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parts focus on what is essential to critical thinking and the fourth on what it is to be a critical thinker.

Jewell’s reasoning taxonomy for gifted children (1996)

Jewell’s taxonomy has three fields: objectives of reasoning; reasoning strategies; and reasoning dispositions. The disposition to adopt thinking about thinking (metacognition) as a habit is very important.

Petty’s six-phase model of the creative process (1997)

Each of the phases (inspiration, clarification, evaluation, distillation, incubation and perspiration) is linked with desirable accompanying mindsets. All phases are essential, but not always sequential. Uncreative people tend to consider few ideas and work with a fixed mindset.

Bailin’s intellectual resources for critical thinking (1999b)

Bailin emphasises critical thinking as the induction into cultural, critical practices and traditions of enquiry; and advocates the infusion of critical thinking into the curriculum. She offers a framework rather than a taxonomy, which identifies the required intellectual resources and habits of mind.

Description and evaluation of productive-thinking frameworks

Altshuller’s TRIZ (Teoriya Resheniya Izibreatatelskikh

Zadach) Theory of Inventive Problem-Solving

Description and intended use

TRIZ is a systematic, creativity and innovation process devised as an aid to practical problem-solving, especially in engineering. It owes much to the work of Genrich Altshuller whose study of patents led him in 1946 to devise an Algorithm for Inventive Problem Solving in the Soviet Union. This algorithm, known as ARIZ, from the Russian, is a part of TRIZ. The first published paper about TRIZ appeared in Russian in 1956 (Altshuller and Shapiro, 1956). It is

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estimated that, by 2002, some 1,500 person-years had gone into the development of TRIZ. The aim is to encapsulate principles of good inventive practice and set them in a generic problem-solving framework (for more details see Altshuller, 1996; 1999; 2000; Salamatov, 1999; Mann, 2002). TRIZ may now be described as a theory of how technology develops, a process and a series of tools to aid thinking to solve practical problems. TRIZ is intended to complement and add structure to our natural creativity rather than replace it. It is claimed to be the most exhaustive creativity aid ever assembled. More recently, it has been adapted to suit non-material problems, such as those that arise in management.

TRIZ helps the would-be problem-solver define a specific problem, see it as a particular kind of problem, identify a potential solution in general terms and translate this into a specific solution. This sequence is illustrated in figure 4.1. Note that TRIZ aims to point thinking in directions that are likely to be productive. It does not provide an algorithm that guarantees a solution: the solver must cross the space S in figure 4.1. In effect, TRIZ is a collection of tools to aid thinking. Although TRIZ has major unique features, development seems to be eclectic and thinking aids from a variety of sources are incorporated.

Fig. 4.1. Classifying a specific problem as an instance of a TRIZ generic problem, using TRIZ tools to identify a generic solution then translating it into a specific solution.

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Problem Definition: in which the would-be solver comes to an understanding of the problem

1.The Problem Explorer provides ways of understanding the problem. These include: a benefits analysis; a problem-hierarchy explorer (the original problem, the broader problem, the narrower problem); a ‘nine-windows’ tool for exploring resources and constraints (in terms of past, present and future; within the system, the system itself, and around the system); and an identification of ‘sore’ points.

2.The Function and Attribute Analysis (FAA) identifies in detail what the solution is expected to do and what its attributes will be. For instance, these can be set out in noun-verb-noun diagrams, rather like concept maps.

3.S-curve analysis locates the problem on a general development curve (S-shaped). For instance, if the current situation lies near the beginning of the curve, solutions are likely to involve improvements to the system. If it lies at the mature (top) end of the S-curve, an entirely new system may be needed as opportunities for further improvements may be few.

4.The Ideal Final Result (IFR) describes the characteristics of the ideal solution to the problem.

Selecting a Problem-Solving Tool

Advice is given on the order in which to try the thinking tools. The order is not intended to be rigid and different authors may suggest different ways of working. It is also possible to construct short versions so that courses from two days to six months duration are offered. It is recognised that short courses are not adequate to do justice to TRIZ and should be seen as taster courses.

Generating solutions: using the tools

1.Technical Contradictions refers to the technical problems identified (e.g. high strength but low weight). The solver uses a matrix to identify which of 40 ‘Inventive Principles’ (strategies) seem to have the potential to suggest a resolution of the contradiction. This use of these 40 generic strategies is said to account for the

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success of hundreds of thousands of patents. For instance, Principle 1– Segmentation, suggests: A. divide a system into separate parts or sections; B. make a system easy to put together or take apart; C. increase the amount of segmentation. All 40 principles are possible ways of improving the functionality of a product by solving relevant problems.

2.Physical Contradictions refers to the physical problems identified (e.g. the object must be both hot and cold). Again, a grid provides Inventive Principles that may suggest solutions.

3.S-Field Analysis involves codifying the problem into a general form. This general form is used to identify those Inventive Principles that may be useful (as these are also expressed in a general form). In addition, additional charts suggest solutions to difficulties raised by the analysis, such as insufficient/excessive relationships.

4.Evolutionary Trends describes patterns of development that have been found to be more or less general amongst solutions to practical problems. These may suggest ways in which a product might be changed (e.g. many boundaries to few boundaries to no boundaries; commodity to product to service to experience to transformation).

5.Resources are what is in or around the system. In identifying these, it draws attention to their existence and directs thought to their potential.

6.Knowledge/Effects refers to the existence of know-what and know-how that has the potential to solve the problem. There are

three resources for identifying these: a) a database of functional effects; b) a database of ways of altering attributes; and c) knowledge resources to be found on-line, through a search of patent databases.

7.ARIZ is a problem-solving algorithm originally devised by Altshuller. It involves: defining the specific problem; technical and physical contradictions; the IFR; the x-component (some magical product that eliminates the contradictions); analysing resources; and selecting and applying the Inventive Principles. ARIZ preceded TRIZ but could be used as a compact or reduced version of it.