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ost college professors evaluate students in their classes using

summative techniques, such as test scores, paper grades, or final course exams. “Tra-ditional assessments,” Cross (1998) stat-ed, “tell students—often too little and too late—how they have done on a test in a course, but not how they are doing as

learners” (6). In contrast, formative evalu-ation provides students with an ongo-ing evaluation of their progress and is designed to improve learning.

Angelo and Cross (1988, 1993) have written extensively about classroom assessment techniques (CATs), which are valuable formative strategies that have applications across various classroom set-tings and disciplines. Their user-friendly manual, titled Class Assessment Tech-niques, provides fifty examples of CATs, classroom situations in which they might

best be used, and step-by-step directions on their implementation. CATs primarily help instructors gain feedback on how well students have learned class mate-rial and thus improve learning. They may also enhance student motivation (Walker 1991) and help foster students’ critical-thinking skills by providing the oppor-tunity to monitor their learning (Angelo 1995). Further, Lieberman, Bowers, and Moore (2001) have noted that an analysis of students’ responses to CATS can pro-vide important feedback to instructors on improving teaching strategies and making necessary modifications to courses.

Since the publication of Angelo and Cross’s manual, a number of reports have appeared in the literature summarizing the use or proposed use of CATs in vari-ous disciplines. These include foreign language (Carduner 2002); English as a second language (Coombe and Kinney 1999); dental hygiene, chemistry, elemen-tary algebra (Cuttic et al. 1999); sociology (Eckert et al. 1997); biology, business management, political science, and litera-ture (Fabry et al. 1997); graduate theolog-ical education (Gaeddert 2003); English composition (Hawkins 1993); education in the humanities (Mann 2000); graduate training in early childhood teacher edu-cation (McNair 2000); and introductory psychology (Walker 1991).

Several findings published during the last fifteen years support the educational value of CATs. For example, using case studies, Cross and Steadman (1996) con-

USING CLASSROOM ASSESSMENT TECHNIQUES

IN AN INTRODUCTORY STATISTICS CLASS

Gary S. Goldstein

M

Abstract. College instructors often provide stu-dents with only summative evaluations of their work, typically in the form of exam scores or paper grades. Formative evaluation, such as classroom assessment techniques (CATs), are more rare in higher educa-tion and provide an ongoing evaluation of students’ progress. In this article, the author summarizes the use of CATs in an undergraduate introductory statis-tics course and present data indicating that students believed CATs increased their understanding of mate-rial and benefited their academic performance. With minor revision, these CATs can be effectively used in other disciplines.

Keywords: classroom assessment techniques, evaluation, statistics

Gary S. Goldstein is an associate professor of psychology at the University of New Hampshire at Manchester. He is also the chair of the Division of Social Sciences.Copyright © 2007 Heldref Publications

78 COLLEGE TEACHING

vincingly demonstrated how several con-cepts in cognitive learning theory (such as attention, deep processing, and metacog-nition) help explain the effectiveness of CATs. Soetaert (1998) summarized self-report data that indicated CATs allowed instructors to clarify topics initially missed by or unclear to students. Fabry and col-leagues (1997) reported that between 82 percent and 93 percent of students who used CATs in political science, biology, lit-erature/writing, and business management classes indicated that CATs contributed to their learning. Walker’s (1991) introduc-tory psychology students who used CATs scored significantly higher on tests than students who took the same course a year earlier without using CATs.

In addition to increasing students’ intellectual understanding of class mate-rial, CATs also improve classroom atmo-sphere: the instructor willingly puts in the extra effort needed to provide formative feedback throughout the semester and is interested in students’ success. This fre-quent and consistent contact may also potentially build and strengthen relation-ships between instructors and students. Students in Cuttic and colleagues’ (1999) study concluded that using CATs was “a positive gesture on the part of the profes-sor to care enough to ask for student input” (88). Other researchers have suggested that CATs empower students because they appreciate having a voice in their learn-ing and believe their views are valued (Fabry et al. 1997; Steadman 1998). Fabry and colleagues further claimed that CATs “increase students’ comfort level and self-confidence” (14). Similarly, Angelo and Cross (1993) indicated that, based on six years of classroom research, the use of CATs lowered classroom barriers between teachers and students, raised students’ lev-els of trust, increased students’ coopera-tion and collaboration, and communicated to students that instructors care about their opinions and ideas. These assertions may be particularly relevant for undergradu-ate courses in statistics, given the level of statistics and math anxiety that often interferes with student learning.

I used CATs extensively in Statistics in Psychology (SIP), an introductory under-graduate course that provides students with an understanding of the use of basic sta-tistical methods in psychological research

and fulfills major and general education requirements. In this article, I describe sev-eral CATs (some from Angelo and Cross’s 1993 text and some that I have created) used in SIP, the rationale for their use, the impact that CATs have on class time, and grading students’ performance on CATs. Most CATs described in this article can be used by teachers in disciplines other than SIP, through minor modifications.

Impact on Class TimeUsing CATs in courses requires

increased preparation by the instructor and additional classroom time. As instruc-tors know, time is a precious commodity in our courses. Angelo and Cross (1993) acknowledged that many faculty cover less material when integrating CATs into courses “because the assessments had convinced them of the need to review, revisit, or reteach important material not learned well enough” (378). However, many CATs take about five minutes of class time to implement, and even those that take longer can provide the instruc-tor with a more focused understanding of concepts misunderstood by students. Therefore, instructors may actually use class time more efficiently to review areas that challenge the majority of students. In describing one of the CATs widely used by instructors—Minute Paper, which is described later in this article—Angelo and Cross (1993) noted that it “provide[s] manageable amounts of timely and use-ful feedback for a minimal investment of time and energy” (148). The same can be said for many other CATs. Additionally, although Angelo and Cross suggested that CATs be administered in the classroom, I have minimized the time costs by assign-ing many CATs as homework.

CATs and Final Course GradeAngelo and Cross (1993) suggested

that students’ responses to CATs should be anonymous and not graded. This prac-tice permits students to be candid about what they do not know and coincides with Angelo and Cross’s views that CATs are formative instruments. In past semesters, I have not graded CATs or required stu-dents to sign their names to CATs that they worked on in or outside of class. Thus, completion of CATs was optional, and this practice led to compliance rates

of 15 percent to 20 percent on assessment techniques assigned as homework. I now require students to complete all assigned CATs but do not grade individual assign-ments. Instead, students can earn up to five points (toward 100 possible points that make up the final course grade) based on the percentage of homework CATs they complete during the semester. Stu-dents who hand in inadequate work have a second opportunity to complete the CAT. Some students find it intimidating to regu-larly disclose their lack of understanding of course material on CATs; therefore, I spend considerable time on the first day of class describing the formative as opposed to summative purpose of CATs, my ratio-nale for using them, and the benefits that accrue to students who complete them. I stress that by asking students to identify themselves, I am able to give them specif-ic feedback over the course of the semes-ter, which will help them learn course material more efficiently and potentially increase their grades. I highlight some of these points in the course syllabus and revisit these issues throughout the semester. Although the contribution to the final grade is minimal (5 percent), the compliance rate for completing the CATs worked on outside of class time increased to nearly 100 percent.

Examples and Rationale for Their Use

Angelo and Cross (1993) provided detailed descriptions of the pedagogical purpose of each CAT listed in their text. A given CAT may serve multiple purpos-es, depending on the classroom setting. Below I describe the CATs used in SIP and the educational goals they serve.

CATs that Deal with Levels of Anxiety and Preparation

There is well-documented literature on math anxiety and a more recent interest in statistics anxiety (Onwuegbuzie and Wilson 2003). Both of these types of anxiety may in part contribute to stu-dents’ apprehension about statistics and impairment in their performance. I used a variation of Focused Autobiographical Sketches (Angelo and Cross 1993), which asks students to write a brief sketch on a dimension of their learning experience. On the first day of class, I asked students

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to write anonymous statements on what makes them most anxious about statis-tics. I read the statements aloud to the class (students who did not wish to have their statement read did not turn it in), dispelling their concerns by showing how many of their fears relate to myths about statistics. Most students described anxiety about their math ability. Success in intro-ductory statistics does not require a spe-cial aptitude in math more advanced than an understanding of solving for unknowns in basic algebra problems. Thus, after reading students’ anonymous responses, I was able to reiterate my contention that most students had an adequate math back-ground for the course. The Background Knowledge Probe (Angelo and Cross 1993), an adjunct I used with the Focused Autobiographical Sketch, assesses stu-dents’ level of preparation for a course or for specific lesson in a course; my Background Knowledge Probe evaluated students’ experience in basic math and algebra skills.

SIP is only one of the many courses in a college curriculum that may be tainted by the mythology cultivated by the student rumor mill. Students’ preconceived judg-ments about classes can lower their expec-tations, which may impair motivation and performance. Thus, the Focused Autobio-graphical Sketch is an effective and easy-to-use tool that provides the instructor with insight into students’ misunderstandings and fears about a given course.

CATs that Assess Understanding of Material and Reasoning Skills

Students with high levels of anxiety about statistics may also be reluctant to ask questions during class for fear that they will expose their inadequacy to peers. Several CATs address this prob-lem. Minute Paper asks students, “What was the most important thing you learned during class?” and “What important ques-tion remains unanswered?” (Angelo and Cross 1993, 148–53). Muddiest Point asks, “What was the muddiest point in the lecture (or homework assignment, dis-cussion, etc.)?” (Angelo and Cross 1993, 154–58). Other phrases can be substituted for “muddiest” to provide the instructor with data about students’ impressions of a given class: “most interesting,” “most bor-ing,” “most useful,” or “most irrelevant.”

These exercises give anxious and non-vocal students a safe opportunity to ask questions about class material and also can provide the instructor with insight on general patterns of students’ faulty rea-soning and misconceptions.

Cuttic et al. (1999) report on a CAT similar to Minute Paper and Muddi-est Point in which students in a dental hygiene class were asked to “make a list of words or phrases that were impor-tant points from the previous class” or “summarize the essence of the class in one sentence” (93). I developed another similar CAT, called “Define the Concept,” which asks students to hand in their defi-nition of an important concept reviewed in that day’s class. After getting students’ approval, I present selected definitions and ask students to comment on how to improve them. This exercise allows students more opportunities to rehearse definitions of concepts and helps them gain a more nuanced understanding of a concept’s complexity. Another CAT, called “Before and After,” asks students to define a specific concept after reading up on an assigned topic (the “before”) and then again after my presentation of the topic in class (the “after”). Feedback on this CAT helps students appreciate ways in which class presentations can help sup-port their understanding of material they initially read about in the text.

I also developed a CAT called “Confu-sion Groups,” in which I dedicate the last five to ten minutes of class time for small groups of about five students to discuss issues about the day’s class that still con-fuse them. I will occasionally use the first five to ten minutes of class for students to discuss issues that confuse them from the previous class. In both cases, students select a spokesperson to present their group’s confusion to the entire class. As another way to explore students’ confu-sion about course material, I occasionally interrupt my presentation and ask students to participate in a CAT called Pairing Up. After asking students to arbitrarily form pairs, I pose a question about the current topic. I ask the first member of the pair to answer, and then the second member to evaluate the first member’s response. Sometimes I pose an additional question to the second member and then ask the first member to evaluate the response.

I often poll the class to determine how many students believe they answered the question correctly. I find this technique useful when there is a lull in the class and students’ attention is waning. The exercise compels students to refocus their attention and monitor their understanding of class material, and it motivates them to ask questions about what currently puzzles them.

CATs like those described in this article may provide instructors with feedback about general patterns of misunderstand-ing in an entire class, as well as prob-lems individual students might have. This information has given me greater insight into common misconceptions that stu-dents have and common errors that stu-dents make for a given topic, which I have summarized in a series of handouts called “Common Misconceptions and Errors.” Such handouts might need to be modified from semester to semester, as the instruc-tor learns more from students about what confuses them. These handouts make excellent study guides for students and also help them realize they are not alone in feeling challenged by the material.

CATs that Assess Ways of Solving Problems and Organizing Material

Documented Problem Solution (Ange-lo and Cross 1993) directs students to provide a step-by-step narrative of their solution to a problem. This CAT gives the instructor insight into students’ problem-solving strategies and the opportunity to point out specific ways students’ thinking may lead them in the wrong direction. It also compels students to reflect on their approach to understanding and solving problems. Angelo and Cross’s (1993) CATs What’s the Principle? (218–21) and Problem Recognition Tasks (214–17) might be used in conjunction with Doc-umented Problem Solution. What’s the Principle? asks students to determine the underlying principle that relates to solving a problem. Problem Recognition Tasks require students to identify the particular type of problem they are asked to solve. Neither requires students to actually solve a problem but instead challenges them to reflect on their approach to a problem.

Empty Outline (Angelo and Cross 1993, 138–41) provides instructors with information on how students structure

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class material. I present students with an outline of the important points of a lecture or series of lectures and instruct them to fill in the “blank spaces.” Instructors can determine the extent to which students should focus on major or minor details by varying the explicitness of the cues in the outlines (or even by presenting no cues and asking students to devise their own outline). I stress that my outline is one of several legitimate schemes students can use to structure class presentations, and that they may have an equally valid way of organizing information presented in class. Angelo and Cross (1993) sug-gested that Empty Outlines help instruc-tors determine whether students grasp important points in a lecture or series of lectures and assist students in developing an organizational structure for mastering the material. I later provide my answers to Empty Outlines (and Documented Problem Solution), which students use as adjuncts to the text and studying tools for exams.

To further help me get a picture of students’ organizational skills, I devel-oped a CAT called Class Notes Review, in which I randomly select and review three students’ class notes each week. In addition to helping instructors learn how well students are following class presentations and effectively organizing their thoughts, reviewing students’ notes can provide insight into whether they are successfully recognizing important points raised in class.

Students’ Evaluation of CATsEach time I taught SIP using CATs (fall

2001, fall 2002, and fall 2003), I gave students the same nine-item evaluation inventory (see table 1). Fourteen out of 16 students in the fall 2001 class, 16 out of 21 students in the fall 2002 class, and all 23 students in the fall 2003 class rated each item on a scale ranging from 1 (strongly disagree) to 7 (strongly agree). Means and standard deviations for the items in the three sections appear in table 1. An exami-nation of the means revealed that students generally believed CATs increased their understanding of class material and rec-ommended I continue using them in SIP and other courses.

Is it possible that requiring CATs (as opposed to making them optional) and

having them contribute to the final grade affects students’ perception of their use-fulness? To test this hypothesis, I com-pared students’ ratings of inventory items in sections in which CATs were optional (fall 2001 and fall 2002) with ratings in the section in which CATs were required (fall 2003). Given that all sections had essentially the same curriculum, assign-ments, and grading system, I combined the students’ ratings of items in the fall 2001 and 2002 sections. I then compared the mean of each item in the combined section with the mean of each item in the fall 2003 section. I conducted two-tailed tests comparing the combined section with the fall 2003 section because I was not certain if requiring students to com-plete CATs would increase or decrease their ratings of the inventory items. An examination of the means indicated that students rated the items more positively in the fall 2003 section than in the com-bined fall 2001/2002 section. However, t tests for eight of the nine items were nonsignificant (all ps ≥ .11, except item

6, p = .09; and item 8, p = .06). Only item 7 (“Completing the learning assessment instruments helped me earn a better grade in the course than I would have had we not completed them”) reached statisti-cal significance, t(51) = 3.23, p = .002. This finding most likely reflects the fact that students in the fall 2003 section could earn up to five points (74 percent of the students earned 5 points; 22 percent earned 4.5 points) toward their final grade by completing CATs.

One needs to temper interpretations based on nonsignificant findings. Students who chose to complete optional CATs in fall 2001/2002 might have differed from students who completed required CATs in fall 2003. They might have been poor students who hoped to get additional feedback from the instructor or highly motivated students who welcomed the opportunity to do extra work. Given these considerations, however, a plausible inter-pretation of these data is that requiring students to complete CATs and having this requirement contribute to their course

TABLE 1. Means and Standard Deviations for Inventory Items for Fall 2001, 2002, and 2003 Sections

Fall 2001 Fall 2002 Fall 2003

M SD M SD M SD

1. The learning assessment instruments 5.29 1.54 5.44 1.41 5.91 0.85 increased my awareness of what I did not understand in the course.2. Feedback I received on the learning 5.43 1.34 5.87 1.06 5.74 1.10 assessment instruments, in either written or oral form, helped me better understand concepts with which I had difficulty.3. The learning assessment instruments 5.46 1.78 6.13 1.15 6.17 1.27 were a good studying tool.4. Completing the learning assessment 5.50 1.45 5.66 1.35 6.00 1.13 instruments helped me to better understand course material.5. Completing the learning assessment 2.67 1.38 2.25 1.44 1.70 1.06 instruments took too much time.6. The learning assessment instruments 1.79 1.31 2.00 1.90 1.26 0.75 hindered my learning of course material.7. Completing the learning assessment 4.29 1.86 4.66 1.62 5.96 1.55 instruments helped me earn a better grade in the course than I would have had we not completed them.8. I would recommend to the instructor that 5.71 1.59 6.38 0.96 6.68 0.48 he continue to use the learning assessment instruments when he teaches the course again.9. Learning assessment instruments like the 5.86 1.46 6.25 1.13 6.41 1.14 ones used in this course would be useful in other courses.

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grade had no detrimental effect on the students’ perceptions of their educational value. On the other hand, requiring CATs as part of the course curriculum increases the likelihood that students will complete them and therefore benefit from receiving feedback from their instructor and reflect-ing on their learning.

An analysis of the students’ grades on the midterm and final exams of the three sections supported this contention. Mid-term and final exams in the three sections were very similar, differing only by a few questions or by the specific value of a statistic or parameter in a given ques-tion. Therefore, a comparison of students’ grades on the midterm and final exams can provide a measure of difference in students’ academic performance in the three sections. Students’ grades on the midterm and final exams in the fall 2001 and 2002 sections (N = 16, N = 21) were not significantly different (p = .65 for the midterm; p = .53 for the final, two-tailed test). Therefore, I combined students’ midterm exam grades in the fall 2001 and 2002 sections and final exam grades in the fall 2001 and 2002 sections, and treated these data as coming from one class. I then used a repeated-measures ANOVA to compare the mean scores on the mid-term and final exams for fall 2001/2002 and fall 2003 (N = 23) sections. Section (fall 2001/2002 versus fall 2003) was the between-condition factor (an independent variable that has, in this case, two lev-els, with a different group of students [fall 2001/2002 versus fall 2003] in each level), and exam score (midterm versus final) was the within-subject factor (an independent variable that is manipulated by testing each student at each level of the variable; in this case, the two levels are midterm and final exam scores). The fall 2001/2002 means for the midterm and final were 74.00 (SD = 13.49) and 63.70 (SD = 20.67), respectively. The fall 2003 means for the midterm and final were 74.39 (SD = 13.44) and 70.17 (SD = 13.81), respectively.

The main effect for section was nonsig-nificant, F(1, 58) = .75, p = .39, indicating that students’ performance on the exams (collapsed across the midterm and final) in the fall 2001/2002 section did not dif-fer from students’ performance in the fall 2003 section. The main effect for exam

score was significant, F(1, 58) = 19.90, p = .0001; students performed better on the midterm than on the final exam. I have consistently observed this pattern in SIP sections taught prior to fall 2001, none of which included CATs as part of the course curriculum. This decrease in scores is most likely due to the more challenging demands of the final, which—unlike the midterm—tests knowledge of inferential (as opposed to just descriptive) statistics.

Because I expected a different pattern of results for students in the fall 2001/2002 and fall 2003 sections, I examined the dif-ferences between the midterm and final exam scores in each of the sections. For the fall 2001/2002 section, the difference of 10.30 units between the midterm and final was significant, t(36) = 5.06, p = .0001. For students in the fall 2003 sec-tion, the difference of 4.22 units between the midterm and final was nonsignificant, t(22) = 1.67, p = .11. Thus, there was a sig-nificant drop in performance between the midterm and final in the fall 2001/2002 section, which did not require CATs, and there was no such significant drop in the fall 2003 section, which required CATs. Further, a drop of 10.22 to 4.22 units represents more than one-half of a letter grade in most instructors’ grading scales.

Requiring CATs resulted in more stu-dents completing them in the fall 2003 section than in the fall 2001/2002 sec-tion. Additionally, as a result of requiring CATs, students may have completed them in a more serious and focused manner, and thus took fuller advantage of their educational benefits. Completing CATs may also have a cumulative effect that students may not fully profit from until the end of the semester, accounting for the lower decline in students’ performance between the midterm and final in the fall 2003 section than in the fall 2001/2002 section. Thus, given students’ overall pos-itive evaluation of the CATs in the three sections and the stronger performance on the final in fall 2003, I suggest that using CATs helped me successfully monitor my students’ progress throughout the course, facilitated their understanding of course material, and increased their learning.

The beneficial effects of using CATs also may be better understood by examin-ing research on the “testing effect.” The testing effect refers to a robust finding that

giving a probe (especially a free-recall test) after a period of original study of material can promote long-term retention and reduce forgetting of that material, even without an additional study between the probe and a final test on the material (see Kuo and Hirshman 1996; Roediger and Marsh 2005). By providing students with an opportunity to retrieve previously studied material, tests may have positive effects on retention of learned material. The regular use of certain types of CATs also provides students the opportunity to retrieve and process material from mem-ory. In my statistics classes, for example, students regularly completed Empty Out-lines and Documented Problem Solutions. Their use may have produced a kind of testing effect, especially during the sec-ond half of the semester when the material was more challenging. A detailed inquiry into the conceptual link between the ben-eficial effects of CATs and the testing effect may provide an interesting line of future research.

NOTESend correspondence to Gary S. Goldstein,

Division of Natural and Social Sciences, Psy-chology Program, University of New Hamp-shire at Manchester, 400 Commercial Street, Manchester, NH 03101; or e-mail gsg@cisunix.unh.edu.

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