A Guided Problem-Based Learning (PBL) Approach: Impact on Critical Thinking

Decision Sciences Journal of Innovative EducationVolume 12 Number 2April 2014Printed in the U.S.A.

C© 2014 Decision Sciences Institute

CONCEPTUAL RESEARCH

A Guided Problem-Based Learning (PBL)Approach: Impact on Critical Thinking

Satish Nargundkar†Department of Managerial Sciences Robinson College of Business Georgia State University,Atlanta, GA, 30302, e-mail: [email protected]

Subhashish SamaddarDepartment of Managerial Sciences Robinson College of Business Georgia State University,Atlanta, GA, 30302, e-mail: [email protected]

Somnath MukhopadhyayDepartment of Information and Decision Sciences College of Business AdministrationUniversity of Texas at El Paso, El Paso, TX, 79968-0544, e-mail: [email protected]

ABSTRACT

The impact of the Guided Problem Based Learning (Guided PBL) approach on CriticalThinking (CT) skills in a core business analysis course was examined. The implementa-tion of this approach included using a textbook created for this purpose, which presentsproblems first, with blank spaces for students to work them out. Discussion of the con-cepts and theory needed to understand and solve the problems, as well as the solutions,come later in the book. This book is referred to as the Reversed Textbook. Students at-tempt to answer questions or solve problems in class with instructor guidance as needed,before discussion of theory. Student learning in sections taught prior to implementingthe Guided PBL method was compared with student learning in sections taught withthe method. Results indicate that the approach motivated learning and improved studentperformance on a departmental final exam by an average of 9%. When measured onCT questions alone, the improvement was on average 24%. Finally, the Guided PBLapproach also improved group task performance by 6%. All the improvements werestatistically significant.

Subject Areas: Problem-Based Learning, Teaching Innovation, and CriticalThinking.

INTRODUCTION

Improving a student’s Critical Thinking (CT) ability is considered to be an im-portant aspect of teaching at the university level by most educators today (Taylor,

†Corresponding author.

91

92 A Guided Problem-Based Learning (PBL) Approach

2010). However, there is considerable debate about how to go about doing it. VanGelder (2005) argues that CT is not a natural activity for humans, and cites Shermer(2002) in saying that humans are pattern-seeking, story-telling animals that prefersimple, familiar patterns over the harder cognitive task of CT. Van Gelder (2005)further suggests that the problem with teaching CT is that many teachers discussthe theory of CT rather than have their students practice it. This is ineffective, heargues, since the only way to improve CT ability, as with any other skill, is topractice doing it. Simply providing challenging course work does not ensure thatstudents will learn to think critically (Bensley, 2010). He suggests that explicit,direct instruction of CT skills is necessary, provides several tips for instructorsto achieve this, including the idea that students must first be motivated to engagetheir minds with the material. Second, CT objectives for the course must be clearlystated.

Active learning strategies have in general been found to be more effectivethan a traditional lecture format in improving measures of problem solving, think-ing, attitude change, or motivation (McKeatchie, Pintrich, Lin & Smith, 1987).In business education, collaborative, project based learning strategies have beenshown to be effective in improving CT skills (Ngai, 2007). Problem based learning(PBL) as a method of instruction to improve CT has been studied extensively in themedical field (Tiwari, Lai, So &Yuen, 2006; Yuan, Williams & Fan, 2008). Whilethe PBL approach is geared towards student directed learning, Meyer (2004) arguesthat CT practice among students must be guided to be more effective, especiallyin areas in which students have no prior knowledge.

In this study a Guided PBL approach is implemented in a required businessanalysis course for undergraduate students to improve their CT ability. The keyresearch questions are:

(1) Does Guided PBL help students perform better overall? and

(2) Does Guided PBL improve CT ability?

LITERATURE REVIEW

Pedagogical literature suggests that there is disagreement about what exactly CT is.It is used too broadly to get a clear idea of how to measure it, and therefore to knowhow effectively it is being taught (Williams, 1999; Bahr & Lloyd, 2010). Despitedisagreement on the definition of CT, there are some accepted elements of CT thatmost researchers agree upon. These include the ability to think deeply about anissue, consider evidence for and against a proposition, and apply reasoning skillsand logical inquiry to arrive at possible conclusions.

Lai (2011), in a survey of the relevant literature, found various definitionsof CT, primarily originating in the fields of philosophy and psychology. Thephilosophical definitions are descriptions of ideals of thinking, such as “disciplined,self-directed thinking that exemplifies the perfections of thinking appropriate to aparticular mode or domain of thought” (Paul, 1992, p. 9). Psychologists, on theother hand, tend to be more pragmatic, and define CT in terms of how humansactually behave, laying out a series of skills and behaviors that a critical thinkermight engage in, such as “seeing both sides of an issue, being open to new evidence

Nargundkar et al. 93

Table 1: Broad classification of pedagogical approaches to CT.

Method Description

Direct This method assumes that CT is a general ability that must be developedthrough stand alone instruction in the process of CT. Proponents ofthis method prefer to teach CT outside of any specific knowledgedomain by creating a general course on CT itself (Ennis, 1989; VanGelder, 2005).

Indirect In this method, CT is assumed to emerge through immersion in a givencontext. In other words, a more rigorous treatment of a specific subjectmatter is considered sufficient for CT to happen, without explicitlymentioning it (Bailin, Case, Coombs & Daniels, 1999; Case, 2005).

Mixed This approach benefits from a combination of the above two approaches.Students are taught the key elements of CT explicitly as theirexperience with CT evolves in a specific knowledge domain such asbusiness, medicine, etc. (Kennedy, Fisher & Ennis, 1991; Paul, 1992).

that disconfirms your ideas, reasoning dispassionately, demanding that claims bebacked by evidence, deducing and inferring conclusions from available facts,solving problems, and so forth” (Willingham, 2007, p. 8). Philosophers criticizethis approach, arguing that one can blindly go through the motions of engaging inthe “right” list of activities without actually thinking critically. The third approachto defining CT comes from the field of education, with Bloom’s (1956) taxonomyleading the discussion with the concept of levels of learning. For pedagogicalpurposes, an actionable definition of CT is necessary. Combining Bloom’s ideaswith those of the psychologists provides a way to operationalize the construct.A student’s thought process cannot be observed as philosophers would have usdo, but explicit problem solving abilities and the ability to gather and analyzeevidence, and make decisions, can be observed. For this study, CT is thus definedas the ability to solve problems, collect and analyze evidence, and use the analysisfor decision making.

The literature on CT is mixed on how it should be taught. Broadly speaking,there are three schools of thought. The first assumes that CT stands alone andshould be taught that way, separate from any other discipline. This is referred toas the direct method. The second approach assumes the reverse – that CT shouldonly be taught through deep immersion in a particular subject, but never directly.This is the indirect method. A third approach simply combines the two, and canbe viewed as the mixed method. Table 1 summarizes the approaches found in theliterature.

STUDENT MOTIVATION AND CRITICAL THINKING

Garcia & Pintrich (1992) found that CT among students in university courses ispositively related to the intrinsic motivation of the students towards learning. Atypical college curriculum includes both required and elective courses. Students


in required courses are often less motivated to study. The motivation for suchstudents tends to be purely extrinsic, a quest for the best grade with the least effort.Ryan & Deci (2000) argue that an effective instructor can move the student froma reluctance to learning towards an acceptance of the goals set by the instructor,and even to internalize the goals. Effective teaching is thus about convincing thestudents of the value of the goals set, making the course relevant to the students’lives, and thereby motivating them to engage their minds fully with the subject.Nargundkar & Shrikhande (2012), in a study of business school students, found thatalong with course organization and clarity, the ability to motivate students is amongthe most important factors that determine the millennial students’ perceptions ofeffective teaching. It is therefore important for instructors to understand how tomotivate students to think critically.

Several approaches have been suggested in the literature to help motivatestudents, and one such approach is Problem-Based Learning (PBL). This con-structivist approach leads to two basic principles: anchoring learning to a largertask, and helping students take ownership of the learning (Savery & Duffy, 2001).The concept of designing courses and curricula around PBL has been applied inseveral fields of study including Engineering, Social Sciences, and Business. Nor-man & Schmidt (1992) reviewed the evidence and found that PBL can result inincreased retention of knowledge over a longer period of time, enhances interestin the subject matter, and increases self-directed learning. The increase in prob-lem solving ability is context specific. There is not enough evidence that problemsolving ability improves in areas other than the one for which the approach isused. Kirshner, Sweller & Clark (2006) on the other hand, based on their under-standing of human cognitive architecture, argue that methods of instruction likePBL that include minimal guidance from the instructor are bound to be less ef-fective than guided instruction. They recommend the use of worked-out examples,which they consider to be the epitome of guided instruction, to help novices learneffectively. Meyer (2004) also argues strongly against purely constructivist ap-proaches to teaching in which the discovery of knowledge is left entirely up to thestudent. He cites research spanning over three decades to emphasize the idea thata guided approach to discovery works better.

The research studies mentioned above suggest that for teaching a core classin which students have almost no prior knowledge of the subject and likely havelow motivation to learn it, a purely unguided PBL approach would probably notwork. On the other hand, the traditional approach of lectures followed by workedexamples and assignments, does little to motivate the students to study a subjectthey are not interested in. The Guided PBL approach provides an appropriatemiddle ground.

IMPLEMENTATION OF GUIDED PBL IN THE CLASSROOM

The Guided PBL approach with a mixed method (see Table 1) of teaching CTwas implemented in a course titled Business Analysis. This is a required coursefor undergraduate business students in their junior year. There are typically upto 45 students in a section. The classroom is set up in a traditional lecture roomwith modern visual aids for instruction, and the ability for students to engage in


impromptu small-group activities. The setup also permits the instructor to walkaround the room to engage with individual students as needed.

The course objectives, broadly, are to help students learn how to analyzebusiness situations, apply quantitative models as needed with the aid of spread-sheets, and interpret model results to support business decision making (a courselike this may typically be labeled Decision Sciences in many institutions). Studentsare evaluated, among other factors, on the basis of a departmental final examina-tion that includes questions at various levels of learning as per Bloom’s taxonomy,including CT. Students are also required to work in groups on two projects duringthe semester in which they demonstrate their ability to analyze a business situa-tion, build spreadsheet models for profitability analysis and forecasting, and writea report detailing their analyses and recommendations. These essentially representgroup level CT tasks.

As part of the implementation of the Guided PBL method in the classroom,one key innovation - a reversed textbook1 for Business Analysis (see Appendix Afor example pages from the book) — was used. Traditional text books begin withgeneral, usually abstract explanations, show examples of worked problems, thenhave exercises at the end of the chapter. They therefore encourage instructors tofollow an order of instruction that begins with lectures on concepts, definitions,procedures, and formulas, and then move towards practical application. This how-ever, is contrary to the principle of Problem Based Learning, which requires that aproblem be introduced first. The innovation here was to create a book that beginswith questions, and provides blank spaces for students to answer conceptual ques-tions or attempt to work out the problems. The second half of the book then offerstheoretical discussion, detailed answers to the conceptual questions, and solutionsto the problems. In essence, the book enables the instructor to reverse the orderof instruction in the classroom to motivate learning. When used appropriately, thefirst half of the book becomes a student-created solution manual.

A typical class session might begin with a business situation. Students areintroduced to the general situation and asked to attempt to solve a problem in thebook or discuss a conceptual issue (see Appendix B for detailed guidelines onimplementing this approach in the classroom). The instructor makes a deliberateeffort to guide the students by offering insights on the problem’s relevance, andthe value that can be created by solving it. However, no specific explanation isprovided as to how to do so. When the semester begins, the problems are usuallyof a kind such that about half the class might be able to solve them based onprior knowledge of algebra and general business. Students are then encouraged totalk with their neighbors in class to solve the problem together. They are awarethat the answers are available in the back, but are encouraged not to look at theanswers. After a few minutes, the instructor asks probing questions, the answersto which help decide how much to ‘nudge’ student thinking with small pieces ofinformation. Eventually the instructor discusses the problem and the solution withthe entire class, continuing to ask probing questions that elicit responses whichlead to key definitions and concepts related to the problem. Finally, the instructor

1Please contact either of the first two authors for more details regarding the reversed textbook.


helps the students go beyond the scope of the current problem and think abouthow it might apply in various other business situations, as well as providing anytheoretical underpinnings as needed.

HYPOTHESES

Referring to the discussion presented in the literature review, students with intrinsicmotivation are likely to perform better than students without the motivation tolearn a subject (Garcia & Pintrich, 1992). Students taking required classes are alsoless likely to be highly motivated to learn the subject. Further, it is possible forinstructors to move the student from extrinsic to intrinsic motivation based on theapproach used in class (Ryan & Deci, 2000). Guided PBL is one such approachavailable to instructors to help motivate students (Kirshner et al., 2006). Oonewould therefore expect that students will perform better overall in a course whentaught with the Guided PBL approach due to increased motivation to learn.

H1: The introduction of the Guided PBL approach with the Reversed Text-book will improve student learning.

The hypothesis is tested by comparing final examination scores of studentswho were taught using two approaches – the traditional approach and the GuidedPBL approach. The details are described in the methodology section.

Similarly, it is expected that students will display improved CT skills in-dividually as a result of having practiced them in and outside the classroom viaassignments in the book designed to help them do so.

H2a: The introduction of the Guided PBL approach with the Reversed Text-book will improve CT at the individual level.

The literature suggests that there is a positive correlation between individ-ual ability of group members and group performance (Bottger & Yetton, 1988).Enhancing individual CT ability should thus improve group performance on CTtasks. It is possible, however, that individual CT skills do not always translate toimproved teamwork. Star individuals may in fact perform poorly in teams since astar may tend to be domineering and alienate team members. Other factors suchas a lack of team cohesiveness or free-loading by some team members, may coun-teract any improvement in individual ability. However, the literature also suggeststhat cooperative learning enhances CT among students individually as well as ingroup work (Johnson & Johnson, 1989; Slavin, 1991). As part of the in-class in-struction for this course, cooperation was encouraged in class discussions in aneffort to build team cohesiveness. It is therefore hypothesized that the Guided PBLapproach to teaching will improve performance in group project tasks as well.

H2b: The introduction of the Guided PBL approach with the Reversed Text-book will improve CT at the group level.


METHODOLOGY

A controlled experiment was used to test the effectiveness of the Guided PBMmethod. The method was used in a required Business Analysis course that hasmultiple sections offered throughout the year. The performance of two groupsof students — referred to as the before and after groups – was compared. Thebefore group consisted of students from four sections (n = 154 students across allsections) of the course taught in the year before the new method was implemented.The after group consisted of students from three sections (n = 114 students acrossall sections) in the year after the implementation. Data were collected from sectionstaught by the same instructor. This ensured that variation due to the ability of theinstructor was controlled for. To control for differences in student ability, a pretestwas conducted at the beginning of the semester for all the students in the beforeand after groups. No statistically significant differences were found, suggestingthat student ability was also controlled for.

To test the first hypothesis, the overall final examination scores of the beforeand after groups were compared, using two-sample t-tests. This examination hasquestions at different levels of learning: Knowledge, Comprehension, and CT,based on Bloom’s (1956) taxonomy. The course coordinator is responsible fordesigning the examination and classifying the questions into the categories. Theexaminations are comprehensive and departmental, and the content of the questionsdid not change during the study.

For hypothesis 2a, it was necessary to look at the students’ individual per-formance on CT tasks. Student performance on only the CT questions from thefinal examinations was compared for the before and after groups (see AppendixC for examples). To test Hypothesis 2b, the before and after student scores onthe projects were compared. As mentioned previously, students in this course areassigned two group projects (groups of 3 or 4 students) that require demonstrationof CT abilities.

RESULTS

H1: Two-sample t-tests were conducted to test for differences in the finalexam scores of the before and after groups. The results are shown inTable 2. In the year prior to using the Guided PBL approach, the averagestudent score in the before group on the departmental final exam was 68%

Table 2: Improvement in Final Exam scores.

Before After

Number of students 154 114Mean Departmental Final Exam Score 68.44 77.02(Maximum possible score = 100)Standard Deviation 11.99 11.34

p < 0.0001


Table 3: Improvement in CT scores.

Before After

Number of students 154 114Mean Score on CT questions only 34.9% 58.0%(Maximum possible score = 100)Standard Deviation 24.8 18.5

p < 0.0001

Table 4: Improvement in team project performance.

Before After

Number of students 154 114Mean Score on Projects 79.6% 85.7%(Maximum possible score = 100)Standard Deviation 5.5 4.9

p < 0.0001

(the median was 69%). The average final examination score climbed to77% (median was 78%) in the year after implementing the method ofteaching (the after group). This is an improvement of almost one lettergrade on average. H1 is thus supported.

H2a: On average, 20% of the questions on the final examination require someCT ability. Results of the average student performance on these questionsare shown in Table 3.

The results show that student performance on CT problems improved signif-icantly due to the use of the Guided PBL approach. The difference was consistenteven when Median scores were considered (35% before and 55% after). H2a isthus supported.

H2b: Data was also collected on student performance on the team projects,and the results of the comparison for the before and after groups areshown in Table 4. CT ability in group tasks showed significant improve-ment. Median scores for the before and after groups were 80% and 85%respectively. The team projects involved spreadsheet-based analysis inwhich students analyzed real or realistic business data, and wrote a reportdetailing their analysis and recommendations. The entire project is thusa CT task. The key question that they must answer is what action wouldthey take as a manager/owner of the business, given their analysis. H2bwas thus also supported by the data.

DISCUSSION

PBL has traditionally been known to improve learning, especially in the medicalfield (Donner & Bickley, 1993; Wood, 2003). This paper contributes to the PBL


literature by adding to the evidence that PBL can be used to enhance CT abilityamong students in a Business School. The Guided PBL approach tested here wasfound to be more effective for a required class than the traditional lecture approach,improving both overall learning as well as CT ability.

The specific innovation of using a reversed textbook to implement the GuidedPBL approach is another contribution of this study. The organization of the bookhelps the instructor implement the teaching strategy more effectively since itprovides no theoretical concepts or solved examples in the beginning. Feedbackfrom students indicates that they find this approach and the reversed textbook to beuseful for their learning. It is rare for students to mention a textbook in a positivelight in the Student Evaluations of Instruction (SEI) at the end of the semester,but this book received several positive comments from students. Overall studentevaluation scores also showed improvement.

While the approach worked well in the experiment presented in this paper,there are potential pitfalls that one should be aware of. A key point is that thereversed textbook alone will not automatically create the improvement in criticalthinking. It must be embedded in the Guided PBL approach. Otherwise, it has thepotential to backfire, since students are not used to working with this kind of abook, and will be expecting a traditional book that explains the concepts at thebeginning of each chapter. The onus is on the instructor to set the expectations ofthe students in terms of how learning will take place, and how the book will beused in and outside the classroom. Suggestions for preparing the instructor and thestudents to use the Guided PBL approach effectively are presented in Table 5.

A possible concern among instructors interested in adopting this approachmay be whether there will be enough time to cover all the material in the course,given the added interactions in the classroom. We have found that the time taken toensure that students learn the content is no more than in the traditional approach.In most instances, the time taken is actually less, since the Guided PBL methodreplaces traditional lectures rather than adding to them. It may take a little longerup front to discuss the issues surrounding the problem, but once that is done,class time is saved as there is little need for repetition of concepts since studentshave been engaged in discovery throughout the class. The additional benefit, asdiscussed before, is that learning occurs at a higher level.

There may be other ways to implement Guided PBL besides using a reversedtextbook. While the reversed textbook is a useful artifact to implement PBL, futurestudies might compare other implementation methods with the reversed textbookapproach. For instance, one could implement PBL through discussion via socialmedia (Boehrs, Samaddar & Mukhopadhyay, 2013). The research presented herecan also be extended by applying Guided PBL in a qualitative course.

The Guided PBL approach using a reversed textbook idea is easily trans-ferable to other domains. The approach encourages students to attempt to solveunfamiliar problems, with enough guidance from the instructor, until they are ableto achieve the learning objectives. It frees the instructor to play the role of relatingconcepts to students’ lives and the business world, achieving the tasks of anchoringproblems to the real world and encouraging students to take ownership of theirlearning. Case study methods are another means of encouraging students to thinkcritically about issues. Both case studies and guided PBL are similar in that they


Table 5: Suggestions for using the Guided PBL approach.

Preparing the students:• On the first day, describe the reversed structure of the book to the students.• Some students may have feel trepidation about not having a traditional textbook,

something they are used to. Work with them on a small problem from the reversedtextbook in the very first class to increase their buy-in and reduce their fear.

• Describe how you will use the book throughout the semester – mainly that they will beworking problems from the book every class and engaging in discussion.

• Emphasize the importance of avoiding the temptation of looking at the answers first inthe back. Put it to them as a challenge – they have the answers anytime they want, butif they want to engage their minds and gain confidence in their ability to solve theproblems, they must work on them in class or at home first before they look at thesolutions.

Preparing oneself (as the instructor)• Get familiar with the book, since the problems from the book will drive the discussion

in class.• To the extent possible, strategize about and practice the various versions of

conversations that might ensue, creating divergent thinking about the problem at hand.• Come up with a strategy to create convergence of the ideas towards the key learning

objective.• Avoid the temptation to give students the answers to questions too quickly. Staying

silent while they attempt to solve a problem is important. If students need guidance, itshould be in the form of questions from the instructor that lead them to the answer,whenever possible.

• Remember that this method is a replacement for the traditional lecture, not somethingto add on to it.

are used to improve critical thinking abilities. The key difference is perhaps theamount of knowledge the student is expected to have prior to using the method.Case studies are typically more comprehensive in scope and are introduced af-ter some formal training in concepts, and principles. The Guided PBL approachprovides the problems first, before students have the knowledge of how to solvethem, and provides them with the guidance to move towards the solution. Addi-tionally, it can be said that case studies tend to be more suitable for broader learningobjectives, while guided PBL may be better suited to specific learning objectives.

Many universities are making efforts in various disciplines to improve CTamong students through a variety of initiatives. Aside from active learning tech-niques within a class, approaches such as interdisciplinary courses are being im-plemented to mimic more of what a student is likely to encounter after college.Real-life issues in business rarely restrict themselves to a single domain. Onemay need a combination of leadership skills, analytical ability, and knowledge offinance, for instance, to tackle a particular problem. However, students typicallylearn these topics independently of each other, and many never make the connec-tion between them. Making each class more relevant by discussing all aspects of areal situation (even if the focus of the course is on one particular aspect) can makethe whole learning process more relevant and meaningful to students.


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APPENDIX A

Illustrative Example

Without any prior discussion of any theoretical approach, the class is asked tosolve a business problem like the following one. The following shows the problemas presented in the reversed textbook including blank workspace.GM is considering designing a new automobile. Their options are a design basedon gasoline engine technology, and one based on a government proposed “Green”technology. The development costs and the wholesale price (all in thousands ofdollars) of the cars are as shown in the table below:

Gasoline GreenTechnology Technology(numbers in $ (numbers in $thousands) thousands)

Wholesale Price/vehicle 25 30Variable Cost/vehicle 15 25Fixed Cost 100,000 200,000

How many automobiles must GM sell for the ‘Green Technology’ to be moreprofitable than the Gasoline Technology?You are in the White House and want to encourage all automakers to adopt the“Green” technology. You cannot provide capital upfront for fixed (development)costs, due to political reasons. However, you can provide a subsidy to GM for everycar sold. How large would you have to make the subsidy if the above numberswere true?

Approach in the classroom

The problem uses a very recent economic and policy issue that motivates students tothink about larger problems facing business and society. The instructor merely facil-itates discussion and students are encouraged to make a decision/recommendation.They may approach the problem whichever way they want, and may interact withthe professor and ask questions. Students work in iterations and by trial and error.The instructor provides guidance or asks questions to keep class discussions fo-cused on getting to the solution of the problem. There are always some studentswho will figure out how to solve the problem, and rest of the class very quicklycatches up with them. They enjoy this self-discovery and get excited about tacklingother similar problems.

This problem is formally known as a Crossover Point analysis. Withouteven introducing the term, if students are asked after solving the problem what


they would call it, more often than not students do come with names that in-volve the words ‘cross-over’ and ‘level’ or ‘point,’ having understood that theessence of solving the problem is finding the point where two profit lines crosseach other on a graph. The instructor then completes the discussion by askingstudents and/or illustrating other applications of this particular type of analysis,or alternate approaches to subsidies, like tax breaks for consumers. Finally, stu-dents are given (or they figure out) the formulaic expression of the crossoverproblem:

At Crossover point,Profit 1 = Profit 2, where Profit 1 and Profit 2 are the profits for two differentalternatives under consideration. Crossover point = (FC1 – FC2) / (CM1 – CM2),where FC1 and FC2 are the fixed costs, and CM1 and CM2 are the contributionmargins for options 1 and 2 respectively.

Solution and discussion to the GM problem as in the Reversed Textbook.

(Note that all numbers are in $ thousand – $10 implies $10,000, and so on).One approach to solving this problem is to compute the Crossover point

between these two options. However, it will lead to a negative crossover point (youshould try this on your own). This does not make sense in practice. What would itmean?An intuitive approach is to compute the contribution margins of each and compare.The contribution margin for the Gasoline Technology option is $10 per unit, while itis $5 per unit for the Green Technology option. This means the profit line is steeperfor the Gasoline Technology option. Also, it has a lower cost up front, which meansthe profit line for Gasoline Technology starts above the Green Technology option,and stays above it, regardless of number of units sold. In other words, Profit forthe Green Technology option starts at a lower point, and can never catch up.Therefore, the subsidy given per unit should make the contribution margin of theGreen Technology option better than the Gasoline Technology option. This meansthe subsidy has to be more than the difference in profit contribution. In this case,it must be more than $5 per unit.

Note to the reader of this paper:

The solution to the problem as presented above is available to the students in theback of the reversed textbook for reference. However, much of what is presented inthe solution already evolves during the class discussion, and students may in factextend the discussion to other questions such as 1) How much more than $5 perunit does the subsidy have to be? 2) What if providing a subsidy as upfront capitalwas possible? How much would be needed to achieve the same goal? 3) Whatif GM decides to go with the Green Technology option for reasons of corporatesocial responsibility? How many units must they sell to breakeven? How would asubsidy affect this breakeven point?


APPENDIX B

Guidelines for implementation for instructors interested in using thisapproach

To illustrate the use of the Guided PBL approach in the classroom, a very smalland simple topic within the broad area of Time Series Forecasting is discussedbelow from two perspectives – the traditional lecture approach and the GuidedPBL approach.

Consider that the objective of the lesson for the day is to ensure that studentslearn the broad concepts of Time Series Forecasting and specifically can apply theNaı̈ve method. A traditional approach would be to talk about the various methodsof forecasting beginning with the Naı̈ve forecast. The instructor describes what it is,writes a formula to represent the forecast as the actual value from the previous timeperiod, and works out an example for the students. Students then use the formulato find the forecast for other practice problems. The instructor then discusses whatit means, where it is applied, and the role of recency of data in choosing theright method. He/she then moves on to the next technique, say moving averages,exponential smoothing, and so on.

To use the Guided PBL approach, the process is essentially reversed. Theinstructor points students to a problem in the reversed textbook that has some salesdata for a company (see Table B1 below) and asks them how they would use it toforecast sales for the next time period.

The discussion begins with asking students how they would proceed in orderto forecast for time period 11. At this point, depending on the class chemistry andprior experience of the students, the discussion could unfold in several differentways. One possible scenario is discussed here. Students begin often by suggestingan average of all of the past data. Some will pull out a calculator and start doingit. The instructor at this point can ask them why they are computing averages. Is itappropriate here? The students will most likely go silent at this point. After furtherprobing by the instructor, some brave soul may suggest looking at a chart of the

Table B1: Sample forecasting problem.

Time Period Sales ($ thousand) Forecast

1 602 673 504 585 626 607 558 629 7110 6511 ???


Figure B1: A scatterplot of the sample time series data.

0

10

20

30

40

50

60

70

80

121086420

$ Th

ousa

nd

Time Period (Quarter)

Sales for XYZ Inc.

data to see what it looks like. If that does not happen the instructor can nudge themin that direction by asking them if a chart might help.2 The instructor then makesa scatterplot of the data in Excel and projects it on screen for the class to see (seeFigure B1). This eases the pressure on the students while the instructor is makingthe chart.

At this point, the instructor can revisit the questions of whether an averageis appropriate and what the forecast for period 11 is. Looking at the graph, somestudent will say that the data look flat. Others will pick up on that and startguessing – typically students will say their forecast is $60 thousand (or 65, or70). The instructor now has two directions in which to take the discussion. First,following up on the comment about the data being flat, the students can be askedhow it matters. What if the data were not flat? What other patterns are possible?How would that change their figuring out the forecast? This leads to a discussionof slopes, positive or negative, and trendlines. It may even go into the idea ofseasonality and cyclicality. The second possibility is to focus on the numbers thatthe students presented as the forecast, and ask them how they came up with thosenumbers. Some will say they just looked at the last number, or the last few, or thatthey saw that the numbers were scattered randomly around the number 60. Theinstructor can now ask them how they would decide which numbers they shouldlook at – only the most recent one, or a recent few, or all of them? The students areat this point becoming aware of the role that recency of data can play in forecasting.

The instructor then asks students for examples of businesses or industrieswhere data need to be very recent for forecasting because the older data are

2It is important to note that instructors cannot make assumptions about how students will respond.Rather, one must be mentally prepared to entertain multiple possibilities, and think on their feet sufficientlyto move the discussion in the appropriate direction to ensure the convergence that the instructor wants canhappen in the planned time for this lesson.


irrelevant. Similarly, what are some businesses that can use much older data?Students generally mention the apparel industry as an example where recent dataare more important because of changes in fashion, and something like a breakfastcereal producer as an example of a business that could use much older data.

Considering that the goal of the lesson is to ensure that students learn toapply Naı̈ve forecasting, the instructor can nudge them towards it by asking themwhat would be the extreme case of using recent data. This will lead them intothe idea of taking only the most recent data point—the sales for the last period– of $65 thousand. Once students see that it is a possible forecast, the instructorcan call their attention to the fact that it is a very simple (and simplistic) method,and the term Naı̈ve Forecast can be introduced. At this point, students completeworking out the problem in the book. Students are then asked what the formulafor computing the Naı̈ve forecast would be in plain English. Students are able toanswer that the forecast for period 11 is the actual value for period 10. It is nowvery simple for them to use mathematical symbols to write out the formula. Theinstructor reminds the students that the discussion of this problem is available atthe end of the reversed textbook. This ends the session.

There are many variations possible to this scenario as the conversation pro-gresses in class. The key element of this process is that to elicit answers fromstudents to most of the important questions, rather than answering them upfrontfor them. The instructor must have the patience to listen to students’ answers,which will most likely not contain the technical terms that the instructor wantsthem to know. One must resist the temptation to give them “the right answer” tooquickly. Note that in this approach all the key points that the instructor wants thestudents to learn, were made through questioning, without any lecture. It beginswith a problem from the reversed textbook, and the solution and discussion areavailable in the back of the same book.

APPENDIX C

Examples of the type of questions that test for CT ability.

(1) You have a business that sells expensive items, which means that yourinventory holding costs are high. Running out of inventory also costs thebusiness, but not as much. If you follow an analyst’s demand forecastsfor your business, which of the following would you prefer to be trueabout her forecasts?

(a) A high MSE with no bias.

(b) A high MSE and a high MAD.

(c) A positive bias with low MSE.

(d) A negative bias with low MSE.

(2) For a certain set of data, forecasts were made using moving averages.The MAD value is + 7.00. If every one of the errors is known to benegative, which of the following can you say with certainty about theBias?


(a) The Bias value will be exactly – 7.00.

(b) The Bias value will be greater than – 7.00 but less than + 7.00.

(c) The Bias value will be exactly + 7.00.

(d) The Bias value will be greater than + 7.00.

(e) Nothing can be concluded about the Bias value.

(3) Before a marketing survey of potential customers was done, John Comp-ton believed there was a 50/50 chance that his music store would becomesuccessful (P(S) = 0.5). The research team determined that for success-ful stores, marketing survey results in the past were favorable 90% of thetime. For unsuccessful stores, the survey results were unfavorable 80%of the time. If the marketing research for John’s store is favorable, whatis the revised probability the music store will be successful?

(a) 0.373

(b) 0.715

(c) 0.818

(d) 0.900

Documents

A Guided Problem-Based Learning (PBL) Approach: Impact on Critical Thinking