reductive sketching to synergize authentic problem solving in engineering
TRANSCRIPT
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Reductive Sketching to Synergize Authentic Problem Solving in Engineering
Leonhard E. Bernold Universidad Tecnica Federico Santa Maria, Valparaiso, Chile
Luis Felipe Gonzalez Böhme Universidad Tecnica Federico Santa Maria, Valparaiso, Chile
Sandro Maino
Universidad Tecnica Federico Santa Maria, Valparaiso, Chile [email protected]
Abstract: As the engineering faculty is encouraged to adopt authentic problem
based teaching the need for students to re-tool their learning skills is increasing.
One such skill is modelling the real world in a way that principles of math and
physics can be utilized. This paper addresses two issues related to sketching for
learning. The first section presents an iterative procedure to verify problem
understanding using abstractive visualization. Building on the rich heritage of
hand-drawing in architectural design and sketch-based reasoning, the text offers
a reductive process to elicit a model as a basis for understanding the problem.
The second part presents the result of an investigation to test the hypothesis that
engineering students’ consider sketching an important skill to support their
learning. Based on the positive first results, the design of a scaffolded approach
to introduce engineering sketching as a critical learning and problem solving skill
is underway.
Introduction and background
Every teacher in engineering has surely experienced the rush of student engaged in a problem-solving exercise to immediately recommend “the” solution before understanding all the relevant issues related to the problem. This well-known phenomenon led Albert Einstein to summarize that “If I had an hour to solve a problem I'd spend 55 minutes thinking about the problem and 5 minutes thinking about solutions.”
Much has been written about strategies to solve problems in science but Pólya’s (1946) four principles are still providing the core elements: 1) Understand the problem, 2) devise a plan of the solution, 3) carry out the plan and check each step, and 4) look back to examine the solution obtained. This, we may say, is the “problem-focused” strategy that is generally adopted by scientists as opposed to the “solution-focused” strategy used by architects and designers to solve problems. According to Lawson (1979), scientists usually focus their attention on discovering the rules that govern the problem at hand, whereas architects learn about the nature of the problem as a result of trying out solutions, i.e., “conjectured solutions” as argued by Cross (1982). To Pólya (1946), one of the basic methods for understanding any problem, not only of geometry, is to draw a figure, that is, to try to find some lucid geometrical representation for the problem at hand. This task is already an important step toward the solution.
Wankat and Oreovicz (1993) in their book, Teaching Engineering, pointed to the importance of the first step in problem solving, ”… students need to practice defining problems and drawing sketches.…(this) is often given very little attention by novices. They need to list the knowns and the unknowns, draw a figure, and perhaps draw an abstract figure which shows
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the fundamental relationships (remember that most people prefer visual learning). The figures are critical since an incorrect figure almost guarantees an incorrect solution.” During their continued research on authentic problem solving applying model elicitation techniques, Diefes-Dux and Salim (2012) found that: “As such, it became clear that students do not have an inherent ability to formulate problems.” Thus, research on enhancing the formulation of the different natures of problems has become of great interest (Jonassen 2010).
Internal and external modeling
Kenneth Craik (1943) was one of the first who suggested that humans create a cognitive structure, the so called mental model of the world that is available for reasoning, decision making, problem solving or in predicting the future. Later, Johnson-Laird (1983) considered mental models “constantly under construction” in a person’s working memory. New concepts in education, founded on constructivist principles, emphasize the importance of a problem as the start of the active learning process guided by the teacher. More specifically, Model-based-Learning (MbL) has become of great interest (Coll, France, and Taylor 2005): “…learning emerges from an interaction between learners’ experiences and ideas, which could be externalized and communicated to others through the construction of artifacts (e.g., models).” External representations of internal models help us to think and communicate complex thoughts. Many writers create drawings and even paintings of scenes before writing fictional books or educational textbooks. Of great importance is the saliency of the problem that has to be modeled with an emphasis on authenticity and relevance to the student’s experience. Sachse, Hacker, and Leinert (2004) particularly emphasized the value of sketching in that it:”… transfers a mental problem solution into a physical object, which the problem-solver may process as the subject of a critical examination, i.e. of his or her metacognitive reflection.” The flexibility of sketching to draw 1-, 2- or 3-d drawings, graphs and diagrams, mathematical symbols, expressions, etc. makes it an inherently effective tool to support the students to switch from one model to another (Louca and Zacharias 2012) representing their internal mental models externally for reflection and scrutiny by others.
Interactive “construction” of problem understanding
The creation and improvement of mental models is considered to be an iterative process. Liu and Stasko (2010) propose the concept that:” … internalization involves the encoding of information abstracted from perception in long-term memory. Since it often does not make sense to assume independent existence of visualizations and their underlying data, information about the data, especially at schematic and semantic levels, may be preserved at the same time.”
Figure 1: Iterative process of forming understanding of an authentic engineering problem
External World Brain
External Model (EM)
Representation of MM
Mental Model (MM) of
Problem Authentic
Problem First Abstraction
Improvement
Improvement
Augmentation of MM 1
Discrepancy 1
Discern Augmentation of MM n
Understanding
of Problem Representation 1
Representation n
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Figure 1 presents a concept to represent the interactive process of abstracting and augmenting the mental model of a real world problem. As depicted, the improvement of the
mental model of a problem depends on recognizing a discrepancy between an external representation of the mental model and the actual problem. This concept is based on scientific methods to elicit the mental process when working on a problem. For example, the think-aloud protocol asks a problem solver to express in words his or her thinking providing an idea about the thinking process that leads to an action (Ericsson and Simon 1993). It is apparent that the iterative cycles only end when the problem is understood. But how do we know that we understand?
While verbal expressions have been found useful to capture the mental model, sketching using the mechanical and sensory systems of arm and eye, is considered another effective method to represent internal models. As represented in Figure 1, being able to compare an external representation with the real world provides the opportunity to recognize discrepancies as a basis for augmenting the mental model. In fact, Briggs and Bodner (2005) argued that the active representation and construction of mental models supplies students with a tool of thinking for model-based reasoning.
Methods of abstraction to foster problem understanding
A core constructivist principle states that gaining understanding is a process that requires the active involvement of the learner. This process is thought to require an iterative interaction between mental and external models with the goal to eliminate discrepancies between the models and the real world problem in such a way that existing knowledge can be employed to develop potential solutions to the problem. This chapter presents three methods that provide unique opportunities to foster this process through an abstraction process that allows the learner to efficiently find the key issues related to a problem while eliminating distracting information.
Abstraction in design
In architecture as in art, every examination of a physical entity or space by means of sketching its visible features is led by a pressing need to capture and reproduce its form, its major divisions (or constituent parts), function (or purpose), and the way of functioning. As with sketching the human figure, to draw a balanced combination of its appearance and the functional virtues is the goal of the artist. Zaidenberg (1945) brakes the study of the drawing of the human figure down into four main topics: (i) The general human form, which comprises learning the generalizations to be made about structure and movement of the human body; (ii) how to “see” the human form, which demands the acquisition of a method for looking at it while simultaneously applying a filter to the artist’s vision that should result in a completely understood and analyzed concept (or idea) of what is seen; (iii) what to “say” about the human form, which involves learning how to control the contributing personal facets which color the understood concept of what is seen; and (iv) the techniques –that is, the personal style– of applying the above three topics which may include speed, pressure and lengths of lines, among others.
Unlike the propositional nature of most design drawings and artistic creations, to Zaidenberg (1945) the inquisitive nature of human figure drawings does not need inspiration or a vision (used in the sense of an epiphany) but rather a method of intelligent elimination of all that is not pertinent to what the artist has to “say” about the figure he or she “sees”. According to Gänshirt (2007), the sketch is originally nothing other than an abstracted and fixed gesture, wherein both temporal and spatial dimensions of some motion sequence have been translated into points, lines, and surfaces. Consistently, Zaidenberg (1945) indicates that portraying a human model requires the artist to first analyze the story behind the pose assumed by the model in order to capture the action of the intention of the assumed pose.
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Thus, an analysis of the major gestures involved in assuming the pose must be made and then a mental conclusion must be translated into a sketch on the paper. This can be seen as a kind of forensic or investigative task by means of which a previous event or a series of events must be reconstructed in order to fully understand the current situation. This forensic-like analysis can likewise be found at the initial stage of building surveying when the surveyor first produces a mental map (sometimes referred to as “perceptual layout” in architectural jargon) of the floor plan which will gradually be enriched with further details such as scale, geometric dimensions, materials, etc. Relevant research in digital building surveying and planning (Donath et al., 2003, Donath and Thurow, 2007, Donath et al., 2008) use on-site freehand sketching as a basis for the development of computer-assisted topological-geometrical models. In archaeological findings and historic building conservation, when there is not much left to see, sketching provides a useful method for figuring out –by inference and deduction– the original form, internal configuration, function, construction procedures or applied materials.
Designers produce many different kinds of drawings for several different purposes. Lawson (2004) distinguishes at least eight which are often mixed together: (1) presentation drawings, (2) instruction drawings, (3) consultation drawings, (4) experiential drawings, (5) diagrams, (6) fabulous drawings, (7) proposition drawings, and (8) calculation drawings. Diagrams, proposition and calculation drawings are sketches architects and designers usually make in the early stages of the design process to collect client requirements and to explore the design space. Goldschmidt (1991) describes these kinds of drawings together as “study sketches”. By this means, design propositions and constraints take form and start interacting with each other as ad hoc design entities at different levels of abstraction in the designer’s representational space. A few lines on paper may represent anything from an entire building to the circulation needs for a community, as Crowe and Laseau (2012) notice. Do and Gross (2001) corroborate such multi-level abstraction capacity of architectural diagrams compared to other domains like electronics. The sketch-based reasoning process itself is described by many (Schön, 1983, Goldschmidt, 2003, Lawson, 2004) as a dialog sustained between the designer and the sketch, or in other words, the designer’s mental model and its representation.
In his outstanding work, Laseau (2001) describes three sketch-based abstraction methods: (a) by distillation, suggesting to draw only that part from the whole that is subject to observation; (b) by reduction, which suggests to distinguish groups of parts from the whole, for instance, by cross-hatching or shading; (c) by extraction, which is to emphasis (for instance, by thicker lines or colored surfaces) a part of the whole while remaining within the context of its system; and (d) by comparison, which suggests to diagram different systems in the same graphic language in order to compare structural rather than superficial characteristics of different systems.
Reductive visual abstraction
Studying the performance or the collapse of a system presented visually, such as the collapse of the Tacoma Narrows Bridge, can be compared to a forensic investigation where visual clues can provide the necessary data to infer cause-and-effect relationship. Based on constructivist principles, this kind of investigation requires the existence of a mental model that can be drawn and build upon. In other words, a child who has never learned plate-tectonic and volcanism will not be able to explain the why so many volcanos exist in Chile. However it was found that a sketching assignment is extremely effective in substantiating or verifying if a student understands new material (Sepasgozar and Bernold, 2012, Siew and Bernold, 2012). Reductive abstraction may offer an excellent venue to help students to actively create a deeply anchored mental model in a formative process. Figure 2cpresents an example of an abstraction process the leads the students step-by-step from a complex real-world problem to a representative model that is reduced to its most relevant elements.
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Due to space limitations, on the initial but most critical visual of the accident is being presented in Figure 2 a). It depicts a busy scene that includes two telescoping-boom cranes, a leaning observation tower sustained by two inclined hoist lines from the cranes. A small building and telephone/power cables suspended from a series poles surround the “leaning tower”.
Figure 2: Process of visual abstraction to identify the cause of a crane collapse
To a student of crane technology the picture should raise some immediate concerns as s/he was “lectured” that hoist lines need to be vertical as cranes are designed and certified for vertical lifting conditions only. Alas, while not all non-vertical line conditions lead to a catastrophic failure the presented case ends with two large truck-cranes laying on the ground. However, Figure 2 a) does not provide any further indication about the cause that could be apparent to anybody but the most experienced crane-engineer. In fact, the authors have found that engineering students have great difficulty to solve the the authentic crane-collapse problem in a structured manner.
The presented reductive abstraction methodology begins in Figure 2 b) by eliminating all the components in the environment clearly not related to the accident. In a second step, also shown Figure 2 b), elements that obstruct the view of the critical objects, cranes and tower, are cut away. The method of artificially removing visual obstacles to see the insides of an object was so expertly used by Leonardo da Vinci. As shown, the small one-story shack has been replaced with a virtual view of the tower base as a perspective extension of the four legs and cross-bracing. In addition, the wooden pole supporting two (phone) lines was deleted and the section crossing the crane boom closed with a virtual section. The final phase of the abstraction process consists of replacing structurally sound elements with symbols. Thus, the intact section of the tower has been replaced with a box, crane booms with solid lines, the pins at the end of the boom with circles, and the cable ropes with dotted lines. What is left are the two crane boom heads with two headache-balls, A + B, and two inclined hoist lines. The imminent question is how did A not suspend vertically from the boom head? According to the second Newton Law (object stays at rest unless a force acts on it) the steel ball stayed in place while the boom head must have accelerated to the right in a quick motion. What could have caused that dynamic force pulling sideways on the head of the boom of crane 2 and, to a lesser extent, on crane 1? As the center of gravity (crossed circle) has moved forward between the two cranes, a force lateral to the motion plane must have been produced The only way such a rapid force can be formed is by the failure of the front leg C the tower is resting on. Due to the vector of the hoist line to A we can infer that the leg closest to the viewer broke. Of course, the next probing question would be: How can such a strong piece of steel suddenly fail?
The first half of the paper discussed theoretical basis for extending the use of engineering sketching into the realm of teaching and learning, specifically as a tool to model an authentic problem. The second section will investigate the question about the disposition of students towards hand sketching, an art that got lost with the rise of computers. Underlying this is the
a) Initial Phase of Crane Collapse b) Reduction and Cut-Away c) Substitution and Final Inference
A
B
C
Crane 1
Crane 2
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hypothesis that today’s students perceive this simple but universal engineering language as a powerful tool.
Survey of students’ disposition towards sketching as a study skill
Before experimenting with students to test the effectiveness of sketching in helping this process the authors decided to measure the readiness or, according to Bloom’s second taxonomy (1956), the affective responses from the students that could be expected. In particular, it would important to know how they would value being able to sketch and to map knowledge. At the same time, a good understanding of their present use of other learning tools is necessary. For this purpose, several questions in a questionnaire survey of 113 engineering students at the University Tecnica Federico Santa Maria (UTFSM) in parallel classes of Physics 110 included related to self-assessment of their study skills and the competencies of a successful student (e.g., sketching and mind-mapping). The students were asked to respond to questions using a four level Likert schema: 1= Highly Disagree, 2 = Disagree, 3 = Agree, 4 = Highly Agree, 0 = I Don’t Know/Does not Apply.
Table 1 presents the summary statistics of mean and standard deviation (STDEV) for selected questions related to active learning, problem based teaching and sketching. It is interesting to understanding that the Mean of 3.49 for question Q 6.3 was the highest for all followed by Q 6.12. Most surprising was the high Mean of 3.23 for Q 6.14 when contrasted with the 1.95 of question Q 4.6. While the responses relative to what a successful student is able to do in terms of metacognition (Q 6.3), use of study skills (Q 6.12), and sketching/mind-mapping (Q 6.14) the very low Mean of 1.95 for Q 4.6 seems to indicate that the students themselves do not apply the learning methods alluded to.
Table 2: Basic statistics of responses to selected questions Likert (1-4)
Q # Statement Subject Mean STDEV
1.4 My study skills are excellent Self-Assessment 2.23 0.79
3.3 The teacher does not spoon-feed the students rather leads us to find the answers to problems
Active Learning 3.42 0.76
3.9 The teacher uses a lot of pictures, videos and other visualization techniques Visualization 2.75 0.89
3.13 The teacher uses real-world problems to explain the relevance of the topic Problem Based
Teaching 3.08 0.99
4.6 As a student I question, underline, summarize, cross-reference when reading the lecture material
Visualization/ Sketching
1.95 0.99
4.9 As a student I find it easier to comprehend new material when it is linked to real-world problems
Problem Based Learning
3.07 0.89
4.10 As a student I benefit more from classes where the teacher coaches me to work on my study skills
Study Skills 3.02 0.86
4.12 As a student I find it very difficult deciding what is most critical in a class text Abstraction 2.24 0.91
6.3 I think that a professional and SUCCESSFUL student is able to evaluate and improve his/her own study performance
Study Skills 3.49 0.61
6.12 I think that a professional and SUCCESSFUL student uses effective study skills appropriate for the different tasks (assignments, projects, journal)
Study Skills 3.46 0.65
6.14 I think that a professional and SUCCESSFUL student models a problem using sketching or mind-mapping
Sketching 3.23 0.79
7.2 My effort as a student (for this class) is excellent Self-Assessment 2.52 0.76
The low responses to the all-encompassing self-assessments of Q 1.4 and Q 7.2 in combination with the Mean of 1.95 for Q 4.6 may, however, indicate that the students are simply not aware of formal study methods although the introduction to the survey included short descriptions of key concepts such as SQR4, learning preferences and study skills. To study possible relations between Q 6.14 (sketching and mind-mapping) and other questions multi variable regression analysis with Excel was executed. The objective was to identify questions/variables with p-values smaller than 0.05 which is accepted as representing a sufficiently strong relationship.
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-4-3-2-1012
0 1 2 3 4 5
Res
idu
als
Residual plot for Q 3.4
Figure 3: Result of a multi-variable regression analysis for Q 6.14 (Value of Sketching and Mind Mapping)
The extremely low R2 value of 7% indicating that the produced model represents the data
poorly a fact that is confirmed by one representative plot of residuals for Q 3.4. Surprisingly,
all the coefficients are very small and, consequently, all the p-values are above 0.05 some of
them with a wide margin.
Results
The survey was designed to inquire if engineering students at UTFSM will value sketching as a tool that would enhance their active learning within a problem-based teaching environment. Reviewing the results of the data analysis paints three different pictures. At first we can affirm that the queried engineering students consider sketching and mind mapping as being an important skill of a successful student. The same holds true for metacognitive capabilities and study skills. On the other hand, they indicate that they themselves don’t use sketching and note taking tools while reading despite the fact that a significant number of students assert that they have difficulties identifying the core messages. It is very reasonable to believe that this is the result of unawareness. This scenario is supported by the low valuation of their own study skills which stays in stark contrast to their perceptions of the study skills exhibited by a professional and successful student. Finally, the multi-variable regression analysis showed no correlations between the students’ valuation of sketching and mind-mapping and other factors related problem-based learning.
Discussion and conclusion
Engineering students who want to become successful problem-based learners require a skill set that is significantly different from the passive copying of lectures and solving of large numbers of similar practice or homework problems. The list of needed competencies encompass metacognition, reading to understand, self-evaluation, etc. but most importantly the ability to model real-world problems before applying scientific principles. However, several research efforts have demonstrated that engineering students lack the skills necessary to accomplish the latter thus they are unable to develop an accurate mental model of the problem as a basis for developing solutions. This paper argues that the established “culture” of hand-sketching can be effectively used to help students learn new knowledge and understand the essence of a real world problem. Mapping models by hand provides
Regression Statistics
Multiple R 0.264692
R2 0.070062
Adjusted R2 -0.04153
Std. Error 0.806921
Observations 113
Coefficients Standard
Error t Stat P-value
Intercept 2.192 0.7222 3.0352 0.0030
Q 1.4 -0.03313 0.1029 -0.3217 0.7483
Q 3.3 0.0364 0.1127 0.3232 0.7471
Q 3.9 -0.0709 0.1071 -0.6618 0.5095
Q 3.13 0.0154 0.1015 0.1518 0.8795
Q 4.6 0.0525 0.0823 0.6383 0.5246
Q 4.9 0.0224 0.0942 0.2385 0.8119
Q 4.10 0.1828 0.1005 1.8183 0.0720
Q 4.12 0.0727 0.0890 0.8171 0.4157
Q 6.3 0.0262 0.1342 0.1953 0.8455
Q 7.2 0.0533 0.1157 0.4606 0.6460
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external representations of the internal model in a visual format. Utilizing the power of the brain to analyze visual images, it allows for an effective means for verification and augmentation in iterative cycles.
The concept of reductive abstraction has an established theoretical basis in architecture containing generalizable structures containing invaluable methodologies to use the visual processing power of the human mind. The paper presents an application of the concept to a forensic investigation of a crane accident from photographs. Reductive abstraction was used to eliminate the unrelated environment and the methodical replacement of the complexity with simple lines and symbols familiar to an engineering students having taken statics.
The final section of the paper offers the outcome of a survey to test if engineering students in a prominent Chilean engineering university would consider the introduction of sketching an important study skill. Based on the survey results, they value highly competencies related to sketching, mind-mapping and study skills. On the other hand, the data also shows, that at present only very few of them are actually utilizing such learning tools. Thus, while the students acknowledge the positive effect authentic problem-based learning as well as the high value of the skills needed to be successful in a learner-centered education environment, their present tool-belt of learning competencies is rather bare.
Based on the result of the presented work, the future effort will focus on scaffolding strategies for advancing sketching as an effective tool to assist students in learning and understanding. A second project will design procedures to scientifically test the effectiveness of reductive sketching in creating accurate mental models of various types of engineering and architectural type problems.
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