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Best Paper PIC I: Applying Knowledge from Educational Psychology and Cognitive Science to a First Course in Thermodynamics

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2012 ASEE Annual Conference & Exposition

Location

San Antonio, Texas

Publication Date

June 10, 2012

Start Date

June 10, 2012

End Date

June 13, 2012

ISSN

2153-5965

Conference Session

NEW THIS YEAR! - ASEE Main Plenary II: Best Paper Recognition & Industry Day Session: Corporate Member Council Speaker

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ASEE Board of Directors and Corporate Members Council

Page Count

21

Page Numbers

25.253.1 - 25.253.21

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https://peer.asee.org/23332

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21

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Stephen R. Turns Pennsylvania State University, University Park

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Abstract

AC 2011-186: APPLYING KNOWLEDGE FROM EDUCATIONAL PSY-CHOLOGY AND COGNITIVE SCIENCE TO A FIRST COURSE IN THER-MODYNAMICSStephen R. Turns, Pennsylvania State University, University Park Stephen R. Turns, professor of mechanical engineering, joined the faculty of The Pennsylvania State University in 1979. His research interests include combustion-generated air pollution, other combustion- related topics, and engineering education pedagogy. He is the author of three student-centered textbooks in combustion and thermal-sciences. He is a Fellow of the ASME and was the recipient of ASEE’s Mechanical Engineering Division Ralph Coats Roe Award in 2009.Peggy Noel Van Meter, Pennsyvlania State University Dr. Van Meter is an Association Professor in the Educational Psychology program at the Pennsylvania State University. She teaches graduate courses on Learning Theory as well as Concept Learning and Prob- lem Solving. Her program of research focuses on students’ learning and problem solving with tasks that involve multiple nonverbal representations and text. She has recently collaborated with faculty members in Engineering on the development of an intervention to support students’ problem solving in statics. c American Society for Engineering Education, 2011APPLYING KNOWLEDGE FROM EDUCATIONAL PSYCHOLOGY ANDCOGNITIVE SCIENCE TO A FIRST COURSE IN THERMODYNAMICSIntroduction The fields of educational psychology and cognitive science have done much to advancethe understanding of how people learn. The overarching goal of this paper is to survey theliterature from these fields to glean the most important, or promising, ideas to improve theteaching and learning of thermodynamics. Our work in this area is just beginning, and thepresent paper lays the groundwork for developing testable strategies and methods to improvethermodynamics pedagogy. The objectives of the paper are, first, to stimulate the thinkingengineering educators in this area, and second, to propose some specific examples ofthermodynamics pedagogy grounded in the findings of educational psychology and cognitivescience. The need to develop teaching methods that can improve the problem solving abilities ofengineering graduates is widely accepted. These methods are most likely to be effective if theyare grounded in a theoretical framework and supported by empirical evidence. In this paper, wepropose instruction that can be implemented in a first course in thermodynamics. The theoreticalframework that guided the development of these methods is one that highlights studentcognition. This framework is organized according to three types of knowledge students mustacquire to become proficient in the domain of engineering. These types of knowledge,declarative, procedural, and conditional, collectively address students’ understanding of conceptsand principles, application of skills and strategies, and awareness and control of learning andproblem solving processes. In this paper, we describe each of these categories of knowledge, including importantcharacteristics, and how the knowledge relates to problem solving. We also discuss specificideas for how instructors can impact students’ acquisition of, and their ability to use, each type ofknowledge. Although this paper discusses how these methods can be applied to a specificthermodynamics course, the principles of instruction can be applied to a variety of engineeringcourses. A graphic overview of the organization of this paper and key points from each sectionare shown in Table 1.A Framework of Student Cognition: Three Categories of Knowledge The knowledge used during problem solving can be broken into different categories.1,2Pol et al.3, for example, identify declarative, procedural, and strategic knowledge as the types ofknowledge required for problem solving. Mayer and Wittrock4 listed six separate categories intheir description of the knowledge needed for problem solving: factual, conceptual, strategic,procedural, metacognitive, and beliefs. In our framework, we collapse Mayer and Wittrock’sfactual and conceptual knowledge into the single category of declarative knowledge; and wecombine knowledge of both skills and strategies in the category of procedural knowledge.Finally, we use the label conditional knowledge for the category that includes both students’metacognitive knowledge and their beliefs about their learning and problem solving. Dividing knowledge into these three category types is a matter of theoretical and practicalconvenience rather than a psychological reality. Although knowledge can be meaningfullycategorized into these three types, it is also true that complex cognitive activity requires thecoordinated use of all three. The advantage of thinking about these as distinct types ofknowledge, however, lies in the direction this provides to the design of instruction. Instruction inpostsecondary science courses has been criticized for an over-emphasis on quantitative orprocedural knowledge while overlooking the importance of teaching students the declarative,strategic, and metacognitive knowledge that also underlies problem solving.5,6 Grounding thedesign of instruction in a theoretical framework that is organized around the range of knowledgetypes addresses these limitations. Table 1. Overview of the Key Characteristics and Instructional Applications of the Three Types of Knowledge Key characteristics Instructional Application  Concepts & Principles  Matrix Notes: Organizes knowledge around principles; draws attention toDeclarative  Comprised of elements organized in a the features that distinguish deepKnowledge knowledge network structure of problems.  Well-organized knowledge supports problem solving  Knowledge of skills and strategies  Worked Examples: Builds procedural fluency.Procedural  Effortful during initial learningKnowledge  Self-explanation Strategy: Applies  Use of procedural knowledge to matrix notes, worked examples, distinguishes strong and weak and independent problems. engineering students  Metacognitive knowledge and beliefs  Explicit explanation and cognitive modeling: Builds knowledge ofConditional  Directs and controls application of when and why some knowledgeKnowledge knowledge applies.  Supports independent use of  Card Sorting: Draws attention to knowledge similarities and differences between problems/principles.Declarative Knowledge Declarative knowledge includes knowledge of concepts and principles. This knowledgeis comprised of elements, which can be defined as a unit of a student’s knowledge that seemsirreducible to him or her.7 Elements are organized together through connections in a knowledgenetwork. The pattern of connections in the network supports the meaning of individual elementsby determining how elements are understood in relation to one another. The knowledge networkoperates through a spread of activation. When one element in a network is thought of, oractivated, that activation spreads along connections and activates other knowledge elements.Those elements that are most closely associated with, or connected to, the activated element aremost likely to also become activated. In other words, when a student encounters a problem andrecognizes the correspondence between a feature of that problem and a stored knowledgeelement, that stored element is activated and activation spreads to other, associated knowledgeelements. These mechanisms show that how a student has organized the elements of theirdeclarative knowledge structure directly influences the probability that a particular set ofknowledge elements will be jointly considered during problem solving. Moreover, it is thepattern of connections across these elements that determines a students’ principledunderstanding. A network is organized around principles when the elements contained in thatprinciple are organized together, and other supportive elements are organized around theprinciple. A student whose knowledge is organized in this manner is able to approach problemsolving through the application of principles. In Figure 1, we show a depiction of one expert'sorganization of the main principles students must learn in thermodynamics. ANALYSIS AND DESIGN OF PRACTICAL DEVICES AND SYSTEMS CONSERVATION OF MASS CONSERVATION OF ENERGY ENTROPY AND EXERGY (1st Law of Thermodynamics) BALANCES (2nd Law of Thermodynamics) PROPERTIES OF MATTER: STATE RELATIONS Figure 1. Key thermodynamic principles provide the basis for the analysis and design of practical devices and systems. Psychological research reveals significant differences in the knowledge organization ofexperts and novices in a domain. Expert’s knowledge is fused around critical principles, whereasthe novices’ knowledge representation is piecemeal and fragmented.8,9 Experts benefit from thisstructure because well-organized knowledge supports problem solving,10 the flexible applicationof knowledge,11 strategy use,12,13 and future learning.37 The aspect of problem solving that may be most affected by how knowledge is organizedis the construction of the problem representation.14,15 The problem representation corresponds tothe internal representation of what the problem requires the solver to do, the elements involved inthe problem, and how those elements should be related.4 A problem solver who accuratelyidentifies the principles involved in a problem is representing the deep structure; one whoseproblem representation is based on the storyline of a problem, however, is constructing a surfacefeature representation. Students, particularly weak students,16,17 have difficulty constructingrepresentations of the deep structure of the problem.9,18 Moreover, there is a significantrelationship between the quality of knowledge organization and the ability to recognize the deepstructure of problems.2,19 A novice problem solver in thermodynamics, for example, may not beable to identify properly the system of interest. Failure to construct an accurate problemrepresentation has been tied to problem solving errors in thermodynamics20 and statics.21 The organization of knowledge is constructed at the time of learning and can beinfluenced by instruction8 and study behaviors.13 In fact, studies comparing the knowledgeorganization of successful and struggling students in postsecondary classrooms shows that moresuccessful students’ express an organizational structure that more closely resembles that ofexperts than do their less successful peers (e.g., Refs. 22, 23). These differences have beenassociated with performance on classroom assessments24 and problem solving measures.2 Taken together, this body of research suggests that one way in which an instructor couldimprove students’ problem solving is by helping students to develop a well-organized knowledgebase and showing how this knowledge applies to specific problems. In a later section, wediscuss ways to promote high quality knowledge organization amongst students inthermodynamics.Procedural Knowledge In our theoretical framework, procedural knowledge includes both the skills andstrategies a student knows. Automated skills include knowledge such as how to applyalgorithms and construct diagrams. Strategies are goal-directed cognitive activities that are notrequired for task completion.25 Examples of strategies used during problem solving include self-questioning,26 self-explanation,17 and sketching.27 Strategic processing during problem solvingcan guide students’ attention, help them to recognize the type of problem, and facilitateknowledge transfer.28 Figure 2 shows examples of key procedural skills from thermodynamics. Identification of System & Boundaries Identification of Interactions with Surroundings Control Mass/Volume Work Interactions Closed/Open System Heat Interactions Mass Interactions Detailed Treatment of Units Use of Tabular or Computer-Based Property Data Identifying Units for Each Quantity Identification of State Region Applying Conversion Factors Interpolation/Software Procedures Figure 2. Procedural skills important in thermodynamics. One cognitive factor important for use of both skills and strategies is the effort requiredfor their execution. The cognitive effort that can be dedicated to any task is limited byattentional resources.4 Effort is determined by the amount of these resources required for a task.Whereas highly effortful procedures requires a large percentage of these resources, less effortfulprocedures require fewer resources. The percentage of attentional resources required by aprocedure determines the percentage of these resources that remain to attend to other aspects ofthe task. A complex thermodynamics problem, for example, may require a student to determinea number of state properties while also deciding on a process path and applying energyconservation. The student for whom determining the properties is effortful will not havesufficient attentional resources remaining to appropriately choose a process path or apply apotentially useful problem representation strategy. Theories of both skill29 and strategy30 acquisition indicate that when a procedure isinitially learned, that procedure will be effortful. This effort is decreased only followingextensive practice.53,54 Differences in the procedural knowledge of engineering students enrolled in a staticscourse were demonstrated in a study by Litzinger et al.17 Participants in this study thought aloudas they solved two analysis problems. A group of successful students from the engineeringcourse were compared to a group of students who had more difficulty with analysis problemsand were struggling in the statics course. The analysis of think alouds and students’ writtenwork revealed several important issues with regard to students’ procedural knowledge. Forexample, both strong and weak problem solvers were unlikely to apply moment equations, whichsuggests students had not strongly encoded knowledge of this procedure and how it should beapplied. Comparisons between the groups of strong and weak students revealed that weakstudents were less likely to apply the procedure of drawing component axes to help them orientthe direction of forces in the problems. One of the most important differences in the proceduralknowledge of these two groups was found when comparing strategy use: Strong problem solversused a self-explanation strategy significantly more often than did weak students. These strongstudents were able to use this explanation strategy to guide recognition of the problem’s deepstructure and to support mapping of declarative knowledge principles throughout problemsolving. The findings from this study suggest that the difficulties students have with solvingnovel problems can be at least partially attributed to weaknesses in their procedural knowledge. Students develop procedural knowledge through their experiences completing problems.The ability to apply these procedures fluently (see Fig. 2), with little effort required, is developedthrough practice. The Instructional Implications section of this paper presents ideas on how thisknowledge can be developed for thermodynamics.Conditional Knowledge Conditional knowledge refers to students’ knowledge of the situations in which particulardeclarative or procedural knowledge should be applied.4,31 This knowledge reflects the students’awareness of when, where, and why other knowledge should be used, and this awarenessunderlies cognitive control during problem solving. That is, a student who knows the conditionsunder which some other particular knowledge should be used is positioned to recognize thoseconditions when they are encountered and, consequently, select the appropriate knowledge. Inthis respect, our definition of conditional knowledge is consistent with frameworks ofmetacognition.32 Our view that this knowledge serves as a control mechanism is consistent withmodels of self-regulation33 and conceptions of how metacognition influences problemsolving.11,34 Table 2. Categories of Thermodynamics ProblemsFixed Mass: State Fixed Mass: Control Volume: Control Volume: Control Volume:Change Instantaneous Instantaneous Steady-State, State Change Steady FlowProblems may Problems typically This category is not The simplest Practical problemsinvolve finding work involve application so much a problem problems involve a here typicallythrough knowledge of 1st law to type, but a general single stream in and involve the emptyingof the path; the determine work rate, framework from out. The 1st and 2nd or filling of a tank orapplication of the 1st heat-transfer, or time which all other laws are typically vessel. Applicationlaw to determine rate-of-change of classes of problems applied to analyze of the 1st lawheat and/or work, or system temperature. can be derived. common devices: requires theto determine the Examples here Conservation of pumps, turbines, integration of thefinal (or initial) include the heating energy is frequently heat exchangers, etc. instantaneous formstate, depending on of a filament with an stated in this form Various simplifying for as controlgivens. Many electrical current and and then simplified. assumptions are volume. This classpossible similar lumped- required depending of problems ispermutations and parameter analyses. on the device. particularly difficultcombinations are This problem type is Process paths may for students.possible. State less common than be specified.relations usually others. Device efficienciesrequired. 2nd law are frequentlyconcepts may or involved.may not be required. With respect to declarative knowledge, a student’s conditional knowledge allows him orher to determine the problem conditions in which a particular principle should be applied. Astudent who has accurately associated these conditions with declarative knowledge elementspossess the ability to recognize the deep structure of a problem, determine the key features thatdistinguish problem types from one another, and consequently, select the correct principle toapply. Table 2 illustrates the types of problems encountered in a first course in thermodynamicsand their distinguishing characteristics. We base these categories on the definition of the system(open or closed) and how time relates to the problem (state change, instantaneous, steady). Wesubsume cycle analysis as a repeated application of state-change or steady-flow processes forsimplicity. Conditional knowledge is also a critical factor in determining students’ use of procedures.In his theory of how automated skills are developed, for example, Anderson29 postulates that theactions of a procedure are stored along with knowledge of the conditions in which the actionsshould be applied. These condition-action pairs are connected together to form a rule-basedknowledge network that drives application of the procedure: When the student encountersconditions that match a stored condition-action pair, that match triggers activation of thecorresponding procedural steps. When the conditions are not accurately specified and tied to theaction, it is unlikely that the correct procedure will be selected. Markman35 points out that thereare differences across individuals in the conditions that are encoded in these condition-actionpairs and that these differences can account for the errors that are made in the actions that areexecuted. Conditional knowledge is also an important determinate of students’ ability toindependently use strategies. Students who know how to use a strategy are typically able toexecute the strategy when prompted but are not able to maintain or transfer the strategy.Students who know when and why the strategy could be used, however, are better able totransfer the strategy to novel situations.4,28 Unfortunately, students’ conditional knowledge is often poorly specified. A study by deJong and Ferguson-Hessler2 demonstrated that the ability to recognize the connections betweenconditional and declarative or procedural knowledge distinguished strong and weak physicsstudents as well as predicted scores on a problem solving measure. In this study, students andexperts were provided a set of cards with each card containing a statement of either declarative,procedural, or conditional knowledge. Each declarative knowledge card stated one conceptualidea, procedural cards specified a problem solving procedure, and conditional knowledge cardsspecified problem solving situations. Both students and physics experts sorted these cards intopiles so that cards that belong together were placed in the same grouping. Weak novices in thisstudy typically sorted cards based on surface features so that, for example, cards that identifiedthe same variables were placed together. The organization expressed by strong students moreclosely resembled the categories compiled by experts. These students were more likely toassociate declarative and procedural knowledge elements with corresponding conditionalknowledge. The quality of sortings were related to performance on a problem solvingassessment covering those principles. Helping students to identify the conditions for applying declarative and proceduralknowledge should be considered a central component of instruction. In doing so, students mustbe shown not only those features that identify a problem as a member of a particular class, butalso those features that distinguish one class of problems from another. Likewise, students’knowledge of problem solving skills and strategies must also be developed in association withthe conditional knowledge that can guide and control the application of procedures.Summary The three types of knowledge described here provide a useful framework for thinkingabout the curriculum, or content, of instruction, but instructors must also be aware that the threetypes develop together. There is, for example, a relationship between the quality of collegestudents’ declarative knowledge organization and the tendency to use deep, rather thansuperficial, study strategies.12,13 Strong students are also more likely to apply strategies towardboth declarative and procedural knowledge than are their weaker performing peers.36 Duringinstruction then, instructors must help students to become aware of these relationships andrecognize how to coordinate the various types of knowledge. In thermodynamics, for example,knowing the state principle, that two independent intensive properties define the state of a simplecompressible substance, can trigger a number of procedures depending upon the problem. Forexample, if only one property is known, some procedure must activate to find a second propertyto define the state. Alternatively, if the state is defined, application of the first law can proceed,if required. Instructors must also be aware that, while these knowledge types speak to the content ofinstruction, one must also consider the methods of instruction.37 The following section beginswith a description and rationale for instructional methods that we believe are congruent with thefindings from educational psychology and cognitive science discussed above.Instructional Applications We advocate instructional methods that use explicit explanation, apply cognitivemodeling, and promote active student engagement. Explicit explanation refers to methods ofinstruction in which teachers provide direct statements explaining what students are expected toknow and how they should know it.38 Cognitive modeling is when the instructor talks out loud toprovide explanations of problem solving processes that are primarily hidden within internalthought processes.39 Explicit explanations given during cognitive modeling teach students howsolution steps are related to problem solving4 and support the development of cognitive andmetacognitive knowledge.40 At the same time, however, we also know that students who are passive recipients ofthese explanations learn less effectively than do students who are actively involved in theirlearning.6,37,41 Prompting the use of deep learning strategies is one way to engage students inactive learning.42 Highlighting the use of these strategies also draws the attention of bothstudents and teachers to the importance of learning how to learn and solve problems. Studentswho attend to these processes are more likely to detect progress toward their learning goals andhave higher self-efficacy relative to their peers who attend to the quality of final products.39 Taken together, these instructional methods can be employed to help students acquiredeclarative, procedural, and conditional knowledge. In the remainder of this section, we shareideas on how this can be achieved in an introductory thermodynamics course. For our purposes,we define an introductory course to cover the content shown in Table 3. Table 3. Topics Covered in a Typical Introductory Thermodynamics TOPIC Introductory Concepts & Groundwork Thermodynamic Properties & State Relations Mass Conservation Groundwork for Energy Conservation – Heat, Work, & Energy Energy Conservation – 1st Law for Thermodynamic Systems Energy Conservation – 1st Law for Control Volumes & Applications 2nd Law of Thermodynamics 2nd-Law Properties, Property Relations, and Isentropic Efficiencies Vapor Power Cycles Gas Power Cycles Vapor-Compression Refrigeration CycleDeclarative Knowledge Figure 1 depicts the four main principles that thermodynamics students must learn: (1)thermodynamic property relations, (2) conservation of mass, (3) conservation of energy, and (4)the second law of thermodynamics. Students must come to understand how these principles areapplied to problems involving closed and open systems, and the role of time in these problems,and how these principles are associated with the features of these problem classifications (seeFigure 2 and Table 2). A goal of instruction in this course is for students to learn how todistinguish problems along these classifications and to understand how the principles apply ineach case. A prerequisite to developing any deep understanding of thermodynamic principles is forstudents to understand the symbolic representations use to describe these principles.43 Althoughthis might seem trivial, many students require time and practice to develop the necessaryvocabulary. Because of the rich content of thermodynamics, many symbols are required.Explicit building of a symbolic vocabulary can be accomplished using in-class exercises,homework, and quizzes. Figure 3 illustrates a quiz that fosters this development. To be successful in thermodynamics, a student must develop a knowledge network inwhich the elements that comprise the four principles are the major organizing component of thenetwork. The student must organize this knowledge relative to the features underlying problemclassifications. Knowledge that allows the student to identify the defining features of problemsmust also be incorporated into this knowledge structure. A. Using words only, define the following terms as they relate fluid mechanics and thermodynamics. Do not just recite the symbols in words; for example, mv2/2 is kinetic energy, not one-half of the mass times the square of velocity. Also give the units of the quantity. Meaning Units a. W _________________________ ________________ b. P _________________________ ________________ c. E _________________________ ________________ d. u _________________________ ________________  Q e. _________________________ ________________ f. h _________________________ ________________ g. mPv  _________________________ ________________ h. q _________________________ ________________ B. The letter vee (upper and lower case) is used to represent several quantities in this course. List these quantities and indicate which vee is used for each. Figure 3. Quiz to assess students’ understanding of symbolic representations. These goals can be achieved through the use of matrix notes, a note taking strategy thatincreases the completeness of students’ notes and encourages the construction of internalknowledge connections that emphasize the organizational relationships across ideas.44 Matrixnotes use a table format in which organizes information according to both unique instances andrepeated categories. Figure 4 shows a completed matrix that could be used in a thermodynamicscourse. In this matrix, the unique instances correspond to the different classification of problemsencountered in the course. These unique instances are given in the headings for each row of thematrix. Columns of the matrix contain the repeated categories that correspond to three of thefour principles. We have also added an additional column labeled defining features. The matrix acts as a framework to organize students’ knowledge throughout the course.Students would start the course with a blank matrix and fill in the blanks as they proceed throughthe course. The structure provided by the columns draws students’ attention to the features thatdistinguish one class of problems from another. Comparing similarities and differences in theprinciples across the problem classes (columns) supports understanding of how the principlesapply to these problems. Once completed, a student can use the matrix as an aid to problemsolving. When given a problem, the student can first inspect the rows to identify the class thatthe problem comes from. That student can then follow each column across that row to see howeach principle should be applied. Once the student has learned the contents of the matrix so thatit is part of the internal knowledge network, this well-organized representation can be accessedwithout having to inspect the external, physical matrix. The entries in Fig. 4 have beenexpressed quite generally; simpler relationships could have been used in many instances. The matrix shown in Fig. 4 provides an organizational structure that spans the entiresemester of the thermodynamics course. The matrix should be introduced early in the semesteras the first problem class is encountered and completed as additional problem classes are coveredthroughout the semester. In keeping with our belief that the best instruction involves explicitexplanation and cognitive modeling, the instructor can take responsibility for selected entries. Matrix notes can also be used to treat selected topics. For example, a matrix could beconstructed for a selection of ideal-gas processes: constant-volume, constant-pressure, andconstant-temperature. Students would then fill in the matrix by writing in the simplified first-lawexpression, useful state relations, and expressions that could be used to calculate work and heatfor the process. Figure 5 shows such a matrix. Having students complete this matrix should helpstudents integrate their knowledge and internalize that special cases follow quite simply from afew general principles. Clearly, the use of matrix notes is not limited to the two examples shownhere; a thermodynamics course is content rich and many opportunities exist for the application ofmatrix notes. For example, matrix notes can very naturally be applied to the topic of steady-flowdevices. Developing matrix notes can also be an active learning exercise using small groups. While the matrices described here are primarily organized around declarative knowledge,this framework can also be used to build connections with procedural and conditionalknowledge. For instance, in addition to the features that define the deep structure of a problemclass, the matrix can also contain information about the derivation of the equation that applies tothat class. Other ideas regarding how procedural and conditional knowledge can be incorporatedwith the matrix are discussed within those sections below.Procedural Knowledge Successful problem solving in complex domains such as thermodynamics requires bothcomponent skills, such as the ability to apply formulas and construct diagrams, as well ascognitive strategies that support learning and problem solving.5,15 One goal for thisthermodynamics course then is for students to build fluency with component skills so that theseskills will become automated and require less effort. A second goal is for students to acquireknowledge of strategies that can be independently applied to support problem solving. To achieve the first goal, we recommend using worked examples to aid development ofskills that can be used fluently with little effort. In the context of cognitive science, workedexamples are defined as samples of problems that show each step of how an expert wouldcomplete the problem.39 Example problems are common in thermodynamics textbooks and assubjects for lectures. Students, for better or worse, depend upon example problems. A well-done worked example allows a student to get into the brain of the expert to understand thethought processes involved in the problem solution. In addition to showing the solution steps fora problem, a worked example can also explicitly document the thinking that went into theexpert’s solution. On the whole, research on worked examples has shown that providingstudents with worked examples leads to better learning of component skills than does providingsample problems that the students complete on their own.45 One reason worked examples maybe effective is because they reduce the amount of attentional resources required during learningof procedural knowledge.46 The current practice of using worked examples in engineeringinstruction is congruent with the findings from cognitive science; thus, rather than disparagingstudents’ use of examples, instructors could consider how to help students use these examplesmost effectively. A course instructor could, for example, annotate textbook examples withverbal explanations of the steps that were taken as a relatively painless way to provide themissing links. Further, as discussed below, students can also be assigned the task of generatingtheir own explanations for the steps in a solution process. We now consider our second goal: increasing students’ knowledge of, and ability toapply, effective problem-solving strategies. Although several strategies could be used to supportthermodynamics problem solving, the strategy we recommend is self-explanation. Self-explanation is a strategy in which students must generate causal explanations of targetedphenomena.47 This strategy directs students to activate their prior knowledge,48 supports theconnection of known principles to problems,17 and supports anticipative reasoning duringproblem solving.49 We recommend this particular strategy because self-explanation can beprompted and taught with relative ease (e.g., Bielaczyc, Pirolli, & Brown50), and the benefits ofthe strategy for learning in engineering has been documented. We recommend incorporating self-explanation with both the matrix notes and workedexamples. Specifically, students can use self-explanation as they take responsibility forcompleting cells of the matrix. For example, when completing the row associated with control Conservation of Conservation of Energy 2nd Law Entropy Defining Features Mass Balances  Fixed Mass: m2  m1  m Q2 , in  1W2 , in 2 Q A process occurs toState Change S    S irrev change the system’s state. 1  1 Q2 , out  1W2 , out 1 T Time is irrelevant. Equilibrium prevails at the  E 2  E 1  E beginning and end of the process.Fixed Mass: m2  m1  m   Qin  Win dS / dt  Q / T  Sirrev  The state of the system isInstantaneous continually changing.    Qout  Wout System descriptions are a snapshot in time.  dE cv / dtControl Volume:Instantaneous m  m   i i  E  E   in out  dE cv / dt  dS cv / dt  Q / T Mass enters/exits the CV, carrying energy with it. m s  m s In Out or    i i i i The state at any location dmcv / dt In Out within the CV is   Qin  Win continually changing. CV  Sirrev descriptions are a snapshot   m (h  i i  Vi / 2  gzi ) 2 in time. Relationships can be used to derive all other In   equations given in this  Qout  Wout matrix.   m (h  i i  Vi / 2  gz i ) 2 Out  dE cv / dtControl Volume:Steady-State, m  m   i i 0 E  E   in out 0  0  Q /T Mass enters/exits the CV, carrying energy with it. m s  m s In OutSteady Flow or    i i i i The state at any location In Out within the CV is fixed.   Qin  Win CV descriptions apply at Sirrev all times. Time is   m (h  i i  Vi / 2  gzi ) 2 irrelevant. In    Qout  Wout   m (h  i i  Vi / 2  gz i ) 2 Out 0Control Volume: m2  m1  E cv , 2  E cv , 1  1 Q2 , in  1W2 , in S 2  S1  1 Q 2 / T The state of a CV changesState Change as a result of mass  mdt   mdt     mi ( hi  Vi / 2  gz i ) dt  2    mi si dt   m s dt  i i entering or exiting with the possibility of heat and In Out In In Out work also occurring. or  1 Q2 , out  1W2 , out m2  m1  m   mi ( hi  Vi / 2  gz i ) dt 2  Out Figure 4. Example of matrix notes applied to key concepts in thermodynamics. Process 1st Law Process & State Work Heat Relations PV1  mRT1 ; PV2  mRT2 1 2 2  PdV  mc (TGeneral Case Q2  1W2  U 2  U 1 2 Q2   T1 ) U 2  U 1  mcv (T2  T1 )  PdV 1 1 v 2 1 H 2  H 1  mc p (T2  T1 ) 1 P  P2 ; T1 / V1  T2 / V2 1 1 Q2  P (V2  V1 )  U 2  U 1 Constant-P Q2  1W2  U 2  U 1 P (V2  V1 ) 1 U 2  U 1  mcv (T2  T1 )  H 2  H1 H 2  H 1  mc p (T2  T1 )  mc p (T2  T1 ) V1  V2 ; T1 / P  T2 / P2 1 Constant-V Q2  1W2  U 2  U 1 Q2  mcv (T2  T1 ) 1 U 2  U 1  mcv (T2  T1 ) 0 1 H 2  H 1  mc p (T2  T1 ) T1  T2 ; PV1  PV2 1 2 Constant-T Q2  1W2  U 2  U 1 PV1 ln(V2 / V1 ) Q 2  1W2 1 U 2  U 1  mcv (T2  T1 )  0 1 1 H 2  H 1  mc p (T2  T1 )  0 Figure 5. Example of matrix notes applied to ideal-gas processes for a fixed-mass system.volumes involving steady state and steady flow, the teacher can prompt the students to use self-explanation to complete the cell corresponding to the conservation of mass principle by askingthem to ‘explain how the conservation of mass applies to these problems’. These studentexplanations should be monitored to ensure students are attending to and including the mostimportant information. Students can also be instructed to use self-explanation when completing workedexamples. Here students can be assigned the task of writing verbal explanations for each step ofthe examples. Students who apply the self-explanation strategy in this manner learn more fromworked examples than do students who do not use the strategy.45 In addition to these uses, students can also be taught to use self-explanation duringindependent problem solving. Using the strategy in this context means that the student wouldexplain each step of the problem as they are completing it, including explanations of how keyprinciples are applied. Similar to how this strategy can be used with worked examples,instructors can encourage this strategy use by assigning the task of writing out theseexplanations. Thus, the homework students turn in would include not only their worked outproblem solution but also their written explanations.Conditional Knowledge Whether acquiring declarative knowledge of principles, or procedural knowledge of skillsand strategies, a student’s ability to independently use this knowledge is affected by his or herunderstanding of when and where this knowledge should be applied.28 Thus, the goals ofbuilding students’ conditional knowledge should also be embedded within the goals for teachingdeclarative and procedural knowledge. We believe this goal can best be achieved by applying the teaching methods of explicitexplanation, cognitive modeling, and active student engagement to the recommended practicesdescribed thus far. An instructor who uses explicit explanation directly tells student what theyare doing and why they are doing it. Thus, when the matrix notes are first introduced, forexample, the teacher should clearly and directly tell the students about the purpose of the matrixand how it should be used. When guiding the students through completion of the matrix, theteacher should engage in cognitive modeling to make visible the thinking that underlies thedecisions that are made. Throughout the semester, the instructor should continue to makeexplicit reference to the matrix, explain how it can be used during problem solving, and bothprompt and model its use. Similar methods can be applied to both worked examples and the self-explanation strategy. That is, the teacher should tell students what they are doing and why, aswell as engage in modeling to support students understanding. When prompting students to usethe self-explanation strategy, it is also important that this strategy be labeled and explained.These explanations can also accompany the teacher’s use of the strategy during cognitivemodeling. Students’ conditional knowledge can also be fostered through activities that draw theirattention to the relationships among principles and to the similarities and differences amongproblems from different classes.4 An activity that can achieve this goal is a form of card sorting.Card sorting is a method used in educational research to infer the organization of participants’knowledge. As an example of how this could be applied to the organization of principles withinthe thermodynamics course, consider giving students a stack of cards on which words are writtento represent key concepts and principles. Students would be directed to sort these cards intopiles so that they place together those cards that belong in the same grouping. In a large class, apencil-and-paper exercise is more practicable. An example list of terms and an expert’s sortingof those terms is shown in Fig. 6. This activity aids learning because it forces students tobecome aware of how they believe these concepts and principles are related. The instructor mayalso use the results of students’ sortings to gain insight into how students understand those terms,much in the same way an educational researcher would use the results to infer the quality of theknowledge structure (cf. Shavelson & Stanton51). Students’ organization of symbolic(mathematical) representations also can be developed and assessed using exercises such as thatshown in Fig. 7. Similar techniques can also be applied to whole problems.52 Students can be givenproblems, such as the two shown in Fig. 8, and told to sort the problems according to the deepstructures that define their class membership. The results of these sortings can be used in thesame manner as the sortings of terms – instructors can infer how students’ understand theseproblems and their ability to detect the deep structure of the problems. The instructor shouldalso engage students in discussion of these sortings to provide the type of training that canimprove their ability to recognize the features that determine deep structure (cf. Quilici &Mayer55). Arrange the following items into several groups of related items. Use as many groups as you need to parse these items. You may also use items more than once. If one of the items in your groups can be considered a heading, underline that term. Items Expert Groupings 1. Pressure State / Properties 2. State Pressure 3. Process Energy 4. Equilibrium Enthalpy 5. Energy Entropy 6. Work Temperature 7. Heat Equilibrium 8. Mass 9. System Process 10. Control volume Adiabatic 11. Conservation principles Isothermal 12. Enthalpy Isentropic 13. Entropy 14. Properties Conservation principles 15. 1st law of thermodynamics Mass 16. 2nd law of thermodynamics ...

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