Critical Analysis Paper for Stephanie Thornton's Children Solving Problems

Jennifer (Juo-Chen) Liu

September 24, 2007

ED 108 Teaching Math & Technology

In Children Solving Problems, Thornton argues that problem solving is a social process and children would experience more success in problem solving if it is done in a social context. She approaches her argument by looking at the historical perspectives of children solving problems. The traditional importance placed on general skills that carries over to other areas of higher cognitive functions made educators looked at problem solving in an abstract way. However, she writes about current views and research that indicate logic and making inferences have less to do with problem solving when compared to the social context that the child is in and the situation of the problem. Furthermore, Thornton provides a discussion of the conceptual tools such as inherent skills and information that children use to manage problem solving.

Thornton uses the studies of Brown, DeLoache, and Karmiloff-Smith to address how children plan to solve problems. According to Brown and DeLoache, the ability of young children to plan is based on the amount of knowledge that they have related to a specific problem, coming up with a solution with the appropriate strategies, and successfully applying their plan. The skills required to solve problems are directly related to a young child’s knowledge and knowing the boundaries of your understandings and strategies come with age and maturation. Once a child recognizes his/her limitations, they are able to select strategies more accurately when faced with a problem. In addition, Thornton states that the works of Brown and DeLoache compliment the theories of Karmiloff-Smith, who has identified three phases that children go through to achieve a solid mastery of a certain component of a problem. The phases that Karmiloff-Smith has identified do not have to happen in order; in fact many children may be in two phases at once. The works of Brown, DeLoache, and Karmiloff-Smith elucidate why the difficulties of problem solving decline as children get older, “Each step forward in planning depends on a step forward in what you know about the specifics of the task. You cannot reflect on the relationship between different courses of action if you cannot represent those actions in a useful way (pp. 59).” As a result, problem solving relies on the gains in the specific knowledge of a task, which are crucial to the development of higher cognitive abilities that enable the child to regulate and understand his/her own problem-solving process.

Thornton believes that children are much more successful at problem solving in a social context. She writes in chapter 5, “Vygotsky shows that the level of skill a child can produce is very much a matter of how much support the child has from the environment – especially from other people (pp.97).” The appropriate interactions between a child and an adult can support their problem solving repertoire because the adult’s organized help aids the development of new skills that the child is not likely to encounter and tackle on his own. Vygotsky’s work suggests that the most effective child-adult scaffolding came when “Parent provides enough support to stretch the child’s problem solving just the right amount: far enough to let the child achieve something new, which he or she could not have done alone, but not so far that the child cannot comprehend or learn from the experience (pp.99).” Vygotsky called this area of skill development, the “zone of proximal development.”

Both children and adults can benefit from collaborative processes such as scaffolded relationships. Thornton gives specific examples as to how a parent can best help their child in problem solving. Children learn the most when parents balance the amount of verbal instruction and demonstration because they get the immediate support that need if verbal commands do not make any sense to them. As a teacher it is important to remember that children will respond differently to verbal instructions depending on their preferred learning style. Therefore, it is beneficial to vary your own instruction by adding hands-on demonstrations that will aid a child in the development of specific or targeted skills. Thornton also mentions that sometimes when you place a novice child together with an expert child, the novice child may not learn as much because the expert child does not know how to scaffold correctly so that he/she can help the novice child solve the same problem. Again, as a teacher, it is important to pay attention to the way that you group students together for collaborative work. Sometimes pairing children of different strengths together can teach them how to work together, but on the other hand if one child is way ahead of the other child in terms of development, one may not be able to communicate effectively and accurately his/her solutions and strategies with their partners.

Thinking back to my own mathematics experiences in elementary school, I rarely remember any kind of teaching strategies that Thornton mentioned in her writings. Mathematics also appeared as a fairly dull subject to me that required numerous drills, worksheets, and memorization tests of the multiplication table. Since I was not exposed to collaborative mathematical learning in my schooling, I find that I am often times caught off guard by the math activities that we do in Dr. Albert’s class. I frequently approach these math activities with no other goal but to solve the puzzle but sometimes the correct solution is not possible unless I interact in specific ways with my group mates. In this case, I think that Thornton’s belief that problem solving happens in a social context makes a lot of sense. The metacognitive process that I have to go through relies on my interactions and dependence on my group mates; it is not only up to me to find a solution. Connecting Thornton’s writing to my own classroom experiences, I have come to learn that mathematical learning is not only a process that only requires one output for every input; rather it is dynamic and conceptual. Now that I have this new knowledge of mathematical learning, I can better assist my students in their learning when I have my own classroom.