Teaching Statistics Courses: some important considerations.

Abstract

Most college students from the behavioral and social sciences are required to enroll in at least one statistics course. Unfortunately, many of these students often attain lower levels of achievement in these courses than in their other classes. Consequently, statistics instructors are faced with the challenge of deciding how to maximize student learning and minimize anxiety and disaffection. Thus, this paper provides a discussion of considerations upon which instructors must reflect in order to address students' needs: context (e.g., undergraduate vs. master's vs. doctoral), content (e.g., measurement vs. evaluation vs. research design), and pedagogical style (e.g., web-based vs. traditional; theory vs. concept vs. application).

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The vast majority of college students from the behavioral and social sciences are required to enroll in at least one statistics course as a required part of their degree programs. Unfortunately, for many of these students, statistics is the most difficult course in their programs of study (Schacht & Stewart, 1990). These students often attain lower levels of achievement in these courses than in their other classes (Onwuegbuzie, Slate, Paterson, Watson, & Schwartz, 2000). Additionally, a significant proportion of these students experience debilitative levels of statistics anxiety while enrolled in statistics courses (Onwuegbuzie & Seaman, 1995). Moreover, many students do not regard statistics to be an essential or relevant aspect of their degree programs, but merely a pervasive hurdle that they must overcome in order to graduate (Gal & Ginsberg, 1994).

Consequently, statistics instructors are faced with the challenge of deciding how to maximize student learning in their classrooms and, at the same time, minimize disaffection and anxiety levels. Indeed, the relatively high levels of underachievement and anxiety that prevail in statistics courses has led to calls for reform in the ways in which students are taught in these classes (Cobb, 1993). Before deciding on how to maximize learning in statistics classes, the instructor must reflect upon the following considerations: the context in which the course is taught, the desired content of the course, and the preferred pedagogical style of the instructor. Considerations regarding the context, content, and pedagogical style are discussed in this paper.

The Context of Teaching Statistics

As noted by Hackett (2001), statistics instructors should "not lose sight of the context in which this teaching occurs" (p. 1). As can be seen in Figure 1, issues related to the context of teaching statistics contains many facets. First and foremost, the statistics instructor should consider the type of institution in which the course is being taught (Figure 1). For example, a Research University likely is significantly different than is a traditional Teaching University with respect to the level of student (e.g., Master's- vs. doctoral-level), type of student body (e.g., statistics vs. non-statistics major), diversity of student body, number of statistics courses in students' program of study, levels of statistics courses (e.g., introductory vs. advanced), status of statistics course (e.g., required vs. elective), and the competence and experience of the statistics instructor. Each of these components, in turn, help to determine the goal of the statistics course. See issue's website <http://rapidintellect.com/AEQweb/sum2003.htm>

As part of determining the goal of a statistics class, the statistics teacher must decide whether his/her students should be prepared to be consumers or producers of research. For instance, if the instructor decides to help students become consumers of research, then he/she may be more likely to focus on the theoretical or conceptual aspects of statistics. Conversely, to prepare students to be producers of educational research, the statistics teacher likely may devote at least some of the course to the instruction of statistical applications, including the use of computer (statistical) software. Thus, all of these facets play an important role in determining the content and pedagogical style, as well as the assessment tools used.

Wilson (2001) noted that "no discussion of the context of teaching statistics would be complete without acknowledgement of the anxiety that students bring to class" (p. 2). Indeed, because the majority of students enrolled in statistics classes typically experience high levels of statistics anxiety (Onwuegbuzie, in press), and that anxiety can debilitate statistics achievement (Onwuegbuzie & Seaman, 1995), instructors should be cognizant of how the statistical milieu might affect students' levels of anxiety.

In an attempt to reduce levels of statistics anxiety in classes, several researchers have advocated the use of humor in statistics classes (e.g., Schacht & Stewart, 1990). Interestingly, in a study of education and business students in graduate statistics courses, Wilson (1996) found that students deemed humor and testing procedures (such as open book/open note testing) to be somewhat effective in reducing their anxiety levels, Moreover, Schacht and Stewart (1990) advocated teaching gimmicks in statistics classes. These gimmicks include using students as the source from which data are collected and allowing students to create the statistical application. Sgoutas-Emch and Johnson (1998) found journal writing to be effective in reducing levels of anxiety, although these authors did not find a statistically significant decrease in anxiety levels.

Most recently, utilizing Onwuegbuzie's (1998) finding of a relationship between hope and statistics anxiety, Dilevko (2000) advocated that statistics and research methodology class activities attempt to assist students in understanding the course objectives, as well as being aware of the goal of statistics in order to control their own learning objectives. Dilevko contended that statistics anxiety can be reduced by improving students' perceived worth of statistics and by decreasing their fear of applying statistical knowledge and principals. According to Dilevko, a two-pronged approach should be employed to reduce statistics anxiety, namely: (a) using current news stories and similar sources to introduce and to explain basic statistical concepts and methodological issues in research; and (b) targeting their fear of application of statistics concepts by introducing students to older articles about subjects of interest, and asking them to read, to understand, and to critique these articles, and to suggest how the research projects described in them could be modified, expanded, and updated. Dilevko asserted that by utilizing these two strategies, the importance of statistics in everyday life can be demonstrated through class discussion of interesting events reported in the popular press.

The Content of Statistics Courses

Once the context of the statistics course has been identified, the statistics instructor has to determine the content of the class. Here the context is essential for planning the statistics curriculum. For example, the content likely will be different for undergraduates versus graduates, as well as for master's versus doctoral students. Similarly, the content is likely to be more advanced for statistics- and research-based majors than for their counterparts. Likewise, different curricula are needed for introductory classes than for intermediate or advanced statistics classes. Whatever the context, statistics instructors should be cognizant that they "do not have enough contact hours with [their] students to cover everything that they need to know to conduct high quality research and to understand the latest developments in the field" (Johnson, 2001, p. 2). Thus, as noted by Johnson (2001), statistics educators "must make many hard decisions about what to include and exclude in [their] courses" (p. 2).

The fact that higher standards in research and statistics (e.g., The American Statistical Association, 1999; Wilkinson & the Task Force on Statistical Inference, 1999) currently prevail, coupled with the fact that our knowledge base in the areas of quantitative-based methodology has rapidly expanded in recent years, there is more necessity for students, particularly at the doctoral level, to take more research methods and statistics courses. Yet, it appears that doctoral curricula and the like have less and less room for research design, statistics, and measurement (Thompson, 1998). In fact, at some institutions students are required to take only one statistics course. At such institutions, choice of topics to be taught is extremely critical (Elmore & Woehlke, 1998). Several additional factors play a role in the content that emerges, including the following: administration support, time, resources, interest in statistics/research, willingness to change, willingness to keep up with the statistics literature, knowledge of the best statistical practices, confidence in statistics/research, experience of teaching statistics, level of instructor anxiety, and competence in teaching statistics. Figure 2 provides a conceptual model of how these factors are related. See issue's website <http://rapidintellect.com/AEQweb/sum2003.htm>

Especially important components of this model are awareness of the most current statistical theory and applications and a willingness to change (Johnson, 2001). As noted by Johnson (2001, p. 20), "it is essential that professors of educational research and statistics keep up on the latest developments in methodology and statistics so that [they] can pass this information along to [their] graduate students 'in training'" [emphasis in original]. Indeed, a statistics instructor who is not well versed with the best statistical practices and/or is unwilling to disseminate these practices is unlikely to develop a cutting-edge curriculum. Unfortunately, the teaching of inappropriate or outdated statistical techniques can lead to students being developed who conduct seriously-flawed theses, dissertations, and other types of research studies. Disturbingly, statistical training has changed little during the last two decades (Aiken, West, Sechrest, & Reno, 1990). Moreover, evidence exists that the majority of published studies and theses/dissertations are seriously flawed, containing procedural, analytical, and interpretational errors (Hall, Ward, & Comer, 1988; Keselman et al., 1998; Onwuegbuzie, 2002; Thompson, 1998; Ward, Hall, & Schramm, 1975). As noted by Onwuegbuzie and Daniel (in press), some of these flaws stem from (a) graduate-level instruction in which statistical techniques are taught as a series of routine steps, rather than as a interactive, reflective, and integrative process; (b) graduate-level curricula that minimize students' exposure to statistical theory and applications; (c) exacerbation of various inaccurate and misleading "mythologies" about the nature of research; (d) increasing numbers of statistics instructors teaching out of their areas of expertise; and (e) a failure, unwillingness, or even refusal to recognize that statistical techniques that were popular in previous years no longer reflect best practices and, more importantly, may now be deemed inappropriate, invalid, or obsolete. Examples of inappropriate statistical practices that are still being disseminated in many statistics courses include (a) not providing evidence that statistical assumptions were checked prior to conducting inferential analyses; (b) not discussing power/sample size considerations; (c) inappropriate treatment of multivariate data; (d) use of stepwise procedures; (e) failure to report reliability indices for either previous or present samples; (f) no control for Type I error rate; and (g) failure to report effect sizes (Onwuegbuzie & Daniel, in press).

An important decision made by statistics teachers relates to the emphasis that should be placed on measurement. Aspects that fall under the auspices of measurement include classical test theory and item response theory. Clearly, the level of statistics course, number of statistics courses in the sequence, level of students, type of student body, and the like largely determine the amount of exposure to measurement issues that students will receive. For example, in an introductory-level course, it is likely that time will prevail to teach only the basics of classical test theory, such as the concepts of reliability and validity. Similarly, the role of qualitative research is another decision that a statistics instructor must make. For example, at some institutions such as Valdosta State University, doctoral students are required to complete a course in mixed methodologies, in which they are taught how to conduct research that utilizes both quantitative and qualitative data either in a parallel or sequential manner (Onwuegbuzie, 2000). The likelihood of statistics instructors using such a pragmatist approach to teaching statistics is a function of their philosophical orientation (i.e., world view), as well as their experience in using mixed methodologies.

Other questions that statistics educators should address are (a) What is the role of program evaluation and research design in statistics classes? (b) Should statistics instructors concentrate more on theory or application? (c) What is the role of computers in statistics classes? (d) Should statistics instructors focus on computational formulae? What should the ratio be between descriptive and inferential statistics? (e) What should be the balance between hypothesis testing and estimation? (f) Should Bayesian statistics play a role in statistics classes? (g) What should be the balance between graphical and analytical techniques? (h) What is the role of meta analyses? (i) How much can we expect reasonably for students to learn within one statistics course and within a series of statistics courses? and (j) What should be the role of action research?

The American Psychological Association (APA) Board of Scientific Affairs, who convened a committee called the Task Force on Statistical Inference, provided recommendations for the use of statistical methods (Wilkinson & the Task Force on Statistical Inference, 1999). Useful recommendations were furnished by the Task Force in the areas of design, population, sample, assignment, measurement, results, analysis, and discussion. At the same time, the Committee on Professional Ethics of the American Statistical Association (ASA) addressed the following eight general topic areas relating to ethical guidelines for statistical practice: (a) professionalism; (b) responsibilities for funders, clients, and employers; (c) responsibilities in publications and testimony; (d) responsibilities to research subjects; (e) responsibilities to research team colleagues; (f) responsibilities to other statisticians or statistical practitioners; (g) responsibilities regarding allegations of misconduct; and (h) responsibilities of employers, including organizations, individuals, attorneys, or other clients utilizing statistical practitioners (The American Statistical Association, 1999, p. 4). Thus, statistics instructors should consider designing their courses with respect to both the APA and ASA recommendations.

Finally, the debate concerning statistical significance testing (cf. Onwuegbuzie & Daniel, in press) makes it clear not only that statistics is a controversial subject matter (Derry, Levin, & Schuable, 1995), but also that it represents an art rather than a science. As such, as recommended by Derry et al. (1995), statistics "should not be taught as a set of final-form, universally accepted concepts that can be handed down by authority and conveyed to students by teachers and textbooks" (p. 52). Moreover, statistics courses should serve to make students cognizant of the major statistical debates (Derry et al., 1995; Johnson, 2001). According to Derry et al. (1995), "students could gain even more by actually discovering and participating in such controversies" (p. 52). Chance (1997) echoes these sentiments, stating that students' most meaningful learning gains arise from debating ideas belonging to different camps.

Pedagogical Style in Statistics Courses

In addition to considering the context and content of statistics courses, instructors must focus on the pedagogical issues. An important aspect of this is how to deliver statistical knowledge (i.e., the media). Central to the delivery system is the role of web-based instruction (i.e., synchronous and asynchronous) in statistics classes. Web-based instruction typically involves the use of computer software and hardware that do not represent the mainstream utilized by college instructors. As such, statistics instructors who use such delivery systems must have an interest in technology, a willingness to use technology, knowledge of various computer software, and a willingness to change. Additionally, the likelihood that this teaching mode will be employed will be greatly facilitated if the statistics teacher should have prior experience of using technology as a teaching aid, as well as confidence in using technology and relatively low levels of technology-related anxiety. Figure 3 presents all these variables in a conceptual model. See issue's website <http://rapidintellect.com/AEQweb/sum2003.htm>

Also presented in Figure 3 are time, resources, and administrator support. Obviously these three components must be in place for delivery systems such as web-based teaching to prevail. The final ingredients in the conceptual model are instructors' learning style and teaching style. For example, if an instructor's learning style is suited to a web-based learning modality, then he/she is more likely to teach using this style. Interestingly, Onwuegbuzie and Daley (1997) found that students who are most similar in learning style to their instructor with respect to persistence orientation, peer orientation, auditory preference, and multiple perceptual preferences tend to obtain higher levels of performance in educational research courses.

Within the statistics classroom, statistics teachers should experiment with different organizational approaches. For example, cooperative learning techniques (Onwuegbuzie, 2001; Onwuegbuzie, Collins, & Elbedour, in press; Onwuegbuzie & DaRos, 2001); and advance organizers (Onwuegbuzie, 1999) could be examined. With respect to the former, Derry, Levin, Osana, Jones, and Peterson (2000) found that a course in which most instruction was anchored to mentored, small-group collaborative activities that simulated complex, real-life problem solving led to meaningful gains in students' reasoning ability. With respect to the latter, Onwuegbuzie (1999) found that students enrolled in the advance organizer sections of a research methodology course obtained higher levels of overall achievement than did their counterparts enrolled in sections in which advance organizers were not utilized by the instructor. As noted by Johnson (2001, p. 2), statistics teachers "must help students become effective users of computer packages (e.g., SPSS, SAS, DataDesk) ... [and] because of the widespread availability of statistical software ... [statistics instructors] can now focus much of [their] effort on teaching students how to correctly use statistical software and how to interpret output." In order to meet the technological needs of students, Valdosta State University required that every statistics and research methodology course take place in a computer laboratory, in which every student enrolled in these classes sits at a computer terminal. (The computer monitor is built into the workstation such that the student's view of the instructor is not impeded.) In these laboratories, the instructor has a computer console positioned at the front of the class containing a computer linked to a projector. Students enrolled in statistics and research methodology courses are then able to learn how to use computer software (e.g., SPSS) in a hands-on, step-by-step manner. Instructors at Valdosta State University believe this to be an effective way of teaching students how to analyze real data.

Conclusion

The present paper has identified considerations upon which statistics instructors must reflect in order to maximize student learning and to minimize student anxiety and disaffection: context, content, and pedagogical style. Once these considerations have been made thoughtfully, along the lines described above, the statistics instructor then will be in a position to begin answering the calls for reform in the ways in which students are taught statistics.

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Anthony J. Onwuegbuzie, Howard University 

Nancy L. Leech, University of Colorado at Denver 

Dr. Onwuegbuzie is an associate professor in the Department of Human Development and Psychoeducational Studies. Dr. Leech is an assistant professor