Problem Posing-Adding a Creative Increment to Technological Problem Solving
University of Minnesota
University of British Columbia
Anne Marie Hill
Perhaps the most privileged of the conceptions of the nature of technology is that it emanates from creative human response to existential problems. Accordingly, to find manifestations oftechnology, technology educators must look to the store of solution strategies that humans have devised over time to cope with life challenges. To teach technology in the classroom, the task, then, is to capture, represent, and fashion this motif of problem and solution into a pedagogy for the subject.
The group of 25 American curriculum leaders who met in the late 1980s to "determine the conceptual framework for technology education" coined this dynamic of problem and problem-resolution "the technological method," a model of which they presented to the profession (Savage & Sterry, 1990, p.6). The model took human needs and wants as its point of departure. It included variables such as technological processes, resources, and technological knowledge. A typology oftechnological problems and solutions was also setforth. Because of the consensus nature of the formulations of the group of 25 and the fact that their work had the imprimatur of the International Technology Education Association (ITEA), the notion that the technological method constitutes the logical way to frame the subject took on great credence.
Two years after the appearance of Savage and Sterry's model, Pucel (1992) offered his own version of "the technological method" at a Mississippi Valley conference of industrial education leaders. He deemed the method to be a component of technological literacy. According to Pucel, the technological method was comprised of seven generic steps that were applicable in any realm of technology. The steps, modestly paraphrased here, were:
- identify an unmet human need,
- clarify the specific technical problem,
- identify relevant existing technical methods and knowledge,
- invent a probable solution,
- determine the social and economic feasibility of the solution,
- modify the solution, and
- implement the solution (Pucel, p. 12).
Pucel sought to illustrate that there was significant separation between his version and others in the technology education literature. He contended that Savage and Sterry's model was a generic problem-solving device. In a subsequent related publication, he explained that the "distinguishing characteristics" of the version he was proposing included it being premised upon the process of invention, and upon the view that technology is created to enhance the quality of human existence (Pucel, 1995, p. 39).
Despite his attempt at separation from Savage and Sterry's model, and his critique that general problem-solving methods are not applicable in the realm of technology, Pucel fell victim of his own critique by himself offering "a set of generic steps which can be applied to any area of technology" (Pucel, 1992, p. 12). His seven steps had the familiar look of a problem-solving formula, primarily because the original model that had been its inspiration (see Bailey, 1978) was itself a problem-solving model. Pucel had condensed four steps of Bailey's six-step model into a single step which he called "invent a probable solution." Bailey's four steps were: (a) specify satisfactory solution characteristics, (b) develop a solution plan, (c) optimize the plan, and (d) produce the solution. Were these four steps to be substituted for his invention step, the result would be an expanded ten-step problem-solving model that would be substantially redundant not just with Bailey's model, but also with Savage and Sterry's.
What can be taken away after examining Savage and Sterry's consensus model, and Pucel's challenge to it, is that representation of the logic of creating technology has become an arena of contestation and theorizing within the field (see also Waetjen, 1989). The contest is not about whether the process or method of technology is akin to problem solving. That may well be a settled issue. But how problem solving should materialize in the technology curriculum and in instruction is unsettled.
The tensions regarding the place of problem solving in our field cannot be divorced from the larger tension surrounding the nature of the technology curriculum. After decades of quest among American adherents for status of technology as a discipline, during which identification and codification of the content of the field has been paramount, technology educators are at a juncture where content is yielding to process as the primary curricular preoccupation. One reason might be that generic processes such as critical thinking, communicating, and problem-solving have become marks of literacy that have appeal both in school and in the workplace (e.g., Carnevale, Gainer, & Meltzer, 1988; Secretary's Commission on Achieving Necessary Skills, 1991). Another related reason might be the internationalization of technology as a subject. For example, British curricular efforts have never gone the disciplinary route, concentrating instead upon design (see Department of Education, 1995; see also Lewis, 1996, for British and American comparisons). The technological method proposed by Savage and Sterry could easily frame the most recent British technology curriculum plans.
But it is questionable whether an abstracted and over-rationalized model of method in technological design is productive for either the student or the technologist. Critique of such a model can come from at least three different directions. First, there is the question of the ontological and epistemological status of a general method of technological problem solving. Second, there is the cultural and gender bias
that is inherent in a model derived from a western corpus of male technologists, and which reflects an overly individualized view of practice. And third, the utilityofgeneralmethods of cognition can be challenged in light of the recent intersection of learning theory and cultural psychology.
While indebted to the work of Dewey in the 1910s and Polya in the 1950s, the notion of methodologically-directed problem solving has been challenged empirically and theoretically. Methods and the choice oftheir adoption are context bound and situation specific. The technological method and design process frame and limit not only student work, but also the way technology educators think about design and problems in teacher education (Custer, 1995; McCormick, Murphy, & Hennessy, 1994; Petrina, 1994).
Nevertheless, problem solving has become the main theme of a genre that includes processes such as designing, experimenting, inventing, and trouble shooting. While these processes have common features, within and between them can be found possibilities for the routine at one end of the spectrum and for the truly creative at the other. But the challenges and implications here for the field of technology education could be appreciated and exploited only if the discourse on problem solving and the technological method changes tenor, by shifting focus from curriculum to instruction, or theoretically from method to situation. This article is intended to begin to shift this discourse.
Our purpose is to add an increment to the literature on problem solving within technology education by focussing attention upon problem posing, or problem finding. This is a neglected aspect of our field within which inheres boundless opportunity for fostering technology-inspired creativity in children. How technologists come to problems, and how they reformulate them in their quest for solution is as important for children to understand as how they ultimately solve these problems. A first implication here for technology teaching is that students must have opportunity to propose problems in the classroom. Their roles as active participants in the enterprise of technology should be acknowledged. They ought to be encouraged to draw upon their own day to day experiences to find problems that they believe require solution. In keeping with a theoretical perspective, a basic premise of this paper is that problem finding opens up new realms of meaning as students co-construct technological knowledge (e.g., Driver et al., 1994; Hill, 1994, 1996, 1997; Hill & Smith, in press).
In what follows we address: (a) theoretical issues' constructivist and socio-cultural frameworks, (b) the idea of problem posing, (c) lessons from mathematics (d) problem-solving in technology education, and (e) problem posing' implications for technology education. The approach is akin to a meta-synthesis (e.g., Noblitt & Hare, 1988) in that discourses outside of the field of technology education are drawn upon for purposes of comparison.
Theoretical Issues: Constructivist and Socio-cultural Frameworks
The recent emphasis on process in technology education lacks theoretical grounding. In the United States, methodological models drawn from stylized notions of cognition, invention and scientific investigation have directed action. As such a model, the technological method may have had political utility in redirecting attention from traditional practice, but the method is constraining. And while it may be argued that classrooms are special environments where control is necessary, the technological and design method should not be legitimized on this basis. Control may neutralize the creativity that most teachers intend to nurture.
It is sobering that "the technological method" or "design process" appears to be ineffective as pedagogy. Classroom studies suggest that students find the methods cumbersome to utilize, and if held accountable, merely retrofit methods and their stages to their actual experience (Chidgey, 1994; Hennessey & McCormick, 1994; Jeffery, 1990a, 1990b; Johnson, 1997; Jones, 1997; McCormick, 1993, 1997; McCormick, Hennessey & Murphy, 1994; McCormick, Murphy, Hennessey, & Davidson, 1996; Rowell, Guilbert, & Gustafson, 1997). The research suggests that the use of methods has become a "ritual," having more to do with classroom culture than the actual solving of a problem (McCormick, Murphy, Hennessey, & Davidson, 1996, p. 10). The findings are consistent with studies of designers, engineers, and scientists (Buchanan, 1992; Cross, Naughton, & Walker, 1986 Latour, 198i; McGee, 1995; Pea, 1993), and in studies of the way problems are solved in everyday life (Lave & Wenger, 1991; Scribner 1986). As Millar and Driver (1987) have suggested, process advocates' portrayals of activity and method in science and technology are "naive and open to criticism" (p. 57). Claims that problem-solving, among other process or "cognitive" skills, is general and transferable are suspect and exaggerated; there is little evidence to suggest that solving one type of problem at work informs problems of the home or school (Howe, 1996; McCormick, 1993; McCormick 1997).
"Process" is made problematic when cast in context of constructivism, and especially troublesome within frameworks of situated cognition and science and technology studies (STS). Here method becomes just another tool among a landscape of cultural artifacts to be used, ignored, or reconditioned in the everyday problems of life and work.
Within constructivism are two core premises: (a) that students actively construct meaning from what they learn, in ways that are consonant with and lend coherence to their experience, and (b) that cognition is functional and adaptive, and serves the experiential world rather than any discovery of an ontological reality. The first premise should not be new to technology educators, but the second challenges orthodox views. The meanings students create as a result of classroom experiences are moderated by complex communications organized within social roles. Knowledge is an adaptation and a function of personal history. Thus, what students come to know will likely be different from what teachers intended (see Osborne, 1996, Phillips, 1995; Wheatley, 1991).
Examining constructivism, Von Glasersfeld (1995), a major proponent, asserts that the theory must be taken in context. One must speak of the "viability" of knowledge, since knowledge is "adaptive." Thus, "there will always be more than one way of solving a problem or achieving a goal" (p. 8). He professes that for the constructivist, learning requires self-regulation and the building of conceptual structures through reflection and abstraction. Problems are not solved by the retrieval of "right" answers, formulas, or methods. "To solve a problem intelligently, one must first see it as one's problem. That is, one must see it as an obstacle that obstructs one's progress toward a goal" (p. 14). Students must arrive at their own problem solving methods and strategies; they cannot rely on a communal strategy.
Advocating a constructivist perspective within mathematics, Wheatley (1991) explained that "(L)earning is accomplished by constructing and elaborating schemes based on experiences" (p. 12). He advocated "problem-centered" learning, where solutions are indeterminate, noting:
Favorable conditions for learning exist when a person is faced with a task for which no known procedure is available. That is, when the learner finds herself in a problematic situation; what is a problem for a person may not be for another. (p. 12)
To understand students' thinking, he suggested that teachers must learn to look at the world through their eyes. Attention shifts from an abstracted and processed world to the students' mind.
Concurring, Simon (1995) asserted that students' thinking and prior understandings must be taken seriously in the design and implementation of instruction. The teacher's knowledge about teaching and the thinking of her/his students evolve simultaneously with changes in the students' knowledge (p. 141). Among the most important insights from constructivism is the issue of paying attention to students' cognition and their interaction with each other. Yet, in constructivism, the social has been under-theorized.
Situated cognition and its variant, learning theories in cultural psychology, have placed constructivists on the defensive. Like constructivism, situated learning is active, and does not serve an ontological reality. But unlike constructivism, it is inherently social rather than individualistic, intricately bound up with language, and socio-historically conditioned. Cognition is distributed across time, environment and community. Here, the unit of analysis is culturally organized human activity (Brown, Collins, & Duguid, 1989; Cole, 1990; Cole & Engestrom, 1993; Howe, 1996; Lave, 1990; Lave & Wenger, 1991; Scribner, 1985; Shweder, 1995).
Pedagogical implications of situated cognition include an emphasis on the social and cultural conditions of learning, and on language. Howe (1996) suggests that students' problems and strategies for their solution should be a starting point for problem-based pedagogy. Problem solving begins with the local, is collaborative, and is enabled by language (occasioned through social interaction and mediated through cultural artifacts). Language is pivotal in knowledge construction. Problems are not solved by individuals, necessarily, but within communities in which students are participants.
For the situationist, the question is what kinds of social environments provide the best context for learning (Greeno, 1997; Lave & Wenger, 1991). Close attention would be paid to the way problems are chosen and structured, and the language used in problem construction or solution.
Where situated cognition offers a theory of learning premised in social practice, enactivism goes beyond, offering a dynamic theory of cultural practice where cognition is ecological and where the collective and the individual change through the profess (Davis & Sumara 1997, p. 115). Collective knowledge and individual understandings co-emerge and interact. Cognition is distributed across individuals and things, is situated in communities, and is occasioned through their interactions. Pedagogy in enactivism recognizes the importance of dialogue. Teachers, as co-participants, acknowledge the share that students have in problems that may be addressed and are responsive to the changes occurring through interaction (Davis & Sumara, pp. 112-116).
In situated cognition and enactivism are theories of the seamless interconnections between psyche and culture. These theories begin to address a world of "thinking through others" (Shweder 1995, p. 77) and thinking through things. They allow for a complex understanding of learning, where things change, and cognition is neither fully personal nor fully social, but situated in activity of individuals and their natural and cultural environment.
We believe that the theoretical frame for problem-solving that we have suggested here has been illustrated in action in exemplary fashion in a study reported by Roth (1995), in which Grade 4 students pursuing an "engineering for children" curriculum in science had the problem of constructing a tower. The curriculum emphasized open-inquiry learning environments, solving problems in ill-defined contexts, and cooperative learning. The children consulted with engineers who visited their classroom. They visited a museum to see an exhibition of bridges, and they saw films on bridges. Students worked on their structures in small groups. Three students were videotaped as they worked on their structure, and their dialogue was analyzed. The analysis showed that the students repeatedly re-framed problems as they negotiated and sought compromise on their solution. "As the conversation evolved, problems were framed and disappeared, solutions were proposed and rejected, and courses of action emerged contingent upon the current state of the construction . . ." (p. 371). The author asserted that "such flexibility in framing and reframing situations has been recognised as an important element in the creativity of engineers" [sic] (p. 371). The students' conversations revealed that "problems did not exist a priori but were constructed in a dialectic relationship between individuals and their settings. A situation that gives rise to a problem to some is unproblematic to others" (p. 371). Consistent with tenets of situated cognition, enactivism, and constructivism, as we have set forth above, the author came to the view that "objects, events, and teacher instructions are unavoidably subject to interpretative flexibility which allowed the students to frame their problems in ways different from those conceived by the teacher" (p. 377). The implication for teachers was that rather than constrain the environments in which children frame problems, they should provide openended activities that are rich in creative possibility.
There are at least three significant implications for technology education that can be drawn from the theoretical framework we have sketched here. First, formulaic problem solving might not yield the creativity teachers seek to foster. Second, students' and teachers' feelings, prior experiences, and language about problems matter. Third, problems ought to be cast under rich social conditions, with students having major roles both in their posing and in their solving.
The Idea of Problem Posing
Central to the idea of problem posing is the conception of students as interactive, social learners involved in the project of knowledge creation (Friere, 1970; Gregson, 1994; Wallerstein, 1987). Freire contrasted problem-posing education with teacher-dominated education, which he deemed "banking" education. He wrote:
Whereas banking education anesthetizes and inhibits creative power, problem-posing education involves a constant unveiling of reality . . .. Students as they are increasingly posed with problems relating to themselves in the world and with the world, will feel increasingly challenged and obliged to respond to that challenge. (p. 68)
Continuing, Friere asserted that "Problem-posing education bases itself on creativity and stimulates true reflection upon reality" (p. 71). It can be seen here that problem posing speaks fundamentally of a philosophy' a disposition to teaching, rather than a technology of teaching. There are no steps to be followed, necessarily. What the teacher must do is completely re-think the assumptions that shape the respective social roles of student and teacher. Students are encouraged away from the sidelines into the game much earlier than is traditional. Their prior knowledge, their language, interests and thoughts' their existence' become respected and acknowledged as valid bases ofthe content of teaching. What the teacher does thereby is create a climate of freedom and risk-taking in the classroom' a climate that engenders creativity. For example, Appleton (1995) reports that the degree of success experienced by students faced with a discrepant event problem in science was based upon the social setting in the classroom and the teaching method employed. The information-seeking behavior of students depended upon information sources made accessible by the teacher.
Finding or posing problems is a quintessentially creative endeavor (see especially Dillon, 1982). Whether the found problem is the presence of a hole in the ozone, or that people who smoke are prone to cancer, those keen enough to call our attention to them distinguish themselves by their astuteness. They help set community agendas that lead to discoveries and inventions that help make the world better.
We may shift this discussion briefly to the dissertation process that culminates graduate study. Many graduate students find the most difficult part of the process to be finding a problem. And indeed, many abandon their studies upon reaching this stage. Students find that while they are prepared with the tools and techniques of research, and while they know the steps and structure of the dissertation, problems do not come easily. Those who venture into the dissertation stage find that much of the delight engendered by their study has to do with the quality of the problem they chose to address. Problem posing lies at the heart of the dissertation process.
Problem-posing is not limited to finding completely new problems. It includes reformulating given or existing ones. Neither is posing discontinuous with problem solving. Duncker (1945) offered the insight that each stage of the solution of a problem constitutes the problem's reformulation. Thus the mediating phases provide opportunity for problem-posing along the way. These re-formulations are products of creative thought. Finding and posing the problem is the critical outer layer of the problem solving process. Once that layer is pealed away, it reveals further layers within which new problems reside' problems that must be addressed as steps in the finding of a grand solution. For example, once it was determined that the Hubble telescope was out of focus, a second layer of problems emerged, having to do with how to re-focus the telescope. That solved, the problem became how to install the new modification. There were opportunities for posing problems all along the way. A second example can be taken from the field of medicine in the realm of AIDS research. The outer layer of this research was finding the cause of the disease. Finding the cure will depend upon the ability of researchers to propose lines of inquiry that add successive increments of success and that converge upon an eventual grand solution.
Posing can occur prior to, during, or after the act of problem solving. Getzels and Csikszentmihalyi (1976) observed artists under experimental conditions, finding that those who kept the problem open longer produced more creative solutions. Artistic success was strikingly related to delayed closure. Keeping the problem open allowed for experimenting.
It has been posited above that problem posing is a high mark of creativity. Henle (1962) offered the view that "in particular cases the important creative task may be precisely to pose a question rather than to answer one" (p. 44). The creative task may be to revise the problem that confronts us, to see it in a new way or in a broader context. Newell, Shaw and Simon (1962) have written that people who have made sign)ficant creative contributions to the advance of science and technology have tended to possess great problem solving powers. These authors viewed creative activity as "a special class of problem-solving activity characterized by novelty, unconventionality, persistence, and difficulty in problem formulation (emphasis added)" (p. 66).
In like vein, Csikszentmihalyi (1994) wrote that:
Many creative individuals have pointed out in their work that the formulation of a problem is more important than its solution and that real advances in science and in art tend to come when new questions are asked or old problems are viewed from a new angle . . . yet when measuring thinking processes, psychologists usually rely on problem solution, rather than problem formulation, as an index of creativity. . . They thus fail to deal with one of the most interesting characteristics of the creative process' namely, the ability to define the nature of the problem. (p. 138)
We believe that this neglect of problem finding is a deficiency that is observable in the discourse on problem solving within technology education. Recent work in this area reveals the potential (e.g., Hill, 1996; 1998). Technological problem solving was situated in real-life, community contexts. These studies have shown that when technological problem solving was taught through design and was open-ended, thereby allowing for problem posing and exploration, student creativity was fostered, and this enriched student learning. As one Grade 11 student said, "It's natural creativity and you get to put your own expression into what you do as well as learn other things that interest you" (Hill, 1998, p. 4).
It is important to distinguish between ordinary problems and novel problems, or, between well-structured and ill-structured problems (Buchanan, 1992). Problem-posing opportunities abound where the situation is novel. In their study cited earlier, Getzels and Csikszentmihalyi (1976) distinguished between "presented" problem situations, where problems have known formulation or an algorithmic method of solution, and "discovered" problem situations, where there are no pre-set solutions, and no predetermined steps to satisfy the requirements of the solution. It is discovered problem situations that best tap creativity, these authors argue. Here the solver, the student, is as likely to pose the problem as the teacher. Thus, on the one hand the problem could be "why is this engine not starting?" where the reason might be known to both student and teacher. Compare this with "how can we make it safer for a wheel-chair bound student to work on this machine?"
Getzels and Csikszentmihalyi (1976) contended that "discovered problems are common not only in fine art, but in all fields where creativity is at issue . . ." (p. 84). In all fields, those who employ an open mode in their consideration of a problem are likely to arrive at more original results.
What this implies is that it might be equally as profitable for students to come to class with problems requiring solution, as it is for the teacher to bring his/her own. Hill and Smith (1996; in press) have found this in their research, where teachers and students found community needs for class technology projects. Students were encouraged to come to class with ideas based on community needs that they themselves had identified. They could select real-life problems for their technology project. This enhanced student motivation, responsibility, and learning.
How can problem posing be actualized? Using the domain of mathematics as context, Brown and Walter (1990) assert that the first step is accepting the givens of the problem, and being able to break free from the clutches of our prior experiences to be able to ask insightful questions about it. An example would be the familiar eggdrop problem. It is possible to view the central question here as "What type of packaging will best cushion the force of gravity when the egg finally hits the ground?" But another line of question could be "How can the effect of gravity be minimized?" One question leads to a packaging quest, the other to a braking quest.
Brown and Walter also suggest that an important step in the problem posing process is to ask "what if not?" That is, "What if this part were to be made not of wood but of plastic?" Or, "What if this were not a round hole but a square one?" These authors agree that posing and solving are connected. The solver must ask "Why did this work? Is this a fluke, or was there some logic at work? Why did my egg not break in the egg drop? Why did my vehicle get so much mileage?" The solution to technological problems is not premised upon magic. The student who solved the problem of the longest bridge must know why her solution worked, or the exercise would have been meaningless.
To recap here, while problem solving is an important facet of teaching across the curriculum, all problem solving processes do not belong in a discourse on creativity, since many problems have known solutions. If the instructor secretly removes a spark plug, and the student figures out that it is a missing plug that prevents the motor from starting, that is problem solving of a kind, but there is little creativity involved. The student merely follows a checklist or an algorithmic fault-finding procedure. The implication for the field of technology education is that more attention needs to be paid to that aspect of problem solving' discovered problems' that focuses upon novelty, for here is the realm of creativity.
Lessons from Mathematics
Technology education can benefit by looking analogously at the experiences of other subjects in the curriculum that have held problem solvingto be fundamental to theirnatures. One subject with such a claim is mathematics, where a discourse based on decades of research in problem solving is evident. Problem posing is emerging from this discourse as the way to make the act of problem solving truly creative.
As in technology education, the field of mathematics has sought to characterize the process of problem solving, and in this regard has relied overwhelmingly upon a model set forth by Polya (1957). Polya's steps were: (a) understand the problem, (b) devise a plan, (c) carry out the plan, and (d) look back, that is, check the result, reflect, and retrace steps. Within the step "devise a plan" inhered opportunities for problem posing. Polya suggested that at this stage in solving a problem, the problem could be varied, through use of analogy or generalization or dropping part of the condition. He wrote that "Variation of the problem may lead to some auxiliary problem" (p. 10). And his entreaty to the solver was "If you cannot solve the proposed problem try to solve first some related problem" (p. 10).
Polya's model remains the dominant problem solving schema in mathematics, informing research and thought on the subject (e.g., Masingila & Moellwald, 1993; McCoy, 1994; Schoenfeld, 1985). Masingila and Moellwald (1993) reported a case where Polya's model was utilized. The case showed that students could be involved in the decision making phase of problem solving, by bringing real world situations into the classroom.
In a review of the status of problem solving in mathematics education Schoenfeld (1983) suggested that Polya's model remains a valid referent. But he cautioned that this model was not easily transmitted in the classroom. The issues are too subtle and complex. And, it is difficult to demonstrate lasting effect of use of the model on students' problem-solving performance.
Silver and Marshall (1990) identified promising findings from problem solving research in mathematics teaching that could influence practice. They found support for metacognitive processes (such as monitoring and evaluation), consistent with Polya's entreaties. Students' beliefs about the nature of mathematics were found to influence their solving proficiency. Further, how students represented math problems was found to be central to their success in solving them. Failure to understand problems correlated with failure to solve them. It was felt that students could benefit from instruction devoted specifically to their understanding of problems. Also, having students work cooperatively was felt to be a promising way to enhance their problem solving competence.
Lester (1994) examined 25 years of published research on problem solving in mathematics, noting evolutionary changes and greater coherence in this line of inquiry. He concluded that while there has been significant progress, work of benefit to teachers still remained to be done with respect to: (a) the role of the teacher in the problem-centered classroom, (b) what actually takes place in such classrooms, and (c) group and whole-class rather than individual problem-solving (p. 672). The last of these areas of need responds to tensions surrounding the claims of constructivists and situationists.
There is the view within mathematics education that affect influences problem solving (e.g., Cobb, Yackel, & Wood, 1989; Thompson & Thompson, 1989). If students are frustrated or discouraged, their ability to solve problems would be impaired. Cobb, Yackel, and Wood (1989) reported on ways in which teachers can utilize the emotional acts of students to shape the norms of a class in ways that enhance problem solving. These authors point out that how teachers respond to fears, joys, or frustrations, influence how children will learn. Ford (1994) found that teachers also may affect student performance by the perceptions they hold of their problemsolving capabilities.
One variable that could be the basis of teacher perception of student capabilities is gender. But in a study of gender differences in problem-solving ability, McCoy (1994) found no differences among third grade students. She did find that the students generally could solve non-routine problems, and could construct good solution processes even when they did not have the right answer. These findings prompted the conclusion that problem solving skill is probably better nurtured than taught. Resonating with this positive view of the ability of children to re-pose and solve problems, English (1993) found that students were able to solve problems by looking back, monitoring their actions and making repairs. The children could interact with the problem materials, develop and modify solution strategies, and detect and correct errors. This ability of students to reflect upon, interrogate and change their solution strategy, is consistent with the idea of problem posing.
Problem Posing in Mathematics Learning
What one observes within the literature on mathematics teaching is an attempt to look critically at problem solving, especially to draw distinction between creative and routine dimensions of it. Differentiation here leads to distinction between convergent and divergent thinking, corresponding respectively with single-solution and multiple-solution problems. It is within this milieu that focus on problem posing as a vector of problem solving in mathematics can be located.
Haylock (1987) proposed problem posing as a means of promoting divergent thinking. He was of the view that problem posing would be a way around the problem of fixation in problem-solving that is, around the burdens on thinking imposed by prior knowledge and by stereotypical ways of seeing things.
Ellerton (1986) compared the quality of problems made up by high achieving math students with that by low achieving ones. The more able students made up more complex problems, could solve them, and could communicate about them better in conversation. The author viewed made-up problems as a tool especially suited for talented students. Also, such problems could serve a diagnostic purpose, if used to find out what a student believes is difficult. Asking children to make up their own problems was a way around the "structured, passive framework that exists in many classrooms" (p. 270). Students could converse with each other about the problems they created.
Brown (1984) emphasized the criticality of students' understanding problems and the need for them to deconstruct and re-pose problems. Students needed to understand the situation from which the problem was derived before attempting to solve it. An important aspect of Brown's advocacy was his idea that students did not necessarily have to solve the problems they pose. Posing was its own reward. Students could share the problems they posed' there could be opportunity for collaboration. As students posed problems, teachers were afforded insight regarding their conception of the subject matter and about cultural aspects of students' problem solving.
Silver (1994) proposed that problem posing was of interest for several reasons, including: (a) its relationship to creativity and exceptional mathematics ability, (b) as a means of improving students problem solving, (c) as a window into students' understanding of math, (d) as a way to improve students' disposition towards math, and (e) as a way to help students become autonomous learners. Problem posing was "central to the discipline of mathematics and the nature of mathematics thinking" (p. 22). According to Silver, the responsibility for formulating and solving problems could rest as much with students as with their teachers. Agreeing with Brown (1984), he opined that students did not necessarily have to work on the problems they posed. They could share their problems with each other.
The new information technologies have added a dimension to the discourse on problem solving in mathematics, and out of that discourse one also sees advocacy for problem posing. This is evident in the case of the Geometric Supposer, a software that helps students make and explore mathematical conjectures. Reflecting upon experiences with teaching via the Supposer, Yerushalmy, Gordon, and Chazan (1993) favored a problem posing approach to mathematics, though they were of the view that since students are not experts, the problems should be posed by teachers. Also reflecting on the possibilities of the Geometric Supposer, Schwartz (1992) advocated the need for students to be taught to question' to propose conjectures. Students should continually ask of the things in their environment, "What is this a case of?" Schwartz opined that to improve the learning of mathematics, "we must expand dramatically the time and attention we devote to the posing of problems" (p. 169).
What are the lessons to be learned from mathematics? A primary lesson is that scholars and practitioners in mathematics have set much store in problem solving over time and have mapped out a many-sided agenda of research aimed at looking at mathematics problem solving from the inside. They have been interested in how to improve the teaching of mathematical problem solving and how to make students better solvers. In this process, they have placed problem posing at the creative end of the problem-solving spectrum and have viewed it as a critical aspect of problem solving pedagogy.
Mathematics, of course, is not technology. But when we look analogically at problem solving research and theorizing in mathematics from the vantage point of technology, it becomes clear that our field can benefit from looking at problem solving from the inside, and from doing so against the backdrop of a many-sided conceptual framework.
Problem Solving in Technology Education
Problem solving becomes manifest in multiple forms within technology education, including experimentation, design, invention, and trouble-shooting. The profession began to show deep interest in it at the end of the decade of the 1980s and through the 1990s, sponsoring manuscripts on the topic (DeLuca & Peterson, 1997; Hatch, 1988). Hatch (1988) provided an excellent survey of the literature, then presented guidelines for the teaching of problem solving in technology classrooms. He distinguished between well structured problems, which required convergent thinking and could be solved via algorithms, and ill-structured problems, which required divergent thinking and solution via heuristics. Well-structured problems abounded in the field of technology, he observed, but were not very useful in developing the skills of the problem solver. On the other hand, ill-structured problems required critical thinking and promoted creative problem solving techniques. This was a very important analysis, congruent with discourses that address the intersection of problem solving and creativity. What Hatch was suggesting was the need to focus upon discovered problems. But these problems were to come from teachers. Noted Hatch, "Educators must . . . be able to highlight problems, challenge and motivate students and then allow students to become actively engaged in seeking solutions" (p. 89).
Setting forth a model for problem-solving research in technology education, Johnson (1988) opined that little work had been done in the field to determine the problems that should be presented to students. Much like Hatch, he seemed to view the teacher as the repository of technological problems. His research model did not explicitly allow that problems could originate with students. This is not to say, though, that problems originating with teachers are undesirable. We have to assume that teachers will bring their knowledge to bear upon the choices they make. Further, if problems promote divergent thinking, they could be the basis of creative thinking through re-formulation and re-posing. But children can pose or find problems too, and including them in the agenda setting for problem solving is an important way in which the frontiers of our field can be pushed. Hill and Smith (in press) provide examples of this in technology education.
In the past decade, a body of research in the vein of problem solving has emerged. In one such study, DeLuca (1991) concluded that to teach technological problem solving, instructional intent and breadth of problem-solving skill to be inculcated are key issues' and that appropriate process and thinking skills must be taught. Some studies have focussed upon trouble shooting, taking into account the context of performance, and delineating differences between expert and novice solvers (e.g., Flesher, 1993; Johnson, 1989).
In terms of its relevance to classroom teachers, an important dissertation study was that conducted by Glass (1992). Glass studied the effects of think-aloud paired problem solving on the processes, thinking, and procedure and solution of technology education students. In this methodology, one student is the designated solver, the other the designated prompter and listener. Students in the treatment group were paired, and were to perform problem-solving tasks by thinking aloud. A no-treatment group was also to solve the problems. A third group, the control group, were of students not currently enrolled in technology. They read the problem statement and took a test. The results were mixed, but supportive of continued exploration of paired-problem solving as a classroom problem strategy. Students in the experimental group outperformed the nonexperimental and control groups with respect to transfer of knowledge from instruction and use of metacognitive thinking. However, except for one of the problems, there was no significant difference with respect to problem representation, that is, understanding of the "facts, elements, and limitations of the given problem statement" (p. 114). Glass set forth many insightful reflections as he looked back on the work. In particular, he came to the view that "there is no substitute for prior knowledge when it comes to problem solving" (p. 132). Further, he conceded that creativity was not controlled for and could have been a confounding factor.
Glass' study is of importance here on a number of fronts. In the first instance, he had helped move the discourse on problem from curriculum theory to technology classroom practice. But further, he was seeking to gain deep insight into the thought processes of children as they solved technological problems. Problem posing is also a way to gain such insight. Again, by focussing on student problem representation, Glass had gotten to the heart of the matter, since, as indicated above, much ofthe difficulties students encounter in solving problems are due to misunderstandings of the task.
The problems students were to solve in Glass' study included London Bridge, where students had to try to design the longest span between the edges of two tables, given two sheets of paper, a stapler, and scissors. A second problem, the Leaning Tower of Pisa, required them to construct the tallest structure that would support the greatest weight, given 20 3" x 5" note cards and 10 paper clips Students got two points for every inch of height obtained, and one point for every ounce of weight supported.
These were clearly interesting problems, carefully chosen by Glass from text material in the field. But the question for the field' for technology teachers who present such problems to students' is What do students learn from such exercises? If the problem has intuitive appeal, then it could be argued that the solution itself is its own reward. But teachers have to be clear on what they want students to learn from such exercises. As discussed earlier in this manuscript, it is critical in technology education classrooms that they understand why their solutions to such problems work. This is an aspect of the teaching of problem solving to which the field probably ought to pay more attention. Sanders (1994) deals with this point, indicating that:
Typically, students build solutions, enter them in the classwide competition, and a 'winner' is identified. Unfortunately, the students generally do not understand why one bridge design is stronger than another or how to improve designs that are inherently weak. (p. 37)
He goes on to say that what is needed here is understanding of principles of science and mathematics, but that "heretofore, that has not occurred" (p. 37). He sets forth a model' design, construct, evaluate--that allows for data gathering and consideration of scientific and mathematical principles (in the context of technology). The evaluation stage of this model is interesting in that it becomes the staging point for re-design, that is, re-posing of the problem.
Beyond the question of student understanding of principles, a problem which Sanders solves in the approach to problem solving he describes, lies the question of ownership of problems. Solving problems teaches students how to be clever and, perhaps, allows the clever among them to stand out. But can the teaching not go further? Why not ask students to conceive of their own problems? Will they not get closer to the innards of technology if they have to shift their creative energy from solving problems to finding them?
Recently, in a midwestern state, a science teacher took a group of children on a field trip to a pond. They caught frogs. One student noticed a deformity in one of the frogs. This was pointed out to the teacher. This observation was passed on to the extension services in the state. It was investigated. Before long the problem had come before the state legislature, and soon was national news. The problem has drawn research funding. The student had found a problem that became a basis for class activities and boundless learning.
Hill (in press) illustrates how technology education teachers can provide problem-posing opportunities for their students. In one instance, she writes of a grade 1 class that approached technology education through writing and producing a play. The teacher and students worked through a consensus building process to decide on the topic. The class then wrote the play and made a final wordprocessed copy on the computer, built the stage, made the characters (dolls and puppets), and rehearsed the play using the made characters. Here they had to investigate different ways to make the characters move. One decision was to use hydraulics. The students then performed the play and videotaped the production. They brought their concerns and imagination into both the creating of the play and its production where there was a wealth of opportunity for technological problem solving. In a second instance, Grade 11 students collaborated with members of the community in contributing to an idea pool based upon community needs. From this pool came practical problems to be solved.
McCormick, Murphy, and Hennessy (1994) conducted inquiry into children's construction of knowledge conveyed through the design process. In their critique of the problem-solving literature, these authors found that despite the stated intent of teachers, students who had received instruction in design did not appear to grasp the big picture suggested by the traditional steps of design. These authors were of the view that the stepwise process erroneously conveys design as a linear process. They cautioned against the notion of a generic problem solving method (see also McCormick, 1993, 1997; McCormick, Murphy, Hennessey, & Davidson, 1996).
Custer (1996) examined how technological problems could be distinguished from other problems. He concluded that what distinguished technological problems was their "goal thrust" component. In the realm of technology, so-called "goal thrust" activities are geared toward creating physical artifacts, and understanding the natural world. Custer proposed a technological processes matrix, in which he sought to separate the main types of problem-solving activities via the logics of complexity and goal clarity. Thus, trial and error, invention, trouble-shooting, and design were categorized.
Custer's model is quite useful, in that it shows that all of the activities within the problem-solving genre must not be lumped together. All problem-solving processes are not of even creative merit. The model shows that invention might be the form of problem solvmg that requires greatest creative effort, due to the open-ended nature of problems, and the high demand for domain knowledge. Custer's invention quadrant provides the greatest potential for the inculcation of creativity through technological problem posing and problem solving.
Problem Posing in Technology Education-Implications
In this article, we have raised issues concerning the technological method, a generic problem solving method, suggesting that greater attention needs to be paid to problem posing, which we believe to lie at the creative end of the problem-solving continuum. Through the 1980s, technology educators' agenda had been to gain recognition of their subject area as a discipline, leading naturally to a concentration on technology education content. More recently there has been concentration on process, almost at the expense of content. At least one of the unsettled issues that arises at this point in our history is how does the process of problem solving materialize into technology education instruction and learning? We have questioned the efficacy of abstract, generic models in light of theory. Moving from generic models to context-bound and situation-specific models shifts the focus from curriculum to instruction and situation where the student as learner plays an important and active role in the equation. This shift is at the heart of this article.
So what are the implications for the teaching of technology when we deem it important that students not just solve problems but also pose them? An important one will be that instruction moves away from students as recipients of teacher knowledge and solvers of teacher-prescribed problems, toward students as active creators of their knowledge.
Clearly, classroom dynamics change, as do roles of students and teachers in such an environment. As students become involved in posing and finding problems by drawing on their life experiences and interests, classroom management must change to accommodate teachers and students co-constructing technological knowledge. The pedagogical dynamics move away from a systematic process with a predetermined teacher problem and right answer that may or may not capture student interest, to one where there is openness and potential for surprise.
Importantly, students engage in meaningful creation, and they are allowed space to work through solutions and acquire insight into why they worked. Teachers become more concerned about what they take away from problem-solving exercises, thus avoiding pedagogy and ready-to-use exercises that result in little more than shallow and questionable learning.
Technology teacher educators have to help future teachers understand the conditions under which children learn best and to set such learning as the central aim of their pedagogy. Future teachers must come to understand that creativity cannot be engendered by mere formula. Rather, that they will have to create the conditions for its expression by exposing their students to the content of technology in the authentic context of laboratories that are rich in technological opportunities in manufacturing, construction, transportation, energy and power, communication, and big-related technologies. Further, they will have to strive for the ideal of a classroom climate that encourages and supports deep thinking, risk taking, inquiring, information seeking, and question asking. Teacher candidates themselves must be made to engage in the process of technological problem posing as part of their preparation. Especially, they should be encouraged to think of problems as needs that may arise from the community. Problems do not have to originate in textbooks; they can come from real-life.
Perhaps the biggest indictment of problem solving as a method of our field, is that it has come to be viewed as being decontextualized and content-independent. For example, students may be asked to create load bearing structures without accompanying instruction in the related principles. That is not how technologists do their work. Technologists possess deep knowledge about the fields in which the practice. It is that knowledge which leads them to understand what they do not know, and what needs to be known. Architects understand architecture' structures, forces, aesthetics, etc. Tool designers understand material properties, and the mechanical forces operating at the interface of tool and work. They know the importance of providing for chip removal. Brain surgeons understand the anatomy of the human brain. Architects, brain surgeons, and tool designers, all technologists, come to insight and to new problems based upon puzzles encountered in their respective fields and their reflections upon them. It is thus foolhardy to conceive of an omnibus problem solving method that would work in all three of their respective domains. People come to problems in the content domains that preoccupy them.
We have shown here that our counterparts in mathematics also have a strong claim upon problem solving. If that claim is legitimate, how then does problem solving in technology education differ from problem solving in mathematics? We think that a key here is that at the end of it all mathematics students come away understanding aspects of mathematics. Accordingly, students in technology education should come away from problem-solving understanding and knowing technology.
Our discussion here raises the issue of creativity as an aspect of technology education teaching and learning to a heightened level of consciousness. It also provokes many practical questions relating to a problem-posing approach to teaching. We believe that there is room here for classroom-based research. Practical questions to be worked out include: What are the respective roles of students and teachers? How does one proceed on a day to day basis? What forms of assessment are appropriate and do students have input? What kind of classroom and laboratory layout is needed? What if the teacher does not have all of the technical knowledge needed to guide students through their projects? Problems of this order are best solved by actual practice, collaboration, and reflection.
We thank Jennifer Thom, graduate student, and member of a seminar class taught by the first author at the University of British Columbia, Summer 1997, for suggesting the topic we explore here as a promising area of inquiry in technology education.
Lewis is Professor, Department of Work, Community and Family Education, College of Education and Human Development, University of Minnesota, St. Paul.
Petrina is Assistant Professor, Technology Studies Program, Department of British Columbia, Vancouver, Canada.
Hill is Assistant of Curriculum Studies, University Professor, Technological Education, Faculty of Education, Queens University, Ontario, Canada.
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