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Conceptos, estructuras y metas. Collin Lynch.
to focus learners on addressing this ambiguity.
Their work is illustrative of the range of definitions and has been frequently cited by others. Voss (2006. Newell. This differentiates them from domains such as Newtonian mechanics. According to this view. Namsoo Shin. Structures.254 C. Simon (1973). using terms like “ill-defined” suggests that one simply has not tried hard enough to develop general methods for problem solving or objectively evaluating the validity of proposed solutions. focused primarily on the structural aspects of constraint-based tutoring systems in ill-defined domains. In this work we present a definition for the terms ill-defined problem and ill-defined domain intended to provide a concise basis for framing and motivating both the discussion in this special issue and future work in this area. Conklin. 1997). cleared. Far from needing to eliminate this ill-definedness. Voss. Shin. Each author approached the topic with a different purpose. it is an opportunity. the fact that a domain or problem is ill-defined should not be an impediment to useful work in AI and education. rather. ethics. & Penner 1983). Aleven. researchers in AI and education should focus on developing systems that address it directly for both functional and pedagogical reasons. David H. Greene. 1992). Mitrovic and Weerasinghe. 1973. We adopt the latter here and. 1982). In addition to these general reviews other authors have focused on specific classes of ill-defined problems such as Design Spaces (Goel & Pirolli. domains like law. James F. Antonija Mitrovic and Amali Weerasinghe (2009) and ourselves (Lynch. In this work we take into account both the cognitive and structural aspects of ill-defined domains and problems. Simon. We then conclude with a survey of related work along these lines. we will clarify a few terms. Simon to illustrate extensions of the General Problem Solver. and Wicked Problems (Rittel & Webber. Shin. In our opinion. and vary in their structure and emphasis. Each served to focus attention on the aspects of ill-definedness of interest to the author. Voss. In our opinion. public policy. Newell sought to address the relationship between a problem’s definition and the abilities of the problem solver. problems are ill-defined until they are surveyed. history. citing other authors where appropriate. 2006). Ashley. and Steven McGee (2003. We will highlight some of the definitions that have followed McCarthy’s before presenting our own. and Voss to examine the process of problem solving in these domains. by contrast. when necessary. we will focus in detail on the work of Reitman. . PREVIOUS DEFINITIONS OF ILL-DEFINEDNESS McCarthy’s original characterization has been reexamined and extended by a number of researchers including Walter Reitman(1964. and strung with barbed wire. 2006). and architecture are inherently illdefined. Jonassen and McGee. Clarification of Terms Before proceeding with this discussion. Post. Jonassen & McGee focused on the educational role of ill-definedness but did not address the role of AI in that process. and Goals this view. Medical Diagnosis (Pople. Minsky sought to differentiate classical search problems from other tasks. as are most of the problems in them. The resulting goal-driven definitions cover many but not all of the same concepts. Alan Newell (1969). We disagree. including new work published in this volume. Herbert A. Lynch et al. 1965). / Concepts. Jonassen. as the work in this volume demonstrates. & Pinkwart. Rather than attempting a complete survey of prior definitions. The words ill-structured and illdefined are often used synonymously in the literature.
expand. Open-textured concepts are common in ill-defined domains such as law where the definitions of concepts such as “negligence. An opentextured concept is one whose application is not automatic but which requires judgment and is contextdependent (Berman & Hafner. are ill-defined. to producing fugues that are “pianistic. both explicitly and implicitly. such as winning a court case. or in music where pieces are structured in terms of “themes” and “voices. restricts him. they must apply relevant knowledge to achieve their goal given their initial position or knowledge. students exercise. he analogizes this process to linguistic transformations where the term “fugue” transforms to “exposition plus development plus conclusion” (Reitman. or structural knowledge such as legal statutes. is performed both to break the problem down and to tease out other relevant constraints. or the principles of linear kinematics and the acceleration constant. In educational settings. Reitman noted that most of the problems addressed by human problem solvers. the knowledge required for problem solving. Newell and Simon: Components as Constraints Minsky’s original characterization was first adapted by Reitman (1964. Although Reitman cautions against taking it too far. a problem is defined by one or more goals that the solver must achieve. pedagogical. They are characterized by relevant declarative. focuses on ill-defined problems while other work focuses on ill-defined domains. perhaps unintentionally. from design to hiring. The domain delineates. 1965). This process of recharacterization. a composer is given a sheet of paper and a pianoforte. We will return to this relationship between domains and problems below. 1965). Domains. rhetorical techniques.” “income. Problems are used functionally to teach students about the domain.” Reitman illustrated his discussion with a think-aloud protocol of music composition collected from an experienced composer. Providing the composer with a piano for example. Structures. In our view. Suppose. some of the work surveyed. the original problem is mapped to many overlapping subproblems where the solution to one subproblem in turn constrains the others. Lynch et al. and Goals 255 have substituted for clarity.” The assigned materials constrain both the problem solving process and the solution. including our own. Additionally.” or “vehicle” are a source of dispute. and refine their command of that knowledge. are conceptual spaces or fields of study such as law and Newtonian mechanics. A solver proceeds through a steady process of transformation or recharacterization of the initially ill-defined problem specification to a better defined and more solvable one. in terms of the declarative or procedural knowledge that students should understand or the professional practice for which they study.” Solvers of ill-defined problems must decide how to “close” the open constraints by filling in the missing problem components. In some cases the problem solver will make an a priori design decision. Reitman. 1985). During this process. In addressing a problem and obtaining feedback. designing a house. problems are defined by a set of initial characteristics and a problem requirement that specifies the task to be performed and the solution criteria. domains are structured pedagogically. In order to do so. selecting a theme for a fugue in turn constrains the choice of counter-themes and the number of voices. as described by Reitman (1965). or calculating the speed of a moving car. by contrast. In Reitman’s formulation a problem is well-defined if the problem solver has access to a complete description of the problem requirements and to all relevant concepts and terms or problem components. for example. It is ill-defined if one or more of these components is left unspecified or is open-textured. / Concepts. and then commanded to “compose a fugue. such as when Reitman’s composer declared his intention at the outset to . For example. In Reitman’s view.C.
While this process is often characterized by monotonically increasing commitments. the composer was free to compose on any theme within the conventions of the piano and the fugue. Voss. the problemsolving context. Reitman’s composer. In Reitman’s example. Lynch et al..256 C. Voss (Voss. Bach wisely chose Frederick’s own “Royal Theme. Voss was concerned with the differences between expert and novice problem solvers and the role of argumentation in ill-defined problems. Voss and his colleagues analyzed a series of expert and novice problem solvers each tasked with addressing the then Soviet Union’s ongoing agricultural problems. King of Prussia. 1979). particularly large-scale social problems. This concept of solver power was noted by Newell (1969) who focused on the relationship between the power or potential of a given problem solver and the problem itself. once commanded Bach to improvise a fugue on the spot with six obbligato voices and a theme of his choosing. In the latter case. Experienced composers are better able to compose novel fugues than novices or non-musicians. or bounding. Simon (1973. and the problem-solving process: . 1983) focused on human problem solvers. abandoned his original theme when it came into conflict with a counter-theme that he developed later on. In the former case.” a set of pieces dedicated to the Emperor (Hofstadter. the design of a warship). this is not always the case. Structures. the solver will reassess a partial solution to identify implicit constraints within it. musical legend holds that Frederick the Great. For instance. / Concepts. solver behavior.. Post. the presence of unspecified components in a problem guarantees that no solution will be universally accepted. & Penner. He provided a more detailed. identifying the following characteristics of ill-defined problems. and the judges involved guarantee a range of viable alternatives. an individual architect designing a home) and when a large-scale project is distributed across separate solvers (e. an architect might come upon a particularly creative or attractive top-floor layout that requires additional supporting walls below. Half-way through the process Reitman’s composer noticed a fourth “voice” in his fugue and continued with that in mind. and Goals produce a three-part fugue. and solver-oriented list of criteria than Simon.” and the resulting fugue made its way into Bach’s “Musical Offering. 1957) in turn noted that many existing models of problem-solving behavior ignored the important role that resource limitations play in guiding. on the other hand. 2006. the addition of a new weapon by the Director of Naval Ordinance might necessitate major structural changes by the Engineer-In-Chief’s office or concessions by the Director of Torpedoes. He specifically characterized ill-defined problems as those for which only weak problem-solving methods are available. Simon (1973) described a similar process in the design domain noting that it occurs both when problems are solved by a single solver (e. In other cases. While a given solution may be acceptable to some. Greene. solutions to those problems. Voss: Rhetorical Problem Solving Like Reitman.g. A master composer of fugues like Bach would find the task far better-defined than a novice with no rules or experience to fall back on. In this case the judge had an implicit preference that was cleverly divined by the great composer.g. for example. According to Reitman (1964). the characterization decisions made by the solver.
and Goals 257 1. and (d) require a large database of relevant information that is often difficult to access. Jonassen. setting new goals. This process was present to some degree in the examples presented by other authors but was not a primary factor in their analyses.” Simon criticized many existing economic theories for assuming that human decision-makers always make optimal decisions. & McGee (Shin. specifically on the cognitive and metacognitive .C. 2003. and Simon. 1997). Jonassen. (b) no unambiguously right or wrong answers. and (b) justify their solutions by means of argument. In his view the experts first frame a problem and then solve it.” He characterizes well-defined problems as being particularly amenable to computer simulation. Voss’ experts focused on identifying relevant factors such as the lack of arable land. for instance. “finding a theme. / Concepts. Solvers of ill-defined problems: (a) divide their work into “problem representation” and “problem solving” phases. Jonassen. and overcome the legacy of previous failures. and generating new conflicts that must be reconciled. Jonassen & McGee: Educational ill-definedness Voss’ work was continued by Shin. Much of his analysis agrees with that of Reitman. however. Voss. Solutions to ill-defined problems: (a) are rarely correct or incorrect but fall on a range of acceptability. Voss was addressing some of the same issues highlighted by Newell (1969) in his discussion of solver power. Newell. and (b) cannot be judged on their own but require some implementation and evaluation to test. This is similar to Reitman’s description. Goel & Pirolli (1992) described a similar process in their discussion of design spaces. His focus. In presenting this. which dealt explicitly with decomposing a problem into subproblems. This is particularly true of his database criterion (1d). Simon countered this by proposing a model of “satisficing” where solvers choose the “best” action they can given a limited amount of processing power and background information. the need for a new design is identified by the First Sea Lord (head of the British Navy) and then passes through a general requirements phase before being passed to each department from Naval Engineering to the Director of Torpedoes. Each group recharacterizes the design according to their needs and makes modifications by imposing new constraints on the problem. When faced with the problem of poor Soviet agriculture. Ill-defined problems: (a) have vaguely stated goals. & McGee. for example. the need to convince ideologically-motivated decisionmakers. on the process by which solution decisions are justified is novel. described problem decomposition in terms of subgoals and subproblems. sometimes repeating the cycle as needed. Greene. for example. Shin. 3.” Voss. This was a more structured form of the process than Reitman described. & Penner (1983) separated the problem-solving process into distinct recharacterization and problem-solving phases. who focused on ill-defined problems in education. Structures. but it is similar to Simon’s (1973) example of warship design in an organizational context where. Lynch et al. and Simon (1957) in his critique of the idealized “economic man. like Reitman. Post. Voss argued that the process of solving ill-defined problems is “rhetorical in nature. 2. (c) unstated or assumed problem constraints.
and Goals skills necessary to solve ill-defined problems and on the process of problem solving. No single definition can be considered “definitive. Unlike previous authors. can be intractably large making explicit representation impractical. ill-definedness is an open-textured concept. its application varies depending upon the authors’ goals. principles. This recharacterization. Their study centered on astronomy problems. and 5) the requirement that learners to make and defend judgments about the problem. and the resulting solution. or solution criteria are un. Jonassen (1997) characterized the solving of ill-structured problems as a design process and highlighted the role of metacognitive strategies such as self-explanation play in problem solving. even in traditionally “well-defined” problems. While each of the provided definitions covers the same or similar problems. are subject to debate. rules and principles are relevant to a solution or their organization. and rules.” Rather. open-textured. In that paper he articulated a multi-step process. or intractable. The first step was identifying an appropriate “problem space” in which to work and articulating the problem’s contextual constraints. Their goal was to highlight the role that metacognition and justification play in the solving of these problems and the fact that solutions to ill-defined problems differ procedurally and pedagogically from well-defined ones. noting that ill-defined problems provide no general rules for deciding cases and very often exhibit inconsistent relationships among concepts. Structures. 4) uncertainty about what concepts. 3) the existence of multiple solutions and multiple solution criteria. in arguing that solvers of ill-defined problems must construct a representation of the problem containing all possible states in order to solve it. They then extended the problem-solving process described by Jonassen (1997). With that in mind:  A problem is ill-defined when essential concepts. & McGee (2003) enumerated a list of characteristics for ill-defined problems including: 1) the absence of one or more problem elements. 2) the presence of vague or unclear goals. The authors departed from earlier researchers. A solver is thus required to structure or recharacterize the domain when working in it. He also highlighted the role of cases in his list of problem criteria. / Concepts. requiring a solver to frame or recharacterize it. notably Simon. Lynch et al. they all serve as functional tools to frame the discussion at hand. This recharacterization is subject to debate.258 C. and procedures for the domain and providing a means to validate problem solutions or cases. relations. Subsequently Shin. such as designing an experiment to verify claims made by another researcher or selecting the best site for a new telescope. . The two are intertwined in his subsequent discussion so we treat them collectively. Shin and his coauthors focused on the pedagogical characteristics of ill-defined problems. and the characterization they choose. In articulating their definition. Jonassen (1997) drew a distinction between ill-structured problems for which multiple solutions exist and ill-defined problems where the definition of the problem or problem components are unclear. relationships.  Ill-defined domains lack a single strong domain theory uniquely specifying the essential concepts.or under-specified. We take Simon’s view that a complete space. Jonassen. PROPOSED DEFINITIONS OF ILL-DEFINEDNESS As the foregoing discussion illustrates.
reinterpreting essential rules and concepts according to the present goal. / Concepts. lack widely accepted domain theories identifying relevant concepts and functional relations. 1973. (2009). identifying clear solution criteria. In our view. 10. This is particularly true of policy debates and other “wicked problems” (Rittel & Webber. 8. and the need for recharacterization. These characteristics have been discussed by other authors on par with absent information and the need for recharacterization. 2006) where solvers must recharacterize a problem in order to transform a mandate to “promote . often distinct. where officers had executed an unwarranted search of a mobile home the advocates choose whether to describe it as a ‘home’ – thus emphasizing the privacy implications – or to describe it as a ‘vehicle’ – thus emphasizing mobility and the risk of flight. 3. It may include redefining aspects of the problem to relate it to relevant domain rules and concepts. involve the need to reason analogically with cases and examples.. In a search and seizure case. for example. open-textured. and require solvers to justify their solutions through argument. involve disagreements among domain experts regarding the adequacy of the solutions. and seek to describe the facts of their case accordingly. The importance of tractability was discussed by both Simon (1973) and Voss (2006). Each characterization aligns the case with different legal principles and precedents. have prior cases that are facially inconsistent. and analogizing or distinguishing the current problem from prior cases. rules. lack clear criteria by which solutions are judged. Hill Jr. and carries with it different implications for the warrant requirement. expend a great deal of effort seeking to clarify and refine their actual goals so as to move from the need to achieve “a lasting peace” to the specific positioning of military forces. and Goals 259 For ill-defined problems this framing/recharacterization is an essential part of the problem-solving process. Diplomats and mediators. cannot be readily partitioned into independent subproblems. or facially inconsistent cases. are not considered to be “solved” when one solution is presented but may be readdressed by multiple. solutions. 7. In addition to aligning the problem with relevant knowledge. 5. This kind of reasoning is common in law where an advocate will choose precedents (prior cases) and legal rules that are advantageous for their client. Lynch et al. arise out of the presence of open-textured. and relations. for example. lack formal or well-accepted methods to verify solutions. there is a causal relationship among them. recharacterization may also make the problem more tractable by moving from impractical standards such as “the optimal chess move” to “a strategic move. 4. A formal algebraic theory. Conklin. a single strong and complete theory cannot be readily defined. 9. Absent such formality in the problem or domain. 6. Features such as the lack of general domain theories. have a large or complex solution space that prohibits one from enumerating all possible characterizations or solutions. for example. involve open-textured concepts and competing domain principles that are subject to debate.C. Forbell et al. requires clearly defined concepts and terms that may be automatically applied to the facts of a given problem and to the background information. Structures. 2. 11. expert disagreement. and intractable concepts. Lane. unspecified and intractable criteria and the consequential need for recharacterization. Due to the presence of unspecified.” Or it may focus the solver on a bounded space of relevant concepts. The problems of negotiation are discussed in detail by Kim. ill-defined problems and domains typically: 1. Durlach.
ill-defined domains lack a centrally organizing domain theory describing the relationship among concepts and providing a means to validate cases. They are not. and to compare. Lynch et al. It is not the case that all ill-defined problems exhibit every one of these characteristics. problems in ill-defined domains tend to be ill-defined. rather than logically by formal rules stating what isn’t Modern and is Punk.. Architecture. Ill-defined domains are often defined in terms of prior cases just as movements or styles of art like Dadaism. has been systematized by theorists such as Alexander (1977.” As one moves along this continuum. Structures. Architects and other artists. Teaching students to work in these domains means teaching them to recognize the varying roles that theories and cases play. We do not view the distinction between well-defined and ill-defined domains as a binary one but as poles on a weak continuum. analogize. As we noted above. “Missionaries and Cannibals”). It is this variability and characterization choice that prompts expert disagreement. by contrast. As a consequence. These conventions are often employed by practitioners to characterize their problems and justify their solutions or to scaffold novice students. rather that the theories are not well-accepted. but exhibit illdefinedness at the “fringes” where the theory begins to break down and otherwise well-defined concepts fail.260 C. and critique alternatives while defining their own. When making an argument in an ill-defined domain. The definitions also frame the problem for future research: How can we design educational technologies that support flexible recharacterization of ill-defined problems and domains? . The proposed definitions are challenged with open questions or selected counterexamples that prompt redefinitions of this seemingly basic concept. it is often necessary to explicitly analogize or distinguish the present work to or from prior cases and competing theories. We believe that these definitions are amenable to work in AI and education. and Punk are defined extensionally by the art or artists within them (e. Modernism. sometimes well after the fact. and to defend the choices made. Nevertheless. are not formally specified. treated as complete and final even by their adherents. Many domains have a well-defined core characterized by a single. They also focus on recharacterization. the role that theories and cases play in structuring the domain and evaluating solutions changes. or are incomplete. strong theory. since debating the relevance of and relationships among concepts means recharacterizing the problems that involve them. They focus attention on the core features that make problems and domains ill-defined. or describing some feature of it. Doctors and diplomats argue about the application of open-textured concepts or past cases to the problem at hand and justify most if not all of their decisions. are rarely asked to justify or even to articulate their design decisions. to select among them. Lakatos (1976) provides an illustration of this process in the domain of geometry. and a pedagogically important aspect of ill-defined problems and domains. When working in such domains it is frequently necessary to enumerate competing concepts and theories as well as conflicting precedents.. however. This is not to say that such domains are free of theories. 1979) who delineated both a functional language for describing “spaces” and rules for its application. At one end lie strictly well-defined problems such as the puzzle problems described by Jonassen (1997) (e. all ill-defined problems share the core need to recharacterize the problem in order to solve it. the central skill for ill-defined problem solving.g. / Concepts.g. for example. In his dialogue students discuss candidate definitions for the concept of a polyhedron. and Goals the general welfare” into programs for highway construction and public education. Man Ray and NOFX). while on the other extreme lie artistic problems such as the need to “express fear in your work.
nor will it change the outcome of the problem. make a crucial difference. No recharacterization of the problem will change the answer nor will it be subject to reasonable debate. the problem includes no open-textured or unspecified concepts. 1 In algebraic terms. Thus. 2001). to novice problem solvers.261 C. Both can involve recharacterization and. all valid representations are equivalent unless one changes the criterion to seek the best or most pedagogically effective representation. Thus. or the same? The first is a standard problem in introductory physics. is it possible to tile the board with dominoes each one covering two adjacent tiles? Fraction Given a proper fraction YX . Neither characterization is. If one considers all possible board sizes. Lynch et al. however is categorically different from the problems of architecture or ethics where no amount of expertise can provide the indisputable answer. underspecified. and Goals Borderline Cases Ill-defined and well-defined problems are often facially similar. It may be solved using kinematics. driven by the presence of open-textured. What is the net force acting on the car? Checkerboard Given a checkerboard with two opposing corners removed. both can appear intractable or underspecified. Similarly. subject to reasonable debate.1 For a student who is unfamiliar with logic and algebra. However. smaller. the solution is:   X (X + 1) o n ⇒ ((X(Y + 1)) o n (Y (X + 1))) ⇒ (XY + X) o n (Y X +Y ) ⇒ X o nY Y (Y + 1)  Thus: (X < Y ) ⇒ X (X + 1) < Y (Y + 1)   & (X = Y ) ⇒ X (X + 1) = Y (Y + 1)   & (X > Y ) ⇒ X (X + 1) > Y (Y + 1) (1)  (2) . or a combination of the two. although the problem necessitates recharacterization it is not ill-defined. however. This characterization is not. Thus the problem is tractable. Problem solvers must recharacterize the problem in terms of a particular set of equations as part of their solution process. This is also the case for the fraction problem. If. Both sets of equations fit into the same theory of classical mechanics. and assumptions regarding its solution. The Checkerboard problem has a lengthy history in AI. in making the distinction between ill-defined and well-defined problems the framing of the problem. if applied correctly. subject to ongoing debate (Buchanan. in the context of physics. This. Structures. The common solution recharacterizes the problem in terms of paired tiles and color matching. the Work-Energy Theorem. however. while there exist a number of viable representations for the fraction problem ranging from pieces of pie to glasses of water. where o n designates the unknown relation. Consider the following problems: Car A 1000kg car rolls down a 30 degree hill. the problem may appear ill-defined as they may not know where to begin. then the space of possible tilings grows large but is still regular. then it becomes ill-defined as creativity is an open-textured concept. / Concepts. or intractable concepts. both are equivalent and. if you add 1 to both the numerator and denominator. will the resulting fraction be larger. one seeks the least-creative solution as in McCarthy (1999). The problem itself is well-defined with a clear logical solution. will produce the same result.
giving them an opportunity to practice these skills in an authentic way. Finally. Voss. Simon. and Goals ILL-DEFINEDNESS. Voss. apply them. Novices. / Concepts. Voss. and Penner (1983) tested the same body of novices both before and after a course on Soviet policy and noted little change in their behavior. meaningful. Greene. Pople (1982) identified a similar issue of early commitment in his work on medical diagnosis. Post. highlighting the importance of domain knowledge in the problem-solving process. and thus motivating to learners.” that is. Structures. for example. policy. This need for guidance was strongly echoed by Shin.262 C. He argued for adopting educational strategies designed to support early exploration of diagnoses. while problem-solving strategies were not a significant predictor of success on ill-defined problems. If. and Penner (1983). and McGee (2003). If. In their analyses Reitman. Shin. AI AND EDUCATION Pedagogical Roles of Ill-defined Problems As Reitman (1964) noted many. by contrast. Jonassen. the task was seen as a political problem then the solver would need to address issues like land reform. a point that was echoed by Jonassen (1997) who described them as “the kinds of problems that are typically encountered in everyday practice. if not most. Lynch et al. of the problems addressed by human problem solvers are illdefined. metacognitive knowledge such as monitoring skills and ability to consider alternate goal formulations was predictive. it was primarily seen as a technical issue then they would address it through education and investment. Jonassen. the job of a practitioner is to deal with this ambiguity. however. and design are ill-defined and are characterized by ill-defined problems. Shin. music. in Shin. in his analysis of the Soviet Agriculture problem noted that the expert problem solvers spent a great deal of time analyzing their characterizations of the problem and considering alternate characterizations. . This group behaved very much like novices. and proceeded to address them separately with little consideration for the interaction among factors or the consequences of their decisions. The pedagogical role of ill-defined problems is to train students in these processes. individuals with expert-level training in scientific reasoning but with no policy experience. Jonassen (1997) argued that ill-defined problems are more interesting. identify the open-textured concepts. In addition to experts in policy formation and novice students. and McGee (2003) who noted that. including metacognitive skills such as goal monitoring and reflection. and in some cases exploit the ambiguity to develop creative solutions. and McGee (2003) further argued that solvers of ill-defined problems employ different skills. than do solvers of well-defined problems. focused exclusively on “low level” factors such as the lack of arable land or the need for more tractors. they further argued that solving ill-defined problems requires domain knowledge that is structured around experiences rather than fundamental principles. Jonassen and McGee all highlight the need to explore alternate problem characterizations.” Some domains such as law. suggesting that the skills required to solve ill-defined problems were not being taught in classrooms. Post. In these domains. as these problems rely more on case-based reasoning than formal derivations. Jonassen (1997) also argued that the domain dependent nature of ill-defined problems compels problem solvers to treat them as “realistic situations” where the solution requires access to a large amount of relevant and well-organized domain knowledge. Jonassen. Voss also examined the behavior of “nonexpert-experts. Greene.
research in the design and use of tutoring systems for ill-defined domains is ongoing. and then to assess and respond to the consequences of their decisions. ICCAT. in the course of negotiation. Jonassen (1997) went further. Lane. 2007) or in leveraging peer guidance (Cho & Schunn. We also described a number of systems that employed one or more of these strategies to provide useful instruction. Their system. a basic recharacterization task. Mitrovic & Weerasinghe.. this is not a complete solution. Some of these systems were constructed around “classical” well-defined models but employed them to facilitate more open ended analysis (e.C. Ogan. and the system guides them in a clear analysis process consisting of noticing key features. help them to frame and recharacterize problems. CATO (Aleven. Others used constraints to express an open but guided domain for exploration (Holland. Hill Jr. 1997). Instead. Durlach. As noted above. support students in the process of recognizing underspecified or open-textured concepts. and the domain lacks strong rules for case comparison. teach them to explore their ramifications. Implementations Developers of tutoring systems or other instructional materials may explore a number of avenues in helping students to address ill-defined problems. weak theory scaffolding. & Weiner. and Goals 263 This brings us back to Minsky’s frontier view of ill-defined problems. & Lynch. receiving feedback.g. thus making the . 2000. Aleven. takes a process-support approach to tutoring. Toth. and Jones developed a tutoring system for intercultural competence (Ogan. collaboration. By contrast. (2009) chose a more model-driven approach to the task of tutoring cross-cultural negotiation. Cultural learning depends heavily on students’ interpretations both of events and language. & Jones. Kim. and then reflecting upon their choices. As the papers in this volume demonstrate. Tutoring systems can be and have been constructed that support these kinds of analyses. 2003)). particularly in scaffolding lower-performing students. Pople (1982) endorsed the development of systems that support the exploration of alternate problem hypotheses to prevent early student commitment. they note that negotiation practice involves characterizing more abstract interests (i. Ashley. The goal of this instruction is to help students in learning to analyze and explain cultural differences. Lynch et al. In a prior discussion (Lynch.. making analyses. we identified four human tutoring strategies that were ideal for incorporation into intelligent tutoring systems: case studies. what one really wants) and then. Students need to both reify their personal goals and to recharacterize the debate in terms of them. 2009). and expert review. assessing whether a given proposal satisfies those desires. articulating a problem-solving process and a series of pedagogical recommendations including the development of case bases and supporting the construction of knowledge bases that reflect real-world knowledge. 2007). 2006). Restricting students to the drained and tilled land will not help them to traverse the swamp. Aleven. researchers in AI and education should develop systems that focus on the ambiguity. Aleven. Forbell et al. or subsets of them.. Structures. 2009) or focused on the support of open discovery in the target domain (Suthers. While such an approach has a place. so as to provide well-defined tutoring environments for instruction. / Concepts.e. & Pinkwart. Still others took a step back from modeling the solutions to a given problem and instead supported the analysis of prior examples (Pinkwart. Students are given an authentic problem in cultural translation. Ashley. Aleven. Under this view researchers in AI and education should focus on defining and structuring ill-defined domains. In their analysis of the problem space. in this case a film clip from the target culture.
They describe extensions to the COMET system that allow it to use preexisting expert solutions and a medical ontology to support novel student solutions. Students using the system enter diagnostic hypotheses using a graphical markup language. explicitly recharacterizing the problem in functional medical terms. (1977). The system employs an ontology and stored expert solutions to recognize when the students employ more general. and Goals problems ill-defined. 13–28. Ill-definedness is an open-textured concept. Berman. In our view these are the root features from which other salient but optional aspects of ill-definedness spring. / Concepts. & Schunn. REFERENCES Aleven. Allen (Eds. New York: Oxford University Press. and Kim et al. 2009). Walter & L. CONCLUSIONS In this article we have examined prior definitions of ill-defined problems and ill-defined domains with the goal of framing discussion of ill-defined problems in an AI and education context. The definitions that we presented here focus on the presence of un. M. E. Alexander. (2003). 183–214). such as a lack of expert agreement and the need to justify solutions. Haddaway and Suebnukarn chose a more explicit focus on the role of recharacterization (Kazi. D. New York.. Kazi. In C. . 150. (pp. Using background knowledge in case-based legal reasoning: A computational model and an intelligent learning environment. 48(3). (1979). Students using the system engage in a simulated negotiation in a game-like setting based upon real-world situations. Their task domain is problembased learning in medicine and the need to support creative student solutions to diagnosis problems. (2001). Lynch et al. & Suebnukarn. open-textured. K. & Hafner. and many researchers have approached it with diverse goals. Unlike Ogan et al. and on the role of recharacterization in addressing them. or intractable concepts in ill-defined problems and domains. Computers and Education. C. V. Saint Paul. New York. Buchanan. Scaffolded writing and rewriting in the discipline: A web-based reciprocal peer review system. C. They receive feedback from the model both as explicit guidance and simulated responses from the in-game characters. Cho. AI Magazine. 183–237. C. Their system. is constructed around a strong domain model that governs system behavior. A Pattern Language. Alexander. 22(3). The Timeless Way of Building. Structures. Creativity at the metalevel: AAAI-2000 presidential address. Obstacles to the development of logic-based models of legal reasoning. C. This allows the students to explore a range of viable diagnoses while still receiving system guidance. Haddawy. G. 409–426. Here the decision to construct an explicit though partially-hidden model enables the system to directly scaffold novices while still keeping a range of open behaviors. B. (2007). New York: Oxford University Press. or more specific variations of the experts’ reasoning. Minnesota: West Publishing Co. Artificial Intelligence.264 C.or underspecified. We then presented our own definitions for ill-defined problems and ill-defined domains with the goal of setting a workable stage for future work.) Computing Power and Legal Reasoning. BiLAT. (1985). The resulting definitions share many of the same essential concepts but focus on aspects of ill-definedness relevant to the authors’ underlying purposes. Instructing students in this ‘real-world’ process of recharacterization is a central pedagogical approach for ill-defined problems that researchers in this field have begun to address.
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