Bloom's framework has been applied in an array of contexts in undergraduate biology education Crowe et al. We used the six levels to create a Weighted Bloom's Index, which summarizes the average Bloom's level of exam questions weighted by the points possible:. To help interpret the index, note that Level 1 and 2 questions test lower-order cognitive skills, Level 3—6 questions assess higher-order cognitive skills Bloom et al.
Levels 1 and 2 in Bloom's taxonomy are considered lower-order cognitive skills; Levels 3—6 are considered higher-order cognitive skills. We calculated a Weighted Bloom's Index for every exam in the study by recruiting three experienced TAs to assign a Bloom's level to every exam question given in each quarter. Although raters knew that they were assessing Biology exam questions, they were blind to the quarter and year.
They were also blind to the study's intent and to the hypothesis being tested by the ratings. Point values for each question were omitted to avoid any bias introduced by high- versus low-point-value questions. Because multipart questions are common on these exams, each rater gave a Bloom's rating to each question part. Each rater assessed exam questions and assigned a total of Bloom's levels.
Including the identical exam, there were a total of exam questions and Bloom's rankings in the study.
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We used the decision rules published by Zheng et al. None of the subsequent questions were discussed as a group to resolve conflicts in ratings. Instead, we assigned the consensus rating when all three raters agreed and the majority-rule rating when two of three raters agreed. When ratings were sequential e. When ratings were nonsequential e. To assess the degree of agreement among the multiple raters, we calculated Krippendorff's alpha—an appropriate measure for ordinal coding data from multiple raters Hayes and Krippendorff, —and the intra-class r.
The Weighted Bloom's Index should accurately summarize the average Bloom's ranking of exams, facilitating comparisons across courses or even institutions. In addition, it should contain information on exam difficulty because students typically perform much better on lower-level versus higher-level questions e. Thus, exams with higher Weighted Bloom's Indices should be harder. As an alternative method for assessing exam difficulty, we created a Predicted Exam Score PES by recruiting three experienced TAs—different from the individuals who did the Bloom's ratings—to predict the average number of points that students would receive on each part of each exam question in the study.
Thus, the PES raters judged the difficulty of exam questions based on 1 an understanding of what had been presented in the textbook and introduced in class and 2 extensive grading experience that made them alert to wording, context, level, and other issues that cause confusion or difficulty. We hypothesized that peer TAs might be more attuned to how undergraduates read and respond to exam questions than faculty are. The PES raters used the same randomized list of identically formatted exam questions as did the Bloom's raters, except that point values for each of the question parts were indicated.
Like the Bloom's raters, the PES raters were blind to the study's intent and the hypothesis being tested with the predicted-points data.
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Work on the PES began with a norming session. This meeting started with each of the three individuals assigning a predicted-average-points value to 25 questions—a total of 58 question-parts—on his or her own. The three then met to discuss their predictions for average points on each question-part until they arrived at a consensus value.
Subsequent questions were assessed individually but not discussed. To arrive at a single predicted-average-points value for each of the exam-question parts after the norming session, we computed the arithmetic average of the three ratings submitted. The goal of the PES was to test the hypothesis that changes in failure rates were due to changes in the difficulty of exams, independent of changes in course design.
The metric should be useful because it is reported in units of average expected points on exams and because exam points predict most of the variation in final grade see Results. Note that because the Weighted Bloom's Index and the PES were computed from data on all exam questions in the study, there was no sampling involved. In cases like this, significance is a judgment about the relevance of observed differences to the hypothesis being tested. In addition, even in the most highly structured course designs, our intent was for exams to remain the primary determinant of final course grade—because exams represent the most controlled type of assessment possible and because exams are the major type of assessment in subsequent courses.
To test the point-inflation hypothesis, we performed simple linear regressions with each student's total exam points in each quarter as the predictor variable and his or her final grade as the response variable. In addition, we computed the 1. These 1. If exams are the major determinant of final grades irrespective of degree of course structure—even when many nonexam points are possible—then R 2 values for the regressions should be uniformly high, the slopes and intercepts of the regression lines should be indistinguishable, and the 1.
Rather, the best-fit distribution followed a binomial error distribution. Consequently, we used analysis of deviance to formally test the hypothesis that the slopes and intercepts of the regressions did not vary across quarters, using a Generalized Linear Model GLM framework Crawley, , p. More specifically, we compared the fit among three linear models 1 incorporating only the covariate exam points, 2 additionally incorporating quarter as a fixed effect, and 3 the full model with an interaction term.
If the additional explanatory variable and the interaction term failed to improve the fit of the GLM, it provides assurance that slopes and intercepts are homogeneous across quarters are not significantly different, using a likelihood ratio test [LRT]. In a longitudinal study of student performance in courses, it is critical to test the hypothesis that changes in failure rates are due to changes in the academic ability and preparedness of the student population at the time of entering each course.
To test this hypothesis, we used the Predicted Grade model introduced by Freeman et al. Because the percentage of missing values was low and the loading of SAT-verbal in the regression model is small, the missing values should have a minimal impact on the analysis. Thus, the substitution for missing values should not bias tests for differences in predicted grade across quarters. We performed linear regressions to compare the Predicted Grade with Actual Course Grade in each quarter of the study, and then used analysis of deviance to assess the robustness of the Predicted Grade model across quarters.
Again, an LRT is used to compare the fit among models; failure to improve the fit of the simplest model provides assurance that slopes and intercepts are homogeneous. To test the hypothesis that students were of equivalent ability and preparedness, we used ANOVA to compare average student Predicted Grade across quarters. In this and other statistical analyses, we checked the assumptions of the statistical tests used. The TAs who ranked questions on Bloom's taxonomy showed a high level of agreement. Using the original values assigned for the norming session questions—not the consensus values—the Kippendorf's alpha among raters was 0.
There was also a high level of agreement among the three TAs who evaluated exam questions for the PES values. Using the original values assigned for the norming session questions—not the consensus values—the intra-class r for the entire data set was 0. The Weighted Bloom's Index summarizes the average Bloom's level per point on an exam; the PES summarizes expert-grader predictions for average points that a class will receive on an exam.
Regression statistics are reported in the text. They are not the averages of the indices from each exam. Across quarters in the study, the regressions of total exam points on final grade were similar, and the average number of exam points required to get a 1.
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Regression analyses: Total exam points as a predictor of final course grade. Across all six quarters of the study, there was a strong relationship between the Predicted Grade and actual grade for each student. These data support the earlier claim by Freeman et al. Analysis of deviance shows that slope and intercept do not significantly vary across quarter. Post-hoc Tukey's Honestly Significant Difference tests demonstrate that this heterogeneity was distributed across quarters in the study: Of the 15 pairwise tests, only six were not significantly different, and these crossed levels of course structure data not shown.
Among five quarters from Spring through Autumn , drop rates varied from 1. Significant heterogeneity occurs when the drop rate of 6. This increase is probably due to 1 a change in enrollment from to , and 2 a change in departmental policy that loosened restrictions on repeating the course. This result is confounded, however, by changes in student academic ability across quarters, reported earlier in the text. To control for student academic characteristics, we constructed a generalized linear mixed-model GLMM to test the hypothesis that level of course structure plays a significant role in explaining the proportion of students failing each quarter.
Specifically, we analyzed the decline in proportion of students failing as a function of those predicted to fail in each quarter at each level of structure. Using multi-model inference MMI , the model with the most explanatory power contained proportion failing as the response variable, with predicted failure proportion and level of course structure treated as fixed effects and quarter treated as a random effect. MMI: Models and comparison criteria. Note that the LRTs are hierarchical: The p value reported on each row is from a test comparing the model in that row with the model in the row below it.
Failure rates controlled for Predicted Grade, as a function of course structure. In this study, low-, medium-, and high-structure courses rely primarily on Socratic lecturing, some active learning and formative assessment, and extensive active learning no lecturing and formative assessment, respectively. The negative association between the Weighted Bloom's Indices and the PES values supports the claim that questions that are higher on Bloom's taxonomy of learning are harder, and both methods of assessing exam equivalence suggest that exam difficulty increased in highly structured versions of the course Table 3, b and c.
It is important to note that the exams analyzed here appear rigorous. Although student academic ability and preparedness varied among quarters, it did not vary systematically with changes in course structure. The results of the GLMM, which controlled for heterogeneity in student preparedness and capability, support the conclusion reported earlier for moderately structured courses Freeman et al.
Thus, the data presented here support the hypothesis that increasing course structure can help reduce failure rates in an introductory biology course—from They are consistent with data from other STEM disciplines suggesting that intensive use of active-learning exercises can help capable but underprepared students succeed in gateway courses e. It is unlikely that this pattern is due to the changes in enrollment or exam format that occurred over the course of the study.
The general expectation is that student achievement is higher in smaller classes, but the lowest failure rate in this study occurred in a quarter with students enrolled—more than double the next largest enrollment. We would also argue that the change in exam format that occurred that quarter, with 2-h-long exams replacing a 2-h comprehensive final, is not responsible for the dramatic drop in failure rate.
The Weighted Bloom's Indices and PES values, for example, indicate that the exams in the altered format were the highest-level and the hardest in the study. We propose that this pattern is due to enrollments in Biology consisting primarily of sophomores who had already completed a three-quarter, introductory chemistry sequence for majors. Thus, it is likely that many underprepared students who might have taken Biology were ineligible, due to a failure to complete the chemistry prerequisite. The experiment to answer this question is underway. It will be interesting to test whether highly structured course designs analyzed here have an impact on this increasingly younger student population.
If the benefit of highly structured courses is to help students gain higher-order cognitive skills, what role do reading quizzes play? By design, these exercises focus on Levels 1 and 2 of Bloom's taxonomy—where active learning may not help. We concur with the originators of reading quizzes Crouch and Mazur, : Their purpose is to free time in class for active learning exercises that challenge students to apply concepts, analyze data, propose experimental designs, or evaluate conflicting pieces of evidence.
As a result, reading quizzes solve one of the standard objections to active learning—that content coverage has to be drastically reduced. The premise is that this information can be acquired by reading and quizzing as well as it is by listening to a lecture. Without reading quizzes or other structured exercises that focus on acquiring information, it is not likely that informal-group, in-class activities or peer instruction with clickers will be maximally effective.
This is because Bloom's taxonomy is hierarchical Bloom et al. It is not possible to work at the application or analysis level without knowing the basic vocabulary and concepts. We see reading quizzes as an essential component of successful, highly structured course designs. This study introduces two new methods for assessing the equivalence of exams across quarters or courses: the Weighted Bloom's Index based on Bloom's taxonomy of learning and the PES based on predictions of average performance made by experienced graders.
These approaches add to the existing array of techniques for controlling for exam difficulty in STEM education research, including use of identical exams Mazur, ; Freeman et al. The Weighted Bloom's Index also has the potential to quantify the degree to which various courses test students on higher-order cognitive skills. In addition to assessing Weighted Bloom's Indices for similar courses across institutions, it would be interesting to compare Weighted Bloom's Indices at different course levels at the same institution—to test the hypothesis that upper-division courses primarily assess the higher-order thinking skills required for success in graduate school, professional school, or the workplace.
The analyses reported here were designed to control for the effects of variation in the instructors, students, and assessments. More remains to be done to develop techniques for evaluating exam equivalence and student equivalence. With adequate controls in place, however, discipline-based research in STEM education has the potential to identify course designs that benefit an increasingly diverse undergraduate population. In the case reported here, failure rates were reduced by a factor of three.
If further research confirms the efficacy of highly structured course designs in reducing failure rates in gateway courses, the promise of educational democracy may come a few steps closer to being fulfilled. David Hurley wrote and supported the practice exam software, Tiffany Kwan did proof-of-concept work on the PES, John Parks and Matthew Cunningham helped organize the raw data on course performance from the six quarters, and Janneke Hille Ris Lambers contributed ideas to the statistical analyses.
The analysis was conducted under Human Subjects Division Review National Center for Biotechnology Information , U. Diane Ebert-May, Monitoring Editor. Author information Article notes Copyright and License information Disclaimer. Freeman et al. This article is distributed by The American Society for Cell Biology under license from the author s.
It is available to the public under an Attribution—Noncommercial—Share Alike 3. This article has been cited by other articles in PMC. Table 1. Failure rates in some gateway STEM courses.
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Open in a separate window. METHODS Course Background This research focused on students in Biology , the first in a three-quarter introductory biology sequence designed for undergraduates intending to major in biology or related disciplines at the University of Washington UW. Student Demographics During the study period, most students had to complete a chemistry prerequisite before registering for Biology ; the majority were in their sophomore year.
Course Design During the six quarters analyzed in this study, the instructor used various combinations of teaching strategies, detailed here in order of implementation. Table 2. Variation in course format. Exam Equivalence across Quarters In a longitudinal study that evaluates changes in failure rates, it is critical to test the hypothesis that changes in failure rates were due to changes in exam difficulty.
Weighted Bloom's Index. Figure 1.
Predicted Exam Score. Student Equivalence across Quarters In a longitudinal study of student performance in courses, it is critical to test the hypothesis that changes in failure rates are due to changes in the academic ability and preparedness of the student population at the time of entering each course.
Figure 2. Table 3. Exam equivalence analyses. Independent ratings Discussed- consensus All three agree Two of three agree Sequential ratings Nonsequential ratings a. Percentage agreement among Bloom's taxonomy raters. Percentage of total ratings 7. Table 4. Student Equivalence across Quarters Across all six quarters of the study, there was a strong relationship between the Predicted Grade and actual grade for each student.
Table 5. Table 6. Average predicted grades across quarters. Evaluating the Drop Rate Among five quarters from Spring through Autumn , drop rates varied from 1. Table 7. Failure rates across quarters. Table 8. Figure 3.
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