A.1 What Is a Teaching Case?

A teaching case is an account of a situation that provides background information, generally comprising a comprehensive history of a problem that includes introductions to multiple players and stakeholders who have a wide range of interests and motivations.

The teaching case can require the students, working individually or in teams, to use this background information (perhaps to be augmented with additional information collected by the students) to

1. describe, interpret, and/or evaluate an action that has occurred and/or
2. address a problem, give a recommendation, make a decision, and/or develop a strategy in order to provide guidance for the future in a realitstic context. Thus, teaching cases may be retrospective and/or prospective.

Retrospective teaching cases often share the actual outcome of the player and stakeholder decisions and strategies they describe. These types of teaching cases require students to (i) develop an understanding of the issue(s) faced by the players and stakeholders, (ii) review how the decisions made and strategies employed by these players and stakeholders lead to the outcome, and iii) compare the outcome to the outcomes that likely would have resulted from other feasible decisions and strategies.

Prospective teaching cases generally do not share the actual outcome of the decisions and strategies they describe. These types of cases require students to (i) identify the issue(s) faced by the players and stakeholders, (ii) generate and compare potential decisions that could be made and strategies that could be employed to address the issue(s), and (iii) make recommendations on the course(s) of action to be taken.

What is not a teaching case? A teaching case is not an extended homework exercise or story problem; a teaching case is more complex and requires far more of the student. It is not a case study, that is, it is not an academic examination of a specific problem or circumstance intended to generalize across populations. A teaching case provides a learning experience for students. Although the situation, players, and stakeholders described in a teaching case may not exist, a teaching case is not contrived; the context, scenario, and problem(s) faced by the players and stakeholders in a teaching case must be relevant to a real problem.

There is no minimum or maximum length for a teaching case, and teaching cases often contain information that is either irrelevant or only tangentially pertinent in order to provide students with experience in assessing the relevancy of information. Cases may also omit or fail to include important information in order to provide students with experience identifying and finding additional information that will be instrumental to effectively addressing a problem, making a decision, or formulating a strategy. Some cases provide data, some require the student to find or collect data, and some cases are data-free (i.e., do not require the student to use actual data in analyzing the case).

A.2 My Motivation for Using Teaching Cases¹

I began teaching at Wright State University's business college immediately after completing my Master's degree in economics. I routinely taught three or four different courses across four sections each academic term. I often taught one or two sections each of the college's second required course in introductory statistics (inference and modelling) at the sophomore level and the college's first and second required courses in introductory operations research (deterministic modelling and stochastic modelling) at the junior level during an academic term. Class enrolments were approximately 40 students, and the math backgrounds of the students were varied and often underdeveloped or weak.

In my first year as an instructor, I quickly realized that my students did not share my enthusiasm for the courses I was teaching. Other faculty members who taught the same courses as I confided that this was common and expected. I became increasingly frustrated, and many of my students and I shared a common source of frustration; after completing these courses, students often still had a weak understanding of the concepts that had been covered.

I thought about this a great deal. The frustration I saw in many of my students was similar to what I had seen in my classmates when I took the same courses just a few years prior. I ultimately decided I could summarize the students' frustrations with three short questions:

• When (i.e., under what circumstances) will I use these concepts and methods?
• Where (i.e., for what problems) will I use these concepts and methods?
• How will I use these concepts and methods?

It occurred to me that I might be able to address all three of these questions effectively through teaching cases. My students had never used the case methodology as a basis for learning, so I was likely limited in what I could do–creating versions of undergraduate introductory statistics and operations research courses for business students that were entirely case-based was not feasible–especially this early in my career as an instructor. Therefore, I decided to develop and utilize a hybrid approach. In my later interactions with other instructors of operations research, statistics, and analytics who have gravitated to the case method, I found that my experience and my motivation are far from unique!

In the hybrid approach I developed, I would continue to devote most class meetings to discussion of the concepts and methodologies to be covered in the course. I would also assign two relatively short (one to two page) cases before each of my three examinations. Analysis of the two cases assigned before each examination would require students to use the concepts and methods that were to be tested over on the ensuing examination, and the students would be given no indication what concepts or methodologies were pertinent to each case. Each student would independently analyze the cases and submit a two-page report on her or his findings for each case. I would devote the class meeting immediately prior to each exam to class discussion of the two assigned cases. The cases would be primarily prospective and would provide students with data. In some cases, relevant facts and/or data would be omitted and students would have to make and assess the potential impact of assumptions. In some cases, irrelevant facts and/or data would be included and students would have to identify and eschew these facts and/or data. I would grade my students on the quality of their analyses, their exposition, and their participation in the class discussions.

In recognition of my students' (and my) lack of experience with the case methodology, I would proceed slowly with the first few cases and temper my expectations. As the term progressed and students gained experience and confidence, I would increase my expectations and adjust my grading accordingly (and I would explain this to my students in advance).

I expected my students' critical thinking, modelling, technical, and analytic skills to improve somewhat after implementation of the hybrid case methodology I had developed, and they did. However, the improvements I saw–in the quality of work, effort put forth, and attitude toward the courses–stunned me. I was particularly gratified to see the weakest responses to questions on exams (which were often embarrassingly poor prior to implementation of the hybrid case method) to be thoughtful, intelligent, and well developed after implementation of the hybrid case method. Students enjoyed the challenge of working on the cases, and they welcomed the opportunity to work on real problems that did not have single well-defined solutions. They also appreciated the opportunity to share their thoughts, opinions, insights, and ideas with each other and their instructor, and even the wariest of students ultimately participated in case discussions.

Of course, implementation of this hybrid case method did not proceed without difficulties. I had to develop case facilitation skills in real time; none of my colleagues used cases, so I had to develop these skills without guidance. Fortunately, my students understood that I was striving to improve their education and were extremely patient. I also had to find sources of cases. There were very few published teaching cases available in statistics or operations research when I began teaching, so I had to write my own cases–six new cases each academic term for each different course I taught–based on my experiences in private industry and consulting as well as those of colleagues, friends, and family. I had a few instances in which one or more students interpreted portions of cases in ways I had not intended. This required me to develop and further refine some interesting case facilitation skills (which I soon concluded was an important part of the case facilitator's repertoire).

I also had to grade the students' written case analyses and participation in case discussions. This was time-consuming, but I did recover some of this time when grading examinations; because my students' performances on the examinations were now much improved, the examinations were far easier to grade. I was concerned about how to cover all of the required course material after giving up approximately 10% of my class meeting time for case discussions. However, I soon found that a student who had the case assignments in hand came to class with a sharper focus, and I was able to get through the same course material in less time.

Finally, I was concerned about how students would react to this increase in their workload–6 case analyses and approximately 12 written pages per student in each course. Again, the outcome was somewhat surprising and extremely gratifying. Not one student complained–to me or in comments on anonymous teaching evaluations–about the additional work. Several thanked me for helping them understand the material in a meaningful way. In later academic terms, several students returned to take other courses from me so that they could further develop their quantitative skills through the hybrid case methodology. My colleagues on the faculty also began reporting that my former students were now more effectively applying concepts from my courses to problems in their courses.

In summary,

• my students' modelling, technical, and analytic skills improved dramatically,
• my workload increased somewhat,
• my students were happier and more frequently reported enjoying my classes,
• my former students applied concepts from my courses to problems in other courses, and
• I enjoyed teaching more than I had before I implemented a hybrid case teaching approach.

All in all, not a bad deal–for me or my students!

I have continued to experiment with the case method over the past 30+ years–using different facilitation styles, implementing teaching cases into large sections, trying different schemes for facilitating class participation–and my results have convinced me that cases are an extremely robust and effective tool for teaching students about the practice of a discipline. Since analytics is a practical discipline, it is logical to conclude that teaching cases are ideally suited to analytics courses.

A.3 Writing a Teaching Case

Authors of teaching cases find topics for teaching cases in two ways: opportunistic and intentional. Each offers its own challenges and difficulties. Once the author has found a topic, she or he must consider several factors when developing and writing the case. This section describes the important considerations that must be made in each of these phases of writing a teaching case.

A.4 Using a Teaching Case

Instructors who wish to use teaching cases face many choices. In addition to selecting appropriate cases for the pedagogical objectives, the instructor must decide on how she or he will assess the students' work on the case assignment (written analyses, class discussions, and/or formal presentations) and she or he must select/develop a style for facilitating in-class case discussions.

A.5 An Example of a Simple Case

A “Boring” Time is a relatively brief teaching case developed by the author to impart understanding and appreciation of the concept of variation in students taking undergraduate introductory business statistics courses. The case, which is generally used early in the academic term, also raises some basic but important issues in design of experiments. Table 1.

In addition to the guidelines discussed in Section 4.2.1, students are given the following grading criteria:

1. Analyses are to be
   • typed or word-processed.
   • double-spaced.
   • two pages maximum of text (not including displays, tables, appendices, etc.).
   • one-inch margins.
   • twelve point type size.
   • Times New Roman font.
2. Each appendix must be referenced in the body of report.
3. Some statistic(s) (numerical measure such as the mean, variance, midrange; graphical display such as a line graph) are to be used.
4. No discussion of how to use software (this includes Excel).
5. The raw data are available for download in an Excel file on the classroom Web site.
6. Students receive full credit unless they egregiously violate these standards.

In analyzing the data provided in this case, students will naturally calculate some summary statistics such as those included in Table B.2.

Summary Statistic	Hole Maker	Shafts & Slips	Judge's Jigs	Drill for Bits
	3.096194829	2.908347920	2.600370430	2.985636918
md	3.113215493	2.912625443	2.600534377	2.887560623
minimum	2.820970546	2.769265229	2.590560135	1.197450108
maximum	3.285616963	3.060279394	2.613596999	4.581084216
range	0.464646417	0.291014165	0.023036864	3.383634108
midrange	3.053293754	2.914772312	2.602078567	2.889267162
s	0.093657619	0.060980033	0.004762979	0.719022438

Based on the sample means, the drill provided by Drill for Bits performed best and the drill provided by Judge's Jigs performed worst. However, students who stop at this point are missing an important characteristic of these data. A line graph or side-by-side boxplots also provide excellent illustrations of this point (see Figure B.1).

Through this graph, students can see both accuracy (How close are the diameters of the holes drilled by one machine to the target of 3 inches) and precision (How consistent are the diameters of the holes drilled by one machine?). They can also see that

• Hole Maker is reasonably consistent (as we can also see in the last row of the table of summary statistics) and routinely overdrills;
• Shafts & Slips is reasonably consistent (as we can also see in the last row of the table of summary statistics) and routinely underdrills;
• Judge's Jigs is extremely consistent (as we can also see in the last row of the table of summary statistics) and always underdrills; and
• Drill for Bits is wildly inconsistent (as we can also see in the last row of the table of summary statistics).

The case does not explain the physical properties of the stainless steel disks or the purpose of the hole, so students cannot discern whether (i) a hole can be rebored or (ii) a hole that is too large is acceptable. This makes assessing the drills provided by Hole Maker and Shafts & Slips difficult. However, if the drills can be recalibrated, the best drill to purchase may be the extremely consistent product produced by Judge's Jigs. This is precisely the ambiguity that I want my students to struggle with when analyzing a teaching case.

Students should also note that assigning each machine to a different employee over the entire life of the experiment could result in a serious bias; the effect of the machine and employee are perfectly confounded. Astute students will recognize this problem and suggest a rotation of the four employees assigned to the four machines. Other students may go further and suggest that Weideman use more than four employees to test the four drills. Here I can use this teaching case to introduce some basic concepts of experimental design in a meaningful way very early in the course.

A.6 Final Thoughts

Because teaching cases afford students low-risk opportunities to assume and ultimately appreciate various roles in typical situations faced by practitioners, they are ideally suited for use in analytics courses. Instructors can use teaching cases to help students understand the answers to three important questions that students frequently ask in analytics courses:

• When they will use these concepts and methods?
• Where will they use these concepts and methods?
• How will they use these concepts and methods?

Many students who have never taken a course that uses the case methodology will be somewhat apprehensive at the beginning of the academic term, but a gentle introduction and early success will quickly alleviate most of their unease. Students will also be less anxious if the instructor provides detailed guidelines and expectations.

There are many approaches to implementing cases into courses. Some instructors design entire courses around the case method, while others (including the author) integrate cases into strategic points in courses. Students can work individually or in teams, and instructors can assess student performance through written analyses, class discussions, and/or formal presentations.

Instructors (including the author) who have integrated cases into analytics courses have reported

• dramatic improvement in students' modelling, technical, and analytic skills,
• increase in instructor workload,
• happier students who enjoy class,
• more frequent application of concepts from my courses to problems in other courses by former students, and
• a more gratifying teaching experience for the instructor.

It is important to reiterate that although the author/instructor will attempt to anticipate all potential student reactions to all of the issues in a teaching case, it is virtually impossible to do so. It is critical that authors spend a sufficient amount of time considering all issues of the case and how they are to be presented, and then be open to revising the case and/or teaching notes to reflect what she or he learns about the case through classroom use. This is also why an author/instructor should test a teaching case in several classrooms before attempting to publish the case.

Finally, an instructor who implements a case methodology into her or his course must be supremely prepared. The instructor must know the case better than any student to avoid surprises, but she or he must also be prepared to deal with surprises. This is what makes teaching with the case method exciting, challenging, fun, and effective.

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