Method 20 List of control questions

Step 1

Step 2

Step 3

Step 4

Main idea and its purpose

Polya’s checklist is most effective in solving educational mathematical and technical problems, however, it can be of help in successfully solving any life problem and is applicable for any domain, such as business, management and invention. It also can be used as a guide to thinking about problems and for researching them in general.

Scope of application, for example, when working with a group of a certain age and composition; in individual work, etc.

This method can be used for individual work (self-checking your activities) and group work (tracking the team's progress).

Application guidance: scope of application, for example, when working with a group of a certain age and composition; in individual work, etc.

The four steps that are vital in solving a problem
1. Understanding The Problem
- What is the unknown? What is the data? What is the condition?
- Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory?
- Draw a figure. Introduce suitable notation.
- Separate the various parts of the condition. Can you write them down?
2. Devising a Plan. Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain a plan of the solution eventually.
- Have you seen it before? Or have you seen the same problem in a slightly different form?
- Do you know a related problem? Do you know a theorem that could be useful?
- Look at the unknown! And try to think of a familiar problem having the same or a similar unknown.
- Here is a problem related to yours and solved before. Could you use it? Could you use its result? Could you use its method? - Should you introduce some auxiliary element in order to make its use possible?
- Could you restate the problem? Could you restate it still differently? Go back to definitions.
- If you cannot solve the proposed problem, try to solve some related problem first. Could you imagine a more accessible related problem? A more general problem? A more special problem? An analogous problem? Could you solve a part of the problem? Keep only a part of the condition, drop the other
part; how far is the unknown then determined, how can it vary? Could you derive something useful from the data? Could you think of other data appropriate to determine the unknown? Could you change the unknown or data, or both if necessary, so that the new unknown and the new data are nearer to each other?
- Did you use all the data? Did you use the whole condition? Have you taken into account all essential notions involved in the problem?
3. Carrying Out The Plan. Carrying out your plan for the solution, check each step. Can you see clearly that the step is correct? Can you prove that it is correct?
4. Looking Back. Examine the solution obtained.
- Can you check the result? Can you check the argument?
- Can you derive the solution differently? Can you see it at a glance?
- Can you use the result, or the method, for some other problem?

The results of applying the method, for example, increasing the ability to go beyond standard solutions, etc.

The emphasis in this method is on being conscious of our problem-solving strategies and on constructing a solution that reflects the steps outlined above.

Instructions for combining creativity methods

1. Determine the goal
Determine why you want to use creative methods in your work and for whom, that is, what is the purpose, goals, meanings, audience, for whom it is happening.
2. Read
Read the description of the methods and recommendations for their use.
3. Choose
Choose those that best suit your purpose and tasks. When choosing methods, pay attention to the fact that they can be conditionally divided into several groups:● procedural, those that help answer the question HOW TO DO IT? How to optimize the process? How to do the process differently?● horizontal, those that answer the question WHO? WITH WHO? FOR WHOM? This is about the distribution of responsibility, and about clarifying the interests, association or for whom we are doing it.● vertical, those related to WHY? WHAT IS A PURPOSE? WHAT IS THE MAIN? It is about clarifying the hierarchy in the structure, the essence of the problem and its solution, what it consists of and what one wants to achieve.
4. Make it specific
Add the missing aspect to the vector. Depending on the task, one of the vectors will be the main one, and the other 2 will be auxiliary.● For example, you need to start the learning process in a different, new way: you choose the most suitable methods for your task and audience, and add methods for vertical and horizontal questions. This will add specificity towards the goal of this process and the distribution of tasks for everyone in the process, will help determine who and what it will be useful for. This creates a habit of thinking in different directions and structuring the process.● For example, the "Blooming Lotus" method allows you to determine the vertical vector, disassemble the problem into components, detail it by seeing the entire system of the problem at the same time, show the connections between different elements and find a solution for each element separately. If we add a horizontal and procedural layer of questions from the SCAMPER method, adding and concentrating on what is still missing, what can be added, what aspect has not yet been revealed, then we will get an even more complete picture and a solution that will cover the maximum fields of the same problem.

5. Сombine methods
Find and add polar aspects. You can combine methods that are more structural with playful ones based on the principle of combining polarities. This can make the process emotional but also structured at the same time. Yes, you can first choose the method that, in your opinion, is most suitable for your problem and task, then immediately determine the one that you would rather not use, which highlights the opposite sides. Moreover, your determined polarity can be conditional, that is, you yourself can determine what is polar in your case, what is the opposite. ● For example, if in one method there is a lot about the connections between elements, their detailed description, diving into the essence of details, then choosing a method that will consider the system of the problem from above, the whole whole, the system as a separate element in the environment around it, this will add scaling in finding a solution.
6. Application time
Different methods require different periods of time when applied. When combining methods, it is better to take this into account by adding a simpler and time-limited method to a method that is time-consuming and more difficult to use.
7. Calibrate the original purpose
During the whole process, calibrate from time to time with the original purpose, goals, meaning for what it all happens and for whom, because in the exciting creative space it can be easy to lose the axis on which the whole process should rest.
8. Experiment
Having created a combination of methods, it is important to experiment and be ready for changes and adaptation of the newly created to the needs, goals and tasks even more, because during the approbation we can just see the fact that was not taken into account. Here we can go back to points 4 and 5, adding aspects that are missing.● Note: try to feel the process, be present in it as much as possible, and allow imperfection and something spontaneous to arise, because the marker of novelty is your surprise, expansion of space and emergence of unexpected details, solutions, ideas.

Instructions for combining creativity methods

1. Determine the goal
Determine why you want to use creative methods in your work and for whom, that is, what is the purpose, goals, meanings, audience, for whom it is happening.
2. Read
Read the description of the methods and recommendations for their use.

5. Сombine methods
Find and add polar aspects. You can combine methods that are more structural with playful ones based on the principle of combining polarities. This can make the process emotional but also structured at the same time. Yes, you can first choose the method that, in your opinion, is most suitable for your problem and task, then immediately determine the one that you would rather not use, which highlights the opposite sides. Moreover, your determined polarity can be conditional, that is, you yourself can determine what is polar in your case, what is the opposite. ● For example, if in one method there is a lot about the connections between elements, their detailed description, diving into the essence of details, then choosing a method that will consider the system of the problem from above, the whole whole, the system as a separate element in the environment around it, this will add scaling in finding a solution.
6. Application time
Different methods require different periods of time when applied. When combining methods, it is better to take this into account by adding a simpler and time-limited method to a method that is time-consuming and more difficult to use.

3. Choose
Choose those that best suit your purpose and tasks. When choosing methods, pay attention to the fact that they can be conditionally divided into several groups:● procedural, those that help answer the question HOW TO DO IT? How to optimize the process? How to do the process differently?● horizontal, those that answer the question WHO? WITH WHO? FOR WHOM? This is about the distribution of responsibility, and about clarifying the interests, association or for whom we are doing it.● vertical, those related to WHY? WHAT IS A PURPOSE? WHAT IS THE MAIN? It is about clarifying the hierarchy in the structure, the essence of the problem and its solution, what it consists of and what one wants to achieve.
4. Make it specific
Add the missing aspect to the vector. Depending on the task, one of the vectors will be the main one, and the other 2 will be auxiliary.● For example, you need to start the learning process in a different, new way: you choose the most suitable methods for your task and audience, and add methods for vertical and horizontal questions. This will add specificity towards the goal of this process and the distribution of tasks for everyone in the process, will help determine who and what it will be useful for. This creates a habit of thinking in different directions and structuring the process.● For example, the "Blooming Lotus" method allows you to determine the vertical vector, disassemble the problem into components, detail it by seeing the entire system of the problem at the same time, show the connections between different elements and find a solution for each element separately. If we add a horizontal and procedural layer of questions from the SCAMPER method, adding and concentrating on what is still missing, what can be added, what aspect has not yet been revealed, then we will get an even more complete picture and a solution that will cover the maximum fields of the same problem.

7. Calibrate the original purpose
During the whole process, calibrate from time to time with the original purpose, goals, meaning for what it all happens and for whom, because in the exciting creative space it can be easy to lose the axis on which the whole process should rest.
8. Experiment
Having created a combination of methods, it is important to experiment and be ready for changes and adaptation of the newly created to the needs, goals and tasks even more, because during the approbation we can just see the fact that was not taken into account. Here we can go back to points 4 and 5, adding aspects that are missing.● Note: try to feel the process, be present in it as much as possible, and allow imperfection and something spontaneous to arise, because the marker of novelty is your surprise, expansion of space and emergence of unexpected details, solutions, ideas.