even with this groundwork established, it remains that there are some tasks that children learn with more facility than others. Thornton suggests that this is due to the meaningfulness of the task: if the task can be connected to something that the child deems worthwhile or important then he or she will be more likely to focus his or her attention on not only completing, but mastering the task. This type of goal oriented problem solving is what Thornton considers meaningful and she notes that this becomes increasingly difficult if the student is asked to “apply an abstract principle or to analyze a situation (105).” To help ease this transition from concrete to abstract problem solving must be encouraged in all facets of the child’s life not simply their academic arena. Later in the chapter Thornton stresses that the scaffolding and encouragement we provide for a child in helping them learn to problem solve has an outstanding affect on the child’s independence and confidence.

In one example Thornton discusses the role of incorporating the child into all tasks to give them a sense of responsibility and necessity. The example she cites is of having a child help in the kitchen to either prepare or clean-up after dinner in order to demonstrate that the child’s presence and help is appreciated and that his or her function in the larger picture of preparing or cleaning-up is integral to completing the task: this reflects what the child is learning about problem solving, that it is to be completed in stages and that no one factor can be omitted while still achieving the desired result. Similarly this encourages the child to look at problems in a fragmented way, that is, to see the different steps or stages that comprise a problem and how they interact. Thornton addresses this at the end of chapter six asking, “Why do human beings go looking for problems to solve instead of just doing things we can already do (126)?” As far as the implications of this question for teachers, it is important that students are encouraged to look for problems in all contexts so that they continue the development of their cognitive abilities and strategies. It is important for teachers to help students cultivate the methodology for problem solving and in particular, for elementary school teachers to promote this type of inquisitive academic and social environment to show student’s that thinking and intelligence are not limited to scores in a test book. Elementary school teachers must implement these devices in their own instruction so as to provide students with a base from which to mature their cognitive capabilities and build up their confidence and independence.

In my own learning experience I have found that when a teacher gives me the tools to build my own knowledge set and skills, my confidence has increased. Similarly I find that I am encouraged to help others achieve the same results because of how I feel regarding the work. I am lucky to have had a childhood filled with chances to participate in activities around the house and I was always encouraged to interact with my peers whether through athletics, art, or group projects: these opportunities enabled me to begin solving social problems in collaboration with others from and early age. Reflecting upon Thornton’s theories I believe that this independence paved the way for me to become an involved problem solver and to seek out opportunities to exercise this knowledge. In elementary school we always had ‘guestimation day’ in which all the classrooms would create a math project for the whole school to try and solve. It was like trick-or-treating around the building solving math problems. For most kids it was a chance to not have class, but for me I loved the opportunity to think logically, to problem solve; I think that this related back to the fact that throughout my childhood I was encouraged in all aspects of my life to problem solve with activities like puzzles, checkers, cooking, computer logic games, etc.

Thornton challenges the reader to answer the question, “Could it be that the processes of solving problems are so fundamental because they provide the very machinery and motor producing cognitive development itself (126)?,” her own essay establishes the answer to this early on by stating that there is a direct positive correlation between a student’s ability to solve a problem and his or her ability to achieve in other academic and social arenas. “Becoming a mature problem-solver is learning the shared assumptions and meanings of our culture (94).”