Session T3E USING DEVELOPMENTAL PRINCIPLES TO ... - ICEE

Session T3E USING DEVELOPMENTAL PRINCIPLES TO PLAN DESIGN EXPERIENCES FOR BEGINNING ENGINEERING STUDENTS Wendy C. Duncan-Hewitt1 , David L. Mount 2 , Steve W. Beyerlein3 , Don F. Elger4 and Judi Steciak 5 Abstract  Experiments with a variety of teaching techniques to improve meaningful learning often are often only partially successful, leaving many students struggling with the abstract and complex knowledge of the engineering disciplines. We hypothesize that decisions about appropriate teaching methods are best made by considering the development of students' intellectual complexity using the “Crux Developmental Model” (CDM) synthesized from a number of disparate theories in the educational, developmental, and complexity literatures. The CDM and its application were assessed and improved over a three-year cycle in the context of a Science and Engineering Camp for teenagers. Our results supported the hypothesis that the CDM: (1) provides a rational method of selecting developmentally appropriate activities to teach specific skills and content, and; (2) provides a tool for customizing learning activities to maximize growth. According to the developmental model, the teenage participants in camp are working at the beginning of the same developmental transition that undergraduates are completing. Thus, we conclude this paper by proposing how the results of this study can be generalized to the undergraduate experience. Index Terms  cognitive complexity, curriculum planning, entering students, guided design, intellectual development, teaching methods.

INTRODUCTION One of the tasks we face in teaching entering Engineering students is to introduce them to the formal concepts and thinking processes of the discipline. These tend to be more abstract, systematic, and complex than the concepts and thinking to which these young people, usually still in their teens, have previously been exposed, leading to failures in comprehension. It became clear that what we needed was a rational method to choose the right teaching method and we turned to theories of education, development, and complexity for some clues. While there is a vast literature, it is sometimes limited in practical utility by the fact that age ranges, subject demographics, or learning domains are too narrow. However a synthesis, the “Crux Developmental Model,” (CDM) described in detail in [1] is easy to apply in many educational settings. The CDM exploits many 1 2 3 4 5

developmental constructivists’ work, including William Perry in [2], Mary Belenky and her colleagues in [3], and Robert Kegan in [4]. The novel aspects of the CDM and its use are twofold: its breadth of application – it can be used with student populations ranging from the adolescent to the postgraduate or returning adult – and its pragmatic marriage of theory with practice. The context in which we tested the CDM was an Engineering and Science Camp for high school students that has been run for the past sixteen years by the University of Idaho’s College of Engineering. This example is pertinent to teachers of most freshmen, and even a significant number of more advanced undergraduates because all the students can be placed within the same developmental stage in the model. The primary difference among the students is the degree to which they have progressed to the next level of development – young adulthood.

THE CRUX DEVELOPMENTAL M ODEL The CDM is based upon leveled intellectual developmental theory (especially neo-Piagetian) extended beyond the years of adolescence into adulthood [5] - [11]. It is comprised of six levels of cognitive complexity (L1 to L6) for which there are defined, qualitative differences in self-concept, thought and value structure, and behaviors. More complex levels incorporate and transcend lower ones. Moreover, each level is, in effect, a “crux:” As in climbing, one needs determination and adequate support and protection (provided by a mentor) if one is even going to try to surmount it. One capable of operating at a higher level of intellectual complexity does not consistently operate at that level. One of the functions of higher complexity is the ability to discriminate between tasks which require a higher order and those tasks for which lower orders are more efficient. We will not describe all the levels, as this information can be found in [1]. However the first five levels are compared briefly in Table I. L2 and L3 are detailed below because this is the developmental transition typical of this age group (and of most beginning undergraduate students). Intellectually, L2 is capable of conceiving entities that one would characterize as “concrete:” things have magnitude, persistence and properties that are distinct from one’s perceptions. If you ask L2 for an abstraction, s/he will

Wendy Duncan-Hewitt, Crux Consulting, 1712 Brookwater Circle, Amarillo, TX, 79124, [email protected] David Mount, Crux Consulting, 1712 Brookwater Circle, Amarillo, TX, 79124, [email protected] Steven W. Beyerlein, Department of Mechanical Engineering, University of Idaho, EPB324K, Moscow, Idaho 83844-0902, [email protected] Don F. Elger, Department of Mechanical Engineering, University of Idaho, EPB324K, Moscow, Idaho 83844-0902, [email protected] Judi Steciak, Department of Mechanical Engineering, University of Idaho, Boise, 800 Park Boulevard, Boise, ID, 83712, [email protected]

0-7803-6669-7/01/$10.00 © 2001 IEEE October 10 - 13, 2001 Reno, NV 31 st ASEE/IEEE Frontiers in Education Conference T3E-17

Session T3E tend to give you an example, not the abstraction itself. L2’s see a few pros, but they won’t see the cons. Goals are shortterm. L2 is able to carry out first-order relational thinking that involves classification, seriation, and causation. Knowledge is “received:” learning is “retaining and returning what others give to me.” Socially, L2 understands that others have distinct points of view, but can’t see how that should impact their own. L2 is motivated by personal intentions and desires and cannot construct obligations and expectations to maintain mutual interpersonal relations. Still unable to construct meaning out of abstract ideas such as “responsibility,” L2 cannot be expected to be a trustworthy member of the community, although s/he is self-sufficient. The “Good” is perceived as something that serves one’s personal interests. Egocentric, opportunistic, and “adolescent,” L2 is also observed in a significant number of adults. L2 is externally motivated – s/he requires an authority to set goals and guidelines. TABLE I Level L1 L2

L3 L4 L5

A COMPARISON OF SOME LEVEL T R A I T S Self-Concept Thoughts Perception of Teacher Impulsive, Single abstractions; To look after me, egocentric, categories of keep control of dependent tangibles things Opportunistic, self- Abstract mapping— T o make it possible protective, wary relating one abstract for me to pass, to concept to another give me the correct information Conformist, selfSimultaneous To approve of my aware, mapping of several efforts cooperative, loyal abstract concepts Conscientious, Abstract systems, To help me become individualistic, systemic principles, competent responsible frameworks Autonomous, Systems of systems, To be a resource as integrated, universal principles I re(construct) my interdependent Self

Intellectually, L3 understands that abstractions, such as the idea of “relationship,” and ideals exist, even if a concrete example cannot be articulated. L3’s thinks logically, hypothetically, and strategically but decision quality varies because they still do not consider every option: they cannot construct a generalized regulatory system. Goals can be relatively long-term and L3 is capable of creating personal meaning from a historical context. L3 can carry out secondorder relational thinking such as analogical reasoning and analysis, but knowledge still is subjective and opinion-based. Perspectives are seen to have equal value, not because of the structure of reasoning per se, but because it is the only way to solve the paradox that people having different opinions might maintain important relationships. Socially, relationships exist as meaningful things of value to L3. Unlike L2, L3 can reflect on here beliefs and motivations. The limitation of L3 self-reflection is that it tends to stop once it generates what seems – to the reflector – to be a logical or chronological sequence of behaviors. Meaning comes from their immediate culture (or one-to-one

relationship) and they believe in conformity and harmony above all else. Although L3’s are beginning to relativize personal importance in their own communities, prejudice is difficult to avoid at this level. They identify with their communities and conform closely to these values and actions. They cannot separate the “self” from relationships because they cannot objectify the associated obligations and influences. The “Good” is directed toward things that maintain relationship. Motivation is still external, but L3 can grow if s/he is asked to seek personal goals. The levels can and should be assessed in a number of ways (e.g., interviews, essays, classroom observation). Performance does not equal ability, so we should be looking for the best performances to make our assessments. At first, one must use a checklist approach similar to that used by beginning psychiatrists making a diagnosis [12]. Experience allows one to construct mental “prototypes” that make assessment much more rapid. An educational bridge for the transition from L2 to L3 exploits teaching that affirms L2 while pushing them towards L3. Able only to negotiate in one direction (through control or appeasement) L2 requires the teacher to be a decisive, discipline-oriented authority. Thinking in “black and white,” L2 wants “correct” information, not ambiguities. An educator whose goal is to help learners grow from L2 to L3 starts with an authoritative style and moves toward being more of a reciprocal motivator/guide as more responsibilities are given and met by the learner. While affirming selfsufficiency, competence, and role differentiation this transformative teacher will demand mutuality and expect trustworthiness. In the process, s/he expects to deal with emotions that arise when L2’s alternately feel constrained and controlled when facing mutual responsibilities and expectations, and then “out of self-control” when they do not meet self-expectations to master their impulses. Teamwork builds commitment to interpersonal expectations, while continued individual assessment affirms identity and discourages the utilitarian use of others’ efforts. Intellectual demands that affirm current capabilities yet push toward Level 3 include: “Have you considered ALL possibilities?” “How are “a” and “b” related?” “How could the positions of “a” and “b” be reconciled?” “How do you interpret…” “Summarize...” L2 to L3 teaching: • Directs the learners to seek correlation and causality and differentiate between them; • Asks for both denotation AND connotation; • Moves from examples to generalized abstractions.

M ETHODS – CAMP LEARNING ACTIVITIES The camp interspersed academic activities with teambuilding and recreational activities. Cooperative learning, discovery learning, journal writing, and assessment were used extensively. Computer technology was used for information processing and modeling. Camp activities taught theory, engineering design and building, modeling (CAD


Session T3E and spreadsheet), and presentation skills (posters, PowerPoint®, web-page design). If the campers were to leave with one new idea, it might be something like this: "Anyone can have fun building and operating a model vehicle, and this was a major component of the camp. However, if one wishes to optimize the performance of that vehicle in a timely manner, physics and engineering theory become essential tools." All camp activities were intended to help the campers come to this conclusion. For the purpose of this paper – assessing the application of the developmental model in the camp setting, we present our observations for the relatively longterm building project and three one-hour academic activities: • An introduction of the engineering concepts of Newtons, Joules and Watts through measurement (mass, distance, ∆t) and calculation. The quantities measured required physical participation – to calculate power, the campers had to time each other running up a flight of stairs. Additionally, they were asked to lis t the assumptions made in each experimental design. • The campers to copy the group results of the preceding experiment into an Excel® spreadsheet and then create various plots, at least one of which had to compare “Work” and “Power.” • An introduction of the concepts of fluid mechanics, including viscous and inertial forces, Reynolds number, and drag coefficient by asking the campers to measure the terminal velocities of spheres of different materials in different fluids. Engineering Design and Building Project

FIGURE. 1 A TEAM OF CAMPERS BUILDING A VEHICLE .

In the ultimate project of the camp, the campers were placed into large teams of six to eight that were split into two subteams in order to build a vehicle (cars, boats, submarines, rockets). Each team was paired with a “mentor” (an undergraduate or graduate student) who was there to ensure safety and to facilitate the design process. At the beginning

of the week, the building activities were highly structured and geared toward safety, introduction of building tools (e.g., table saws), and constraints (e.g., materials that could and could not be used). Later in the week, the activities were unstructured as the teams planned and undertook their building and testing. The vehicles were entered in a competition on the last day. Scoring was not as simple as awarding the most points to the vehicle that was the fastest, went the furthest, etc. Instead, the goals involved reliability, reproducibility, and optimization.

RESULTS AND DISCUSSION Academic Activities – Intellectual Dimension In a normal classroom situation, one might assure understanding through testing. Such testing is not “fun,” so one probes understanding by different methods in a camp environment. The way we assessed understanding was either to ask the campers to apply the knowledge or to explain it during the activities. Understanding of the various concepts taught in the three activities described above ranged from complete (but only for a small number of campers: one student commented that we were making approximations in the calculation of power) to nil. The more complex concepts, e.g. Reynolds number, drag coefficient, were not understood at all. When asked to hypothesize why glycerin is so viscous relative to water, a participant answered “…because it is so dense.” Campers, when asked to define “power” confused it with “work” and “strength.” Campers dutifully undertook the calculations and made the plots, but derived no understanding from this work. Sometimes lack of understanding could be inferred by the fact that no entries were made in the notebooks; for example, “assumptions” was invariably left blank. Some abstract concepts were understood only in the form of their concrete examples. For example, campers, when asked to define “force” answered variously: “something that acts on a body”, “gravity”, “like a push on a swing”, “like Darth Vader.” During the spreadsheet activity, the campers had no difficulty in creating simple bar charts but “got stuck” when attempting a 2 dimensional plot – even though they had done such plotting in school. Teams, when faced with a spreadsheet designed to graph changes in an outcome when several variables are altered, didn’t know where to start until they were assisted, step-by-step, by a facilitator. The concepts with which the campers coped included (a) Distinguishing weight and mass (although most could not give another example of a quantity “like weight,” i.e., another force; (b) Acceleration; (c) The meaning of a bar chart; (d) How an Excel® spreadsheet works, and (e) Terminal velocity. The CDM provided some explanations for these observations. L2 is competent at abstractions to the extent that they can be referred directly to the concrete. Thus,


Session T3E abstractions such as speed, mass, and even acceleration can be understood. Abstractions of greater order (than abstract abstractions): Reynolds numbers, drag coefficients, viscosity, force, energy, power -- are much more difficult (if not impossible) for L2 to understand. While L2 often graphs in 2D competently, it requires memorization, recognition, and application of an algorithm. A 2D graph requires that the students understand the significance of the relationship between variables (L3 concept). Thus, although graphing problems can be excellent teaching tools from a developmental perspective, there must be appropriate intervention by the facilitators. This was the case during the camp, since the class was small enough that the two facilitators could work with each team of campers until they could complete the plot and explain its significance within the time allotted. It is practicable to help L2 “jump the gap in understanding” for concepts of intermediate abstraction such as “force,” by asking questions that probe for understanding. For example, a list of the concrete examples generated by the learners can be returned to them with the task of formulating a generalization or abstraction that encompasses all of them. Students can be probed for the “meaning” of relationships and asked for related examples. On the other hand, it might be prudent to redesign more abstract classes such as the fluids laboratory to omit abstruse concepts. In retrospect, much of the theory would be useful only at a more advanced level. If the projects were extended over weeks or months, and the campers took greater pains to document their construction successes and failures, the need for theory MIGHT become apparent. Then learning the theory would become important enough to sustain their attention, even in the face of conceptual difficulties. In higher education, instructors often spend a great deal of time trying to create and teach according to an abstract framework. In teaching this knowledge, we tend to start by teaching the abstract categories and then we move to increasing detail and concreteness, ending with examples and problems. We do this believing that we are giving the students a gift of a pre-packaged shortcut. According to complexity theory, we learn in the opposite direction to that in which we remember. This suggests that we teach a discipline by starting with the concrete. Then we can help the students construct and/or understand abstract generalizations and laws to explain patterns. We can finally show the students how the structure of the course reflects this abstract organization.

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How much power can your body generate by running up and down one flight of stairs? • How much power is one horsepower? • How many people running up and down the stairs would it take to “run” your house? • If electricity costs 7 cents/kWh, how much money could you save by doing the stairs to genera te the power? In order to answer these questions which all have a personal meaningfulness, the students were given an experiment to perform: they were asked to weigh themselves and then time how long it takes them to ascend a flight of stairs whose height they measure. From these data, they used given equations to calculate power and convert it into various units of differing familiarity. However, before being given materials and permission to proceed to the “hands-on” part of the activity, they were required to answer critical thinking questions and thereby generate a “theory” to take with them as they performed the measurements. The critical thinking questions provided a framework for the analysis of results. The high degree of student engagement was evident from the noise level generated during the activity and the participation in the post-exercise debriefing. As answers to the questions in the exercise were taken up when the full group reconvened, thereby encouraging accountability, the structure of the activity provided for gentle correction of wrong answers and opportunity to “show off” for those who got the answers right. Corrections were made in a manner that minimized the embarrassment of error (the instructor posted a number of answers before indicating correctness without identifying the “offending” team) yet provided evidence for the need to check results. L2s like competition and “showing off”, while reassurance is a positive reinforcement for L3 development. Additionally, L2s “require” closure and concrete answers so having a concrete problem such as “How feasible is it for me to try to watch TV while generating the power needed to keep it turned on?” generate enthusiasm for the exercise. The spreadsheet activity was just as successful as the one described above, however it required much more intervention on the part of the facilitators. In part, this was because pairs of campers were being introduced to Excel® in a hands-on computer laboratory. The facilitators had to circulate rapidly and constantly to ensure that all the groups kept up and didn’t become involved in computer-play (e.g., surfing the web). When these campers (L2) finished the spreadsheet activity, they resorted to “play” – gossiping, surfing the internet, etc. Some, however, continued to Academic Activities – Procedural Dimension explore features of the software beyond the assignment One especially successful activity taught force, energy and expectation. These contrasting behaviors can be explained power (L3) through measurement (L2). We believe that by greater progress in the transition to L3 by the latter group. some of the teaching techniques used by the instructor lent The primary need for intervention arose each time the to his success, despite the fact that some of the concepts pairs of campers completed a sub-task of the activity: then, were a stretch for L2. First, the facilitator set the stage for the facilitators ensured that the intended learning was this activity by asking questions that framed the abstract achieved by asking probing questions. When understanding concept of “power” in terms to which they could relate: was incomplete or incorrect, further questions were asked, or 0-7803-6669-7/01/$10.00 © 2001 IEEE October 10 - 13, 2001 Reno, NV 31 st ASEE/IEEE Frontiers in Education Conference T3E-20

Session T3E the campers were asked to repeat and check their procedures. In comparison, the fluid mechanics activity resulted in far less excitement and appeared to be soporific for some. The developmental model indicated that the “procedural failure” had a number of origins: • Lengthy periods of uninterrupted lecture to “explain” the abstractions, but less feedback; • Lack assessment of understanding of concepts of intermediate complexity (e.g., viscosity) before using them to calculate even more abstract concepts; • A more tenuous link between experiment (concrete), the calculations (completely abstract), and the topics of the critical thinking questions (completely abstract); • The closure period was used to plot calculations, but not to probe the campers’ understanding. Teaching for this activity might be modified in the following ways to facilitate the L2 à L3 transition: • Engaging students’ interest with concrete situations; • Posing questions which the students might ask of themselves given these situations; • Requiring “deep” active thinking by asking and requiring answers to critical thinking questions that forced them to abstract from the concrete; • Encouraging group accountability by insisting upon validation of answers using checking algorithms (such as unit analysis); • Requiring individual accountability by calling on group members at random (rather than a group spokesperson), forcing them to ensure that all members understand; • Simplifying or eliminating higher-level concepts; • Collecting answers in a large group session after working at a team level and then exploring correctness and meaning before proceeding with the plotting step. Vehicle Building – Intellectual Dimension The engineering design process is iterative. During the first design session the campers were taught that one hypothesizes a design based upon one’s current theory(ies), designs, builds, and tests – then revises theory and design based upon the results and tries again until the design specifications (in this case the vehicle score) are met. We rationalized that a scoring scheme appropriate for the L2 to L3 transition should be based on two variables (requiring L3 understanding of relationship) rather than just maximized performance on one variable (something that L2 finds easier to understand). We avoided greater complexity since the resulting degree of abstraction (and non-linearity) prevents meaningful learning and use of the score. In practice, the campers did not adhere to the design process and often tended not to use a prototype’s score to plan the next prototype. They would predict success (based usually on aesthetics rather than theory) and then, upon failure, make random and irrational design modifications.

Sometimes the goals of optimization and reproducibility were abandoned altogether as the teams pursued the more exciting goals of “maximization” or even “design radicalness.” We believe that the facilitation and not the score or the design process were responsible for this disappointing result. It is essential to ensure that the process actually is used and then to debrief scoring after each trial. Despite formal plans to do so, team mentors were reluctant to follow through, an example of a mismatch between intent and performance. Strict adherence to the process, analysis and assessment were perceived by the mentors to be “not fun” or “boring” for the campers and they tended to neglect them. Perhaps this should not have been surprising – most of them voiced their desire to please the campers as their primary goal, even before the camp began. Future improvements are procedural – we must teach the mentors ways in which a scientific protocol can be made to appear “fun.” Perhaps a game structure would be most appropriate: adolescents enjoy rule-laden games all the time, as long as scoring is tied directly to the rules. In other words, the final competition score must reflect adherence to the process as well as the achievement of a design goal (which otherwise occurs randomly). Vehicle Building – Procedural Dimension At L2, even when a sub-team is composed of “only” four members, it is expected that there will be difficulty in coming to consensus since each person literally identifies with his design concept. Therefore, in light of the fact that mentors were reluctant to intervene, it was not surprising that were few instances of high-quality teamwork and cooperation. For example, it was not unusual for a team member to: • make a commitment then arrive at the next meeting with a task undone; • play computer solitaire rather than collaborate; • daydream during theory classes in the expectation that the others would pick up the slack; • not consult with others before acting; • procrastinate, etc. Many of these behaviors are typical of L2. Frequent, more intimate mentor interventions could address each of these transgressions. Instead, our L2 campers resolved these “insurmountable” disagreements according to the CDM. Often, but not always, there was one member who was louder or more willful whose wishes became the team’s goals even when scientific evidence said otherwise. In some groups with more than one strong-willed member, we repeatedly observed a behavior which skirted the consensus/compromise objective of teamwork: design disagreements led to “splitting” of sub-teams into even smaller units (consisting perhaps of only one individual), building and testing designs independently, participating with the remainder of the team in a superficial manner. Consensus was not reached easily afterwards either, possibly


Session T3E because, short of catastrophic failure, they could not agree on decision criteria. The feeling was – “Well, so what? My model might work better than yours NEXT time.” There was not enough time really to assess performance reliability in a way that was convincing to the other team members. To surmount these problems in the future, mentors could ask the campers to predict the score prior to each launch for their particular design. Testing would be followed by a thorough debriefing of the results, with hypotheses made as to contributing factors, forcing suggestions beyond the obvious and typical “more power” and “less weight” responses. This might push the teams to consider the more sophisticated principles of the vehicle design such as drag or gearbox ratio. An additional activity might involve displaying each team’s prototype prior to launch and asking each person independently to predict the relative success of that prototype in achieving the target. This approach might squelch the typical L2 predilection for “aesthetic” design, pushing them to “fall back” on scientific principles pertinent to the vehicle. In more general terms, it is desirable for the teams to go through several design prototypes, permitting them to see the benefit of the design-build-test cycle typical of engineering projects. Due to the usual time constraints of a week-long camp experience, it is essential for the project not to exceed the thinking, mechanical skills and patience possessed by the campers, but detailed enough to hold interest. Therefore, the construction needs to be a compromise of complexity and time, balancing challenge and the number of iterations possible within the time limits.

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ACKNOWLEDGMENT Sponsors for the North Idaho Science Camp include the National Institute for Transportation Technology (NIATT), Idaho Space Grant Consortium, Albertson Foundation, and GTE along with other regional foundations.

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http:://www.cruxconsulting.org. A paper entitled "“A dialogical theory of intellectual complexity” is being submitted to The Journal on Excellence in College Teaching.

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CONCLUSIONS - APPLICATION FOR BEGINNING UNDERGRADUATES Contrary to the hopes of Piaget, but consistent with the CDM, most beginning undergraduate students have not yet attained “formal operations” (L3 and L4) but are still in transition from L2. Yet some of their performances, such as their ability to follow directions and to memorize a large amount of information, can fool us into thinking that they understand – and therefore can apply – what they have been taught, when this is really not the case. The difficulties and successes that the campers had with both content and process can be expected to be experienced by beginning undergraduates. Thus, many of the suggestions given in the RESULTS section can be applied to improve teaching at the undergraduate level. These results supported the hypothesis that in assessing HOW a student knows using the CDM, we can predict the degree to which they will be challenged or frustrated by alternative educational methods and curricula, ultimately allowing us to optimize the transformative potential of our teaching. For entering undergraduates this suggests: • Teach examples then facilitate students’ construction of abstractions, expecting this to be a difficult, iterative affair that will need close intervention. Finally, assess

students’ understanding of the abstractions by asking them to solve new concrete problems. Use team-based learning to build an internalized concept of relationship, anticipate the problems that will occur and intervene aggressively, but always assess knowledge individually. Do not expect entering students independently to use and understand all the elements of the iterative design process. Take each step independently, assess explicitly, and lead them through the iterations.

[10] Koplowitz, H. “A Projection Beyond Piaget’s Formal-Operations Stage: A General System Stage and a Unitary Stage” in M.L. Commons, F.A. Richards, and C. Armon (Eds.) Beyond Formal Operations -- late adolescent and adult cognitive development, Praeger, New York, 1984, p. 272. [11] Fischer, K.W., Hand, H.H., and Russell, S. “The Development of Abstractions in Adolescence and Adulthood, “ in Commons, M.L., Richards, F.A., and Armon, C (Eds.), Beyond Formal Operations -late adolescent and adult cognitive development, Praeger, New York, 1984. [12] Luhrman, T.M. Of Two Minds, Knopf, New York, 2000, p.41.
