Students' perceptions on factors of statistics anxiety and instructional strategies.
Key words: statistics anxiety, learning statistics, teaching statistics
Statistics anxiety is defined as anxiety that occurs as a result of encountering statistics in any form and at any level (Onwuegbuzie, DaRos, & Ryan 1997). In classrooms, statistics anxiety is noticeably common among students whose academic background includes little previous statistical or mathematical training. Onwuegbuzie, Slate, et al. (2000) stated that 75% to 80% of graduate students in the social sciences appeared to experience uncomfortable levels of statistics anxiety which negatively affected learning (Onwuegbuzie & Seaman 1995).
Consequently, statistical analysis became the lowest academic skill for graduate students in the social sciences (Huntley, Schneider, & Aronson 2000). The dilemma is that almost all graduate students in the social sciences need to take statistics as part of their academic training. How training programs should help graduate students address statistics anxiety and help them learn statistics more effectively is important.
Statistics anxiety is not only due to the lack of training or to insufficient skills, but is also due to misperception about statistics and negative experiences in previous statistics classes. For instance, students often think they do not have enough mathematics training to do well in statistics classes. The fear of failing the course causes a delay in enrolling in statistics courses for as long as possible, and the delay often leads to failure to complete degree programs (Onwuegbuzie 1997). The lack of self-efficacy and the high anxiety in statistics keep many students away from engaging in research work or furthering an academic career (Blalock 1987; Caine et al. 1978; Schacht & Stewart 1990; Zeidner 1991).
The prevalence of statistics anxiety among graduate students in the social sciences has called for researchers' and educators' growing attention in the last decade. In the literature, statistics anxiety has been extensively studied in two major areas--measurement of and factors contributing to statistics anxiety. In the early stage, statistics anxiety instruments were derived from measurement of math anxiety, including the Statistical Anxiety Scale (Pretorius & Norman 1992) and the Statistics Anxiety Inventory (Richard & Woolfolk 1980). The Statistics Anxiety Rating Scale (STARS), developed by Cruise and Wilkins (1980) and Cruise, Cash, and Bolton (1985), is recently studied by Baloglu (2002) for its psychometric properties. More recently, Watson et al. (2003) incorporated the STARS along with a survey of attitude toward statistics into a multimedia program--EncStat (Encouraged About Statistics)--that aimed at identifying students with statistics anxiety or negative attitudes toward statistics.
The factors contributing to students' anxiety are broad. Forte (1995) found several factors that were applicable to social work students who experienced statistics anxiety. These factors were minimal previous math preparation, late-in-career introduction to quantitative analysis, general anti-quantitative bias, lack of appropriation for the power of analytical models, and lack of mental imagery useful in thinking about quantitative concepts. Another investigation found that evaluation concern, fear of failure, and perfectionism were responsible for statistics anxiety (Walsh & Ugumba-Agwunobi 2002).
Onwuegbuzie and Wilson's (2000) comprehensive review classified the factors associated with statistics anxiety into three categories: (a) situational factors, such as math experience (Baloglu 2001, 2003; Betz 1978; Hong & Karstensson 2002; Pan & Tang, 2004; Roberts & Bilderback 1980; Tomazic & Katz 1988; Wilson 1997; Zeidner 1991), statistics experience (Sutarso 1992), computer experience (Zimmer & Fuller 1996), and research experience (Trimarco 1997; Pan &Tang, 2004); (b) dispositional factors, such as math selfconcept or self-esteem (Zeidner 1991), scholastic competence or multiple intelligences (Birenbaum & Eylath 1994; Daley & Onwuegbuzie 1997; Onwuegbuzie 2000c), perfectionism (Onwuegbuzie & Daley 1999; Walsh & Ugumba-Agwunobi 2002), hope (Onwuegbuzie 1998a), and procrastination (Onwuegbuzie 2000a; Walsh & Ugumba-Agwunobi 2002); and (c) personal factors, such as learning style (Onwuegbuzie 1998b; Wilson & Onwuegbuzie 2001), age (Baloglu 2003: Pan & Tang, 2004), gender (Baloglu 2003; Benson 1989; Benson & B&alos 1989: Betz 1978; Demaria-Mitton 1987; Hong & Karstensson 2002; Roberts & Bilderback 1980), and ethnicity (Bell 1998; Onwuegbuzie 1999).
Unfortunately, few studies have examined methods to reduce the anxiety in learning statistics for graduate students in the social sciences (Onwuegbuzie & Wilson 2000). Schacht and Stewart (1990) found that students in statistics classes where humorous cartoon examples were incorporated felt a reduction in their level of anxiety. Smith, Miller, and Robertson (1992) and Sgoutas-Emch and Johnson (1998) reported that journal writing was apparently effective in reducing anxiety, although these authors did not find a statistically significant decrease in anxiety levels. Forte (1995) argued for an effective teaching approach that incorporated computer usage, real-world applications, humor, statistical language practice, and group-learning principles. Dolinsky (2001) suggested creating a collaborative environment in which active learning strategies were used as the primary method to teach statistics. Recently, Pan and Tang's (2004) study shows that the combining application-oriented teaching methods with instructors' attentiveness to students' anxiety is a significantly effective way to reduce students' anxiety in learning statistics. These teaching methods reveal promising, initial efforts to reduce students' statistics anxiety, but more innovational strategies of teaching statistics are needed (Huntley et al. 2000).
The purpose of this current study was to gain more understanding of students' perceptions on factors contributing to their anxiety in learning statistics and potentially helpful instructional strategies. A focus group study was used to explore what factors students think impede their statistics learning and contribute to their anxiety in learning statistics and whether the instructional strategies employed in the classroom helped them reduce their statistics anxiety and learn statistics effectively. The research questions were (a) What factors do students perceive to be contributing to their anxiety in learning statistics? (b) What instructional strategies do students feel helpful to lessen their statistics anxiety and to learn statistics effectively? The importance of understanding students' perceptions lies in the fact that no strategies will work if students cannot make any sense of their learning process.
Seven voluntary students were recruited from a 30-student graduate course on statistical methods offered by the College of Education at a Midwest urban university. Specifically, these 7 students included 1 Asian student, 2 African Americans, and 4 Caucasian Americans. There were 2 male and 5 female students. The mean age was 33.86 with a standard deviation of 6.20. All but one was pursuing a doctoral degree. Three of the students majored in Counseling, two in Educational Foundations, and two in Communication Sciences and Disorders. All of them had at least one (M = 3.43, SD = 1.27) mathematics, statistics, or other quantitative courses in their previous degrees. The participants also reported that they had research experience (M = 2.86, SD = 1.07) rated on a 5-point Likert scale (1 = little experienced through 5 = very experienced).
Data Collection Method
We conducted a focus group interview as the data collection method. "A focus group interview is an interview with a small group of people on a specific topic" (Patton 2002, p. 385) and "it can get high-quality data in a social context where people can consider their own views in the context of the views of others" (p. 386). The purpose of this study was to examine students' perceptions on the factors contributing to their statistics anxiety and instructional strategies that might be helpful for them to learn statistics effectively. The format of focus group aligns well with the research goal because seeking reaction to shared experiences is one of the functions of the focus group interview. Interactions among participants also enhance data quality. It is a cost-effective data collection method as well.
The participants were in the same statistics class. In that class, several instructional strategies were employed to reduce the anxiety and enhance learning outcome. The instructional strategies used in the class were classified into two categories: application-oriented teaching methods and instructor's attentiveness to students' anxiety. In the first category, the students were requested to write an essay biweekly to their bosses or friends about what they have learned in the class using layperson's language based on a real example from their work or daily life. The students were also asked to critique a published quantitative journal article, which allowed students to apply the course content to evaluate quantitative research.
In regard to reducing the anxiety, the instructor had tried the following strategies: (a) an orientation letter was sent out a week prior to the class to get the students oriented to the expectations of the class, such as textbooks, necessary background knowledge in math, and available resources for help if students had any concerns or questions; (b) the instructor maintained flexible and extra office hours and conducted an interim class survey addressing the students' concerns; (c) the students could bring a note sheet to the final exam. Preparing the note sheet functioned as a means of reviewing the course materials and summarizing course content; and (d) the students also had an option to take the course on a Pass/Fail basis as an alternative to the regular letter grading system, which dramatically reduced their anxiety about doing poorly in the class.
At the end of the class after the final exam, the students were recruited to participate in the study using focus group to explore effective statistics learning. 7 students out of 30 students in the class volunteered to participate. The questions in the focus group interview solicited the participants' responses on the following four areas: (a) what factors made them anxious about learning statistics, (b) positive and negative experiences in learning statistics, (c) teaching methods that helped them reduce the anxiety, and (d) teaching methods that helped them learn statistics. The participants were also asked to provide any suggestions that would help graduate students learn statistics more effectively.
At the end of the quarter, the focus group was conducted in a quiet, private room in the same building where the students took their class. One of the researchers played the role of moderator, and the other was in charge of video taping the interview session. The participants were briefed about what a focus group was and what they needed to do in the interview. They were informed about their rights to withdraw from the study and were told that their confidentiality would be guarded. The moderator also ensured that everyone had an opportunity to express their views and concerns if there were any. At the end, both researchers thanked the participants for their contributions.
The focus group interview lasted about 1 hour. The moderator asked the questions and then invited the participants to provide their responses and reactions to the questions. Every participant was given opportunity to respond; if the participants did not have any reaction to a particular question, they might choose to pass. The participants were briefed on the process of focus group interview and encouraged to respond not only to the questions from the moderator but also the responses from their group members. The participants did interact well because they knew each other from class and seemed comfortable to each other. The researchers noticed that the group agreed with each other more often than differing on the issues. The moderator also emphasized that there were no right or wrong answers and that all input was appreciated.
The videotaping of the focus group interview was transcribed verbatim by a research assistant and the transcribing process was double-checked by the researchers to secure the validity of the transcription. The transcripts were independently coded by the researchers for analysis. In their independent coding process, the researchers looked for the common themes from the participants' responses to the same questions and then grouped the same or similar responses into a category. The data were reduced into several categories pertaining to two major themes: factors contributing to statistics anxiety and helpful instructional strategies. Finally, the researchers compared and discussed their coding and themes identified for consensus. The researchers did not find any major disagreement on coding or interpretation of the repeated words.
Factors Contributing to Statistics Anxiety
In responding to several questions probing factors contributing to statistics anxiety, the participants provided a variety of responses (see Table 1 for a summary). Four patterns were identified: fear of math, lack of connection to daily life, pace of instruction, and instructor's attitude. The anxiety of math deficiency was echoed by almost all the participants. One participant said, "I was never very good at math so that's what makes me more anxious." Another student said, "For me too, I have a fear of math I may get stuck half way in solving the problem." "I have a math phobia," still another agreed. Several students indicated that statistics had little to do with their daily-life problems and made it difficult to learn. For instance, one student said, "It's not connected to anything that I normally do.'" Another student echoed, "It doesn't feel important by day to day." The pace of instruction was mentioned because some students felt that intensity of graduate curriculum (i.e., one quarter for one subject) seemed to be a problem, compared to undergraduate courses where one spends a whole academic year on a particular subject. There was one student who stated that she did not have anxiety about learning statistics because she liked problem-solving process.
In regard to negative experiences, several students mentioned how an instructor in their previous statistics class had harmful impact on their view of themselves and statistics. The sample statements were: "You didn't want to ask a question, some people were ridiculed;" and "I didn't feel like the instructor was interested in how I was doing in the class or cared, and that did make a lot of differences." Taking an exam was another difficult thing that the participants agreed upon as negative experience. Lastly, the intensive pace of instruction was again mentioned as a negative impact on their learning. One student said, "I need soak time [to digest the materials]." Helpful Instructional Strategies
The majority of the students listed examination methods and evaluation criteria as the important instructional strategies that would be helpful for them to reduce the anxiety (see Table 1 for a summary). They preferred to have many small quizzes, case studies, and projects for course evaluation rather than a heavily weighted final exam. One student said, "I would prefer we do the exercise and have to show our work, what would work for me, I thought the exam was too time intensive." "It's very anxious because you have so much to do and such a chunk of your grade and if I bomb there, then I just get a bad grade," another student expressed the same feeling. Being given an option to take the course on a Pass/Fail basis also helped some students because they knew they could pass but not necessarily got a B or above grade which is required by the graduate school. "Note sheet" was generally liked by the participants; however, one student felt that the note sheet was not so helpful because of difficulty in organizing information on one sheet.
Pertaining to the helpful instructional methods for learning statistics, the responses of the participants could be categorized into 3 major areas (see Table 1). Practical application was the most frequently brought up strategy in the discussion. The specific approaches included working on real-world problems, applying the statistics in a research project, reinforcing the concepts through homework, and communicating what has been learned in class to other people. They stated, "I would like more practice in solving more problems," "developed a study and then applied what we learned," "more examples, more problem solving ... kind of walking through the steps, ... and I think I learn by repetition," "I really liked the assignment where we had to explain to a friend, because again.... once I started to type it out I realized that I had a lot of questions, do I really understand this," and "I even like the overlapping of the assignment with the exercise." The other helpful ways were flexible availability of assistance by the teaching staff as well as by lecture notes which were available prior to class. "Presentation of the lectures are very helpful," and so was "their availability" (referring to teaching assistant and instructor). The third area the participants felt helpful was their hope to have a small class size and some in-class small group activities.
When asked about their positive experience in the statistics class, the participants expressed their appreciation of real-world examples and practical exercises/problem solving (see Table 1). They particularly liked the example being carried through for illustrating different concepts. The participants indicated their "aha" moments came when "pulling things together in the real world" and "things come together and make you understand." They felt "real stories help" and "examples were really good." The other positive experiences the participants identified included orientation of the class, lecture notes on the Electronic Blackboard available prior to the class, and flexible availability of assistance by instructors and teaching assistants.
Statistics anxiety is prevalent among graduate students in the social sciences. Measurement of and factors affecting statistics anxiety have been focuses of much research during the past 20 years. Few studies have examined what students' experiences were in learning statistics in class. This study used a focus group study to explore what factors contributed to students' anxiety about learning statistics and what instructional strategies could be potentially helpful in reducing their anxiety and to assist them to learn statistics effectively. The findings revealed that contributing factors range from misconception or mystified belief about statistics to instructor's attitude to lack of connection to real-world problems. The results also illustrated that practical application was the most effective teaching strategy identified by the participants of the focus group.
In addition to the math phobia and misconception about statistics, the instructor's attitude was another important factor for students' statistics anxiety. If the instructor can be sensitive to students' concerns and attentive to their worries, it is possible to help graduate students in the social sciences learn statistics more effectively. The participants in this study revealed that the orientation letters from the instructor prior to the class were helpful. The reasons were probably not only because the letter informed the students about what to expect and how to be ready for the class, but also it was a sign that the instructor cared about students' learning. Encouragement from instructors (Wilson & Onwuegbuzie 2001), humorous teaching style (Forte 1995; Schacht & Stewart 1990; Wilson 1998), and addressing the anxiety and providing coping strategies to students (Dillon 1982; Pan & Tang, 2004; Wilson 1998) were suggested in the literature to be effective instruction practices for reducing students' statistics anxiety.
The responses from the participants consistently favored the teaching strategies that use more practical application, real-life stories and case examples. One of the contributing factors for statistics anxiety was lack of connection to the real world. It seems that when the lectures and assignments gear towards real-life problems and illustrate how statistics can be useful, misconceptions about statistics can be dispelled. Applying the class contents to daily life and actual research articles makes learning statistics more meaningful. Many participants also stressed the importance and helpfulness of having one example carried through so that they can see clearly how statistics can address different aspects of the problem. The literature, in fact, supports the findings of this study. Forte (1995), Pan and Tang (2004), and Wilson (1998) suggested that applying statistics to real-world situations be helpful in alleviating anxiety in statistics classes. Dunn (1996), Dolinsky (2001), Pan and Tang (2004), Smith, Miller, and Robertson (1992), and Sgoutas-Emch and Johnson (1998) also found that writing assignment was an effective way to help students to form positive attitudes toward to statistics. Applying the statistical concepts to solve real-life problems also give students opportunities to reinforce what they have learned, which addresses the pace issues that many participants feel as a problem.
The participants indicated that fear of failure was one of the causes of anxiety. Therefore, if instructors can eliminate the source for their failure--examination, students at least can focus more on learning rather than outcome evaluation. For instance, several methods used in the class, such as optional grading system, more flexible office hours, orientation letter, and the note sheet, were all measures that made it easier for students to pass the course. From the participants' responses, it was clear that these measures were helpful in addressing the psychological part of their statistics anxiety. Availability of assistance is important because knowing they can ask for help any time, students will not feel frustrated when they are stuck.
The findings of this study revealed that teaching statistics more effectively required instructors be attentive to students' anxiety and to employ multidimensional teaching approaches. Anxiety can be addressed by instructors' attitudes and multiple ways of evaluating students' learning outcome. The grades of the course can be composed of different assignments with each weighting not too much, so that if students do not well in one particular assignment, they still have chance to make up their grade from other assignments. The assignments should be designed to give students opportunities to reinforce learned concepts. More importantly, the instruction in the class as well as the assignments need to be application-oriented, i.e., practical real-world problem solving. Problem-based learning (PBL; Boud & Feletti 1991) may be a reasonable choice for instructional method. Other suggestions based on the findings from this study were small class size, although implementing small class size sometimes is beyond instructors' control: small group exercises: and cases/examples carried through for illustrating various notions.
Some researchers may be concerned about the generalizability of the current study with a single focus group interview on only 7 voluntary participants. Although the information was sought from the single focus group, the purpose of this study was not to make general statement about statistics anxiety for all graduate students in the social sciences. Rather, this study was to try to provide potentially useful suggestions for instructors and students to explore a means of reducing statistics anxiety. In further research, it would be desirable to conduct multiple focus groups and target on each subpopulation by one of the multiple focus groups. The multiple focus groups would give us a more complete picture of students' perceptions on factors contributing to statistics anxiety and instructional strategies that would help them to learn statistics effectively. Moreover, it would be also interesting to have the qualitative findings in this study followed by experimental quantitative researches looking at the relationship between a decrease in anxiety and an increase in students' performance.
In summary, the statistics anxiety prevalence among graduate students in the social sciences can be addressed from both supportive environment and multidimensional instructional strategies. The supportive environment helps students reduce their anxiety, and the application-oriented instruction makes it easier for students to learn statistics more effectively.
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Wei Pan, Ph.D., Assistant Professor of Quantitative Educational Research. Mei Tang, Ph.D., Associate Professor of Counseling, University of Cincinnati.
Correspondence concerning this article should be addressed to Dr. Wei Pan, Division of Educational Studies, University of Cincinnati, P.O. Box 210002, Cincinati, OH 45221-0002; Email: firstname.lastname@example.org.
This research was supported by a pedagogy grant from the College of Education, Criminal Justice, and Human Services at the University of Cincinnati. The authors are indebted to Robert Kallmeyer for collecting and managing the focus group interview data. The authors are also thankful to Haiyai Bai for useful comments.
Table 1 Summary of Results from Focus Group Interview Theme Factor Factors contributing to statistics anxiety Math phobia Lack of connection to daily life Pace of instruction Instructor's attitude Helpful instructional strategies Practical application Real-world example carried through Orientation prior to class Multiple evaluation criteria Flexible availability of assistance