A Factor Analysis of Primary Mental Processes for Technological Problem Solving
Roger B. Hill
The Universtiy of Georgia
Robert C. Wicklein
The University of Georgia
Issues related to problem solving and strategies for helping students learn how to solve problems in efficient and creative ways are a key element in several recent school reform initiatives (National Academy Press, 1996; National Council of Teachers of Mathematics, 1989; Secretary's Commission on Achieving Necessary Skills [SCANS], 1991). Educators, parents, and business leaders have sought to make the classroom more reflective of an environment where students will need to be lifelong learners, using creative activities that challenge their abilities to think critically and solve problems that have more than one correct answer.
Educators within the field of technology education have also given considerable attention to the concept of problem solving with specific focus on solving technological problems (Halfin, 1973; Hutchinson & Hutchinson, 1991; Hutchinson & Karsnitz, 1994; Todd, 1990). Solving technological problems is a key element underlying all of the processes identified in the recently published A Rationale and Structure for the Study of Technology (1996) produced by the Technology for All Americans Project.
Custer (1995) distinguished technological problem solving from other forms of problem solving and provided a clear rationale for including it as an essential component in technology education instruction. Using Newell and Simon's (1972) concept
of problem space, Custer notes the distinctive characteristics of technological problem solving with respect to resources, primary processes, and goal thrust. Emphasis is placed on goal thrust
The problem space or context in which problems are solved is very significant when considering how best to develop problem-solving skills. For effective instruction to occur in this arena, teaching strategies should be based on situated learning and cognitive apprenticeship models (Duncan, 1996). Approached from this perspective, the knowledge, primary processes, and goal thrust typical of solving technological problems in real-world settings are important to know about and understand.
Technological processes like analyzing, designing, and prototyping are labels used by technologists to describe activities that are a part of their work. Medical professionals use terms like evaluating, diagnosing, and clinical trials to describe similar functions. Some have argued that these terms are linguistic terms that have developed within the cultures of various professional fields (Custer, 1995) and that these terms share much in the way of cognitive and practical processes. That observation, however, does not diminish the importance of the terms and the professional culture from which they come, when establishing a context for situated learning.
As technology educators have approached the task of teaching technological problem-solving skills, a variety of approaches have been used (Johnson, 1994; Johnson, 1996; Maley, 1986; McCade, 1990; Pucel, 1995; Sellwood, 1989; Tidewater Technology Associates, 1986; Waetjin, 1989; Wicklein, 1997; Wright, Israel, & Lauda, 1993). Traditionally these activities have been presented in a rather static or detached form as a problem-solving module or presentation of a specific problem-solving formula. Teachers have been unsure of the critical components needed to consistently reinforce the concepts of technological problem solving or to develop new instructional areas that integrate problem solving in creative ways. Without these critical components teachers are left with traditional problem-solving formulas or mechanistic procedures that fail to adequately prepare students in this critical area. Efforts have been needed to more clearly define the primary processes involved in technological problem solving.
The primary processes used to solve technological problems are based on mental methods of inquiry. These intellectual or mental processes often interface with manipulative activities, but the key elements to be examined in this study are the mental processes used to solve technological problems. For purposes of this discussion, mental processes have been operationally defined as the cognitive portion of the primary processes component in the problem space of technological problem solving.
A factor analytical procedure was used in this study to synthesize key themes or constructs representative of the mental processes used in technological problem solving. These themes were developed to provide a basis for process-based technology education curriculum designs. Process-based designs have been proposed as an alternative to traditional designs based on technical content (Savage & Sterry, 1991; Todd, 1990; Hutchinson & Hutchinson, 1991; Wicklein, 1993) and are much more consistent with applications of cognitive learning theory needed to successfully develop problem-solving skills.
This study represented a continuation of prior research on the mental processes employed when solving technological problems. Harold Halfin, in his 1973 dissertation entitled Technology: A Process Approach, identified 17 mental processes and methods of inquiry that were consistently used by technologists to solve problems. He suggested that these constructs could be used as an integral framework for the development of technology education curriculum. In a more recent analysis, Wicklein and Rojewski (1998) revalidated and updated Halfin's original work. Wicklein and Rojewski completed a modified Delphi study that confirmed the 17 original mental processes and methods of inquiry that Halfin analyzed. They also identified 10 additional items for a total of 27 mental processes, all of which were deemed necessary for problem solving within the context of the present technological society. These processes consisted of analyzing, communicating, computing, contexts, creating, customer analysis, defining problem(s), designing, establishing need, experimenting, innovating, interpreting data, managing, measuring, modeling, constructing models/prototypes, monitoring data, observing, predicting, questioning/hypothesizing, researching, searching for solutions, conducting a technology review, testing, transfer/transformation, values assessment, and visualizing. In addition to the identification of these terms, working definitions were developed and analyzed through the modified Delphi process (see Table 1).
Table 1 Mental Processes and Definitions From Delphi Study (Wicklein & Rojewski, 1998)
Analyzing - The process of identifying, isolating, taking apart, breakdown down, or performing similar actions for the purpose of setting forth or clarifying the basic components of a phenomenon, problem, opportunity, object, system, or point of view. Communicating - The process of conveying information (or ideas) from one source (sender) to another (receiver) through a media using various modes. (The modes may be oral, written, picture, symbols, or any combination of these.) Computing - The process of selecting and applying mathematical symbols, operations, and processes to describe, estimate, calculate, quantify, relate, and/or evaluate in the real or abstract numerical sense. Contexts - Understanding the social, cultural, organizational, etc. context for the task. Creating - The process of combining the basic components or ideas of phenomena, objects, events, systems, or points of view in a unique manner which will better satisfy a need, either for the individual or for the outside world. Customer Analysis - The process of evaluating inputs of the receiver or technology. Defining Problem(s) - The process of stating or defining a problem which will enhance investigation leading to an optimal solution. It is transforming one state of affairs to another desired state. Designing - The process of conceiving, creating, investing, contriving, sketching, or planning by which some practical ends may be effected, or proposing a goal to meet the societal needs, desires, problems, or opportunities to do things better. Design is a cyclic or iterative process of continuous refinement or improvement. Establishing Need - The process of determining the degree of need for the technological problem or solution. Experimenting - The process of determining the effects of something previously untried in order to test the validity of an hypothesis, to demonstrate a known (or unknown) truth, or to try out various factors relating to a particular phenomenon, problem, opportunity element, object, event, system, or point of view. Innovating - Taking existing "know-how" and being able to implement it in new situations. Interpreting Data - The process of clarifying, evaluating, explaining, and translating to provide (or communicate) the meaning of particular data. Managing - The process of combining the basic components or ideas of phenomena, objects, events, systems, or points of view in a unique manner which will better satisfy a need, either for the individual or for the outside world. Measuring - The process of describing characteristics (by the use of numbers) of a phenomenon, problem, opportunity, element, object, event, system, or point of view in terms which are transferable. Measurements are made by direct or indirect means, are on relative or absolute scales, and are continuous or discontinuous. Modeling - The process of producing or reducing an act or condition to a generalized construct which may be presented graphically in the form of a sketch, diagram, or equation; presented phyiscally in the form of a scale model or prototype; or described in the form of a written generalization. Models/Prototypes - The process of forming, making, building, fabricating, creating, or combining parts to produce a scale model or prototype. Monitoring Data - The process of collecting and recording data and time conditions related to problem occurrence. Observing - The process of interacting with the environment through one or more of the senses (seeing, hearing, touching, smelling, tasting). The senses are utilized to determine the characteristics of a phenomenon, problem, opportunity, element, object, event, system, or point of view. The observer's experiences, values, and associations may influence the results. Predicting - The process of prophesying or foretelling something in advance, anticipating the future on the basis of special knowledge. Questions/Hypotheses - The process of asking, interrogating, challenging, or seeking answers related to a phenomenon, problem, opportunity, element, object, event, system, or point of view. Researching - The process of becoming familiar with the background information necessary to investigate the problem. Knowing what type of information to look for and where to locate it. Searching for Solutions - The process of examining multiple options when attempting to resolve technological problems. Technology Review - The process of evaluating the performance of a solution at an appropriate time in the future. Testing - The process of determining the workability of a model, component, system, product, or point of view in a real or simulated environment to obtain information for clarifying or modifying design specifications. Transfer/Transformation - The process of transferring across areas or fields to new situations. Values - The process of understanding the role of the technician's and other's values in deciding on courses of action. Visualizing - The process of perceiving a phenomenon, problem, opportunity, element, object, event, or system in the form of a mental image based on the experience of the perceiver. It includes an exercise of all the senses in establishing a valid mental analogy for the phenomena involved in a problem or opportunity.
The work by Wicklein and Rojewski (1998) resulted in a comprehensive compilation of problem-solving constructs. A key problem not resolved in the previous work was that the list was not very user-friendly for practical applications. Using this lengthy list to develop and assess technology education curriculum would be very difficult. Curriculum designers and classroom practitioners would likely struggle to assimilate the complete listing of mental processes into any given instructional activity. A more concise set of constructs was needed that encompassed all of the items while at the same time simplifying the overall scope of the mental processes.
Purpose and Research Question
The purpose of this study was to systematically identify the themes or key constructs representative of the mental processes necessary for solving technological problems. Reducing the complete listing of mental processes to a shorter and more usable list was a practical step necessary to facilitate application of research previously completed. The research question formulated to guide this study was as follows: What list of constructs best summarizes the comprehensive list of mental processes identified by Wicklein and Rojewski (1998) as necessary for solving technological problems?
The population for this study consisted of the members of the International Technology Education Association (ITEA). This group, representative of professional technology educators, consists of persons who are knowledgeable about technology and adept at systematic methods of solving technological problems. Given the limitations of budget and the constraints of time, this population was accessible and had the expertise needed to contribute to the study. ITEA members were also considered to be appropriate participants because the goal of the study was to generate constructs that would be applied within the context of technology education instruction.
To identify the selected population, a database of the 3,818 professional members of the ITEA was obtained in electronic form. It was determined that a random sample of 361 would be ideal to provide an accurate representation of this population (Krejcie & Morgan, 1970). The random number generator in Microsoft Access was used to generate the necessary random sample. A total of 361 questionnaires were mailed to potential respondents identified in the random sample. Initially 144 (39.9%) were returned and an additional 81 (22.4%) were received after follow-up letters were sent out. Materials were coded to provide tracking of returned instruments and follow-up mailings were used to encourage respondent participation. The number of returned questionnaires totaled 225 with no significant differences detected between initial and follow-up responses. Due to missing or incomplete date, a total of 212 (58.7%) usable instruments were obtained.
Respondents included 33 (15.6%) females and 179 (84.4%) males. The age range for half of the respondents was 26-45 years, with 106 (50.0%) in this category, and most of the rest were in the 46-65 range, with 99 (46.7%) of respondents. A total of 134 (63.2%) of the respondents had been teaching for more than 15 years, so considerable experience was represented in the sample. Respondents worked in positions ranging from elementary to post-secondary with representation in each category listed on the questionnaire. Table 2 provides complete details for the demographic data for the respondents who returned usable questionnaires.
A questionnaire was constructed for use in the study and was validated using a panel of respondents similar to those included in the population for the study. Minor modifications were made to address issues raised in the validation process and the instrument was mailed to the selected sample. The questionnaire included a section for demographic data (gender, age, years teaching, and position), a list of the 27 mental processes identified in Wicklein's Delphi study, and a brief definition of each listed mental process.
Table 2 Frequency Counts for Respondents by Gender,
Age, Years Teaching, and Position
Grouping Variable Frequency Percent
Gender Females 33 15.6 Males 179 84.4 Age 26-45 106 50.0 46-65 99 46.7 Over 65 2 0.9 Years Teaching Less than 1 3 1.4 1 - 2 5 2.4 3 - 5 21 9.9 6 - 15 49 23.1 More than 15 134 63.2 Position Elementary 6 2.8 Middle School 58 27.4 High School 76 35.8 Post-secondary 23 10.8 Supervisory 31 14.6 Other 18 8.5
The instrument used a stem of, "Please circle a number to indicate how often each of these mental processes is used in solving technological problems". It was followed by the following scale for rating standards for each item: 1 = Never; 2 = Almost Never; 3 = Seldom; 4 = Sometimes; 5 = Usually; 6 = Almost Always; and 7 = Always. This scaling is similar to that which was recommended by Nunnally (1978). The Likert scale responses for each of the 27 mental processes provided the raw data for this study.
The conceptual basis for requesting the perceived frequency of use of mental processes as a basis for developing representative constructs for mental processes used by technologists was the belief that related processes would have similar patterns of use and importance. For example, if frequency patterns were analyzed for use of terms like external thread, major diameter, minor diameter, pitch, lead, crest, root, form, and series, a unifying concept for these terms might be identified. Since all of these terms are related to threaded fasteners, frequency of use would logically be similar and "thread specifications" might serve as an appropriate label to summarize the terms. In a similar manner, a logical approach to identifying representative constructs for the mental processes used by technologists was to analyze frequency of use in solving problems.
To identify a concise list of explanatory constructs from the responses collected, a factor analysis was used. This procedure was similar to that used in a study by Wicklein and Hill (1996) and Hill and Petty (1995) and addressed the research question developed to guide the study. Factor analysis is a technique for achieving parsimony by identifying the smallest number of descriptive terms to explain the maximum amount of common variance in a correlation matrix (Tinsley & Tinsley, 1987). The factors developed embody the meaning of the 27 original items within a more concise and useable list.
Principal-components analysis was used to extract the initial factors identified in the statistical treatment of the data. Orthogonal rotation using a Varimax procedure was then used to minimize the number of loadings on a factor, thus simplifying the structure and making the solution more interpretable. Potential factor solutions with from two to ten factors were examined and solutions with factors having an eigenvalue of less than one were eliminated. Additional inspection of factor solutions also considered the number of items loading on each factor, with preference to solutions with more than one item loading on a factor. Careful consideration was given to each factor solution that met all of these criteria and the final solution was selected to provide the most parsimonious representation of the data collected.
Using squared multiple correlations as the initial communality estimates, principal-components analysis of the data was completed followed by Varimax orthogonal rotation. A five-factor solution provided eigenvalues greater than one for all factors. A scree test was performed and it also supported a five-factor solution. The factor matrix produced by this process provided a meaningful and concise list of constructs representative of the mental processes being studied.
In response to the research question developed to guide this study, a five-factor solution was identified after careful analysis of the data. For each factor a label which captured the essence of the loading items was identified. The constructs identified were researching the problem, searching for solutions, innovation, analyzing data, and evaluating results. In interpreting the items that loaded on each factor, the .30 level is a generally accepted minimum factor loading because it indicates that approximately 10% of the variance for a corresponding variable has been explained by a factor (Tinsley & Tinsley, 1987). Using these criteria, the five factors collectively explained all of the 27 mental processes on the questionnaire and accounted for 45.9% of the total variance. The end result was a manageable list of factors that capture the meaning of the mental processes used in solving technological problems.
Decisions about labels to attach to factors generated by the statistical process were made by the researchers after considerable examination and discussion about the mental processes included under each factor. While the process was a subjective one, the choices reflect careful consideration of the definitions of each mental process clustered under a factor. Definitions of mental processes along with an item listing for each factor have been included in this report so that other researchers and scholars can consider alternative labels if they so choose.
Factor 1. Researching the Problem
This factor was comprised of items related to gathering data about the problem and considering the needs to be met. The mental processes that loaded here included questioning and probing to determine the nature of the problem and determining the various aspects of the problem that needed to be considered. Determining the degree of need was also imbedded in this factor. Table 3 provides factor loadings, item means, standard deviations, and a list of the mental processes that loaded on this factor.
Table 3 Variable Loadings and Item Means for Factor 1:
Researching the Problem
.63969 5.53 1.22 researching .62031 5.03 1.27 questions/hypotheses .51290 5.04 1.15 transfer/transformation .50121 4.80 1.23 values .44948 5.15 1.24 establishing need
Factor 2. Searching for Solutions
The items that loaded on this factor were descriptive of mental processes needed to manage the search for problem solutions. The concept of measurement, necessary to objectively consider potential solutions, was also reflected in the response pattern for this factor. The factor loadings, item means, standard deviations, and the actual items which loaded on factor 2 are provided in Table 4.
Table 4 Variable Loadings and Item Means for Factor 2:
Searching for Solutions
.59134 5.40 1.19 managing .57504 5.09 1.15 measuring .55756 5.59 1.11 searching for solutions .51609 5.11 1.34 technology review .38273 5.98 1.09 communicating
Factor 3. Innovation
This factor was made up of mental processes necessary to design and create innovative solutions to a problem. The conceptual frame of this factor included evaluating inputs of the receiver of the technology, reconsidering the problem definition, and then moving toward the synthesis of ideas and materials necessary for an effective solution. Table 5 provides factor loadings, item means, standard deviations, and the actual items that loaded on the third factor.
Table 5 Variable Loadings and Item Means for Factor: Innovation
.57673 5.29 1.24 creating .57124 5.82 1.09 defining problem(s) .55665 6.06 1.01 designing .49832 5.91 1.03 innovating .48294 4.89 1.17 customer analysis
Factor 4. Analyzing Data
This factor was made up of items that involved mathematical reasoning and manipulation of data. Computing, analyzing, visualizing, and modeling were all a part of this factor. Interpreting the results of data analysis for predictive purposes was also included. The factor loadings, item means, standard deviations, and the mental processes that loaded on the fourth factor are provided in Table 6.
Factor 5. Evaluating Results
The mental processes identified with this factor encompassed the activities needed to test a problem solution. Collecting and recording data, observing, and prototyping were all associated with this factor. The factor loadings, item means, standard deviations, and the mental processes that loaded on the fifth factor are provided in Table 7.
Table 6 Variable Loadings and Item Means for Factor 4:
.53088 4.97 1.24 computing .50602 5.61 1.36 predicting .45848 6.01 .98 analyzing .44232 5.56 1.24 visualizing .43397 5.39 1.25 modeling
Table 7 Variable Loadings and Item Means for Factor 5:
Loading Item Mean SD Item
.76100 5.17 1.35 monitoring data .62487 5.53 1.18 models/prototypes .42684 5.75 1.13 testing .42396 4.86 1.35 observing
As these findings are considered, it is important to note that the order in which the factors are listed is not a significant feature for their interpretation. They are listed in order by magnitude of variance explained for each factor, but no sequential order is intended. As a concise list of steps necessary for technological problem solving, the factors should not be considered in a linear fashion. They comprise components in a process, sometimes used simultaneously, sometimes successively, and sometimes in an iterative manner. They provide a parsimonious list of constructs intended to capture the essence of the mental processes used in solving technological problems.
It was the intent of this study to identify the primary factors representative of the mental processes and methods of inquiry used to solve technological problems. Using a factor analysis process, five major themes were identified that are typically employed when solving technology-related problems. The factors identified can be appropriately integrated into the framework for technology education curricula. Efforts to verify and refine the previous research of Halfin (1973) and Wicklein and Rojewski (1998) met with successful results.
The five factors identified in this study provide a stable and workable platform for technology teachers to establish a strong curriculum with mental processes used by technologists as a central feature. By employing these factors in the design of technology education curriculum, teachers and students can be assured that the curriculum rests on a solid foundation that will not be out-of-date within a short period of time. If the focus of technology education instruction is directed toward these problem-solving processes, technology teachers would not be bound by the limitations of their laboratories (e.g., having or not having the latest technological device). Certainly, the latest technological equipment is nice to have and is often conducive to student and teacher enthusiasm. Without it, however, sound problem-solving strategies can still be developed and students can benefit from instruction toward a real-world problem-solving context that is transferable beyond the classroom.
It is very interesting that Wicklein and Rojewski's (1998) initial Delphi research on the identification and prioritization of the essential mental processes used by technologists to solve problems also described five categories of mental processes. The results of their classification were very similar to the five factors of this study. They described their categories as analysis, conceptualization, creativity, investigation, and social. Although the titles differed from the findings in this research, the concepts were following similar paths. The related titles are: analysis [delphi] vs. analyzing data [factor analysis], conceptualization [delphi] vs. searching for solutions [factor analysis], creativity [delphi] vs. innovation [factor analysis], investigation [delphi] vs. researching the problem [factor analysis], and social [delphi] vs. evaluating results [factor analysis]). The parallelism of these two research projects indicates that the mental processes maintain a strong consistency which can contribute to greater generalizability and application within the classroom.
Another potential benefit of this research is related to assessing student achievement in technology education instructional activities. Hill (1997) developed a technique for observing students as they complete technological problem-solving activities to determine how often and how frequently various mental processes are being employed. A simplified form of this assessment could be developed using the five factors from the factor analysis. The end result might be a more effective tool for evaluating student progress and greater assurance that effective technological problem-solving skills are being developed.
A final conclusion refers to the similarities that the identified mental process factors have with some of the more traditional formulas currently being used to describe problem solving. Problem-solving guidelines have been described in several current technology education textbooks as well as in the professional literature (Bransford & Stein, 1984; Hutchinson & Karsnitz, 1994; Tidewater Technology Associates, 1986). This close parallelism strengthens both the traditional formulas of problem solving as well as the results from this new research. This study provides needed data and valuable instructional options to support and enhance efforts of teachers who are currently employing problem-solving strategies in their curriculum.
The mental processes that were identified in this research can serve as a foundational basis for future curriculum planning for technology education. By integrating these processes, technology educators can create comprehensive approaches to technological problem solving that are not limited by tools, equipment, and laboratories. Further efforts will need to be undertaken to establish the viability and practicality for the mental process approach for the technology education curriculum. The following recommendations are put forward as possible next steps in this design procedure.
1.Develop specific instructional activities that incorporate the mental processes with appropriate technologies for use in secondary-level technology education programs. Efforts are now underway to create a series of learning activities that incorporate the mental processes for technology education students. By using both overt and covert means to develop and apply the methods, students will be actively engaged in the learning process.
2.The mental methods identified in this research could be used to evaluate current technology education curriculum. Existing curriculum could be analyzed to determine the extent to which it currently employs the mental methods of inquiry. Based on this evaluation, educators could enhance or revise their existing curriculum to better address the identified mental methods.
A word of caution to educators who may use these mental processes as a basis for curriculum development is that the factors are not intended as a hierarchical mechanism for problem solving or curriculum development. The identified mental methods are not in order of importance nor would they all necessarily be used in any given technological problem. It is conceivable that a number of the processes be employed in a given problem, but would not necessarily follow any specific order.
The overall results of this study were encouraging. A radical, new perspective of problem solving was not the result, but an effective and parsimonious list of factors representative of the key mental processes used in solving technological problems was identified. The similarity of the factors to both traditional models of problem solving and to recent research on the mental processes tended to confirm the validity and reliability of the results. Application of these constructs can be an effective element in the ongoing efforts to improve instruction in the field of technology education.
Hill is an Associate Professor in the Department of Occupational Studies, The University of Georgia.
Wicklein is an Associate Professor and Coordinator of Graduate Studies, Department of Occupational Studies, The University of Georgia. and the element of dealing with creation of physical artifacts as a distinguishing characteristic of technological problem solving.
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