Psychological Reports: Sociocultural Issues in Psychology 2014, 115, 1, 297-310. © Psychological Reports 2014
REDUCING STATISTICS ANXIETY AND ENHANCING STATISTICS LEARNING ACHIEVEMENT: EFFECTIVENESS OF A ONE-MINUTE STRATEGY1, 2 CHEI-CHANG CHIOU Department of Accounting National Changhua University of Education, Taiwan YU-MIN WANG
LI-TZE LEE
Department of Information Management National Chi Nan University, Taiwan
Department of Accounting Information Overseas Chinese University, Taiwan
Summary.—Statistical knowledge is widely used in academia; however, statistics teachers struggle with the issue of how to reduce students' statistics anxiety and enhance students' statistics learning. This study assesses the effectiveness of a “one-minute paper strategy” in reducing students' statistics-related anxiety and in improving students' statistics-related achievement. Participants were 77 undergraduates from two classes enrolled in applied statistics courses. An experiment was implemented according to a pretest/posttest comparison group design. The quasi-experimental design showed that the one-minute paper strategy significantly reduced students' statistics anxiety and improved students' statistics learning achievement. The strategy was a better instructional tool than the textbook exercise for reducing students' statistics anxiety and improving students' statistics achievement.
Statistical knowledge is widely used in multiple fields of academia as well as in non-academic practice. Consequently, more and more undergraduates, and even postgraduates, of diverse backgrounds have had statistics included in their lists of compulsory courses (Onwuegbuzie & Leech, 2003). Likewise, the knowledge of applied statistics is gaining in importance for students in business schools (Carlson, 1999). Without doubt, statistics is an important field of study. For many undergraduate and postgraduate students, statistics is among the most formidable courses in their curriculum plans (Feinberg & Halperin, 1978; Schacht & Stewart, 1990; Onwuegbuzie & Leech, 2003). Many researches indicated that when undergraduate students encounter concepts, questions, cases, and instructional or test situations concerning statistics, they are likely to develop severe anxiety (Feinberg & Halperin, 1978; Zeidner, 1991; Onwuegbuzie, 1998; Onwuegbuzie & Leech, 2003). Onwuegbuzie (1998) Address correspondence to Yu-Min Wang, Department of Information Management, National Chi Nan University, Taiwan or e-mail ([email protected]). 2 The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this research under NSC 96-2413-H-018-007. Ted Knoy is appreciated for his editorial assistance. 1
DOI 10.2466/11.04.PR0.115c12z3
23-PR_Chiou_140039.indd 297
ISSN 0033-2941
05/08/14 5:22 PM
298
C-C. CHIOU, ET AL.
pointed out that such anxiety is experienced by as many as 80% of postgraduate students. Anxiety related to statistics engenders a negative perception of statistics among the students, and is even regarded as a major obstacle to acquiring a degree (Onwuegbuzie, 1998; Onwuegbuzie & Leech, 2003). Furthermore, quite a number of non-statistics majors consider statistics of no importance or little relevance to the subject they are studying, regarding it rather as an unavoidable hurdle on their way to graduation (Onwuegbuzie & Leech, 2003). These research results evidently demonstrated that statistics anxiety is a current prevailing issue deeply concerning undergraduate and postgraduate students. Statistics anxiety involves a complex array of emotional reactions which may cause discomfort at medium levels or at higher levels can entail severe consequences such as apprehension, fear, nervousness, panic, and other negative results (Onwuegbuzie, Da Ros, & Ryan, 1997; Onwuegbuzie, 2004) which impede learning. Published literature supports the idea that statistics anxiety or statistics test anxiety are negatively associated with learning (Zeidner, 1991; Lalonde & Gardner, 1993; Onwuegbuize & Seaman, 1995; Teman, 2013). Ruggeri, Dempster, Hanna, and Cleary (2008) conducted research to examine student expectations and experiences of statistics learning. They showed that poor communication with a professor and worries about course failure are major reasons for statistics anxiety. There are two types of anxiety: state anxiety and trait anxiety (Westerback & Long, 1990). State anxiety refers to a temporary state of anxiety aroused by a specific situation (Cross & Huberty, 1993). Trait anxiety is related to a personality characteristic rather than a temporary feeling (Beasley, Long, & Natali; 2001). Therefore, Onwuegbuzie, et al. (1997) regarded statistics anxiety as a state anxiety. Since state anxiety is a reaction to an external situation, the situation can be improved; the anxiety may be treated and relieved through counseling (Richardson & Suinn, 1972). Smith (2000) indicated that if mathematics teachers can integrate more effective instructional strategies into their teaching, then mathematics anxiety may be reduced and students' self-concepts enhanced. Similarly, statistics anxiety may be alleviated via instructional strategies. One-minute Paper Strategy Although few studies exist on the use of instructional strategies for relieving statistics anxiety, this does not mean that such anxiety cannot be reduced but rather that more empirical research is needed in this regard. Nonetheless, the literature proposed some effective coping methods, e.g., addressing the anxiety (Dillon, 1982), using humor (Schacht & Stewart, 1990), using collaborative learning (Dolinsky, 2001), applying statistics in practical settings (Stallings, 1993; Thompson, 1994; Pan & Tang, 2004), etc. Thus, it may be concluded that statistics anxiety can be reduced by means
23-PR_Chiou_140039.indd 298
05/08/14 5:22 PM
REDUCING STATISTICS ANXIETY
299
of instructional strategies. Huntley, Schneider, and Aronson (2000) and Pan and Tang (2004, 2005) indicated that to mitigate statistics anxiety it is necessary to develop more innovative instructional strategies. Therefore, this study employs a strategy advocated by Harvard University (Light, 1990; Almer, Jones, & Moeckel, 1998), called a one-minute paper in courses on statistics, to study whether or not it is conducive to relieving statistics anxiety and enhancing the learning achievement of statistics. With the one-minute paper strategy, students take several minutes at the end of each class to answer the following two questions: “What is the most important concept you learned in class today?” and “What questions remain unanswered?” Their answers, which are anonymous, are given to the instructor to read after class. Ruggeri, et al. (2008) examined students' expectations and experiences when learning statistics. They showed that poor communication between instructors and students is a main reason for statistics anxiety. The one-minute paper can encourage students to relay their most important questions to teachers. Teachers can then give students useful feedback and answers to their learning responses. Thus, the one-minute paper technique can effectively improve social dynamics between instructors and students and thereby minimize students' discomfort (Maier & Panitz, 1999). Through active interaction between students and teachers, a situation of harmony and unanimity can occur between students and teachers in a classroom (Harwood, 1996), and the effects of students' negative emotions are reduced. The one-minute paper is a writing-to-learn exercise, i.e., based on cognitive elaboration theory (Ackerman, 1993). Writing-to-learn uses writing as a means of learning material instead of as an end. This approach is built on constructivist learning theory and is a pedagogical application of cognitive theory to a writing process (Bereiter & Scardamalia, 1987; Tynjälä, 1998). Writing one-minute papers engages students in a focused exercise requiring cognitive elaboration that can be used as an activity to summarize or clarify questions, or to support or specify information learned (Reder, Charney, & Morgan, 1986). The key notion underlying elaboration theory is that learners must develop a meaningful context into which subsequent ideas or skills can be integrated. Successful elaboration improves learning performance by motivating learners, focusing their attention on relevant information, and facilitating integration of information (Mayer, 1980; Hamilton, 1989). The learning benefits of the one-minute paper strategy accrue when students actively think about what they did and did not learn during a class (Almer, et al., 1998). Chizmar (1994) asserted that the one-minute paper empowered students, encouraged students to reflect on class material, and forced them to review and synthesize what they learned in their own
23-PR_Chiou_140039.indd 299
05/08/14 5:22 PM
300
C-C. CHIOU, ET AL.
words (Panitz & Panitz, 1999). With this learning activity, students can immediately review what was learned in class and enhance their memory by searching for the right answers. This active learning can enhance understanding and critical thinking, improving students' learning achievement (Latchaw, 1995; Tynjälä, 1998). Although many studies have discussed the contributions of the oneminute paper strategy to instruction and class management, they largely have focused on general conceptual principles or case studies. No study empirically investigated whether the one-minute paper strategy would help reduce statistics anxiety and improve statistics learning achievement. Hypothesis 1. Students who write one-minute papers will have higher scores on statistics tests. Hypothesis 2. Students who write one-minute papers will have lower statistics anxiety scores. METHOD Participants In total, 77 undergraduate sophomore students enrolled in an applied statistics course from two classes participated. According to scores released from the Taiwan College Entrance Examination, these students had similar mathematical ability and all were accounting majors at the same university. They all had completed a calculus course successfully. Therefore, they had similar mathematics knowledge. For the treatment class (8 men, 30 women), students' average age was 19.5 yr. (SD = 0.7). For the comparison class (30 women, 9 men), students' average age was 19.4 yr. (SD = 0.6). Experimental Design This study employed the quasi-experimental unequal control group design. One class was assigned to the treatment group (n = 38), and the other class was assigned to the comparison group (n = 39). The one-minute paper strategy was used in the treatment group's class, but not in the comparison group's class. The teacher and textbook—“Statistics for Business and Economics” by Anderson, Sweeney, Williams, and Chen (2011)—for both groups were the same to avoid confounding effects. No student had prior experience with the one-minute paper. Each class was taught for 3 hours per wk. Study duration was 18 wk. Procedure The study was quasi-experimental, with a treatment and comparison group representing intact classes of a single course. First, the course and
23-PR_Chiou_140039.indd 300
05/08/14 5:22 PM
REDUCING STATISTICS ANXIETY
301
basic statistical concepts were introduced in Week 1. The course syllabus was distributed to each student. Statistics topics in Chapters 1 and 2 in the textbook were taught during Weeks 2 and 3. All participants took a statistics achievement Pretest and a statistics anxiety survey in Week 3. The quasi-experimental treatment began in Week 3. The instructor, topics, instructional materials, exercises, and textbook for both groups were identical. However, the one-minute paper strategy was used in the class of the treatment group only. Students in this group were asked to write short answers to the above two questions in the 5–10 min. at the end of every class. The time allowed to write a one-minute paper is based on suggestions by Cross and Angelo (1988) and Kloss (1993). The instructor can understand the students' learning experiences and misconceptions through these one-minute papers. Students received feedback from the instructor in the next lecture. Students could use this feedback as a review tool to enhance their learning. This process continued until the semester ended. For the comparison group, a 5–10 min. textbook exercise review was administered at the end of every class and students were asked to take it home to find the answer by themselves. The time of the 5–10 min. exercise review in the comparison class was in accordance with the time of writing one-minute papers in the treatment class. In the beginning of the next class, the teacher first reviewed the material taught in the last class. The two classes thus experienced the same in-class and practice times and both groups were encouraged to ask questions during or after classes. This process also continued until the semester ended. Finally, both groups completed a statistics anxiety survey and statistics achievement tests in Weeks 10 and 18 (Posttest 1 and Posttest 2). The pretest evaluated students' initial statistics knowledge and statistics anxiety. Posttests were administered to assess the treatment effect. Measures Achievement.—Learning achievement in this study means students' cognitive achievement, which was measured by students' examination scores. Students' cognitive achievement represents cognitive objective, one of the instructional objectives which include knowledge, comprehension, application, analysis, synthesis, and evaluation. Each statistics achievement test (i.e., Pretest, Posttest 1, and Posttest 2) had 10 multiplechoice items and four calculation items. The test items were selected from the question pool in the textbook and were based on course progress. The students scored four points for each correct answer to multiple-choice items and 10 points for each correct answer to calculation items. The full score was 100 points. To conform to the requirement of validity, questions for three tests were examined using a two-way specification table with
23-PR_Chiou_140039.indd 301
05/08/14 5:22 PM
302
C-C. CHIOU, ET AL.
sections for knowledge, comprehension, application, analysis, synthesis, and evaluation, respectively. The topics in the statistics achievement Pretest included “the nature of statistics” and “organizing data.” For example, one question was “Some hotels ask their guests to rate the hotel's services as excellent, very good, good, and poor. This is an example of an a. ordinal scale. b. ratio scale. c. nominal scale. d. interval scale.” The Kuder-Richardson (KR) 20 reliability coefficient was .88. The split-half reliability was .86. The statistics achievement Posttest 1 covered themes relating to descriptive measures, probability, random variables, and discrete probability distributions. For example, one question was “When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the (a) relative frequency method, (b) subjective method, (c) classical method, (d) posterior method.” The Kuder-Richardson (KR) 20 reliability coefficient was .92. The split-half reliability was .89. The statistics achievement Posttest 2 included topics about continuous probability distributions, sampling, and sampling distributions. For example, one question was “Which of the following statements about a discrete random variable and its probability distribution are true? (a) Values of the random variable can never be negative, (b) Negative values of f(x) are allowed as long as ∑ f(x) = 1, (c) Values of f(x) must be greater than or equal to zero, (d) The values of f(x) increase to a maximum point and then decrease.” The Kuder-Richardson (KR) 20 reliability coefficient was .87. The split-half reliability was .85. Statistics anxiety.—The Statistics Anxiety Rating Scale (Cruise & Wilkins, 1980; Cruise, Cash, & Bolton, 1985)’s is a widely used instrument for measuring students' statistics anxiety or feelings of anxiety resulting from conducting statistical analyses (Hsiao, 2010). The scale contains 51 items. In Cruise, et al. (1985)’s research on statistics anxiety of 1,150 students, six major dimensions were loaded from factor analysis. The factor scores were loaded between .48 and .86, while the value of Cronbach's α was between .68 and .94 in their study. The test-retest reliability coefficient was between .67 and .83 in the 5-week study of 161 students (Cruise, et al., 1985). Three of the six dimensions (i.e., Interpretation Anxiety, Test and Class Anxiety, and Fear of Asking for Help) measure anxiety about statistics. The other three dimensions (i.e., Worth of Statistics, Computation Self-concept, and Fear of Statistics Teachers) address perceptions and attitudes toward statistics. Interpretation Anxiety is concerned with the anxiety underwent when a student is faced with making a decision from or interpreting statistical data. Test and Class Anxiety measures the anxiety entailed when taking a statistics class or test. Fear of Asking for Help men-
23-PR_Chiou_140039.indd 302
05/08/14 5:22 PM
REDUCING STATISTICS ANXIETY
303
tions the anxiety experienced when asking a fellow student or professor for help in understanding the material covered in class or any type of statistical data, such as that contained in an article or a printout. Worth of Statistics refers to a student's perception of the relevance of statistics. Computational Self-Concept measures the anxiety involved when attempting to solve mathematical problems, as well as the student's perception of her/ his ability to do mathematics. Fear of Statistics Teachers is concerned with the student's perception of the statistics instructor (Onwuegbuzie, 2004). All item responses were given on a five-point Likert scale, with anchors 1: Strong disagreement and 5: Strong agreement. The score range was from 51 to 255. The internal consistency reliability of the six-dimension subscales, as measured by Cronbach's α coefficient (and split-half reliability coefficient), was as follows: Interpretation Anxiety .88 (.90), Test and Class Anxiety .82 (.83), Fear of Asking for Help .6 (.7), Worth of Statistics .92 (.92), Computational Self-Concept .76 (.8), and Fear of Statistics Teachers .81 (.85). The coefficients were similar to those obtained by Baloglu (2002). RESULTS Achievement Table 1 shows descriptive statistics and group comparisons at Pretest, Posttest 1, and Posttest 2. There were no significant differences between the treatment group and comparison group on achievement or anxiety at Pretest. Students in both groups had similar statistics knowledge and anxiety prior to conducting the one-minute paper treatment. Since Pretest scores may have influenced the quasi-experimental effect (i.e., the one-minute paper strategy), one-way analyses of covariance (ANCOVA) were applied to assess the quasi-experimental effect. Pretest scores on achievement (and anxiety in a separate analysis) were covariates and Posttest 1 scores of achievement (or anxiety) were dependent variables. The ANCOVA could be applied according to homogeneity of variance tests (Posttest 1: F = 0.18, p = .67; F = 0.56, p = .46; Posttest 2: F = 0.29, p = .59; F = 2.35, p = .13). Furthermore, the Shapiro-Wilks tests of normal distributions for two dependent variables, achievement and anxiety scores, were not statistically significant (Posttest 1: W = 0.98, p = .24; W = 0.97, p = .06; Posttest 2: W = 0.97, p = .09; W = 0.98, p = .29). Table 2 shows results of the analyses of covariance at Posttests 1 and 2. Empirical results indicate that the one-minute paper strategy significantly improved learning achievement and significantly reduced anxiety of students at both posttests. Therefore, Hypotheses 1 and 2 were both supported. Mean differences in learning achievement between the experiment group and control group at Pretest, Posttest 1, and Posttest 2 were −4.01,
23-PR_Chiou_140039.indd 303
05/08/14 5:22 PM
304
C-C. CHIOU, ET AL. TABLE 1 DESCRIPTIVE STATISTICS AND GROUP COMPARISONS (T TEST AND ANCOVA) Variable
Group
n
M
SD
Treatment
38
63.63
12.21
Comparison
39
67.64
15.75
Treatment
38
168.37
25.69
Comparison
39
169.74
27.79
Comparison With Pretest df
t
p
75
−1.25
.22
75
0.23
.82
75
2.86
.06
Cohen's d
Pretest Achievement Anxiety Posttest 1 Achievement Anxiety
Treatment
38
75.00
14.50
Comparison
39
68.54
16.02
Treatment
38
114.21
29.46
Comparison
39
182.77
25.72
75
10.89
< .001‡
75
2.23
.03†
0.93 0.06 2.11 −0.47
Posttest 2 Achievement Anxiety
Treatment
38
78.17
14.29
Comparison
39
70.13
17.14
Treatment
38
105.95
28.06
Comparison
39
176.89
26.09
75
11.50
< .001‡
1.19 0.16 2.43 −0.26
†p < .05; ‡p < .01.
6.46, and 8.04, respectively. The experimental group had superior learning achievement over time. The increase over time in the experimental group was more apparent than that in the control group. Writing OMPs should further enhance learning achievement in statistics over time. The mean differences in statistics anxiety scores between the experimental group and control group at Pretest, Posttest 1, and Posttest 2 were −1.37, −68.56, and −70.94, respectively. The experimental group had significantly lower statistics anxiety than the control group. Writing OMPs should further reduce learning anxiety in statistics over time. Students' Attitudes Toward One-minute Papers After the posttest, students were asked a question regarding their attitudes toward one-minute papers. “Do you think the one-minute papers are helpful to you? How helpful are they and do any improvement needs to be made?” The result indicated that all of the students considered the one-minute papers to be helpful. Some respondents noted the following: Student A: My first impression on one-minute papers was that the teacher put much effort into teaching. I was very touched by him because no others seemed concerned about individual student learning. When writing the weekly papers, I realized that a big advantage of the one-min-
23-PR_Chiou_140039.indd 304
05/08/14 5:22 PM
305
REDUCING STATISTICS ANXIETY TABLE 2 ANALYSIS OF COVARIANCE: POSTTESTS 1 AND 2 Dependent Variable
Source
SS
df
MS
F
η2
Posttest 1 Statistics achievement
Statistics anxiety
Covariate
6602.63
1
6602.63
44.75†
0.38
Treatment
1570.70
1
1570.70
10.64†
0.13
Error
10919.06
74
147.56
Covariate
27776.35
1
27776.35
69.75†
0.49
Treatment
87815.81
1
87815.81
220.53†
0.75
Error
29446.89
74
398.20
Posttest 2 Statistics achievement
Statistics anxiety
Covariate
7588.36
1
7588.36
50.45†
0.41
Treatment
2240.38
1
2240.38
14.89†
0.17
Error
11131.13
74
150.42
Covariate
15560.00
1
15560.00
29.20†
0.28
Treatment
94811.98
1
94811.98
177.95†
0.71
Error
39427.49
74
532.81
†p < .01.
ute papers is that it helped me to integrate class contents with deeper impressions. Student B: When writing the one-minute papers, I can clarify my mind regarding the class content and review lessons. Moreover, I received answers in the following class meeting. Student C: I marked some misconceptions and wrote them down in the papers for later review at home. In the following class lectures with explanations of answers, I could pay attention to acquiring a better understanding. Student D: It helped me to better comprehend and reorganize major concepts, and enabled me to record major concepts in class and to ask questions. Student E: I paid more attention in class because I had to fill out the papers. It enhanced student-teacher interaction and communication as well as improving teaching quality. Student F: It can help me to recall lessons as well as to figure out the application of each equation. When learning new complicated concepts, I got confused about the function of equations. Therefore, the checklists enabled me to not only reflect on and categorize materials but also to recognize my own problems and connect with prior knowledge. It allowed me to consider whether the misconception was due to the lecture or to my being inattentive in class.
23-PR_Chiou_140039.indd 305
05/08/14 5:22 PM
306
C-C. CHIOU, ET AL.
In summary, most students believed that the one-minute papers played an important role in helping students to promptly review lessons and in recording their problems as notes for consulting with teachers in the next meeting. Moreover, students used the one-minute papers as a powerful reviewing tool to reorganize key points and prepare for examinations. It not only improved students' concentration in asking questions but also improved the quality of teaching through regular student-teacher interactions. Examples of responses to a question about improving the one-minute papers are as follows. Student A: I did not know where to start when I received the papers, and questions in the one-minute papers could be more specific in case students would merely write down equations. Student B: Instead of a long drawn-out explanation, major concepts provided would be good enough. It should leave us with more time for independent thinking. Student C: I would like the papers to be available right in class so I could write down questions immediately without omissions. Student D: It would be much better if I could find answers right before the end of the class session. Student E: I would like a Likert-scaled form to narrow down my answers since sometimes I do not know how to write down my answers. DISCUSSION This study investigated whether the one-minute paper strategy reduces students' statistics anxiety and improves learning achievement in an applied statistics course. Quasi-experimental results indicated that the one-minute paper strategy significantly reduced students' statistics anxiety and enhanced their learning achievement. Poor communication between students and teachers is typically a cause of statistics anxiety (Ruggeri, et al., 2008). Liu (2012) also indicated that students' negative perceptions of teacher-student relationships negatively affected students' trait test anxiety. From students' points of view, the one-minute paper strategy enhanced student-teacher interactions and improved teaching quality. As Panitz and Panitz (1999) indicated, the one-minute paper strategy is a student-centered technique that activates interactions between students and teachers, thereby enhancing students' learning effectiveness and decreasing learning distress. Through such interactions, harmony and understanding between students and teachers in the classroom are supported (Harwood, 1996). Therefore, students may experience excitement about learning and reduced anxiety (Chizmar, 1994; Latchaw, 1995). As students are asked to complete the one-minute paper exercises, they must recall and think about major concepts taught in the class. The one-minute papers can push students to search actively for main concepts
23-PR_Chiou_140039.indd 306
05/08/14 5:22 PM
REDUCING STATISTICS ANXIETY
307
and unanswered questions. This process drives students to review periodically and think about their learning outcomes. Thereby, learning achievement and anxiety improve. The results also showed that the one-minute paper's effect in reducing statistics anxiety was larger than the effect improving learning achievement. As shown in Table 2, the effect sizes of the one-minute papers on statistics anxiety were large (0.75, 0.71). The effect sizes on statistics achievements were small (0.13, 0.17). The one-minute paper is a studentcentered writing-to-learn approach (Catalano, 1995) that encourages students to provide feedback to teachers. This approach helps teachers establish a rapport with a large class of students and provides insights into students' learning difficulties and learning perceptions (Harwood, 1996). That is, through one-minute papers teachers can identify students' learning problems and misconceptions and quickly adapt their instruction during future classes. Therefore, students' anxiety can be reduced promptly. However, improvement to learning achievement is a gradual and complex process. Students must patiently engage in learning and understand each topic to gain knowledge and learning achievement. The one-minute papers will probably require more time and more applications for best effect in improving statistics achievement. Limitations Some limitations must be noted. Students were not assigned randomly to treatment and comparison groups. The empirical results may have been influenced by internal validity. For example, students' mathematical ability may have differed. The effects of writing one-minute papers on enhancing statistics achievement and reducing statistics anxiety seemed to increase over time. More rigorous and longitudinal studies could assess this time course. The reliability of the Statistics Anxiety Rating Scale may have influenced the results. Future studies could include other measures to enhance the generalizability of the results. Conclusions Many studies have indicated that statistics anxiety and statistics test anxiety are negatively associated with learning (Elmore & Vasu, 1980; Zeidner, 1991; Lalonde & Gardner, 1993; Onwuegbuzie & Seaman, 1995). Therefore, reducing statistics anxiety is a crucial problem. The one-minute paper strategy is useful because it can quickly reduce students' statistics anxiety and improve learning performance. The following issues should be addressed before using the one-minute paper strategy in a specific course: Should one-minute papers be provided at the beginning or end of class? Should students answer the question: “What question or questions remain unanswered for you?” in an
23-PR_Chiou_140039.indd 307
05/08/14 5:22 PM
308
C-C. CHIOU, ET AL.
open-ended form or in a Likert form? Should answers for one-minute papers be provided immediately or in the next class meeting? Should answers for one-minute papers be given in a keynote form or in a detailed form? REFERENCES
ACKERMAN, J. M. (1993) The promise of writing to learn. Written Communication, 10(3), 334-370. ALMER, E. D., JONES, K., & MOECKEL, C. L. (1998) The impact of one-minute papers on learning in an introductory accounting course. Issues in Accounting Education, 13(3), 485-497. ANDERSON, D. R., SWEENEY, D. J., WILLIAMS, T. A., & CHEN, J. C. (2011) Statistics for business and economics. Mason, OH: Thomson Learning. BALOGLU, M. (2002) Psychometric properties of the Statistical Anxiety Rating Scale. Psychological Reports, 90, 315-327. BEASLEY, T. M., LONG, J. D., & NATALI, M. (2001) A confirmatory factor analysis of the Mathematics Anxiety Scale for children. Measurement & Evaluation in Counseling & Development, 34(1), 14-26. BEREITER C., & SCARDAMALIA, M. (1987) The psychology of written composition. Hillsdale, NJ: Erlbaum. CARLSON, W. L. (1999) A case method for teaching statistics. Journal of Economic Education, 30(4), 52-58. DOI: 10.1080/00220489909595938 CATALANO, G. D. (1995) Some ideas on the teaching of engineering science: a student centered approach. Journal of Engineering Education, 84(1), 21-24. CHIZMAR, J. F. (1994) Total quality management (TQM) of teaching and learning. Journal of Economic Education, 25(2), 179-190. CROSS, K. P., & ANGELO, T. A. (1988) Classroom assessment techniques: a handbook for faculty. Ann Arbor, MI: Univer. of Michigan, National Center for Research to Improve Postsecondary Teaching and Learning. CROSS, R. W., & HUBERTY, J. J. (1993) Factor analysis of the State-Trait Anxiety Inventory for children with a sample of seventh- and eighth grade students. Journal of Psychoeducational Assessment, 11(3), 232-241. DOI: 10.1177/073428299301100303 CRUISE, R. J., CASH, R. W., & BOLTON, L. D. (1985) Development and validation of an instrument to measure statistical anxiety. Proceedings of the Section on Statistical Education, Alexandria, VA: American Statistical Association. Pp. 92-98. CRUISE, R. J., & WILKINS, E. M. (1980) STARS: Statistical Anxiety Rating Scale. Unpublished manuscript, Andrews Univer., Berrien Springs, MI. DILLON, K. M. (1982) Statisticophobia. Teaching of Psychology, 9(2), 117. DOLINSKY, B. (2001) An active learning approach to teaching statistics. Teaching of Psychology, 28(1), 55-56. ELMORE, P. B., & VASU, E. S. (1980) Relationship between selected variables and statistical achievement: building a theoretical model. Journal of Educational Psychology, 72(4), 457-467. FEINBERG, L., & HALPERIN, S. (1978) Affective and cognitive correlates of course performance in introductory statistics. Journal of Experimental Education, 46(4), 11-18. HAMILTON, R. (1989) The effects of learner-generated elaborations on concept learning from prose. Journal of Experimental Education, 57, 205-217.
23-PR_Chiou_140039.indd 308
05/08/14 5:22 PM
REDUCING STATISTICS ANXIETY
309
HARWOOD, W. S. (1996) The one-minute paper: a communication tool for large lecture classes. Journal of Chemical Education, 73(3), 229-230. HSIAO, T. Y. (2010) The Statistical Anxiety Rating Scale: further evidence for multidimensionality. Psychological Reports, 107(3), 977-982. HUNTLEY, D., SCHNEIDER, L., & ARONSON, H. (2000) Clinical interns’ perception of psychology and their place within it. The Clinical Psychologist, 54(4), 3-11. KLOSS, R. J. (1993) Stay in touch, won't you? Using the one-minute paper. College Teaching, 41(2), 60-63. LALONDE, R. N., & GARDNER, R. M. (1993) Statistics as a second language? A model for predicting performance in psychology students. Canadian Journal of Behavioral Science, 25(1), 108-125. LATCHAW, J. S. (1995) Assessment and community. Paper presented at the 46th annual meeting of the Conference on College Composition and Communication, San Diego, CA, March 23-25. (ERIC Document Reproduction Service No. ED 385839) LIGHT, R. J. (1990) Explorations with students and faculty about teaching, learning, and student life. The Harvard assessment seminars, first report. Cambridge, MA: Graduate School of Education and Kennedy School of Government. LIU, Y. Y. (2012) Students' perceptions of school climate and trait test anxiety. Psychological Reports, 111(3), 761-764. MAIER, M. H., & PANITZ, T. (1999) End on a high note: better endings for classes and courses. (ERIC Document Reproduction Service No. ED 448446) MAYER, R. E. (1980) Elaboration techniques that increase the meaningfulness of technical text: an experimental test of the learning strategy hypothesis. Journal of Educational Psychology, 72(6), 770-784. ONWUEGBUZIE, A. J. (1998) The dimensions of statistics anxiety: a comparison of prevalence rates among mid-southern university students. Louisiana Educational Research Journal, 23, 23-40. ONWUEGBUZIE, A. J. (2004) Academic procrastination and statistics anxiety. Assessment & Evaluation in Higher Education, 29(1), 3-19. ONWUEGBUZIE, A. J., DA ROS, D., & RYAN, J. M. (1997) The components of statistics anxiety: a phenomenological study. Focus on Learning Problems in Mathematics, 19(4), 11-35. ONWUEGBUZIE, A. J., & LEECH, N. L. (2003) Assessment in statistics courses: more than a tool for evaluation. Assessment & Evaluation in Higher Education, 28(2), 115-127. ONWUEGBUZIE, A. J., & SEAMAN, M. (1995) The effect of time and anxiety on statistics achievement. Journal of Experimental Psychology, 63(2), 115-124. PAN, W., & TANG, M. (2004) Examining the effectiveness of innovative instructional methods on reducing statistics anxiety for graduate students in the social sciences. Journal of Instructional Psychology, 31(2), 149-159. PAN, W., & TANG, M. (2005) Students' perceptions on factors of statistics anxiety and instructional strategies. Journal of Instructional Psychology, 32(3), 205-214. PANITZ, T., & PANITZ, P. (1999) Assessing students and yourself using the one minute paper and observing students working cooperatively. (ERIC Document Reproduction Service No. ED 453262) REDER, L. M., CHARNEY, D. H., & MORGAN, K. I. (1986) The role of elaborations in learning a skill from an instructional text. Memory and Cognition, 14(1), 64-78. RICHARDSON, F. C., & SUINN, R. M. (1972) The Mathematics Anxiety Rating Scale: psychometric data. Journal of Counseling Psychology, 19, 551-554.
23-PR_Chiou_140039.indd 309
05/08/14 5:22 PM
310
C-C. CHIOU, ET AL.
RUGGERI, K., DEMPSTER, M., HANNA, D., & CLEARY, C. (2008) Experiences and expectations: the real reason nobody likes stats. The British Psychological Society, 14(2), 75-83. SCHACHT, S., & STEWART, B. J. (1990) What's funny about statistics? A technique for reducing student anxiety. Teaching Sociology, 18, 52-56. SMITH, K. B. (2000) Effects of a cooperative teaching approach on math anxiety in beginning algebra. Focus on Learning Problems in Mathematics, 22(2), 1-17. STALLINGS, W. M. (1993) Return to our roots: raising radishes to teach experimental design. Teaching of Psychology, 20(3), 165-167. DOI: 10.1207/s15328023top2003_7 TEMAN, E. D. (2013) Factorial invariance of the Statistical Anxiety Rating Scale across sex and students' classification. Comprehensive Psychology, 2(1), 1-11. THOMPSON, W. B. (1994) Making data analysis realistic: incorporating research into statistics courses. Teaching of Psychology, 21(1), 41-43. DOI: 10.1207/s15328023top2101_9 TYNJÄLÄ, P. (1998) Writing as a tool of constructive learning: students' learning experiences during an experiment. Higher Education, 36(2), 209-230. WESTERBACK, M. E., & LONG, M. J. (1990) Science knowledge and the reduction of anxiety about teaching earth science in exemplary teachers as measured by the science teaching State-Trait Anxiety Inventory. School Science and Mathematics, 90(5), 361374. ZEIDNER, M. (1991) Statistics and mathematics anxiety in social science students: some interesting parallels. British Journal of Educational Psychology, 61(3), 319-328. Accepted May 21, 2014.
23-PR_Chiou_140039.indd 310
05/08/14 5:22 PM
REDUCING STATISTICS ANXIETY AND ENHANCING STATISTICS LEARNING ACHIEVEMENT: EFFECTIVENESS OF A ONE-MINUTE STRATEGY1, 2 CHEI-CHANG CHIOU Department of Accounting National Changhua University of Education, Taiwan YU-MIN WANG
LI-TZE LEE
Department of Information Management National Chi Nan University, Taiwan
Department of Accounting Information Overseas Chinese University, Taiwan
Summary.—Statistical knowledge is widely used in academia; however, statistics teachers struggle with the issue of how to reduce students' statistics anxiety and enhance students' statistics learning. This study assesses the effectiveness of a “one-minute paper strategy” in reducing students' statistics-related anxiety and in improving students' statistics-related achievement. Participants were 77 undergraduates from two classes enrolled in applied statistics courses. An experiment was implemented according to a pretest/posttest comparison group design. The quasi-experimental design showed that the one-minute paper strategy significantly reduced students' statistics anxiety and improved students' statistics learning achievement. The strategy was a better instructional tool than the textbook exercise for reducing students' statistics anxiety and improving students' statistics achievement.
Statistical knowledge is widely used in multiple fields of academia as well as in non-academic practice. Consequently, more and more undergraduates, and even postgraduates, of diverse backgrounds have had statistics included in their lists of compulsory courses (Onwuegbuzie & Leech, 2003). Likewise, the knowledge of applied statistics is gaining in importance for students in business schools (Carlson, 1999). Without doubt, statistics is an important field of study. For many undergraduate and postgraduate students, statistics is among the most formidable courses in their curriculum plans (Feinberg & Halperin, 1978; Schacht & Stewart, 1990; Onwuegbuzie & Leech, 2003). Many researches indicated that when undergraduate students encounter concepts, questions, cases, and instructional or test situations concerning statistics, they are likely to develop severe anxiety (Feinberg & Halperin, 1978; Zeidner, 1991; Onwuegbuzie, 1998; Onwuegbuzie & Leech, 2003). Onwuegbuzie (1998) Address correspondence to Yu-Min Wang, Department of Information Management, National Chi Nan University, Taiwan or e-mail ([email protected]). 2 The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this research under NSC 96-2413-H-018-007. Ted Knoy is appreciated for his editorial assistance. 1
DOI 10.2466/11.04.PR0.115c12z3
23-PR_Chiou_140039.indd 297
ISSN 0033-2941
05/08/14 5:22 PM
298
C-C. CHIOU, ET AL.
pointed out that such anxiety is experienced by as many as 80% of postgraduate students. Anxiety related to statistics engenders a negative perception of statistics among the students, and is even regarded as a major obstacle to acquiring a degree (Onwuegbuzie, 1998; Onwuegbuzie & Leech, 2003). Furthermore, quite a number of non-statistics majors consider statistics of no importance or little relevance to the subject they are studying, regarding it rather as an unavoidable hurdle on their way to graduation (Onwuegbuzie & Leech, 2003). These research results evidently demonstrated that statistics anxiety is a current prevailing issue deeply concerning undergraduate and postgraduate students. Statistics anxiety involves a complex array of emotional reactions which may cause discomfort at medium levels or at higher levels can entail severe consequences such as apprehension, fear, nervousness, panic, and other negative results (Onwuegbuzie, Da Ros, & Ryan, 1997; Onwuegbuzie, 2004) which impede learning. Published literature supports the idea that statistics anxiety or statistics test anxiety are negatively associated with learning (Zeidner, 1991; Lalonde & Gardner, 1993; Onwuegbuize & Seaman, 1995; Teman, 2013). Ruggeri, Dempster, Hanna, and Cleary (2008) conducted research to examine student expectations and experiences of statistics learning. They showed that poor communication with a professor and worries about course failure are major reasons for statistics anxiety. There are two types of anxiety: state anxiety and trait anxiety (Westerback & Long, 1990). State anxiety refers to a temporary state of anxiety aroused by a specific situation (Cross & Huberty, 1993). Trait anxiety is related to a personality characteristic rather than a temporary feeling (Beasley, Long, & Natali; 2001). Therefore, Onwuegbuzie, et al. (1997) regarded statistics anxiety as a state anxiety. Since state anxiety is a reaction to an external situation, the situation can be improved; the anxiety may be treated and relieved through counseling (Richardson & Suinn, 1972). Smith (2000) indicated that if mathematics teachers can integrate more effective instructional strategies into their teaching, then mathematics anxiety may be reduced and students' self-concepts enhanced. Similarly, statistics anxiety may be alleviated via instructional strategies. One-minute Paper Strategy Although few studies exist on the use of instructional strategies for relieving statistics anxiety, this does not mean that such anxiety cannot be reduced but rather that more empirical research is needed in this regard. Nonetheless, the literature proposed some effective coping methods, e.g., addressing the anxiety (Dillon, 1982), using humor (Schacht & Stewart, 1990), using collaborative learning (Dolinsky, 2001), applying statistics in practical settings (Stallings, 1993; Thompson, 1994; Pan & Tang, 2004), etc. Thus, it may be concluded that statistics anxiety can be reduced by means
23-PR_Chiou_140039.indd 298
05/08/14 5:22 PM
REDUCING STATISTICS ANXIETY
299
of instructional strategies. Huntley, Schneider, and Aronson (2000) and Pan and Tang (2004, 2005) indicated that to mitigate statistics anxiety it is necessary to develop more innovative instructional strategies. Therefore, this study employs a strategy advocated by Harvard University (Light, 1990; Almer, Jones, & Moeckel, 1998), called a one-minute paper in courses on statistics, to study whether or not it is conducive to relieving statistics anxiety and enhancing the learning achievement of statistics. With the one-minute paper strategy, students take several minutes at the end of each class to answer the following two questions: “What is the most important concept you learned in class today?” and “What questions remain unanswered?” Their answers, which are anonymous, are given to the instructor to read after class. Ruggeri, et al. (2008) examined students' expectations and experiences when learning statistics. They showed that poor communication between instructors and students is a main reason for statistics anxiety. The one-minute paper can encourage students to relay their most important questions to teachers. Teachers can then give students useful feedback and answers to their learning responses. Thus, the one-minute paper technique can effectively improve social dynamics between instructors and students and thereby minimize students' discomfort (Maier & Panitz, 1999). Through active interaction between students and teachers, a situation of harmony and unanimity can occur between students and teachers in a classroom (Harwood, 1996), and the effects of students' negative emotions are reduced. The one-minute paper is a writing-to-learn exercise, i.e., based on cognitive elaboration theory (Ackerman, 1993). Writing-to-learn uses writing as a means of learning material instead of as an end. This approach is built on constructivist learning theory and is a pedagogical application of cognitive theory to a writing process (Bereiter & Scardamalia, 1987; Tynjälä, 1998). Writing one-minute papers engages students in a focused exercise requiring cognitive elaboration that can be used as an activity to summarize or clarify questions, or to support or specify information learned (Reder, Charney, & Morgan, 1986). The key notion underlying elaboration theory is that learners must develop a meaningful context into which subsequent ideas or skills can be integrated. Successful elaboration improves learning performance by motivating learners, focusing their attention on relevant information, and facilitating integration of information (Mayer, 1980; Hamilton, 1989). The learning benefits of the one-minute paper strategy accrue when students actively think about what they did and did not learn during a class (Almer, et al., 1998). Chizmar (1994) asserted that the one-minute paper empowered students, encouraged students to reflect on class material, and forced them to review and synthesize what they learned in their own
23-PR_Chiou_140039.indd 299
05/08/14 5:22 PM
300
C-C. CHIOU, ET AL.
words (Panitz & Panitz, 1999). With this learning activity, students can immediately review what was learned in class and enhance their memory by searching for the right answers. This active learning can enhance understanding and critical thinking, improving students' learning achievement (Latchaw, 1995; Tynjälä, 1998). Although many studies have discussed the contributions of the oneminute paper strategy to instruction and class management, they largely have focused on general conceptual principles or case studies. No study empirically investigated whether the one-minute paper strategy would help reduce statistics anxiety and improve statistics learning achievement. Hypothesis 1. Students who write one-minute papers will have higher scores on statistics tests. Hypothesis 2. Students who write one-minute papers will have lower statistics anxiety scores. METHOD Participants In total, 77 undergraduate sophomore students enrolled in an applied statistics course from two classes participated. According to scores released from the Taiwan College Entrance Examination, these students had similar mathematical ability and all were accounting majors at the same university. They all had completed a calculus course successfully. Therefore, they had similar mathematics knowledge. For the treatment class (8 men, 30 women), students' average age was 19.5 yr. (SD = 0.7). For the comparison class (30 women, 9 men), students' average age was 19.4 yr. (SD = 0.6). Experimental Design This study employed the quasi-experimental unequal control group design. One class was assigned to the treatment group (n = 38), and the other class was assigned to the comparison group (n = 39). The one-minute paper strategy was used in the treatment group's class, but not in the comparison group's class. The teacher and textbook—“Statistics for Business and Economics” by Anderson, Sweeney, Williams, and Chen (2011)—for both groups were the same to avoid confounding effects. No student had prior experience with the one-minute paper. Each class was taught for 3 hours per wk. Study duration was 18 wk. Procedure The study was quasi-experimental, with a treatment and comparison group representing intact classes of a single course. First, the course and
23-PR_Chiou_140039.indd 300
05/08/14 5:22 PM
REDUCING STATISTICS ANXIETY
301
basic statistical concepts were introduced in Week 1. The course syllabus was distributed to each student. Statistics topics in Chapters 1 and 2 in the textbook were taught during Weeks 2 and 3. All participants took a statistics achievement Pretest and a statistics anxiety survey in Week 3. The quasi-experimental treatment began in Week 3. The instructor, topics, instructional materials, exercises, and textbook for both groups were identical. However, the one-minute paper strategy was used in the class of the treatment group only. Students in this group were asked to write short answers to the above two questions in the 5–10 min. at the end of every class. The time allowed to write a one-minute paper is based on suggestions by Cross and Angelo (1988) and Kloss (1993). The instructor can understand the students' learning experiences and misconceptions through these one-minute papers. Students received feedback from the instructor in the next lecture. Students could use this feedback as a review tool to enhance their learning. This process continued until the semester ended. For the comparison group, a 5–10 min. textbook exercise review was administered at the end of every class and students were asked to take it home to find the answer by themselves. The time of the 5–10 min. exercise review in the comparison class was in accordance with the time of writing one-minute papers in the treatment class. In the beginning of the next class, the teacher first reviewed the material taught in the last class. The two classes thus experienced the same in-class and practice times and both groups were encouraged to ask questions during or after classes. This process also continued until the semester ended. Finally, both groups completed a statistics anxiety survey and statistics achievement tests in Weeks 10 and 18 (Posttest 1 and Posttest 2). The pretest evaluated students' initial statistics knowledge and statistics anxiety. Posttests were administered to assess the treatment effect. Measures Achievement.—Learning achievement in this study means students' cognitive achievement, which was measured by students' examination scores. Students' cognitive achievement represents cognitive objective, one of the instructional objectives which include knowledge, comprehension, application, analysis, synthesis, and evaluation. Each statistics achievement test (i.e., Pretest, Posttest 1, and Posttest 2) had 10 multiplechoice items and four calculation items. The test items were selected from the question pool in the textbook and were based on course progress. The students scored four points for each correct answer to multiple-choice items and 10 points for each correct answer to calculation items. The full score was 100 points. To conform to the requirement of validity, questions for three tests were examined using a two-way specification table with
23-PR_Chiou_140039.indd 301
05/08/14 5:22 PM
302
C-C. CHIOU, ET AL.
sections for knowledge, comprehension, application, analysis, synthesis, and evaluation, respectively. The topics in the statistics achievement Pretest included “the nature of statistics” and “organizing data.” For example, one question was “Some hotels ask their guests to rate the hotel's services as excellent, very good, good, and poor. This is an example of an a. ordinal scale. b. ratio scale. c. nominal scale. d. interval scale.” The Kuder-Richardson (KR) 20 reliability coefficient was .88. The split-half reliability was .86. The statistics achievement Posttest 1 covered themes relating to descriptive measures, probability, random variables, and discrete probability distributions. For example, one question was “When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the (a) relative frequency method, (b) subjective method, (c) classical method, (d) posterior method.” The Kuder-Richardson (KR) 20 reliability coefficient was .92. The split-half reliability was .89. The statistics achievement Posttest 2 included topics about continuous probability distributions, sampling, and sampling distributions. For example, one question was “Which of the following statements about a discrete random variable and its probability distribution are true? (a) Values of the random variable can never be negative, (b) Negative values of f(x) are allowed as long as ∑ f(x) = 1, (c) Values of f(x) must be greater than or equal to zero, (d) The values of f(x) increase to a maximum point and then decrease.” The Kuder-Richardson (KR) 20 reliability coefficient was .87. The split-half reliability was .85. Statistics anxiety.—The Statistics Anxiety Rating Scale (Cruise & Wilkins, 1980; Cruise, Cash, & Bolton, 1985)’s is a widely used instrument for measuring students' statistics anxiety or feelings of anxiety resulting from conducting statistical analyses (Hsiao, 2010). The scale contains 51 items. In Cruise, et al. (1985)’s research on statistics anxiety of 1,150 students, six major dimensions were loaded from factor analysis. The factor scores were loaded between .48 and .86, while the value of Cronbach's α was between .68 and .94 in their study. The test-retest reliability coefficient was between .67 and .83 in the 5-week study of 161 students (Cruise, et al., 1985). Three of the six dimensions (i.e., Interpretation Anxiety, Test and Class Anxiety, and Fear of Asking for Help) measure anxiety about statistics. The other three dimensions (i.e., Worth of Statistics, Computation Self-concept, and Fear of Statistics Teachers) address perceptions and attitudes toward statistics. Interpretation Anxiety is concerned with the anxiety underwent when a student is faced with making a decision from or interpreting statistical data. Test and Class Anxiety measures the anxiety entailed when taking a statistics class or test. Fear of Asking for Help men-
23-PR_Chiou_140039.indd 302
05/08/14 5:22 PM
REDUCING STATISTICS ANXIETY
303
tions the anxiety experienced when asking a fellow student or professor for help in understanding the material covered in class or any type of statistical data, such as that contained in an article or a printout. Worth of Statistics refers to a student's perception of the relevance of statistics. Computational Self-Concept measures the anxiety involved when attempting to solve mathematical problems, as well as the student's perception of her/ his ability to do mathematics. Fear of Statistics Teachers is concerned with the student's perception of the statistics instructor (Onwuegbuzie, 2004). All item responses were given on a five-point Likert scale, with anchors 1: Strong disagreement and 5: Strong agreement. The score range was from 51 to 255. The internal consistency reliability of the six-dimension subscales, as measured by Cronbach's α coefficient (and split-half reliability coefficient), was as follows: Interpretation Anxiety .88 (.90), Test and Class Anxiety .82 (.83), Fear of Asking for Help .6 (.7), Worth of Statistics .92 (.92), Computational Self-Concept .76 (.8), and Fear of Statistics Teachers .81 (.85). The coefficients were similar to those obtained by Baloglu (2002). RESULTS Achievement Table 1 shows descriptive statistics and group comparisons at Pretest, Posttest 1, and Posttest 2. There were no significant differences between the treatment group and comparison group on achievement or anxiety at Pretest. Students in both groups had similar statistics knowledge and anxiety prior to conducting the one-minute paper treatment. Since Pretest scores may have influenced the quasi-experimental effect (i.e., the one-minute paper strategy), one-way analyses of covariance (ANCOVA) were applied to assess the quasi-experimental effect. Pretest scores on achievement (and anxiety in a separate analysis) were covariates and Posttest 1 scores of achievement (or anxiety) were dependent variables. The ANCOVA could be applied according to homogeneity of variance tests (Posttest 1: F = 0.18, p = .67; F = 0.56, p = .46; Posttest 2: F = 0.29, p = .59; F = 2.35, p = .13). Furthermore, the Shapiro-Wilks tests of normal distributions for two dependent variables, achievement and anxiety scores, were not statistically significant (Posttest 1: W = 0.98, p = .24; W = 0.97, p = .06; Posttest 2: W = 0.97, p = .09; W = 0.98, p = .29). Table 2 shows results of the analyses of covariance at Posttests 1 and 2. Empirical results indicate that the one-minute paper strategy significantly improved learning achievement and significantly reduced anxiety of students at both posttests. Therefore, Hypotheses 1 and 2 were both supported. Mean differences in learning achievement between the experiment group and control group at Pretest, Posttest 1, and Posttest 2 were −4.01,
23-PR_Chiou_140039.indd 303
05/08/14 5:22 PM
304
C-C. CHIOU, ET AL. TABLE 1 DESCRIPTIVE STATISTICS AND GROUP COMPARISONS (T TEST AND ANCOVA) Variable
Group
n
M
SD
Treatment
38
63.63
12.21
Comparison
39
67.64
15.75
Treatment
38
168.37
25.69
Comparison
39
169.74
27.79
Comparison With Pretest df
t
p
75
−1.25
.22
75
0.23
.82
75
2.86
.06
Cohen's d
Pretest Achievement Anxiety Posttest 1 Achievement Anxiety
Treatment
38
75.00
14.50
Comparison
39
68.54
16.02
Treatment
38
114.21
29.46
Comparison
39
182.77
25.72
75
10.89
< .001‡
75
2.23
.03†
0.93 0.06 2.11 −0.47
Posttest 2 Achievement Anxiety
Treatment
38
78.17
14.29
Comparison
39
70.13
17.14
Treatment
38
105.95
28.06
Comparison
39
176.89
26.09
75
11.50
< .001‡
1.19 0.16 2.43 −0.26
†p < .05; ‡p < .01.
6.46, and 8.04, respectively. The experimental group had superior learning achievement over time. The increase over time in the experimental group was more apparent than that in the control group. Writing OMPs should further enhance learning achievement in statistics over time. The mean differences in statistics anxiety scores between the experimental group and control group at Pretest, Posttest 1, and Posttest 2 were −1.37, −68.56, and −70.94, respectively. The experimental group had significantly lower statistics anxiety than the control group. Writing OMPs should further reduce learning anxiety in statistics over time. Students' Attitudes Toward One-minute Papers After the posttest, students were asked a question regarding their attitudes toward one-minute papers. “Do you think the one-minute papers are helpful to you? How helpful are they and do any improvement needs to be made?” The result indicated that all of the students considered the one-minute papers to be helpful. Some respondents noted the following: Student A: My first impression on one-minute papers was that the teacher put much effort into teaching. I was very touched by him because no others seemed concerned about individual student learning. When writing the weekly papers, I realized that a big advantage of the one-min-
23-PR_Chiou_140039.indd 304
05/08/14 5:22 PM
305
REDUCING STATISTICS ANXIETY TABLE 2 ANALYSIS OF COVARIANCE: POSTTESTS 1 AND 2 Dependent Variable
Source
SS
df
MS
F
η2
Posttest 1 Statistics achievement
Statistics anxiety
Covariate
6602.63
1
6602.63
44.75†
0.38
Treatment
1570.70
1
1570.70
10.64†
0.13
Error
10919.06
74
147.56
Covariate
27776.35
1
27776.35
69.75†
0.49
Treatment
87815.81
1
87815.81
220.53†
0.75
Error
29446.89
74
398.20
Posttest 2 Statistics achievement
Statistics anxiety
Covariate
7588.36
1
7588.36
50.45†
0.41
Treatment
2240.38
1
2240.38
14.89†
0.17
Error
11131.13
74
150.42
Covariate
15560.00
1
15560.00
29.20†
0.28
Treatment
94811.98
1
94811.98
177.95†
0.71
Error
39427.49
74
532.81
†p < .01.
ute papers is that it helped me to integrate class contents with deeper impressions. Student B: When writing the one-minute papers, I can clarify my mind regarding the class content and review lessons. Moreover, I received answers in the following class meeting. Student C: I marked some misconceptions and wrote them down in the papers for later review at home. In the following class lectures with explanations of answers, I could pay attention to acquiring a better understanding. Student D: It helped me to better comprehend and reorganize major concepts, and enabled me to record major concepts in class and to ask questions. Student E: I paid more attention in class because I had to fill out the papers. It enhanced student-teacher interaction and communication as well as improving teaching quality. Student F: It can help me to recall lessons as well as to figure out the application of each equation. When learning new complicated concepts, I got confused about the function of equations. Therefore, the checklists enabled me to not only reflect on and categorize materials but also to recognize my own problems and connect with prior knowledge. It allowed me to consider whether the misconception was due to the lecture or to my being inattentive in class.
23-PR_Chiou_140039.indd 305
05/08/14 5:22 PM
306
C-C. CHIOU, ET AL.
In summary, most students believed that the one-minute papers played an important role in helping students to promptly review lessons and in recording their problems as notes for consulting with teachers in the next meeting. Moreover, students used the one-minute papers as a powerful reviewing tool to reorganize key points and prepare for examinations. It not only improved students' concentration in asking questions but also improved the quality of teaching through regular student-teacher interactions. Examples of responses to a question about improving the one-minute papers are as follows. Student A: I did not know where to start when I received the papers, and questions in the one-minute papers could be more specific in case students would merely write down equations. Student B: Instead of a long drawn-out explanation, major concepts provided would be good enough. It should leave us with more time for independent thinking. Student C: I would like the papers to be available right in class so I could write down questions immediately without omissions. Student D: It would be much better if I could find answers right before the end of the class session. Student E: I would like a Likert-scaled form to narrow down my answers since sometimes I do not know how to write down my answers. DISCUSSION This study investigated whether the one-minute paper strategy reduces students' statistics anxiety and improves learning achievement in an applied statistics course. Quasi-experimental results indicated that the one-minute paper strategy significantly reduced students' statistics anxiety and enhanced their learning achievement. Poor communication between students and teachers is typically a cause of statistics anxiety (Ruggeri, et al., 2008). Liu (2012) also indicated that students' negative perceptions of teacher-student relationships negatively affected students' trait test anxiety. From students' points of view, the one-minute paper strategy enhanced student-teacher interactions and improved teaching quality. As Panitz and Panitz (1999) indicated, the one-minute paper strategy is a student-centered technique that activates interactions between students and teachers, thereby enhancing students' learning effectiveness and decreasing learning distress. Through such interactions, harmony and understanding between students and teachers in the classroom are supported (Harwood, 1996). Therefore, students may experience excitement about learning and reduced anxiety (Chizmar, 1994; Latchaw, 1995). As students are asked to complete the one-minute paper exercises, they must recall and think about major concepts taught in the class. The one-minute papers can push students to search actively for main concepts
23-PR_Chiou_140039.indd 306
05/08/14 5:22 PM
REDUCING STATISTICS ANXIETY
307
and unanswered questions. This process drives students to review periodically and think about their learning outcomes. Thereby, learning achievement and anxiety improve. The results also showed that the one-minute paper's effect in reducing statistics anxiety was larger than the effect improving learning achievement. As shown in Table 2, the effect sizes of the one-minute papers on statistics anxiety were large (0.75, 0.71). The effect sizes on statistics achievements were small (0.13, 0.17). The one-minute paper is a studentcentered writing-to-learn approach (Catalano, 1995) that encourages students to provide feedback to teachers. This approach helps teachers establish a rapport with a large class of students and provides insights into students' learning difficulties and learning perceptions (Harwood, 1996). That is, through one-minute papers teachers can identify students' learning problems and misconceptions and quickly adapt their instruction during future classes. Therefore, students' anxiety can be reduced promptly. However, improvement to learning achievement is a gradual and complex process. Students must patiently engage in learning and understand each topic to gain knowledge and learning achievement. The one-minute papers will probably require more time and more applications for best effect in improving statistics achievement. Limitations Some limitations must be noted. Students were not assigned randomly to treatment and comparison groups. The empirical results may have been influenced by internal validity. For example, students' mathematical ability may have differed. The effects of writing one-minute papers on enhancing statistics achievement and reducing statistics anxiety seemed to increase over time. More rigorous and longitudinal studies could assess this time course. The reliability of the Statistics Anxiety Rating Scale may have influenced the results. Future studies could include other measures to enhance the generalizability of the results. Conclusions Many studies have indicated that statistics anxiety and statistics test anxiety are negatively associated with learning (Elmore & Vasu, 1980; Zeidner, 1991; Lalonde & Gardner, 1993; Onwuegbuzie & Seaman, 1995). Therefore, reducing statistics anxiety is a crucial problem. The one-minute paper strategy is useful because it can quickly reduce students' statistics anxiety and improve learning performance. The following issues should be addressed before using the one-minute paper strategy in a specific course: Should one-minute papers be provided at the beginning or end of class? Should students answer the question: “What question or questions remain unanswered for you?” in an
23-PR_Chiou_140039.indd 307
05/08/14 5:22 PM
308
C-C. CHIOU, ET AL.
open-ended form or in a Likert form? Should answers for one-minute papers be provided immediately or in the next class meeting? Should answers for one-minute papers be given in a keynote form or in a detailed form? REFERENCES
ACKERMAN, J. M. (1993) The promise of writing to learn. Written Communication, 10(3), 334-370. ALMER, E. D., JONES, K., & MOECKEL, C. L. (1998) The impact of one-minute papers on learning in an introductory accounting course. Issues in Accounting Education, 13(3), 485-497. ANDERSON, D. R., SWEENEY, D. J., WILLIAMS, T. A., & CHEN, J. C. (2011) Statistics for business and economics. Mason, OH: Thomson Learning. BALOGLU, M. (2002) Psychometric properties of the Statistical Anxiety Rating Scale. Psychological Reports, 90, 315-327. BEASLEY, T. M., LONG, J. D., & NATALI, M. (2001) A confirmatory factor analysis of the Mathematics Anxiety Scale for children. Measurement & Evaluation in Counseling & Development, 34(1), 14-26. BEREITER C., & SCARDAMALIA, M. (1987) The psychology of written composition. Hillsdale, NJ: Erlbaum. CARLSON, W. L. (1999) A case method for teaching statistics. Journal of Economic Education, 30(4), 52-58. DOI: 10.1080/00220489909595938 CATALANO, G. D. (1995) Some ideas on the teaching of engineering science: a student centered approach. Journal of Engineering Education, 84(1), 21-24. CHIZMAR, J. F. (1994) Total quality management (TQM) of teaching and learning. Journal of Economic Education, 25(2), 179-190. CROSS, K. P., & ANGELO, T. A. (1988) Classroom assessment techniques: a handbook for faculty. Ann Arbor, MI: Univer. of Michigan, National Center for Research to Improve Postsecondary Teaching and Learning. CROSS, R. W., & HUBERTY, J. J. (1993) Factor analysis of the State-Trait Anxiety Inventory for children with a sample of seventh- and eighth grade students. Journal of Psychoeducational Assessment, 11(3), 232-241. DOI: 10.1177/073428299301100303 CRUISE, R. J., CASH, R. W., & BOLTON, L. D. (1985) Development and validation of an instrument to measure statistical anxiety. Proceedings of the Section on Statistical Education, Alexandria, VA: American Statistical Association. Pp. 92-98. CRUISE, R. J., & WILKINS, E. M. (1980) STARS: Statistical Anxiety Rating Scale. Unpublished manuscript, Andrews Univer., Berrien Springs, MI. DILLON, K. M. (1982) Statisticophobia. Teaching of Psychology, 9(2), 117. DOLINSKY, B. (2001) An active learning approach to teaching statistics. Teaching of Psychology, 28(1), 55-56. ELMORE, P. B., & VASU, E. S. (1980) Relationship between selected variables and statistical achievement: building a theoretical model. Journal of Educational Psychology, 72(4), 457-467. FEINBERG, L., & HALPERIN, S. (1978) Affective and cognitive correlates of course performance in introductory statistics. Journal of Experimental Education, 46(4), 11-18. HAMILTON, R. (1989) The effects of learner-generated elaborations on concept learning from prose. Journal of Experimental Education, 57, 205-217.
23-PR_Chiou_140039.indd 308
05/08/14 5:22 PM
REDUCING STATISTICS ANXIETY
309
HARWOOD, W. S. (1996) The one-minute paper: a communication tool for large lecture classes. Journal of Chemical Education, 73(3), 229-230. HSIAO, T. Y. (2010) The Statistical Anxiety Rating Scale: further evidence for multidimensionality. Psychological Reports, 107(3), 977-982. HUNTLEY, D., SCHNEIDER, L., & ARONSON, H. (2000) Clinical interns’ perception of psychology and their place within it. The Clinical Psychologist, 54(4), 3-11. KLOSS, R. J. (1993) Stay in touch, won't you? Using the one-minute paper. College Teaching, 41(2), 60-63. LALONDE, R. N., & GARDNER, R. M. (1993) Statistics as a second language? A model for predicting performance in psychology students. Canadian Journal of Behavioral Science, 25(1), 108-125. LATCHAW, J. S. (1995) Assessment and community. Paper presented at the 46th annual meeting of the Conference on College Composition and Communication, San Diego, CA, March 23-25. (ERIC Document Reproduction Service No. ED 385839) LIGHT, R. J. (1990) Explorations with students and faculty about teaching, learning, and student life. The Harvard assessment seminars, first report. Cambridge, MA: Graduate School of Education and Kennedy School of Government. LIU, Y. Y. (2012) Students' perceptions of school climate and trait test anxiety. Psychological Reports, 111(3), 761-764. MAIER, M. H., & PANITZ, T. (1999) End on a high note: better endings for classes and courses. (ERIC Document Reproduction Service No. ED 448446) MAYER, R. E. (1980) Elaboration techniques that increase the meaningfulness of technical text: an experimental test of the learning strategy hypothesis. Journal of Educational Psychology, 72(6), 770-784. ONWUEGBUZIE, A. J. (1998) The dimensions of statistics anxiety: a comparison of prevalence rates among mid-southern university students. Louisiana Educational Research Journal, 23, 23-40. ONWUEGBUZIE, A. J. (2004) Academic procrastination and statistics anxiety. Assessment & Evaluation in Higher Education, 29(1), 3-19. ONWUEGBUZIE, A. J., DA ROS, D., & RYAN, J. M. (1997) The components of statistics anxiety: a phenomenological study. Focus on Learning Problems in Mathematics, 19(4), 11-35. ONWUEGBUZIE, A. J., & LEECH, N. L. (2003) Assessment in statistics courses: more than a tool for evaluation. Assessment & Evaluation in Higher Education, 28(2), 115-127. ONWUEGBUZIE, A. J., & SEAMAN, M. (1995) The effect of time and anxiety on statistics achievement. Journal of Experimental Psychology, 63(2), 115-124. PAN, W., & TANG, M. (2004) Examining the effectiveness of innovative instructional methods on reducing statistics anxiety for graduate students in the social sciences. Journal of Instructional Psychology, 31(2), 149-159. PAN, W., & TANG, M. (2005) Students' perceptions on factors of statistics anxiety and instructional strategies. Journal of Instructional Psychology, 32(3), 205-214. PANITZ, T., & PANITZ, P. (1999) Assessing students and yourself using the one minute paper and observing students working cooperatively. (ERIC Document Reproduction Service No. ED 453262) REDER, L. M., CHARNEY, D. H., & MORGAN, K. I. (1986) The role of elaborations in learning a skill from an instructional text. Memory and Cognition, 14(1), 64-78. RICHARDSON, F. C., & SUINN, R. M. (1972) The Mathematics Anxiety Rating Scale: psychometric data. Journal of Counseling Psychology, 19, 551-554.
23-PR_Chiou_140039.indd 309
05/08/14 5:22 PM
310
C-C. CHIOU, ET AL.
RUGGERI, K., DEMPSTER, M., HANNA, D., & CLEARY, C. (2008) Experiences and expectations: the real reason nobody likes stats. The British Psychological Society, 14(2), 75-83. SCHACHT, S., & STEWART, B. J. (1990) What's funny about statistics? A technique for reducing student anxiety. Teaching Sociology, 18, 52-56. SMITH, K. B. (2000) Effects of a cooperative teaching approach on math anxiety in beginning algebra. Focus on Learning Problems in Mathematics, 22(2), 1-17. STALLINGS, W. M. (1993) Return to our roots: raising radishes to teach experimental design. Teaching of Psychology, 20(3), 165-167. DOI: 10.1207/s15328023top2003_7 TEMAN, E. D. (2013) Factorial invariance of the Statistical Anxiety Rating Scale across sex and students' classification. Comprehensive Psychology, 2(1), 1-11. THOMPSON, W. B. (1994) Making data analysis realistic: incorporating research into statistics courses. Teaching of Psychology, 21(1), 41-43. DOI: 10.1207/s15328023top2101_9 TYNJÄLÄ, P. (1998) Writing as a tool of constructive learning: students' learning experiences during an experiment. Higher Education, 36(2), 209-230. WESTERBACK, M. E., & LONG, M. J. (1990) Science knowledge and the reduction of anxiety about teaching earth science in exemplary teachers as measured by the science teaching State-Trait Anxiety Inventory. School Science and Mathematics, 90(5), 361374. ZEIDNER, M. (1991) Statistics and mathematics anxiety in social science students: some interesting parallels. British Journal of Educational Psychology, 61(3), 319-328. Accepted May 21, 2014.
23-PR_Chiou_140039.indd 310
05/08/14 5:22 PM
