understanding_problems

Annotations by Ben Wilbrink

The strong conception here is that of the problem-based curriculum.

Deanna Kuhn (2005) is a protagonist.

George Pólya is, according to Allen Newell (1980)

Allen Newell seems to be one, though he is not actively involved in instructional design

Ronald Giere might be one

Ronald N. Giere (1988). Explaining science, a cognitive approach. University of Chicago Press.

Deanna Kuhn (2005). Education for thinking. Harvard University Press.

Edward A. Silver (Ed.) (1985). Teaching and learning mathematical problem solving: Multiple research perspectives. Erlbaum. questia

Patrick W. Thompson: Experience, problem solving, and learning mathematics: Considerations in developing mathematics curricula ()
- p. 190: "A third theme is that to learn mathematics is to learn mathematical problem solving. This is in contrast to the common view that one learns a set of mathematical skills and then learns to apply them to solve problems (e.g., GagnŽ, 1983). However, the essential feature of constructing mathematical knowledge is the creation of relationships, and creating relationships is the hallmark of mathematical problem solving. I will return to this point in the next section and later in case studies."
- p. 191: "By a mathematics curriculum I mean a selected sequence of activities, situations, contexts, and so on, from which students will, it is hoped, construct a particular way of thinking."
- p. 192 problem-based curricula: "From a constructivist perspective, any curriculum aimed at promoting mathematical thinking must, by the very nature of the phenomenon, be problem based."

Herbert A. Simon (1978). Information-processing theory of human problem solving. In W. K. Estes (Ed.) (1978). Handbook of learning and cognitive processes, volume 5, Human information processing (271-295). Hillsdale, New Jersey: Lawrence Erlbaum.

p. 287: ill-structured problems "A production system (...) containing a rich repertory of recognition processes and associated with a large store of information in longterm memory, would produce precisely the kind of continually changing problem space that has been observed in protocols of subjects solving such problems."
Ofwel: Herbert Simon schakelt moeiteloos een tussenfase van complex begrijpen van van probleemstellingen tussen: vertalen, modelleren, omwerken, alternatief formuleren, verbiden met bekende/verwante/eenvoudiger eerder opgeloste problemen die nieuwe aspecten aan kunnen dragen waarop mogelijk vruchtbare producties passen voor de oplossing of voor het oplossingsplan voor het voorliggende probleem.

Earl D. Sacerdoti (1975). The Nonlinear Nature of Plans. In Proceedings of the Fourth International Joint Conference on Artificial Intelligence (IJCAI-75), 206-214. pdf retrieved november 2008

abstract "We usually think of plans as linear sequences of actions. This is because plans are usually executed one step at a time. But plans themselves are not constrained by limitations of linearity. This paper d escribes a new information structure, called procedural net, that represents a plan as a partial ordering of actions with respect to time. By avoiding premature commitments to a particular order for achieving subgoals, a problem-solving system using this representation can deal easily and directly with problems that are otherwise very difficult to solve"
p. 207: "NOAH (Nets of Action Hierarchies) is a problem solving and execution monitoring system that uses a nonlinear representation of plans"
Earl D. Sacerdoti A Structure for Plans and Behavior. Doctoral thesis
- Abstract "This report describes progress to date in the ability of a computer system to understand and reason about actions. A new method of representing actions within a computer's memory has been developed, and this new representation, called the "procedural net," has been employed in developing new strategies for solving problems and monitoring the execution of the resulting solutions. A set of running computer programs, called the NOAH (Nets Of Action Hierarchies) system, embodies this representation. Its major goal is to provide a framework for storing expertise about the actions of a particular task domain, and to impart that expertise to a human in the cooperative achievement of nontrivial tasks. A problem is presented to NOAH as a statement that is to be made true by applying a sequence of actions in an initial state of the world. The actions are drawn from a set of actions previously defined to the system. NOAH first creates a one-step solution to the problem, then it progressively expands the level of detail of the solution, filling in ever more detailed actions. All the individual actions, composed into plans at differing levels of detail, are stored in the procedural net. The system avoids imposing unnecessary constraints on the order of the actions in a plan. Thus, plans are represented as partial orderings of actions, rather than as linear sequences. The same data structure is used to guide the human user through a task. Since the system has planned the task at varying levels of detail, it can issue requests for action to the user at varying levels of detail, depending on his/her competence and understanding of the higher level actions. If more detail is needed than was originally planned for, or if an unexpected event causes the plan to go awry, the system can continue to plan from any point during execution. In essence, the structure of a plan of actions is as important for problem solving and execution monitoring as the nature of the actions themselves."

November 15, 2008 \ contact ben at at at benwilbrink.nl

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