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**Problem-Based Learning in Quantitative Classes**

Bruce K. Blaylock,

Jerry M. Kopf,

*Blaylock, PhD. and
Kopf, PhD. are Professors of Management in the **College** of **Business** and Economics*

**Abstract**

Although a number of authors
have reported results of using Problem Based Learning (PBL), there are few
examples of how to take a current event and turn it into a problem-based
learning opportunity. The purpose of this paper is to demonstrate how a
statement of Presidential Candidate Barak Obama during the 2008 presidential
campaign was used to implement PBL in a quantitative course. Students were more actively engaged in the
learning process, more responsible for their own learning, and more emotionally
involved in learning.

**Introduction**

Many students of quantitative analysis and statistics leave these classes convinced they will never use that subject matter in their careers. Sadly, some of them are absolutely right because the way a topic is taught often determines what students can do with the information acquired (Mayer & Greeno, 1972). A number of studies have documented and lamented the challenges faced by faculty teaching quantitative courses (see Bridges et al.,1998; Cerrito, 1999; Lomax & Moosavi, 2002; Schumm et al., 2002; Stork, 2003). Previous studies have argued that the use of collaborative, group-based, learning projects (CL) would overcome some of the identified challenges. For example, students had less anxiety when studying statistical topics (Schacht & Stewart, 1992; Helmericks, 1993), greater satisfaction with the learning (DePotter, 1995; Perkins & Saris, 2001), and performed better (Wybraniec & Wilmoth, 1999; Auster, 2000).

Other authors have suggested extending the collaborative approach by using real

problems as the motivation and focal point for learning (See
Boud, 1991; Hanson, 2006; Hmelo-Silver,
2004; Norman & Schmidt, 2000). PBL
is an instructional strategy in which students are confronted with real
problems and strive to find meaningful approaches to the issue. PBL motivates students to “learn to learn”
by challenging them to solve real problems they may not know exactly how to
solve. Instead of focusing on teaching
students how to solve imaginary problems, which may have little relevance to
the student, PBL starts with the need to solve a real problem, and then looks
for appropriate techniques. In other
words, the need to solve a problem
comes before learning techniques to solve the problem (Boud, 1985; Boud and Feletti, 1991; Woods, 1985). This approach to learning contrasts with
prevalent teaching strategies where the concepts, presented in a lecture
format, precede "end-of-the-chapter" problems.

The role of the faculty member in a PBL environment changes
from someone who provides the answer to a problem to that of a coach or mentor
who helps students learn how to solve a problem. According to Mykytyn,
et. al. (2008) the instructor has three responsibilities in the PBL
environment:

1)
Help learners develop knowledge about the problem being
investigated;

2)
Identify resources, respond to questions, and introduce
tools or knowledge as it is requested and needed by students; and

3)
Assist students with discovering the solution to the
problem.

The purpose of this article is to assist faculty with
implementing PBL in quantitative courses.
The class we selected was a
quantitative analysis course, which is required by most accredited colleges of
business. We used a controversial
statement made by Presidential Candidate Barak Obama during the 2008 campaign
as the learning vehicle for several quantitative topics. It is not the intent of this article to
present empirical evidence of the impact of PBL on learning--many other authors
have done that and are cited throughout this paper. Instead, we will
attempt to provide some details on how PBL was implemented, the steps involved,
some of the difficulties encountered, and some observations about both the
challenges and benefits. Hopefully,
sharing our experiences will aid other faculty members who are looking for ways
to enhance engagement and learning in quantitative courses.

**Implementing PBL**

An assertion made by then Presidential Candidate Obama
(2008) gave all statistics and quantitative analysis instructors an opportunity
to use this historic political year as a learning vehicle. In a campaign speech candidate Obama said, “You
know the other day I was in a town hall meeting and I laid out my plans for
investing $15 billion a year in energy efficient cars and a new electricity
grid and somebody said, 'well, what can I do?
What can individuals do? You know
what? You can inflate your tires to the
proper levels and that if everybody in

Even though Presidential Candidate Obama later admitted he
may have been caught up in the passion of the political season with the above
claim, and even though there are several valid sources for secondary analysis for
his claim, the problem still provides an opportunity to stress the importance
of critically evaluating all assertions, not just politically motivated
assertions, but advertisements, sales claims, internet postings, etc.

Presentation of the Problem

Knowles (1990) suggested an essential characteristic of the
successful adult learning environment is an affective (emotional) as well as an
intellectual attachment to the subject.
The first step toward creating a PBL environment is to establish a
personal connection between the problem and the students. Since many students have financial
responsibility for a car, it was very easy to induce an emotive furor in the
classroom by showing a YouTube video (See reference list) of Mr. Obama’s
statement and posing the question, “Will this part of Mr. Obama’s energy plan
cause the price you and I pay for gas to decline?” The initial discussion allowed students to
express whether or not they believed the assertion. As is typical, the discussions were filled
with statements of “I believe…” or “I think…”
Such a discussion allows the instructor to distinguish between an
assertion or a statement of opinion and a statement of fact that can be systematically
supported with data.

The learning questions

By asking, “How do you know?” the faculty member can
challenge students to think about how they can support their opinions. As the faculty member and students ponder
that query the faculty member can help students realize their opinions have
often been formed from the statements of those with a particular viewpoint or
vested interest in the answer. They also
need to realize if they are to critically examine the assertion, they must
begin assessing what they know factually about it, what they don’t know, and
create a plan to obtain answers to the later.

Eventually, the above discussion turned to the questions of
what was needed to support or refute Mr. Obama’s statement. The following themes emerged:

1)
His statement implied a significant number of people
drive with under inflated tires.

2)
Mr. Obama’s statement implied correcting the under
inflated tire problem will save enough gasoline to make an alternative energy
policy, off-shore drilling, unnecessary.

3)
Finally, Mr. Obama’s statement implied correcting the
problem will lower fuel costs to all consumers.

The required quantitative analysis class at an AACSB
accredited business school was divided into groups of 4 – 6 members following
the introductory discussion. They were
tasked with the following:

o
Create a list of questions that must be answered
in order to address the above themes and evaluate the accuracy of Mr. Obama’s
statement;

o
How you will answer those questions either
though primary or secondary data; and

o
How will you convert the data into usable
information?

At this point students were emotionally engaged in the
process of solving this problem, but not necessarily confident of their
abilities to do so. The majority of
groups had difficulty with logically organizing their thoughts and articulating
relevant questions most likely because they had never been asked to do so in
previous learning environments. One of
the benefits of PBL is that it provides students an opportunity to practice
structuring issues which require a sequence of logic rather than a simple
response to singular isolated questions, thus promoting analytical skills for
inquiry.

In PBL students are not only encouraged to determine what
they don’t know, they are asked to create a plans for learning about those
topics, developing research plans for collecting data, conducting analysis, and
testing assertions. Instead of providing
students the “correct” answer to textbook problems, the instructor’s role is to
facilitate problem solving, not to provide all the answers.

Over the period of one class and outside-of-class meetings, student
groups developed the following list of questions:

1)
What percentage of cars has under inflated tires?

2)
How much are the tires under inflated?

3)
How many miles per gallon (MPG) are lost at each level
of under inflation?

4)
How many vehicles are on the road?

5)
Are cars, Sports Utility Vehicles (SUVs), and trucks
impacted equally by under inflation?

6)
How many miles are being driven by vehicles on the
road?

7)
How much gas is being wasted?

8)
If this amount of gas were saved, what would be the
impact on the price at the pump?

Planning the Study

To address the first question, students realized they would
need a sample to determine the percentage of under inflated tires. An advantage of PBL over traditional
pedagogical approaches is discovering and solving analysis problems that may
not come up when using textbook data.
For example, students realized they would need a sample to determine the
percentage of under inflated tires, but unlike end-of-the-chapter problems,
they also needed to determine the sample size required to have a meaningful
margin of error. Furthermore, they had
to create a plan for taking the sample. On the latter, students were very
creative. Some of their ideas included checking tire
pressures by:

·
Stationing themselves at gas stations;

·
Attending the upcoming Atlantic Coast Conference
football game;

·
Going to the local shopping mall;

·
Using the parking lots at the University; and

·
Going to the Department of Transportation where
citizens conduct business related to their cars.

Students had to select the best idea from their list of
alternatives, which forced them to consider the criteria upon which they would
base the decision. With a little guidance
from the instructor, students discovered the sample should be representative of
the population for which they are making estimates. Clearly, none of the data gathering
approaches they initially considered would allow them to generalize on a
national scale. Following a short “lecturette,” the class decided they would like to limit
their study to estimating the number of students on their own campus who have
under inflated tires, which caused the remaining questions to be modified. Even though the groups could not complete the
study as originally envisioned, they still had an interesting, which they were
motivated to pursue, and which required an identical analysis.

How data is analyzed is a concomitant decision to what data
must be collected. As students settled
on an approach to their data gathering, they began thinking about the
analysis: “How would they estimate the
percentage of cars with under inflated tires based on their sample?” Again, with some questioning from the
instructor, students recalled creating confidence intervals. Since the study groups were interested in the
proportion of cars with under inflated tires, they focused on creating
confidence intervals for proportions. An
enterprising student discovered a website (Dimensions Research, 2008) that
showed them how to calculate confidence intervals for proportions. None of the students had previously learned
how to create confidence intervals about proportions, but with the information
they knew (how to build confidence intervals for means), and a relevant
question about estimating the percentage of cars with under inflated tires for
which they didn’t know the answer, they were motivated to learn on their own
how to implement new quantitative tool.

To assess the impact of under inflation students needed to
know more than merely the proportion of cars with under inflated tires; they
also needed to know the degree to which tires were under inflated. Consequently, they changed the data to be
gathered to include the proper inflation for the tire (reported on the exterior
of most tires) and the actual tire pressure.

Their next problem was sample size. Problems at the end of chapters merely state
a sample size with no explanation as to why or how the sample was selected. When faced with real problems; however, such
information must be determined by those conducting the study. Students again discovered what they did not
know and were motivated to ascertain how to select an appropriate sample
size. Most sample size approaches
required knowledge of the population standard deviation, a parameter students
did not have. Another “lecturette” on the subject provided students with enough
information to compute sample size based on a subset of their data and to
calculate a sample standard deviation to estimate the population standard
deviation.

Gathering Data

For most students, gathering primary data was a new
experience. They had to determine what
data was to be gathered, in what form it should be, how many observations, and
from what sources. Since the research
question was changed to estimating gas saved within the University community,
students sought permission from University officials to check tire pressures in
the University’s parking.

A number of secondary data sources were used to address
questions 3 – 6 on the students’ list:

- Number of University vehicles
registered by vehicle type (University Parking Services);
- Impact of under inflation on gas
mileage (See reference for fuel economy);
- National MPG averages for cars,
trucks, and SUVs (AAA Gas Watchers Guide); and
- National average of miles driven (BNET).

Analysis

The next challenge facing students was how to use the
secondary and primary data collected in the data gathering phase of the
project. Success at overcoming previous
planning and data gathering issues gave students confidence to enter the
analysis phase of the project. They first
organized their primary data into two categories: under inflated and properly inflated tires. Students agreed if tires were over inflated
they were placed in the properly inflated category (over inflation does not
impact gas mileage, but does pose a safety hazard). Students computed a confidence interval for
the proportion of University cars with under inflated tires. To properly interpret the analysis, students sought
the correct interpretation of the confidence interval through readings they
found on the internet. The confidence
interval allowed them to determine a range for the number of University cars with
under inflated tires. Next, by using the
secondary data on MPG and average miles driven for each category of vehicle, the
students calculated the amount of gasoline that range of vehicles would use if
their tires were properly inflated.

Students now had an estimate of the amount of gasoline their
fellow students should be using if their tires were properly inflated. They turned their attention to estimating wasted
gasoline caused by under inflated tires.
They created a histogram of the amount of under inflation for each
vehicle category. These weightings
combined with the loss of MPG efficiency reported in secondary data allowed
them to calculate a weighted average estimate of the quantity of gas being
used. They aggregated that information
for each vehicle type, and subtracted it from it the amount of gas that would
be used with proper inflation, thus yielding the quantity of gasoline being
wasted.

**Impact on Student
Learning**

Many PBL studies have documented the benefits of learning
strategies that more fully engage students in active, group-based problem
solving (See Hmelo-Silver, 2004; Norman &
Schmidt, 2000; Hansen, 2006). The goal of this study was not to empirically
replicate previous studies. We did,
however, seek anecdotal evidence of its effectiveness by inviting students to
comment on the experience. We also
examined the perceptions of learners in the PBL environment with perceptions of
learners in a more traditional pedagogically-based quantitative analysis
course. We addressed those perceptions
through the framework of successful learning described by Knowles (1980).

Anecdotal statements from student can be represented by the
following:

- “I
never really understood confidence intervals and didn’t believe they were
useful to anyone. I believe I do
understand what they represent and can see many applications in my major.”
- “The
project was difficult because it required us to think in ways other
professors have not asked us to do.
I did get a lot out of the project and believe I could successfully
complete a similar one now.”
- “I
liked the project because the topic was current and real.”
- “This
is a better way to learn math.
Other classes have been memorizing a formula or work this
problem. Dick and Jane stuff. ”

Lest the reader feels like PBL pleases everyone, there were
minority comments similar to these:

- “This
was entirely too much work. Why
don’t you just tell us how to do it?”
- “What
a waste of time. All this stuff has
been done before. I found
information on the internet that disproved the (Obama) statement. What’s the point?”

Knowles (1980) provided the following list as essential
characteristics of the successful adult learning environment:

1.
Learning is a process.

2.
Tlearner must be actively
involved in the learning experience.

3.
Each learner must be responsible for his or her own
learning.

4.
The learning process has an affective (emotional)
component.

5.
Adults learn by doing.

6.
Problems and examples must be realistic and relevant to
learners.

7.
Adults relate their learning to what they already know.

8.
An informal environment works best.

9.
Variety stimulates.

10.
Learning flourishes in a nonjudgmental environments.

11.
The instructor’s responsibility is to facilitate. The
participants’ responsibility is to learn.

A questionnaire developed by Blaylock et. al, (Forthcoming) was created to examine student perceptions on the above characteristics. The questionnaire was distributed to students exposed to the PBL environment and those who took the class where traditional presentation methods were used. Using simple t-tests we found students in the PBL environment were significantly more involved in the learning process, got more emotionally engaged with the subject matter, and relied more on previous knowledge to advance their understanding.

**Conclusion**

Our analysis indicated that using a statement of Presidential
Candidate Barak Obama during the 2008 presidential campaign to implement PBL in
a quantitative course did have a positive impact on student engagement. The results show that students were more
actively engaged in the learning process, more responsible for their own
learning, and more emotionally involved in learning. The analyses used in this
PBL Project were not extremely difficult and did not require sophisticated
quantitative skills; however, because it did require students to actually
create a methodology for examining the problem, the experience had many more
learning opportunities. Furthermore,
since students were responsible for designing their study including analysis
techniques, most were more motivated to devote the necessary time to
discovering what they needed to learn and to learn it. Implementing PBL can also be a challenge for
instructors who are use to a very structured, lecture based format. An area for future exploration would be to
investigate the extent to which instructors in quantitative course feel
comfortable using CPBL learning strategies, and the extent to which they have
the facilitation and group work skills needed to successfully implement such a
strategy.

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