Psy 416:Reasoning and Problem Solving

Erwin Segal

I. Modal view

Cognitive psychologists generally consider the domain of their investigations individual cognitive agents. These agents are people or other individuals that for the sake of the research can substitute for people, usually animals or other computational systems (implemented computer programs). The actions of an agent are presumed to be due to its current competence or else due to relatively permanent changes in its competence due to learning.

Cognition and problem solving is thought of conceptually as being context free. A person incorporates a model of the problem space in her head and then applies operators, defined by the logical structure, to move through the space until a goal is achieved. If the goal is not reached failure would be explained by claiming that the problem solver did not know the appropriate operators or that she did not spend enough time on the problem.  In this model, the environment plays a minimal role. It is simply the source of the problem and the data and the recipient of the results. Problem solving and other thinking is the execution of learned or innate procedures "in the head."

Very little research in cognitive psychology focuses on the details of the situation. Usually research and analyses consider particular stimulus situations only as input to study the details of the internal cognitive or neural representations.

Standard questions for such cognitive psychologists include:

What does an agent know?
How does the agent acquire knowledge?
How is knowledge represented in the agent?
How does the agent use that knowledge for reasoning or action?

II. Alternate viewpoint

Some cognitive scientists argue that the particular actions and decisions that are made are more intimately involved with aspects of the situation than is obvious from the usual focus on the agent.
Situation centered views of problem solving have been gradually gaining steam. They go by various names and there is no consensus of what it is all about, but there is definitely some important issues involved. The broad issue is the belief that properties of cognition, as well as details of behavior, depend a great deal on details of the conceptual, social, cultural, or physical context. There is often an interplay between the contexts and the cognition that would not be discovered without broadening the analysis.

The units to be studied as cognitive systems are thus are not individual agents or minds, but individuals in different contexts. The Ceci and Roazzi chapter on reserve gives examples and data on how conceptual and cultural contexts have major influences on what effective procedures can be accessed in dealing with certain tasks. The Ed Hutchins article on reserve describes a cognitive analysis of a commercial airliner's cockpit. From this perspective problem solving does not reside in the head, but rather resides in a dynamic interaction between the person and the environment. By enlarging the unit for cognition we increase the likelihood that we can see the dynamic interplay of internal and external properties of the system. Importantly, even the algorithms and heuristics used by the system are not the same as those that a researcher might propose if she considered the agent independently of the system.

Some problems which seem to require analytic analysis of contexts to fully explain.

1. Subtracting one multidigit number from another.
2. Building a house of cards
3. Writing a paper on creativity
4. Landing an airplane without crashing
5. Playing in the violin section of an orchestra
6. Finding the coefficient of friction in a physics problem
7. Docking an Aircraft Carrier

Ed Hutchins asks "How many people on an Aircraft Carrier actually know how to dock it?"

The answer he gives is "None."

Consider the role of different contexts in problem solving.

1. If two people, A and B, work on a problem together A can add to what B has done "on line." The contribution by A to the solution may have been something that was not in the problem solving schema that she had available until the new information was received. Furthermore, her own idea might not have made sense to her without the information received from B.
2. Most people who write papers, music, or poetry, edit their works. They generate it and then evaluate the results and modify it. The drafts serve as inputs to the process and are part of the problem domain. Effective procedures include recursively reading what has just been written, evaluating it, and editing it. Obviously the manuscript being revised is part of the system needed to understand the effective procedures used to solve the problem.
3. In the assigned Anzai article, how the problem solvers developed and used diagrams played an important role in solving the problems. From the perspective taken here, the diagram is part of the system solving the problem. Having the diagram changes the details of the algorithm used to solve the problem. Algorithms often include external diagrams.
4. If someone has a logic problem to solve, (e.g. the 'Donald+Gerald=Robert' problem) it may be impossible without writing down different partial solutions as a memory enhancer, prop or crutch.
5. If 3/4 of a shapeable substance is needed, one can make it into a disk, cut through it vertically and horizontally and use 3 pieces. If 3/4 of a cup of a liquid is needed one may pour it up to the 3/4 cup line of a measuring cup, or maybe fill a half cup and a quarter cup. If 3/4 of a rectangular solid is needed, one find the center of the length and the center of one of the halves, cut it at that point and take the larger piece. Each are different procedures for the particular physical object to be dealt with.
6. Given a particular problem, one can often find a solution that gives an answer to the needed precision by making use of a variety of estimation heuristics available in the current situation. Examples in the text about how a shopper compares values across products shows different heuristics dependent upon the values of the objects being compared. notes on context

• Given any problem there are an innumerable number of algorithms or heuristics that might be used to solve it. The ones that are used are not due to random processes, but rather they depend upon conditions of experience, training and the situation. Without the appropriate previous experience, members of different cultures and subcultures do not interpret problems the same way.
• Many algorithms and heuristics are parts of dynamic systems, or make use of on-line information, and cannot be completed outside of the environment in which they take place.
• Parts of the algorithm may be externalized and available when needed, parts may be independently done by different agents at the appropriate time.
• Information may be time sensitive and fed by one component to another component when needed. Different activities often have to be coordinated in time and space in order to get problems solved.
• The bottom line is that reasoning and problem solving is often contextualized and there are pressures to make both the internal computations or memories less difficult and to make use of physical and social inputs that are available.
• Cultural differences in Thinking
  

1. Predict location of geometric shapes or play video game with same algorithm
2. Predicting races or stock markets
3. Add numbers or price sets of products (These are reported in Ceci and Roazzi)
4. African American students, East Asian students, and Women taking tests at major universities.