“good problem-solver" の概念規定は，ストラティジーおよびメタ認知を特定する営みにおいて実現されている。実際，ストラティジー/メタ認知の表現として導入される言い回し“Ｘをする”は，
“good problem-solver はＸをすることができる”
という言い回しを妥当とするものであり，“good problem-solver”の含意になることで逆に“good problem-solver”の概念を規定するものになっている。
以下は，Flavell,1979，Lester,1978,Lester,1983，Garofalo and Lester,1985 の中で挙げられているストラティジー，メタ認知を，（中には，表現を変えつつ）ピックアップしたものであるが，これらは確かに，“good problem
solver"/“poor problem solver”の含意として，逆に“good problem solver"/“poor problem solver”の概念を規定するものになっている：
- Having a good mathematical background
- Having a good variety of experience with problems
- Perseverance
- Tolerance for ambiguity
- Positive attitudes
- Resistence to distraction
- Field independence
- Divergent thinking
- Distinguishing relevant from irrelevant information
- Quickly and accurately seeing the mathe-matical structure of a problem
- Generalizing across a wide range of similar problems
- Remembering a problem's formal structure for a long time
- Knowing that most problems can be solved in more than one way
- Knowing that many interesting problems take more than 1 or 2 minutes to solve)
- Knowing that some problems may have more than one correct answer whereas others may have no answer, due to insufficient information
- Realizing the importance of organizing information
- Willingness to engage in problem solving
- Doing good mathematical achievement
- Good visual perception
- Viewing problem solving as a multifacted complex of processes
- Knowing that many problems allow multiple solution methods
- Choosing approaches to problems
- Avoiding blind alleys
- Allocating problem-solving resources
- Having good skill in organizing information
- Good reading ability
- Good spatial ability
- Good verbal and general reasoning ability
- Good spatial ability
- Makeing a good combination of the followings:
- Making a table
- Drawing a diagram
- Organizing a list of information
- Gessing and testing
- Trial-and-error
- Looking for a pattern
- Looking for an inductive argument if there is an integer parameter
- Systematizing
- Inference
- Using and/or developping visual aids
- Simplifying the problem
- Using and/or developping simpler problems
- Trying a similar approach with fewer variables
- Establishing subgoals
- Recalling and using previous experiences
- Arguing by contradiction or contrapositive
- Identifying goals and subgoals
- Global planning
- Local planning (to implement global plans)
- Performing local actions
- Monitoring to progress of local and global plans
- Trade-off decisions (e.g., speed vs. accuracy, degree of elegance)
- Having not only adequate knowledge but also sufficient awareness and control of that knowledge
- Monitoring one's task understanding and regulate one's strategy usage
- Selecting strategies to aid in understanding the nature of a task or problem
- Planning courses of action
- Selecting appropriate strategies to carry out plans
- Monitoring execution activities while implementing strategies
- Evaluating the outcomes of strategies and plans
- Revising or abandoning nonproductive strategies and plans
- Self-questioning and self-answering in the sense of monitoring：
- problem comprehension stage ──
What are the relevant and irrelevant data involved in the problem?
Do I understand the relationships among the information given?
Do I understand the meaning of all the terms that are involved?
- goal analysis stage ──
Are there any subgoals which may help me achieve the goal?
Can there subgoals be ordered?
Is my ordering of subgoals correct?
Have I correctly identified the conditions operating in the problem?
- plan development stage ──
Is there more than one way to do this problem?
Is there a best way?
Have I ever solved a problem like this one before?
Will the plan lead to the goal or a subgoal?
- plan implementation stage ──
Am I using this strategy correctly?
Is the ordering of the steps in my plan appropriate, or could I have used a different ordering?
- solution evaluation stage ──
Is my solution generalizable?
Does my solution satisfy all the conditions of the problem?
What have I learned that will help me solve other problems?
- Evaluation of orientation and organization:
- Adequacy of representation
- Adequacy of roganizational decisions
- Consistency of local plans with global plans
- Consistency of global plans with goals
- Evaluation of execution:
- Adequacy of performance of actions
- Consistency of actions with plans
- Consistency of local results with plans and problem conditions
- Consistency of final results with problem conditions
- Understanding what such variations as
abundant or meager,
familiar or unfamiliar,
redundant or densely packed,
well or poorly organized,
delivered in this manner or at that pace,
interesting or dull,
trustworthy or untrustworthy
imply for how the cognitive enterprise should best be managed and how successfully its goal is likely to be achieved
- Knowing what strategies are likely to be effective in achieving what subgoals and goals in what sorts of cognitive undertakings
- Escaping from the followings:
- Using only a random trial-and-error strategy in solving process problems, if they are unable to decide on a computation to perform
- Coordinating simultaneously the multiple conditions present in a problem
- Ignoring one or more conditions as they work on a problem
- Recognizing the need to coordinate multiple conditions but not being able to do so
- Forming problem representations based on syntactic interpretations only
- Crunching numbers
- Failing to gain “good" understanding of the problem statement before beginning to try to solve the problem
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