Analytical and quantitative thinking skills are core components of science but can be challenging to teach in introductory biology courses. To address this issue, modest curriculum modifications, including methods of hypothesis testing, data collection, and statistical analysis, were introduced into existing exercises in an introductory biology laboratory course. After completing the updated course, students demonstrated improved ability to understand and interpret statistical analyses. Furthermore, students were more likely to understand that hypothesis development and quantitative data analysis are important parts of biology. This study indicates that small changes to laboratory curricula can effect important changes in student learning and attitudes.

When revising scientific curricula, an important goal is to create changes that reflect scientific practice and enhance the learning experience. As many national organizations have stated, these goals can be accomplished by providing active learning experiences with inquiry-based activities that require hypothesis testing and data collection (National Research Council, 2003; Handelsman et al., 2004, 2007; Project Kaleidoscope, 2006). Furthermore, because collecting and interpreting quantitative information is central to evaluating scientific hypotheses, it is also important to introduce students to analytical and quantitative thinking skills when revising curricula (National Research Council, 1996).

In undergraduate biology majors as diverse as wildlife biology (Cooper et al., 2001) and neuroscience (Boitano & Seyal, 2001), educators have called for greater emphasis on quantitative skills, notably the use and interpretation of statistical tests. Instead of learning quantitative skills in biology courses, many biology students take separate courses in mathematics, statistics, or psychology departments. This separation between biological knowledge and quantitative skill sets often causes students to view these two fields as disconnected (National Research Council, 2003). As a consequence, they do not learn how to correctly apply their mathematical knowledge to solve a scientific problem (A'Brook & Weyers, 1996; Metz, 2008). Because experimental design, data analysis, and problem solving are integral parts of scientific practice, a major goal of our curricular revisions was to provide authentic activities to teach students how to apply statistical methods to analyze biological data.

Significant problems with curricula are often addressed by implementing major curricular changes, completely revising courses. However, these types of modifications are often difficult to implement because they require a large investment in time and resources by course instructors and/or educational institutions. We decided to investigate how making small-scale curriculum changes to an existing introductory biology course could impact students' abilities to design experiments, perform data analysis, and solve problems. Introductory Biology at our institution is composed of two separate courses in which students must co-enroll: (1) a lecture that meets for 50 minutes three times a week and (2) a lab that consists of a 50-minute pre-lab lecture (with about 150 students) and a 3-hour laboratory that meets once a week (with a maximum of 16 students per lab section). Different faculty members teach the lecture and the lab, and students receive separate grades on their transcripts for each course. We focused our curricular changes on the laboratory component as a logical place to introduce methods of data analysis, hypothesis development, and quantitative tasks.

To address the need for increased quantitative skills, we introduced inquiry-based quantitative tasks into an existing laboratory curriculum that was primarily observation-based. Metz (2008) demonstrated that including quantitative analyses as a part of biology instruction can improve students' abilities to make the crucial link between statistical concepts learned in a mathematics course and their application for analysis of a biological data set. Similarly, we revised existing exercises of dissection or histological examination to ask students to collect and analyze data along with making their observations. When possible, laboratory exercises were modified to be inquiry-based, such that students first developed hypotheses and tested them, applying the principles of "scientific teaching" laid out by Handelsman et al. (2004) and adhering to suggestions from national organizations that inquiry-based exercises allow students to engage in the more effective form of active learning (PKAL, http://www.pkal.org; National Research Council, 2003; Handelsman et al., 2004; DeHaan, 2005). The curricular changes we describe were easily made in one summer, were complementary to the biology instruction content of the course, and did not require any new equipment.

For example, in one exercise, the existing version asked students to dissect a crayfish, making note of the structure and function of certain anatomical parts (Table 1 contains a summary of changes). While the original exercise focused on invertebrate anatomy, the exercise was easily modified to focus on testing a hypothesis by starting with the question, "Are female crayfish a different size than male crayfish?" By asking the students to answer a question, we required them to actively engage with the material in order to develop a scientifically credible hypothesis, and link the hypothesis back to biological concepts. Crayfish chela size is known to be a sexually dimorphic trait (e.g., Elser et al., 1994); thus, students can draw on the current scientific literature to help them formulate a hypothesis. To test their hypotheses, students had to collect only one piece of data that they had not been previously asked to gather: the body length of their crayfish. To analyze their data, students were taught how to perform basic graphic and statistical analyses (histograms, t-tests) during lab, and then had to apply these skills in a homework assignment, providing evidence to support their interpretation of the results. Some laboratory exercises introduced both hypothesis development and testing, but most provided questions to the students. Example modules are available at http://www.barnard.edu/hspp/cdOrganismal_Evolution_BIO_Lab.htm.

**Table 1.**

Lab Topic
. | Previous Curriculum
. | Modified Curriculum
. | Statistical Analysis (Modified Curriculum)
. |
---|---|---|---|

Animal Form and Function | Students dissected crayfish, focusing on structure and function of anatomy | Students performed same dissection but also investigated the question: Are male and female crayfish the same size? | t-test |

EKG | Students measured their own EKG while lying, sitting, and after exercise | Students designed an experiment to measure their own EKG after performing activities of their choice | ANOVA |

EMG | Students measured EMG from 7 levels of forearm clenching | Students performed same exercise but analyzed data more rigorously | Regression |

Animal Chemotaxis | Students investigated chemotaxis of C. elegans to different concentrations of volatile compounds | Students performed the same exercise but analyzed data more rigorously | Regression |

Plant Embryo Germination | Students removed corn embryos from seed and grew on defined media | Students performed similar exercise but analyzed data more rigorously | ANOVA |

Plant Transpiration | Students investigated the effect of light on the rate of transpiration | Students designed an experiment to investigate the effect of an environmental variable on the rate of transpiration | t-test |

Lab Topic
. | Previous Curriculum
. | Modified Curriculum
. | Statistical Analysis (Modified Curriculum)
. |
---|---|---|---|

Animal Form and Function | Students dissected crayfish, focusing on structure and function of anatomy | Students performed same dissection but also investigated the question: Are male and female crayfish the same size? | t-test |

EKG | Students measured their own EKG while lying, sitting, and after exercise | Students designed an experiment to measure their own EKG after performing activities of their choice | ANOVA |

EMG | Students measured EMG from 7 levels of forearm clenching | Students performed same exercise but analyzed data more rigorously | Regression |

Animal Chemotaxis | Students investigated chemotaxis of C. elegans to different concentrations of volatile compounds | Students performed the same exercise but analyzed data more rigorously | Regression |

Plant Embryo Germination | Students removed corn embryos from seed and grew on defined media | Students performed similar exercise but analyzed data more rigorously | ANOVA |

Plant Transpiration | Students investigated the effect of light on the rate of transpiration | Students designed an experiment to investigate the effect of an environmental variable on the rate of transpiration | t-test |

To determine the impact of these curricular changes, we compared students' responses on a survey at the beginning and end of the semester, designed to measure the students' abilities in or attitudes about two areas: (1) Quantitative skills: Will students improve their ability to collect and analyze basic biological data as determined by their abilities to interpret basic statistical tables and figures? (2) Concepts: Will students gain an increased understanding that hypothesis development and testing is the engine of biological science (as opposed to memorization)? Will students also learn that quantitative skills are indispensable for interpreting the results of research? We found that small-scale curricular modifications had a significant impact on student learning and attitudes.

## Methods

### Curriculum Changes

The modifications described in this paper affected one semester of an introductory biology course focused on physiology, ecology, and evolution. Since a large-scale overhaul of the curriculum was not practical, we focused on making small-scale changes to the existing curriculum. Many existing labs asked students to make detailed observations of different organisms without introducing methods of data analysis. Furthermore, the exercises provided little opportunity for students to formulate hypotheses or design experiments. In the revision process, the general topic and overall framework of each lab exercise was not altered, as the labs were coordinated with material presented in the lecture. Thus, the lecture instructors did not design any changes in order to implement our laboratory curricular modifications. Instead, portions of existing exercises were redesigned by adding in methods of data collection and analysis, and/or reframing the exercise to allow for increased student inquiry. These curriculum modifications were easily implemented over the course of one summer.

Of the 11 lab exercises taught in the semester, six were modified (summarized in Table 1). Four of these labs were chosen because the existing versions included data collection but not analysis. These labs were reframed such that students were asked to collect data to answer a question, and to use appropriate statistical analysis to interpret their data to answer that question. For example, during one lab that focused on electromyography, students measured the electrical signals generated after forearm clenching and were asked if they thought that increasing the force of their clench would cause a direct increase in electrical output from their forearm muscles. They then used linear regression analysis to analyze their data.

The other two reframed labs were chosen for modification because the existing version had asked students to test predeveloped hypotheses (summarized in Table 1). For example, the original version of one lab asked students to measure the electrical activity generated by their heart after lying down, sitting, and jumping. This lab was modified such that students were asked to design an experiment in which they performed an activity of their choice that might affect their EKG. Students chose to test the effect of things such as the exercise, drinking caffeine, or listening to music. They then analyzed their data using analysis of variance and wrote a lab report detailing their experimental findings. In both labs that were updated, students were given the chance to practice testing hypotheses, collecting data, and analyzing data from experiments they designed.

### Assessment Tool

One hundred fifty-nine students in 12 laboratory sections responded to the survey during the first laboratory meeting of the semester, and of those, 141 also responded to the same survey during the last laboratory meeting of the semester (but before the final laboratory exam), and granted permission to use their survey results for this study. The survey was distributed on paper to students in the beginning of the laboratory periods. The survey tool is available in Appendix 1. Students also signed a consent form before answering the survey.

### Analysis

Data for the 141 students who responded in both the preclass and postclass surveys were matched with the students' final laboratory course grades. Pre- and postclass responses on quantitative skills questions were analyzed using paired t-tests. Pearson correlations were used to analyze relationships between students' background and their acquisition of quantitative skills, and multiple linear regressions were used to examine how quantitative skills learning and student background predicted course performance. All analyses were performed using the statistical software R (http://www.r-project.org).

## Results & Discussion Skills

Analysis of answers on the pretest showed that many students did not know how to apply statistical analysis skills to answer biological problems, answering only 1 out of 4 skill-based questions correctly (median number of questions answered correctly) (Table 2 and Figure 1). There was no correlation between success on the pretest and prior preparation in statistics (r^{2} = 0.13; number of courses taken previously that focused mainly on statistics and initial skills score), indicating that even students who had learned basic quantitative analysis skills had trouble applying their knowledge to biological data sets.

**Table 2.**

Question
. | Pretest
. | Posttest
. | Percent Improvement
. |
---|---|---|---|

1. Interpreting scatter plot and regression | 54.3% | 78.6% | +24.3 |

2. Interpreting t-test results | 19.3% | 86.4% | +67.1 |

3. Interpreting bar plot | 22.9% | 47.9% | +25.0 |

4. Understanding bar plot data | 40.7% | 47.1% | +6.4 |

Question
. | Pretest
. | Posttest
. | Percent Improvement
. |
---|---|---|---|

1. Interpreting scatter plot and regression | 54.3% | 78.6% | +24.3 |

2. Interpreting t-test results | 19.3% | 86.4% | +67.1 |

3. Interpreting bar plot | 22.9% | 47.9% | +25.0 |

4. Understanding bar plot data | 40.7% | 47.1% | +6.4 |

Interestingly, there was no correlation between number of statistics courses taken (up to 3 courses) and success in this course, indicating that students with little prior statistical preparation did not appear to be at a disadvantage in the modified curriculum. However, students with prior backgrounds in biology were more likely to succeed in this course, an outcome that was expected because, presumably, these students could draw on their previous biological knowledge to help them succeed in portions of the lab course requiring that knowledge (such as learning anatomy). However, prior background in biology did not affect students' ability to learn statistical analysis skills, as there was no correlation between number of prior biology courses and performance on the posttest (Table 3).

**Table 3.**

Variable
. | Estimate
. | SE
. | P
. |
---|---|---|---|

How many biology courses have you taken? | 1.18 | 0.60 | 0.050 |

How many courses have you taken which focus mainly on statistics (e.g., Biostatistics, Statistics for Behavioral Scientists, Probability)? | 0.97 | 1.05 | 0.356 |

What year are you in college? | –1.03 | 0.66 | 0.120 |

Quantitative skills score postcourse | 2.28 | 0.57 | <0.001 |

Variable
. | Estimate
. | SE
. | P
. |
---|---|---|---|

How many biology courses have you taken? | 1.18 | 0.60 | 0.050 |

How many courses have you taken which focus mainly on statistics (e.g., Biostatistics, Statistics for Behavioral Scientists, Probability)? | 0.97 | 1.05 | 0.356 |

What year are you in college? | –1.03 | 0.66 | 0.120 |

Quantitative skills score postcourse | 2.28 | 0.57 | <0.001 |

A comparison of pre- and posttest answers indicated that students were able to learn basic data analysis skills when they were introduced in the context of a biology course (Figure 1 and Table 2). Overall, statistical analysis skills improved, the number of correct questions rising from a median of 1 of 4 on the pretest to 3 of 4 on the posttest (paired t-test, t = 10.56, P << 0.001). Students improved the most in analysis methods that were introduced multiple times. For example, 85% (120/141) were able to correctly interpret a t-test results table (used in three separate labs), and 77% (109/141) were able to correctly answer a question about regression analysis (used in only one lab). In a multiple regression also accounting for years in college, number of previous biology courses, and number of previous statistics courses, students who performed better on skill questions earned a higher grade in the course (Table 3; multiple linear regression, r^{2} = 0.138, P < 0.001), which suggests that students who were able to grasp data-analysis skills were also better able to grasp basic biological concepts.

### Concepts

To determine whether our curricular modifications affected students' attitudes about the importance of data collection and interpretation in biology, we asked the students to respond to statements about the importance of quantitative thinking, quantitative skills, and hypothesis-driven approaches to biology on a Likert Scale survey that we developed (see Appendix).

At the end of the course, students were more likely to agree with the statement "Understanding statistics is very important for biologists," which indicates that these curricular changes affected the way students viewed the role of quantitative skills in biology (Figure 2 and Table 4). In fact, students with the largest attitude change regarding this topic earned higher course grades.

**Table 4.**

Question
. | Pretest (September)
. | Posttest (December)
. | % Change
. |
---|---|---|---|

An experiment can prove a hypothesis is true | 3.26 | 2.71 | –16.80 |

Understanding statistics is very important for biologists | 4.22 | 4.56 | +8.16 |

A good experiment will always yield the same results | 2.62 | 2.80 | +6.70 |

The goal of an experiment is to resolve a biological question with certainty | 2.65 | 2.57 | –3.17 |

Variability in data is usually due to measurement error, not natural variability | 1.78 | 1.81 | +1.61 |

Outliers in your data set represent mistakes | 1.96 | 1.94 | –1.10 |

Unexpected data does not provide useful information | 1.34 | 1.34 | –0.35 |

Question
. | Pretest (September)
. | Posttest (December)
. | % Change
. |
---|---|---|---|

An experiment can prove a hypothesis is true | 3.26 | 2.71 | –16.80 |

Understanding statistics is very important for biologists | 4.22 | 4.56 | +8.16 |

A good experiment will always yield the same results | 2.62 | 2.80 | +6.70 |

The goal of an experiment is to resolve a biological question with certainty | 2.65 | 2.57 | –3.17 |

Variability in data is usually due to measurement error, not natural variability | 1.78 | 1.81 | +1.61 |

Outliers in your data set represent mistakes | 1.96 | 1.94 | –1.10 |

Unexpected data does not provide useful information | 1.34 | 1.34 | –0.35 |

In the largest change in attitudes, at the end of the course, the students agreed much less with the statement "An experiment can prove a hypothesis is true." This suggests that, through the process of performing hypothesis testing, students were able to grasp that the goal of testing hypotheses is to confront alternative hypotheses with data, and to ask whether the data can be used to reject the null hypothesis. This was one of the goals that we had in redesigning the curriculum.

Interestingly, students' attitudes did not change about how to deal with "messy" data. For example, there was little change in how students responded to the statement that "variability in the data is usually due to measurement error, not natural variability." This suggests that our curriculum reforms may have used examples that were clear-cut and did not give students a chance to deal with the type of "messy" data that real-life science often yields. Because one goal of the lab exercises was to demonstrate key concepts from the lectures, exercises with largely variable data sets were not developed. However, because there is variability in biological systems, it is important to teach students how to interpret more complex data. To address this issue, it may be possible to further modify certain labs to allow students to ask a question that might generate less clear-cut data. One would predict that students would be most successful when asked to analyze a "messy" data set if they were to use a statistical method that was previously introduced for analysis of a more clear-cut data set.

## Conclusions

The need for undergraduate biology curricula to incorporate quantitative skills throughout all courses, even introductory courses with nonmajors, is clear. We have modified existing laboratory exercises in an introductory laboratory-based course by adding quantitative components as well as active learning approaches. Because only modest curricular modifications were made, these changes were easily implemented with a minimum investment of time and resources by the course instructor. Under the new curriculum, students were able to learn quantitative skills and concepts without detracting from the core content of the exercises, and without necessarily having any previous exposure to statistical concepts. Furthermore, these curricular changes affected the way in which students viewed the importance of statistical analysis in biology. These examples show how small changes to existing laboratory curricula can impart large changes in attitudes about the nature of science. These types of modest curricular changes should allow today's undergraduate biology students to better rise to the challenges they will face in future coursework, research, and teaching.

## Acknowledgments

Curriculum development was supported by a Hughes Science Pipeline Project grant to Barnard College from the Howard Hughes Medical Institute. We thank J. Sircely for assistance with curriculum development and P. Hertz for support. We thank A. Rogat and M. Wallenfang for excellent and constructive comments. The use of the survey was approved by the Columbia University Institutional Review Board (human subjects # FWA00001512).