Talk:Problem solving/Archive 1

Early comments
The majority of the article is a contribution of User:JoachimFunke with supporting articles published at:
 * http://www.psychologie.uni-heidelberg.de/ae/allg_en/mitarb/jf/jofu_pub.html

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Very.

the link above does not work...

I added a note on the TRIZ method in "see also" section. I guess it should be integrated into the European Research part, but didn't quite know how to do it... -- User:Jose Icaza on 29 february 2004

--- Added section entitled "Characteristics of Difficult Problems" based on open source work of Dorner and Funke. ThreePD 01:30, 10 February 2006 (UTC)

I removed the "Problem Solving Skills For The Real World" link. I apologise if I offended whoever made the link - but the linked page does not actually contain any information about problem solving - rather, it looks like a product promotion. I therefore feel that it is an inappropriate link for an encyclopedia.--New Thought 21:12, 5 March 2006 (UTC)

Characteristics of Difficult Problems
It seems that a characteristic is missing. There needs to be a characteristic of "Uncertain Relevance". i.e. A determination often has to be made as to the relevance of many factors when considering a problem. It may not be obvious to what degree any factor is relevant, from "very relevant" through to "not relevant".

DannyStevens 13:36, 8 June 2006 (UTC)

Danny, I partially agree with you, in that as soon as we "identify" concepts as "belonging" within a problem space we are essentially wrestling with the mental task of determining whether that particular concept is relevent or irrelevent to the problem space. As well, in reality, this concept attribute is very likely a continuous function, rather than the binary value we frequently attempt to reduce it to. However, given the way you have described Uncertain Relevance, it seems to me that you are talking about an attribute of a particular information item or fact related to the problem, rather than a characteristic of the complex problem itself. [That is - unless you really mean that we often don't know whether a complex problem is worth solving or not (irrelevance of the problem solving goals) - in which case I completely agree].

So then, expressed as a characteristic of the complex problem space, this issue presents itself as Intransparency. We are never quite clear on what concepts or facts or parameters belong within the problem space as a whole and which ones don't. If this issue presents itself at the beginning of the problem formulation, I have called it Commencement Opacity i.e. we are confused right at the outset regarding how to characterize the problem. Alternatively, if we believe we know the characteristics of the problem at the beginning but then later we are bogged down by additional concepts or facts, or experience a void of necessary concepts or facts, during the problem solving activity, then in this case I have subcategorized this phenomena as Continuation Opacity.

In summary, I completely agree with you that there exists a characteristic called Uncertain Relevance, however, I believe that this characteristic belongs to a particular fact or concept as it is being assessed for "belonging" within the problem space. Also, since there is this characteristic of Uncertain Relevance belonging to each concept within the problem space, it creates an overall characteristic of Intransparency in the overall complex problem solving activity. Indeed this issue can only really be addressed by defining and clarifying relationships between the subordinate atomic facts and concepts.

I hope this adequately explains my reasoning about the terms that have been presented.

ThreePD 15:26, 1 September 2006 (UTC)

Should the link to dynamics (time constraints) point to the "dynamical systems" article instead?

Problem solving in mathematics education
Is this topic sufficiently distinct to form a separate article? In the last 25 years Problem Solving has become a major part of mathematics education, and a major part of the constructivist vs back-to-basics debate. Whole curricula have been set up around problem solving, and each new development in state standards and NCTM standards has included reevaluation of problem solving. There have been volumes of literature produced on this topic. Jd2718 07:17, 26 November 2006 (UTC)

Hyphenation
Does anyone know why problem-solving redirects here and not vice-versa? We should standardize
 * problem-solving would function as an adjective, eg "a problem-solving approach." vs minus the hyphen working as the noun: "Problem solving is a teachable skill" Jd2718 04:41, 5 March 2007 (UTC)