



By Paul Filmore
Present education often has a dysfunctional approach in that it gives students knowledge and examples of how to solve problems using that knowledge, and then assumes that the student will (somehow, by a process similar to osmosis) understand how to solve further problems in that domain. In reality there appears to be little focus on teaching how to solve problems systematically, particularly reallife problems that are "messy" and extend into a number of domains. This paper is based on six years of teaching systematic problem solving in the United Kingdom (U.K.) and the special place that the Theory of Inventive Problem Solving (TRIZ) has in this arena. Key areas covered are:
The author previously wrote a detailed guide that details how the author taught TRIZ to undergraduates and postgraduates.^{4} The basic teaching philosophy has been little modified when running training workshops for industry.
The following are some of the key areas which were introduced when teaching TRIZ, to lay the foundations on which TRIZ tools can be established:^{4}
There are many books on problem solving. The starting place is often by introducing a process, an example of which is shown in Figure 1.
Adapted from Problem Solving in Groups^{13} 
What is not clear in Figure 1 is that the first three stages can be time consuming and a significant part of the project work. Most students leap in at stage 4 by immediately trying to solve the problem. This is where the "systematic" in systematic problem solving comes in, i.e., problem solving that at the outset defines the problem and then follows a process. The process should also include feedback loops, so that if at one stage the solutions appear too limited, then one needs to go back to an earlier stage.
The area of problem solving skills is considered a high priority skill area in postgraduate, Master of Science (MSc) development. Directors of five universities covering a number of MSc programs stated that "identification of problem essentials, initiative and originality were highly rated."^{12} This was also reported as important from the employer's perspective when recruiting graduates. "Developing strategies to change mindsets" was mentioned by employers under problem solving requirements.
How is it possible to stop students from immediately starting to solve a problem? The author's approach is to get the students to gain the awareness of this danger by attempting to solve simple problems. The key to this is that the examples must be simple and the students must have fun. A minimum of two different types of problems need to be used before the message sinks in – take the students twice around the learning cycle.
As an example, consider the problem in Figure 2 – the first problem given to students. The approach is to gradually illicit more and more ideas, and for the ideas to get more and more creative. Students then start to realize that they have been making assumptions that have been limiting their ability to solve the problem.
Courtesy Hannah Filmore 
Common assumptions about this problem include:
When all the student assumptions have been listed, it is a good idea to introduce the (TRIZ) idea of available resources and then list them. Examples are:
At this point it is useful to point out that symmetry, dimensionality, etc. may be resources – even drop a loaded hint that the solution would not be possible with a perfectly circular moat. The solution of putting one plank across the right angle of the moat and then the other on top and to the far side is not important. It is getting the students to see that it is their thinking that gets in the way of solving a problem – otherwise there would not be a problem!
A simple second problem is wellknown – how can the nine dots, shown in Figure 3, be connected using no more than three lines, without lifting the pencil off the paper. (The author suggests that students who know the solution do not tell others and if someone discovers the solution then they keep it hidden and only show the lecturer.) When students have had five minutes to generate solutions, the teacher can go back and suggest that again the reason that they cannot answer the problem is that they are making assumptions and, thus, limiting their thinking. After a pause, the lecturer can ask the students to list their assumptions. Usually when a student says that the lines have to terminate on a spot (i.e., the lines cannot go beyond the outer series of spots), then a number see the solution.

The final comment on this solution is that it is solved by thinking outside the box – a phrase that many students have heard while not realizing its implications! Problem solving is all about really understanding the problem before starting to solve it. TRIZ has a number of tools to do this, including functional and resource analysis. Other tools define the constraints and widen thinking with time (past, present, future) and size (subsystem, system, supersystem).^{11}
Before defining the problem, stage 1 of the problem solving process is brainstorming or mindstorming. In the author's experience, many engineers and postgraduate students do not understand that brainstorming requires using the creative hemisphere of the brain and that the moment that any hint of analysis enters (e.g., laughing at a suggestion), then the logical hemisphere takes over (as it has been trained to do, especially for engineers and scientists) and stops the creative flow of ideas. The author now introduces the concepts of convergent (logical) and divergent (creative) thinking. The problem solving process is then to alternate using these ways of thinking illustrated in Figure 4.

In the problem definition and analyze the problem stages, the author likes to introduce "The Six Word Diagram" from Rudyard Kipling's poem, which starts:
I keep six honest servingmen
(They taught me all I knew);
Their names are What and Why and When
And How and Where and Who
This equates to the following question set:
This links with TRIZ's problem hierarchy explorer tool and to the ideal final result problem definition questionnaire.^{11}
A detailed look at how people learn and how this work has been taken on into how organizations learn can help explain how to deal with psychological barriers.
The book Creative Problem Solving reports the work of Ned Herrmann on brain dominance.^{6} Dominance, cognitive (thinking) processes, or preferred modes of knowing all have advantages in quick response time and higher skills level, which is why people default to a particular thinking process. Hermann developed the Herrmann brain dominance instrument (HBDI) and from the results concludes that there are four separate dominances:
Adapted from Creative Problem Solving^{9} 
As seen in Figure 5, the preferences "A" and "B" correspond to the leftbrain hemisphere (i.e., the logical, structured areas) and the "C" and "D" relate to the rightbrain hemisphere (i.e., the creative and holistic thinking areas). These relate to creative problem solving mindsets (Figure 5, right). A key point is that preferences are influenced by a person's (school and college) teaching and that individuals can strengthen nondominate preferences by the careful choice and practice of specific activities (e.g., daydreaming and sketching) for developing quadrant 4.
The author has found that initially considering the barriers to creativity is a practical approach that students can relate to easily. Some barriers include:
This leads to awareness that there are different barriers within individuals and within a company/ organization, as seen in Figure 6. This creativity model helps illustrate a realization of the holistic nature of being an effective problem solver.
Adapted from "Enhancing Creativity in Science & Engineering"^{1} 
How does utilizing the above techniques in learning facilitation (teaching) help develop systematic problem solving? And what are the implications for TRIZ adoption? There is a problem with teaching problem solving – if the teacher moves from a problem toward the solution then the student is in the dark until the last moment. On the other hand, if the teacher starts with the solution, "the solution is viewed as ‘obvious,' often to the point of being almost facile. In fact the very ‘obviousness' of a solution is very often used as a test of how ‘right' the solution is. The more ‘obvious' the answer, the better the solution."^{10}
This is why the author thinks that the teacher has to first develop an awareness in the students that they themselves are the reason why a solution is not being found! This awareness has to encapsulate the habits of:
In the author's experience, it is only after developing an awareness of these barriers that students can appreciate the need for tools that help with this breakthrough process. It is now that the basic TRIZ tools can be introduced. Looking at a good case study is essential and then looking at the results that show if TRIZ is effective.^{4,5}
Why has TRIZ not yet taken off fully? The author appreciates that TRIZ appears to the overworked engineer as just another one of many new tools/processes [Six Sigma, quality function deployment (QFD), functional analysis, failure mode and effects analysis (FMEA), Taguchi, total quality management (TQM), Lean, etc.]. What has though not been made clear is the ability of TRIZ to challenge mindsets (that are open to being challenged) and, thus, deliver breakthrough change. (See Table 1, below.) It should though be emphasized that TRIZ can often complement these other techniques, such as combining TRIZ and Taguchi.^{15}
Being provocative, the author suggests that engineering education has failed by emphasizing compromising/balancing of tradeoffs, and school science/technology education has failed by emphasizing logical thinking. The author believes that children should be taught in primary schools to analyze a problem in terms of what sort of problem it is, change it into a contradiction, look for the ideal, etc.
Table 1: Initial Ideas for How TRIZ Helps Break Mindsets So That Problem Solving Becomes Easy  
TRIZ Tool/Approach  Points Helping to Break Mindsets 
Resources and constraints  • Help understand and define the problem • Clarify that everything may available as a resource 
Functional analysis  • See the problem visually/holistically/overview as a system of interactions 
Ideal final result (IFR)  • Balance tradeoffs is a limited way of thinking; start with the ideal and work backwards to a practical position • Help identify the benefits • Some things are free – believe it! 
Contradictions  • Do not use the word "problem" – defining a contradiction in terms of an improving and worsening pair(s) makes the issue seem more manageable • Formulate the contradiction in terms of, for example, space or time, further helps to open possibilities of understanding 
Contradiction matrix  • Resource of solution triggers • Brainstorm or use other creative approaches (e.g., synetics) starting with these given triggers 
Trends  • There is a (physical) limit where putting in large effort will get very little reward (i.e., little increase in efficiency/ideality) • Other industries have jumped Scurves already – why reinvent the wheel? • The difference between incremental and breakthrough thinking (i.e., jumping Scurves) • Which trends have you not considered as being relevant? 
Nine windows  • Gets away from the present and systems level thinking, by forcing one to consider the past and future and sub and supersystem levels 
Problem hierarchy tool  • Elucidates why an individual wants to solve the problem and what is stopping her • Defines broader and narrower problem levels 
This paper shows that making people aware of their limiting thinking preferences, their assumptions, and their initial limiting problem understanding and definition greatly enhances their problem solving abilities. TRIZ tools can be appreciated more widely by recognizing their mindset breaking potential.
Originally published at TRIZCON2007.
Dr. Paul Filmore has been teaching creativity, personal, professional, entrepreneurial and research skills for more than 10 years, at the University of Plymouth, UK. He introduces TRIZ to firstyear engineering degree students and technology Masters (postgraduate) students. Dr. Filmore runs an innovation consultancy, The Insight Centre, where TRIZ and other systematic problemsolving skills predominate and have been augmented by research and practical understanding of how disruptive innovation thinking can help to further break mindsets. Contact Paul Filmore at pfilmore (at) plymouth.ac.uk.