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Journal of Education for Business

ISSN: 0883-2323 (Print) 1940-3356 (Online) Journal homepage: http://www.tandfonline.com/loi/vjeb20

Using Graphic Organizers to Improve the Teaching

of Business Statistics

Danilo Sirias

To cite this article: Danilo Sirias (2002) Using Graphic Organizers to Improve the Teaching of Business Statistics, Journal of Education for Business, 78:1, 33-37, DOI: 10.1080/08832320209599695

To link to this article: http://dx.doi.org/10.1080/08832320209599695

Published online: 31 Mar 2010.

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Using Graphic Organizers to

Improve the Teaching of

Business Statistics

DANILO SlRlAS

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Saginaw Valley

State University University Center,

Michigan

tatistics is an important course for

S

business students. In fact, statistics is part of the core requirements not only for business students, but also for students majoring in other fields such as education, psychology, and other social sciences. Despite the relative importance of statistics, many students and alumni rank its value as very low com- pared with other business courses

(Zanakis

& Valenzi, 1997). Yet, man-

agers are expected to have good data- analysis skills, an important component

of the decision-making process.

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A clear

gap exists between the need for data- analysis skills and the perceptions that students have about the importance of statistics.

When listening to students express their concerns about learning statistics, I basically hear the same reservations. Common phrases used by students to describe the obstacles that they face include the following: “The problems look so overwhelming, I do not even know where to start”; “there are so many variables and formulas and I do not know how all these things relate”; “I am not good in math”; and “when the teacher does the problems on the board,

it looks so easy, but when I

try, I get

confused.” Other researchers have reported similar complaints (Lan, Bradley, &

Parr,

1993).

How are teachers dealing with these

ABSTRACT. In this article, the

author proposes the use of one of the tools of the Theory of Constraints- referred to as the prerequisite tree-as a framework for providing structure to the development of graphic organizers used in introductory statistics courses. Even though statistics is an important course for business majors, students often do not have an easy time understanding the material. Graphic organizers could be a strategy to help students overcome their concerns. The author provides guidelines for implementation of graphic organizers in the classroom, especially in statistics.

problems? In a survey of statistics teachers, Strasser and Ozgur (1995) found that respondents spent 80% of class time lecturing and the rest of the time handling questions and answers, which left little or no time for extensive cases or student presentations. The survey did not ask how lecturing time was used by the instructors, but the coverage of statistics textbooks and the nature of students’ concerns would suggest that most coverage deals with solving statistics problems, as opposed to teaching concepts or learning computer software. What makes solving statistics problems such a difficult task for students? The literature suggests that the math problems are challenging because they entail a mixture of words, numbers, special symbols, and graphics (Braselton &

Decker, 1994). Statistics possesses the same characteristics that make math a difficult subject. The challenge for students is in providing order to a set of seemingly disorganized concepts. A methodology that allows students to see how concepts, numbers, and special symbols interrelate is clearly needed. Such methodology should also break statistics problems into smaller subproblems so that students can have a more systematic method to solve them. Graphic organizers are a response to these needs.

Graphic Organizers

Educational research suggests that understanding can be defined as con- nection among pieces of information (Ginsburg, 1977). For achievement of concept connectedness, researchers have developed graphic organizers as metacognitive tools to enhance understanding. Graphic organizers are “visual displays teachers use to organize information in a manner that makes the information easier to understand and learn” (Meyen, Vergason, & Whelan, 1996, p. 132). A discussion of all types of graphic organizers is beyond the scope of this article, but an extensive overview of various mapping techniques can be found in Jonassen, Beiss-

ner, and Yacci (1993).

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September/October 2002 33

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It is not clear how graphic organizers work or do not work (Rice, 1994). How- ever, some researchers have suggested that graphic organizers allow students to store information in both spatial and verbal formats, providing an additional retrieval path for remembering informa-

tion (Kulhavy, Lee,

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& Caterino, 1985).

Regardless of how and why graphic organizers work, educational theorists agree that knowledge must be structured-have some level of organiza- tion-to be retained and easily accessi- ble from long-term memory (Anderson, 1995; Farnham-Diggory, 1992).

Despite the apparent advantages of such organizers, there appear to be no clear guidelines for implementing a graphical organizer strategy (Merkley &

Jefferies, 2001). Even worse, some textbooks may have graphic organizers that can cause more confusion than understanding (Robinson, 1998). Several studies in the field of statistics have dealt with the use of concept maps to teach (Schau & Mattern, 1997; Zwan- eveld, 2000), but they do not touch upon the problem-solving aspect. In this article, I use the Theory of Constraints (TOC) as a framework for providing structure to the development of graphic organizers that can be used in an introductory course in statistics. I present an overview of the TOC and a description of one of its thinking tools, the prerequisite tree. Using an example, I also describe how the prerequisite tree can

be adapted to teach statistics.

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The Theory of Constraints

The TOC is a management philoso- phy developed by Goldratt (1997). One of the basic principles of TOC is that there are very few numbers of variables (referred to as constraints) preventing a system from achieving its goals. The reason for this is that systems are com- posed of interrelated and interdependent links working together to achieve a pre- determined goal. Depending on how these interdependencies are built, inter- vening in one link may or may not have an impact on the whole system. To be stable, systems must have very few leverage points; otherwise, chaos will occur. The idea, then, is to construct a description of a system in such a way

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Journal of Education for

Business

that it is possible to determine the key leverage points and the type of interven- tion needed to obtain a desired result.

The heart of the TOC, at this point in its development, is a set of logical tools known as the thinking processes (TP). These tools are based on strict logical procedure and have been used in myriad business applications. TP tools include the current reality tree, the cloud, the future reality tree, the negative branch, the prerequisite tree (PrT), and the tran- sition tree. Specific details about the TP are available in the literature (Dettmer, 1997; Scheinkopf, 1999). My purpose in this article is to show how one of the tools, the PrT can be adapted to teach statistics.

Within TOC, a PrT is a tactical tool used for planning the execution of an objective. Constructing a PrT consists of two steps: (a) building an intermediate objective (10) table and (b) constructing an intermediate objective map.

Building an 10 Table

The first step in building an I 0 table is to ensure a clear understanding of the objective to be accomplished. In TOC, the objective is referred to as the “ambitious target.” Once the ambitious target has been defined and clarified, the next step is to generate all the obstacles pre-

venting one from achieving the target. A

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mechanism for generating a list of obstacles is to ask the question, “What is blocking the implementation of this goal?” This process continues until no more obstacles can be found. The main objective of having a list of obstacles is to break down the ambitious target into subproblems that are more manageable. Brealung down a problem into smaller parts is known to facilitate its solution.

Next, solutions referred to as 10s are given to each one of the obstacles. Each I 0 should be determined in such a way that, as a result of its implementation, the obstacle disappears or its influence ceases to block the implementation of the goal. For example, if an obstacle is “we do not have the expertise to perform this task in this department,” then possible 10s are “we conduct a training program,” or “we simplify the task.” In the former 10, providing training that will bring the required expertise to the

department eliminates the obstacle. In the latter scenario, the I 0 does not elim- inate the obstacle, but it creates a situa- tion in which the obstacle is irrelevant.

The procedure consists of taking an obstacle and then asking for suggestions as to how to overcome it. In some cases, several 10s may be candidates for over- coming an obstacle. Logically, the I 0 that is easiest to implement or the least expensive should be selected. Addition- al research may be needed to make a better decision in selecting the appropri- ate 10. At the end of this process, each obstacle should have a corresponding I 0 with a high level of likelihood that it will overcome the obstacle. Completing this step results in a final list of obstacles and intermediate objectives. This list is referred to as an I 0 table.

In determining an 10, we could hit a wall and not come up with a specific way to overcome an obstacle. In this case, the recommended course of action is to simply write down the I 0 as the opposite of the obstacle and perform a separate PrT analysis on that I 0 later in the process. If separate analyses are conducted for difficult IOs, the result is a set of interconnected PrTs as opposed to a single PrT.

Constructing an 10 Map

The 10s at this point are a disorganized array of seemingly unrelated tasks. The next step is to convert this list into a plan. To accomplish this, one must put 10s into a logical sequence by determining (a) which 10s should be worked on first, which second, and so

forth and (b) which 10s can be worked on in parallel with other 10s.

To do this, one must determine which 10s are direct, logical prerequisites for achieving the ambitious target-in other words, which 10s must be achieved before the ambitious target can be accomplished. These 10s themselves also have immediate prerequisites that are found through use of the same logic. The process continues until all 10s are connected either to the ambitious target or to another 10. The connections among 10s can be depicted as a logical tree referred to as the I 0 map, a graphical representation of the final plan, including all intermediate objectives and

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the logical implementation sequence

(see Figure 1).

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The Prerequisite Tree and Statistics

Let us examine some important issues and strategies surrounding the teaching of statistics. First, for many

students, solving a statistics problem

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is

an ambitious target. Second, as I men- tioned in the introduction, statistics is a combination of words, numbers, special symbols, and graphics that are logically connected. Finally, statistics problems are solved through a series of interrelated steps not necessarily sequenced in a linear fashion. These characteristics make the PrT-a logical tool that breaks down a problem into manageable subproblems-a good candidate for a graphic organizer for statistics classes.

Some modifications to the PrT process are needed for accommodating the specific characteristics of statistics problems. The construction of an I 0 table is unnecessary because the steps for solving statistics problems are already determined. I 0 maps can present the steps needed for solving a given problem in boxes that provide space for students to take notes. Each box repre- sents a specific skill that students need to master to solve a problem successful- ly. Sometimes a skill is just the ability to use a calculator, but, in other cases, good conceptual understanding, such as determining the right alternative hypothesis, is required.

In Figure

2, I show an example of a

modified I 0 map for the topic of interval estimation. I 0 maps are handed out to students as a tool for working out their statistics problems. Students are

FIGURE 1. Intermediate Objective (10) Map

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I

+

I 0 2

.

I 0 6

told that boxes without any arrows com-

ing into them are usually data to be gathered from the problem. For example, in Figure 2, three pieces of data are

needed:

X,

n, and the level of confi-

dence. Once the data are available, the procedure outlined in the diagram can be applied. A box with arrows coming into it signals that all previous steps must be completed first because they are logical prerequisites. The steps outlined in Figure 2 indicate that the stu- dents must complete three steps before calculating e.

Boxes are interrelated not only through steps within a diagram but also through diagrams. For example, in Fig-

ure 2, the step “find

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2 on the table” was

covered in a previous diagram showing how to use the normal distribution table. If needed, the instructor can refer students back to a previous diagram, thus promoting one of the important aspects of graphic organizers-that students build new meanings based on previous knowledge (Novak, 1991). This is based on schema theory, which states that “information that fits into a [student’s] existing schema is more easily under- stood, learned, and retained than information that does not fit into an existing schema” (Slavin, 1991, p. 164).

Notice that the last step in the diagram asks students to interpret their results. The purpose of this is twofold. Because they have to interpret the results, students need to go beyond learning the steps mechanically. Beins (1993) found that requiring students to provide written conclusions improves both computational and interpretative skills. Also, students can check whether their final solutions make sense. For instance, an answer such as “the proba- bility of an event is 2.25” should raise a flag, because probabilities cannot be greater than 1 .O.

In class, I usually give three copies of the diagrams to the students, along with an extra page for taking notes. First, I

model; I work one exercise on the board to demonstrate the procedure related to the topic. Then, I provide students with guided practice; they work an example themselves and ask questions if they are having difficulties with a specific step. They keep a blank copy of the diagram in case they need to practice one more

September/October 2002 35

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FIGURE 2. Finding a Confidence Interval for the Proportion

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I

Interpret

your answer

I

,

problem with it. To finish the topic, I

have students practice individually on several homework problems. Students are warned that in the exam they cannot use the diagrams but that they should use them as a guide to learn the differ- ent procedures. This sequence of tasks follows the scaffolding model of teaching (Gainen & Willemsen, 1995).

Discussion

The diagrams have been very successful in my classes (see Appendix for examples of students’ comments), and the average grade has improved. Because I 0 maps break down statistics problems into manageable parts, students can concentrate on solving por-

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Journal

of

Education for Business

tions of a procedure rather than being overwhelmed with the whole problem. Students can also verify their work as they go through the problems in class by comparing their intermediate step results with their neighbors’. By contin- uously referring back to the steps in the diagrams, they can self-monitor their learning and progress. Self-regulated learning has been associated with several cognitive and behavioral benefits (Lan, Bradley, & Pan; 1993).

This process provides an important benefit that could also explain the better performance: Students take much better notes. Graphic organizers provide a very practical way for taking clear and precise notes (Sakta, 1992). After completing one diagram, students have a

clear example of how a problem is to be worked and can easily refer back to it. This happens regardless of how disorganized an instructor may be in writing a problem on the board. As long as they are aware of which step is being worked on, students will have clear notes depicting all the steps in a given procedure. Enhanced note-taking can lead to better performance (Katayama &

Robinson, 2000).

An additional benefit of the use of such graphic organizers is that coverage of class content takes less time. The main reason for this is that students ask more focused questions, because they can refer to a specific step in the diagram instead of asking the instructor to do the whole problem over. The extra time can be used for other activities, such as group projects or case studies with actual data-effective teaching practices suggested in the literature (Strasser & Ozgur, 1995).

Furthermore, continuous improve- ment can be encouraged. When students are having trouble with a specific step, they can be assigned homework problems and activities to overcome that specific obstacle. For instance, one semester I noticed that several students were having difficulties finding the Z value from a table when they were con- ducting a hypothesis-testing problem. To help them overcome that insufficien- cy, I created assignments targeted to that specific skill.

An instructor can also use the diagrams as a grading tool. Similar graphic organizers called fill-in maps have been used for assessment purposes (Schau &

Mattern, 1997). Along the same line, Roberts (1999) has provided several examples of the use of concept maps as an assessment tool. An instructor can assign points or percentages to each step in the diagrams and grade exams accordingly. Again, the results of the grading process can be used in determining where improvements need to be made to increase the quality of the course.

Future Research

Because the results at this point are only anecdotal, additional research, such as an experiment, is needed for

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testing the benefits of using the PrT

process i n statistics classes. It would be

useful to understand which variables have a greater influence o n performance. For example, does performance improve because of better notetaking?

Or is it a result of the higher self-effca-

cy that students develop with improved self-confidence? Does self-regulated behavior play a role?

Other questions pertain to the possi- bility of applying the same methodology to other analytical subjects, such as

quantitative methods and higher level statistics, in which the problems are

highly structured, as they are in introductory level statistics. O n e important issue is whether students can transfer the skill of breaking down a problem into smaller parts to other areas of their academic lives, such as writing papers

and preparing presentations.

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REFERENCES

Anderson, J. R. (1995). Learning andmemory: An

integrated approach. New York: John Wiley. Beins, B. C. (1993). Writing assignments in sta-

tistics classes encourage students to learn inter- pretation. Teaching Psychology, 20(3),

Braselton,

S., & Decker, B. C. (1994). Under-

standing graphic organizers to improve the reading of mathematics. The Reading Teaches 48(3), 276-28 1.

Dettmer, W. (1997). Goldratt’s Theory of Con- straints. Milwaukee: ASQC Quality Press. Farnham-Diggory, S. (1992). Cognitive process in

education (2nd ed.). New York: HarperCollins. Gainen, J., & Willemsen, E. W. (1995). Reenvi- sioning statistics: A cognitive apprenticeship approach. New Directions for Teaching and Learning, 6I(Spring) 99-108.

Ginsburg, H. P. (1977). Children’s arithmetic. New York: D. Van Nostrand Co.

Goldratt, E. (1997). Critical chain. Great Barring- ton, MA: North River Press.

Jonassen, D. H., Beissner, K., & Yacci, M. (1993). Structural knowledge: Techniques for repre- senting, conveying, and acquiring structural knowledge. Hillsdale, NJ: Erlbaum.

Katayama, A. D., & Robinson, D. H. (2000). Get- ting students “partially” involved in note-taking using graphic organizers. The Journal of Exper- imental Education, 68(2), 119-133.

161-164.

Kulhavy, R. W., Lee, B. J., & Caterino, L. C. (1985). Conjoint retention of maps and related discourse. Contemporary Educational Psychol-

Lan, W. Y., Bradley, L., & Pan, G. (1993). The effects of a self-monitoring process on college students’ learning in an introductory statistics course. Journal of Experimental Education, 62( I), 2 6 4 0 .

Merkley, D. M., & Jefferies, D. (2001). Guide- lines for implementing a graphic organizer. The Reading Teaches 54(4), 350-357.

Meyen, E. L., Vergason, G. A., & Whelan, R. J.

(1996). Strategies for teaching exceptional chil- dren in inclusive settings. Denver, CO: Love. Novak, J. D. (1991). Clarifying with concept

maps. The Science Teaches 58(7), 4 5 4 9 .

Rice,

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

G. E. (1994). Need for explanations in

graphic organizer research. Reading Psycholo-

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gy,

AS, 39-67.

Roberts, L. (1999). Using concept maps to mea- sure statistical understanding. International Journal of Mathematical Education in Science and Technology, 30(5), 707-717.

Robinson, D. H. (1998). Graphic organizers as aid to text learning. Reading Research and Instruc- tion, 37(Winter), 85-105.

Sakta, C. G. (1992). The graphic organizer: A blueprint for taking lecture notes. Journal of Reading, 35(6), 482-484.

Schau, C., & Mattern, N. (1997). Use of map techniques in teaching applied statistics courses. The American Statistician, 51(2), 171-175. Scheinkopf, L. J. (1999). Thinking for a change.

Boca Raton, FL: St. Lucie Press.

Slavin, R. E. (1991). Educationalpsychology (3rd ed.). Needham Heights, MA: Allyn & Bacon. Strasser, E. S., & Ozgur, C. (1995). Undergradu-

ate business statistics: A survey of topics and teaching methods. Interfaces, 25(3), 95-103.

Zanakis,

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

S. H., & Valenzi, E. (1997). Student anx-

iety and attitudes in Business Statistics. Journal of Education for Business, 73(1), 10-16. Zwaneveld, B. (2000). Structuring mathematical

knowledge and skills by means of knowledge graphs. International Journal of Mathematical Education in Science and Technology, 31(3), 393414.

ogy, 10, 28-37.

APPENDIX STUDENT COMMENTS

“I do feel that the diagrams helped me,

but they only helped me in breaking do[wn] the steps of how to do the problems. For example, at the top of the diagrams you have to find two or three variables first, and then put them all into the equations. I liked this part because I was able to determine

what variables were given, and which vari-

able I needed to find. This step also helped

me on the exam because I was able to use

the correct equation for the problem that contains those variables. So basically, I did

find the diagrams useful.”

“I was the one who got 87 on the first test and then 100 on the second [Author’s note: this student got 100 on the final exam too].

I was also one of the people who finished within a half hour on the second test. I must credit this to your new teaching technique-the prerequisite trees. These helped me study for the second exam by allowing me to come to a better understanding of each variable before plugging numbers into a formula. I knew which formulas to use on the exam because I knew what each number

represented. By using the prerequisite trees, I came to realize what the procedure was for each type of problem, and it became clear to me which formula to use for each problem. Thanks to these trees I only had to read a problem once over [sic] before I knew what to do when normally I may have to read a problem over three or four times before fully understanding it. This is why I finished so quickly and still got a good score. Thank you! Your new technique is great!”

“The presentation and utilization of these ...g raphical models.. .that you present- ed through the semester has allowed me to fully understand the concepts of this course. More importantly, I believe that I

can apply these models in my job responsi- bilities today in order to make me more efficient at work. These models allowed [me] to see the process before attacking the problems. The concepts were demonstrated in the textbook, but these models made it much easier. To relate, it’s like going on a trip to a place you’ve never been to. If you look at a map first, and see where your [sic] at, and where you want to go. It’s a lot easier than just getting into your car and travel- ing down the road looking for street signs and the like. I really wish these tools would

have been made available in my previous &on Statistics class, but that’s history now. Again, thanks for the clever idea and 1 will definitely put these tools to good work for future real-world situations. I am also going

to recommend to anyone who will be taking one of these two courses to try to sign up for your class based on my successes.”

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