What is a problem?

A problem can be seen as an obstacle, a challenging situation that involves gaps between current and desired situations.

Problems vary across the disciplines. Math problems are analysed and solved with mathematics methods, while social ones may need introspection, behaviourism, and experimentation to find solutions.

Problems also vary in terms of degree. Some problems require more thinking and systematic planning and procedures to get solved while others rely only on routine procedures and so are easier to solve.

This means that the type of problem or challenge determines the approach to solving it. In addition, understanding the problem is key to identifying a solution.

Problem solving definition

Our students need to understand that problem-solving concerns not only numerical solutions, as mathematics. Various problems do not use numbers.

Indeed, problem-solving is about transforming an existing problem state into a desired one.

The process involves bringing up change to reach what we want. So, we can generate new ideas as a result of searching or reflecting, understanding, and combining existing information. These ideas are key to solving that problem.

Problem solving process

It is also known as the ‘problem-solving cycle’ as problems keep arising.  The steps described below are common to solving most problems. So, you can teach these to your students.

1. Defining the problem

Before asking students to think about any solution to a problem, we should ask them first to identify what the problem is.  Defining the problem is the hardest part as students engage in a higher-order thinking process.

You can help them out by addressing the following questions:

What causes the problem? Where, when, and how is it occurring? Why is this occurring? Who is most affected?

Students can work individually or in groups to write their answers to those questions. They discuss and compare their answers to understand the problem at hand.

2. Identifying a technique

After defining the problem, it is time to identify the technique to solve it.  There are different problem-solving techniques. Here are some examples:

• Abstraction

It means breaking down the problem into smaller problems and finding a solution for each.

• Brainstorming

This works with a group where each member suggests a solution and then they discuss their ideas and come up with an optimum solution.

• Hypothesis Testing

This includes making assumptions to explain the problem at hand and proving them through doing research.

• Analogy

Here, students find a problem (source) that is similar to the problem they need to solve (target) and map the solution of that source problem onto the target problem.

• Reduction

Reduction is a combination of both abstraction and analogy. Students will have to break the problem down through abstraction and by using analogy they will have to identify solutions to those smaller problems.

• Trial and Error

Students will have to try and use all the different solutions that they might find to solve a problem. Then, they will identify which solution worked best to solve the problem. They might not find an accurate solution in the first go.

3. Selecting the most feasible solution

Students need to generate alternative solutions, then select the most feasible one. To do so, they need to consider:

• Which solution will solve the problem in the short term as well as the long term?
• Is that solution consistent with the organizational goals?
• What are the possible outcomes?
• Will it cause other unanticipated problems?

 

4. Planning how to implement the solution

To plan how to use their most feasible solution to solving a problem, ask your students to:

• Set SMART goals for their plan;
• determine the steps that should be taken to use this solution,
• identify the type of information needed to bring that solution,
• estimate the time to solve the problem;
• define the necessary resources (people, materials, etc.).

 

Students need to remember that ongoing observation and reflection are necessary to monitor the implementation of the solution. Along that process, it is necessary to evaluate their plans and make the necessary decisions to attain their goals.

5. Checking if the problem has been solved

This is the final stage of the problem-solving process. It involves evaluating the obtained results and measuring the effectiveness of the plan.

So, besides finding out whether or not the hypothesis is accurate, students need to evaluate the observed outcome to decide on the effectiveness of their solution.

They also need to reflect on their mistakes and the kinds of decisions they should have made to improve further their problem-solving skills.

To conclude, problem solving is the act of defining a problem, identifying the technique to solve it, selecting a solution and setting a plan to implement it, and then evaluating the final outcomes or results. Involving students in such a process is necessary to develop their critical thinking skills in this ever-changing world. So, integrate problem-solving activities is worth it.