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The Decision Sciences Journal of Innovative Education
A Short, Simple Learning Curve Classroom Exercise
John Paxton
School of Business and Technology
Wayne State College
Wayne, NE 68787
Abstract
Making learning curves "real" to students is sometimes a difficult task. This difficulty may be overcome by using identical LegoÒ building block sets in an experiential classroom exercise.
Introduction
Having taught learning curve units to both undergraduate and MBA classes over the last twenty years, I was looking for some way to "make this material real" to my students. Conventional teaching examples did not seem to make an impression on the students; they all seemed as if this were merely one more academic exercise to be endured prior to graduation. A "hands-on" experience was necessary.
Learning Curves: a quick summary
Learning curve theory states that, as the volume of practice is doubled, the time required for a task is reduced by a stable, predictable increment, usually expressed as a percentage. For example, an 80% learning curve means that the second repetition will take 80% of the time it took for the first exercise, and that the fourth repetition will take 80% of the time it took to do the second repetition. In general,
time on task = (time for first unit)(run number) (learning curve constant)
where
learning curve constant = ln (learning curve rate)/ln (2).
In most texts, the model is conventionally shown as
Y = a X b.
The Exercise
This exercise is designed for business undergraduate and MBA students. I do not believe that this exercise would be appropriate for those having advanced coursework, a strong math background, or both.
I purchased five identical LegoÒ sets; in my case, this was set #5918, a small desert vehicle with driver, comprised of twenty-nine pieces. I believe that any small LegoÒ set would work with this protocol, as long as the assembly is not too simple. These cost about $4.00 each. I eliminated all extraneous pieces (in this case, some desert wildlife). I transferred the remaining pieces to "snap lid" containers (microwave containers, like those sold as "Zip-loc"â); in each container, I also enclosed the pictorial instruction sheet. This was for ease of transportation to and from the classroom and for ease of storage, since the original LegoÒ boxes were not meant to be re-used.
This exercise is the first thing presented in the learning curve unit. The students have no prior briefing or lecture material. This precludes "experience contamination" where the students know in advance what's supposed to happen; in this way, the students have a stronger belief in the experiment's validity and reliability because they know that the results they see were not "rigged".
For the exercise, I have the class divide itself up into groups of four or five students, each of which gets one LegoÒ set and a "calculations" form for each student. ("Demonstration groups" may work better with larger class sizes.) Each group needs to have at least one member with a watch having a second hand (or a digital watch with a stopwatch function). Next, I give instructions to the class as a whole. In each group, one student is the assembler, one student is the timer, and the rest are recorders. (Each student receives a form, shown in Appendix One, prior to the start of the exercise. To be filled out during the exercise, this gives each student a permanent record of the exercise. The instructions for the exercise are shown in Appendix Two.) The assemblers are instructed to assemble the vehicle four times, with complete disassembly between each iteration. The timer is to tell the assembler when to start, and then record the time of completion of each assembly in the appropriate space on the form. At the end of the fourth assembly, one of the recorders graphs the assembler's performance [assembly time = f(run number)] while the other recorders finish the "step-at-a-time" calculations on the lower half of the form.
Since the learning curve percentage depends production doubling, this protocol gives each group two such doublings – one between Run One and Run Two and the second between Run Two and Run Four. The observer/calculators are instructed on their form to calculate both of these and then to average the two. If the first unit (i.e., Run One) takes four minutes to assemble, and the second unit takes 3 minutes to assemble, a doubling has occurred and the learning curve rate is
3/4 = 0.75 or a 75% learning curve.
If, then, the fourth unit (another doubling) takes 2.19 minutes to assemble, we'd have
2.19 / 3 = 0.73 or a 73% learning curve.
Averaging the two, the assembler demonstrates a 74% learning curve.
When these calculations are finished for each of the five groups, I have each group report their average learning curve percentage, writing them on the board. Treating each of these percentages as a sample data point, we then have several data points from which to calculate a "grand mean" class learning curve average. Over the past three years (seven sections of Operations Management), these class averages are consistent around learning curve percentages of 70 - 75%.
At this point, I then begin to lead the class through the theory of learning curves, ending the class session with these figures: this learning curve percent means that the learning curve constant is
ln(0.74) / ln(2) = -0.434.
A learning curve constant of –0.474 gives us a forecasting model of
Time on task = (4 minutes)(Run number) –0.434 .
The Results
When my students see that they actually do exhibit learning curve behavior, they become much more involved; further, they begin to believe that their future subordinates (and husbands, wives, and children) may actually exhibit this behavior as well. The exercise is well received by the students (apparently a welcome relief from lecture), with the assemblers cheered on by their teams as they work. While no formal testing has been done on the long-term effectiveness of this technique, it does liven up a lecture topic and helps to convince the student that, at least in this one case, the material is not all theory.
The exercise takes about thirty minutes to complete, including the group and class calculations; I usually spend the remainder of the fifty-minute period explaining the significance of the results and their application in the "real world". I believe that this is a period well spent because it does seem to convince many students that "learning curve behavior" is not just an academic abstraction, but a "real world" artifact.
Following this first class session, I go into normal "lecture mode", but throughout the following lectures, I draw attention back to the exercise. For example, when the learning curve constant "b" is introduced, I have the students take out their data sheets and calculate "b" for their group. When we begin to use the model for forecasting, their first forecasts are made using their own group data (i.e., "How long would it take to make the eleventh unit? How long would it take to make all eleven units [the cumulative time]?")
Potential Problems
The single biggest potential problem is the loss of parts. I warn my students to be careful to be sure that all the parts get back into the containers at the end of the exercise; I then check each container after the class to see that this has been done. So, far, I've been lucky (no parts having been lost), so the warning is worthwhile.
Another potential problem is group sizing; if the groups are too large (i.e., greater than four or five students), too many students will become bored and restless, causing the exercise to become unruly and disruptive. In larger classes, perhaps a couple of "demonstration groups" in the front of the class would work better.
A third problem, which I cover in the instructions prior to the experiment, is the conversion of "seconds" into "tenths of a minute". Without this instruction, students, in the past, have tried to divide minutes and seconds (i.e., 2:36 [two minutes, thirty-six seconds], rather than 2.6 [2.6 minutes]), producing very strange results. Simple telling the students to divide the number of seconds by sixty and rounding to the nearest single decimal (i.e., thirty-seven seconds becomes 0.6 minutes, so two minutes and thirty-seven seconds becomes 2.6 minutes) has worked well for me.
Appendix One: Calculations Sheet (one per student)
Time 1:______________________
Time 2:______________________
Time 3:______________________
Time 4:______________________
++++++++++++++++++++++++++++++++++++++++++++
Divide Time 2 by Time 1
Time 2 à
____________ = ______________(Answer 1)
Time 1 à
Divide Time 4 by Time 2
Time 4 à
____________ = ______________(Answer 2)
Time 2 à
Add Answer 1 to Answer 2
_______________ + _______________ = _____________
(Answer 1) (Answer 2) (Answer 3)
Divide Answer 3 by 2
Answer 3à _______________/2 = ____________ (Answer 4)
Post Answer 4 on the board.
++++++++++++++++++++++++++++++++++++++++++++
Note: Answer 4 is the average learning curve percentage for this individual for this task, measured over four repetitions.
============================================
Appendix Two: Instructions
1. Assemble the model four times, recording each time in its appropriate slot and disassembling the model completely between each run. (If you don't specify "completely", some groups, seemingly in competition with other groups, will just break the model into major subassemblies, subverting the experiment.)
2. Record times as minutes and tenths of a minute (explain here conversion of seconds to tenths of a minute).
3. Be careful not to lose any of the parts; they're small and will get away from you unless you're careful.
4. At the end of the fourth run, have one member of your group graph the performance (run number on the horizontal axis, time for that run on the vertical axis).
5. Have another group member complete the calculations on the sheet, posting Answer Four on the board when it's completed. (Teaching note: Run this experiment, with yourself as the assembler, in the privacy of your office first. This will give you a "feel" for the learning curve percentage with the particular LegoÒ model you're using.) Watch as the number are posted; they should be in your same experimental range range. If they're not, have the students check their calculations.
6. When all group results are posted, find the
mean (i.e., [result 1 + result 2 + … result n]/n). This you
may then use as a springboard into the formal lecture.
Vita
John Paxton holds a PhD in Management from the University of Nebraska. He has taught Management for twenty-four years, primarily at Wayne State College in northeast Nebraska. Comments, suggestions, critiques and questions may be directed to jopaxto1@wsc.edu.
