Problem-solving

Discovery Deduction Induction Abduction Transformation Problem-solving Diagnose Language Prediction Metacognition



Aquiring cognitive skill levels

People learn new cognitive skills over time, through experience and/or education.  One method for evaluating the cognitive skill levels one has acheived is based on Bloom's Taxonomy. Of course there are other method's, but this one is easy to use, easy to follow, and provides a path, of sorts, for acheiving incremental improvements over time.

From Wikipedia

Knowledge

Knowledge involves recognizing or remembering facts, terms, basic concepts, or answers without necessarily understanding what they mean. Its characteristics may include:

  • Knowledge of specifics—terminology, specific facts
  • Knowledge of ways and means of dealing with specifics—conventions, trends and sequences, classifications and categories, criteria, methodology
  • Knowledge of the universals and abstractions in a field—principles and generalizations, theories and structures

Example: Name three common varieties of apple.

Comprehension

Comprehension involves demonstrating an understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating the main ideas.

Example: Compare the identifying characteristics of a Golden Delicious apple with a Granny Smith apple.

Application

Application involves using acquired knowledge—solving problems in new situations by applying acquired knowledge, facts, techniques and rules. Learners should be able to use prior knowledge to solve problems, identify connections and relationships and how they apply in new situations.

Example: Would apples prevent scurvy, a disease caused by a deficiency in vitamin C?

Analysis

Analysis involves examining and breaking information into component parts, determining how the parts relate to one another, identifying motives or causes, making inferences, and finding evidence to support generalizations. Its characteristics include:

  • Analysis of elements
  • Analysis of relationships
  • Analysis of organization

Example: List four ways of serving foods made with apples and explain which ones have the highest health benefits. Provide references to support your statements.

Evaluation

Evaluation involves presenting and defending opinions by making judgments about information, the validity of ideas, or quality of work based on a set of criteria. Its characteristics include:

  • Judgments in terms of internal evidence
  • Judgments in terms of external criteria

Example: Which kinds of apples are best for baking a pie, and why?

Synthesis

Synthesis involves building a structure or pattern from diverse elements; it also refers to the act of putting parts together to form a whole. Its characteristics include:

  • Production of a unique communication
  • Production of a plan, or proposed set of operations
  • Derivation of a set of abstract relations

Example: Convert an "unhealthy" recipe for apple pie to a "healthy" recipe by replacing your choice of ingredients. Explain the health benefits of using the ingredients you chose vs. the original ones.

 

A problem is an obstacle to achieving a goal. The traditional, rational approach to problem solving is:

  1. Clarify description of the problem, including domain,
  2. Analyze causes and remember any new ones,
  3. Identify alternative solution methods for each cause and remember new ones,
  4. Assess each alternative,
  5. Choose one,
  6. Implement it,
  7. Evaluate whether the problem was solved or not. 

To determine if a cause or solution is known use abductive reasoning. If no cause is apparent, then diagnose using Mill’s methods or Fault Diagnosis methods to identify the specific cause. If no solution is apparent, then try one, then another, of the solution-seeking techniques.

Solution-seeking techniques

  • Abstraction: solving the problem in a model of the system before applying it to the real system
  • Analogy: using a solution that solved an similar problem from an unrelated domain. 
  • Case Based Reasoning: uses cases, instead of rules, to solve a problem.
  • Brainstorming: (especially among groups of people) suggesting a large number of solutions or ideas and combining and developing them until an optimum is found
  • Divide and conquer: breaking down a large, complex problem into smaller, solvable problems
  • Hypothesis testing: assuming a possible explanation to the problem and trying to prove (or, in some contexts, disprove) the assumption
  • Lateral thinking: approaching solutions indirectly and creatively
  • Means-ends analysis: choosing an action at each step to move closer to the goal
  • Method of focal objects: synthesizing seemingly non-matching characteristics of different objects into something new
  • Morphological analysis: assessing the output and interactions of an entire system
  • Reduction: transforming the problem into another problem for which solutions exist
  • Research: employing existing ideas or adapting existing solutions to similar problems
  • Root cause analysis: eliminating the cause of the problem
  • Scientific Method: using a hypothesis and three phase reasoning to determine the cause of an unexpected observation.
  • Trial-and-error: testing possible solutions until the right one is found.

  

Analogy

Analogy may be used for propositional or behavioral reasoning.

 

The reasons for using analogy for behavioral reasoning are to determine how did it happen, how do I make it happen, what will happen to it, or why did it happen. The requirements for using this method are: a specific rule must be known, either a case (cause) or a fact (effect) is known, and the case or fact must be similar to the case or fact of the specific rule.  The method used includes abstracting the case or fact, then using abduction if the fact is known or deduction if the case is known to find a similar specific rule..

 

A special method of reasoning called Case-based reasoning is used to create a new procedure from a known procedure. Case-based means using a rule based on a prior single event or observation.

Case-based reasoning process

Case-based reasoning is a method for creating a new procedure based on a single prior  event or observation. This method has been formalized for purposes of computer reasoning as a four-step process.

  1. Retrieve: Given a target effect, retrieve Case-based rules from memory that are relevant to causing it. A Case-based rule consists of a specific procedure and a specific effect, and, typically, annotations about how the procedure was derived.
  2. Reuse: Map the procedure from the previous Case-based rule to the target effect. This may involve adapting the procedure as needed to fit the new situation
  3. Revise: Having mapped the previous procedure to the target situation, test the new procedure in the real world (or a simulation) and, if necessary, revise
  4. Retain: After the procedure has been successfully adapted to the target effect, store the resulting experience as a new Case-based rule in memory.

Example

  1.  
    1. Retrieve: Fred wants to prepare blueberry pancakes. Being a novice cook, the most relevant experience he can recall is one in which he successfully made plain pancakes. The procedure he followed for making the plain pancakes, together with justifications for decisions made along the way, constitutes Fred's retrieved case.
    2. Reuse: Fred must adapt his retrieved solution to include the addition of blueberries.
    3. Revise: Fred adapted his pancake solution by adding blueberries to the batter. After mixing, he discovers that the batter has turned blue – an undesired effect. This suggests the following revision: delay the addition of blueberries until after the batter has been ladled into the pan.
    4. Retain: Fred records his newfound procedure for making blueberry pancakes, thereby enriching his set of stored experiences, and better preparing him for future pancake-making demands.