Chapter 11 Problem Solving
1. How can I summarize this reading in a few sentences?
We solve problems everyday but seldom do we stop and think about why we are so capable of doing so. This chapter explains our problem solving abilities. Problem solving occurs when we have a desired goal in mind and we must overcome obstacles and/or find the important information we need to reach the goal. Every problem contains three parts: the initial state, goal state, and the obstacles.
In solving a problem, the first step is understanding the task at hand. In order to due this, you need to form an accurate mental representation and pull from your previous experiences. To truly understand the problem, you must be able to determine what information is most relevant to arriving at the solution. This is an obstacle for many young minds! Once an understanding of the problem is reached, the problem solver moves on to finding a good way to represent the problem. There are several different ways to represent a problem, such as, symbols, matrices, diagrams, and visual images. An important topic that was covered in this reading is the situated-cognition approach. This approach suggests that students transfer what they are learning in the classroom to everyday problem solving. Due to this, students should have experience solving mathematical problems that are similar to what they might face in the real world. This approach also states that people often learn a skill in a certain situation and later have difficulty transfer the knowledge when it is taken out of context.
There are several different problem solving strategies discussed in this reading. The well known algorithm usually works as long as it is applied correctly. The analogy approach is a common choice for problem solving. This is where you apply a previously solved problem that is similar to the current attempted one. The means-ends heuristic involves dividing the problem into sub-problems and the hill-climbing heuristic is one of the simplest methods. Like the name suggests, the solver continues to select alternatives that seems to lead directly to the goal.
Things that effect problem solving include your level of expertise, experiencing a mental set, and functional fixedness.
Creativity is a rather broad topic that was also discussed in this chapter. It seems to go hand in hand with problem solving. Defining creativity seems to be controversial. According to the text, “creativity requires finding a solution that is novel, high quality, and useful” (Matlin, 2009, p.389). J.P. Guilford proposed creativity should be measured in terms of divergent production. Robert Sternberg suggests creative people produce a creative idea when no one else in interested in the idea. Once it has become popular, they move on to another new idea. Sternberg and Lubart state a person must poses six characteristics to be a wise creative person. They are intelligence, knowledge, motivation, an encouraging environment, an appropriate thinking style, and an appropriate personality.
2. How does it fit into what I have learned already in this course?
To become an effective problem solver, one must be aware of their cognitive abilities. The information being taken into long term memory and stored for future use must be encoded richly and valuably. To problem solve, one must self-regulate their cognitive abilities. Since prior knowledge is so important, our memory must be accessed and our general knowledge also plays a part in problem solving. Without the previously learned material, problem solving information would be much more abstract.
3. What am I still not clear on?
I understand the difference between intrinsic and extrinsic motivation and times weh both would be appropriate. What I am still a little confused about is how teachers are supposed to keep from stifling creativity, covering necessary curriculum, and not employ extrinsic motivation techniques. I think someone is doing a workshop on this subject. I will keep my eye on blackboard.
4. How would apply this to my own teaching/work?
I am applying this now in my classroom. This year, I made it a personal goal to not have any of my students cry during the ISAT session 3 math test. And they didn’t! I have been focusing on mathematical problem solving at least one day a week in my math class. It has really helped my students overcome the fear of attacking the dreaded word problems. I found the information about obstacles of problem solving helpful in understanding what my students are facing. Many of my students struggle with mental set.
5. What proof does the author offer that makes me believe this is valid? Do I believe it? Why?
I am wondering why the author chose to devote a section to creativity. It seems as if it was there to simply tell us is applies to problem solving but the whole area is controversial. There are only two researchers and their studies presented. If it fits in so well with problem solving, I need more information.
6. Why is this important? What does it help improve or explain or predict?
Any time we have the opportunity to learn how to help our students it is important. I believe the information about situated-cognition approach to help explain why some students have some many problems applying what they have learned from their personal life to the classroom and vice versa.
7. When would I actually use this – under what kind of circumstances and for what kind of students?
All of my students can benefit from learning new approaches towards problem solving. I have never heard of the actual term hill-climbing heuristic. I believe many of us use this strategy but my third graders will love hearing this term.
8. Are there other ways to accomplish the same thing that are faster, cheaper, and/or better?I am going back to the intrinsic and extrinsic motivation to answer this question. Just how many studies have been done in this area? It seems as if this is an area that keeps coming up with the same results no matter how it is tested or researched. The motivation behind the task does influence the final task. What I see is an easier way. Try to vary your tasks so that the students are doing things they enjoy, at least at times.