It’s been no big deal that students encounter a problem that is complex, in order to solve this problem its advised that you are able to identify and problem-solving is the process of applying a method.
Problem-solving need to be explicitly taught in a way that can be transferred across multiple settings and contexts.
Problem-solving is an on-going process activity in which we take what we know to discover what we don’t know. It involves overcoming obstacles by generating hypotheses, testing those predictions, and arriving at satisfactory solutions.
Helping your students grow to be people who will be successful outside of the classroom is equally as important as teaching the curriculum.
Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.
Understand the problem. It’s important that students understand the nature of a problem and its related goals. Encourage students to frame a problem in their own words.
Describe any barriers. Students need to be aware of any barriers or constraints that may be preventing them from achieving their goal. In short, what is creating the problem? Encouraging students to verbalize these impediments is always an important step.
Identify various solutions. After the nature and parameters of a problem are understood, students will need to select one or more appropriate strategies to help resolve the problem. Students need to understand that they have many strategies available to them and that no single strategy will work for all problems. Here are some problem-solving possibilities:
Create visual images. Many problem-solvers find it useful to create “mind pictures” of a problem and its potential solutions prior to working on the problem. Mental imaging allows the problem-solvers to map out many dimensions of a problem and “see” it clearly.
Guesstimate. Give students opportunities to engage in some trial-and-error approaches to problem-solving. It should be understood, however, that this is not a singular approach to problem-solving but rather an attempt to gather some preliminary data.
Create a table. A table is an orderly arrangement of data. When students have opportunities to design and create tables of information, they begin to understand that they can group and organize most data relative to a problem.
Use manipulatives. By moving objects around on a table or desk, students can develop patterns and organize elements of a problem into recognizable and visually satisfying components.
Work backward. It’s frequently helpful for students to take the data presented at the end of a problem and use a series of computations to arrive at the data presented at the beginning of the problem.
Look for a pattern. Looking for patterns is an important problem-solving strategy because many problems are similar and fall into predictable patterns. A pattern, by definition, is a regular, systematic repetition and may be numerical, visual, or behavioral.
Create a systematic list. Recording information in list form is a process used quite frequently to map out a plan of attack for defining and solving problems. Encourage students to record their ideas in lists to determine regularities, patterns, or similarities between problem elements.
Try out a solution. When working through a strategy or combination of strategies, it will be important for students to …
Keep accurate and up-to-date records of their thoughts, proceedings, and procedures. Recording the data collected, the predictions made, and the strategies used is an important part of the problem-solving process.
Try to work through a selected strategy or combination of strategies until it becomes evident that it’s not working, it needs to be modified, or it is yielding inappropriate data. As students become more proficient problem-solvers, they should feel comfortable rejecting potential strategies at any time during their quest for solutions.
Monitor with great care the steps undertaken as part of a solution. Although it might be a natural tendency for students to “rush” through a strategy to arrive at a quick answer, encourage them to carefully assess and monitor their progress.
Feel comfortable putting a problem aside for a period of time and tackling it at a later time. For example, scientists rarely come up with a solution the first time they approach a problem. Students should also feel comfortable letting a problem rest for a while and returning to it later.
Evaluate the results. It’s vitally important that students have multiple opportunities to assess their own problem-solving skills and the solutions they generate from using those skills. Frequently, students are overly dependent upon teachers to evaluate their performance in the classroom. The process of self-assessment is not easy, however. It involves risk-taking, self-assurance, and a certain level of independence. But it can be effectively promoted by asking students questions such as “How do you feel about your progress so far?” “Are you satisfied with the results you obtained?” and “Why do you believe this is an appropriate response to the problem?”
Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions:
- Does the answer make sense?
- Does it fit with the criteria established in step 1?
- Did I answer the question(s)?
- What did I learn by doing this?
- Could I have done the problem another way?
Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem-solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem-solving skills, a teacher should be aware of principles and strategies of good problem-solving in his or her discipline.
Novices in a particular field typically have not yet developed effective problem-solving principles and strategies. Helping students identify their own problem-solving errors is part of helping them develop effective problem-solving skills.
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