Online Strategies To Improve Quantitative Skills in Microbiology Laboratory Classes.

Biology is an increasingly quantitative science. Thus, it is important that undergraduate biology curricula include frequent opportunities for students to practice their quantitative skills. This can create a substantial grading burden for faculty teaching online and/or large enrollment courses, but the "formula question" feature present in many learning management systems (LMS) offers a solution. Using this feature, faculty set up a basic scaffold for an algebraic word problem, and the LMS can then automatically generate and grade many different versions of the question. In this paper, we describe the use of "formula questions" in an undergraduate microbiology course and specifically focus on how the strategic use of algebraic word problems at multiple points throughout the semester can help build quantitative literacy. Key to the success of this approach is that faculty provide a review of foundational mathematical skills early in the semester, even in upper-level classes. This should include reacquainting students with formatting conventions (e.g., rounding and scientific notation), familiarizing them with any idiosyncrasies of the technology platforms, and demonstrating how to solve math problems using spreadsheets. This initial effort increases student success when more complex problems are introduced later in the semester. Though the tips summarized in this paper focus on undergraduate microbiology teaching laboratories using Canvas, the approach can easily be modified to help students develop their critical thinking and quantitative reasoning skills at other levels and in other disciplines.

INTRODUCTION

As life sciences research becomes more interdisciplinary and quantitative, biology educators are seeking new and creative ways to help students learn to analyze and interpret large and complex data sets. To successfully engage in these more advanced analyses, students must first have a solid grasp of core mathematical concepts and confidence in their quantitative skills. Although some colleges have established curricula that integrate the teaching of biology and mathematics (e.g., references 1 to 4), most instead rely on individual instructors to address quantitative literacy in individual classes. Microbiology laboratory courses provide an excellent venue for students to apply quantitative thinking to biological problems, though this becomes more challenging when courses have a large enrollment and/or are online. One way to address this challenge is to use learning management systems (LMS) to compose algebraic word problems so students can practice problem-solving skills. Word problems are especially effective for developing quantitative literacy because they support metacognition and require students to construct an answer rather than recall one from memory (5). The “formula” question type found in many LMS can make it easier for faculty to incorporate word problems frequently throughout the semester (Fig. 1). The formula question goes by different names in different LMS (Table 1), but all function similarly—the student is presented with a question that includes one or more numerical values and is expected to perform a calculation using those values. The LMS inserts different random numbers into the question each time it runs, making it possible to generate hundreds of versions of the question, which can be automatically graded based on a formula provided by the instructor. This article describes several tips and tricks for using the formula question framework to incorporate word problems into an upper-level microbiology laboratory. The approach can be applied in a variety of courses at all levels.

FIG 1

Framework for incorporating formula questions into microbiology laboratory classes, highlighting the importance of foundation skills and the opportunity for cumulative learning to deepen student understanding of quantitative concepts.

TABLE 1

Question type used to create formulas in several common learning management systems

Learning management system (LMS)	Question type	Instructional website
Blackboard Ultra	Calculated formula	https://help.blackboard.com/Learn/Instructor/Ultra/Tests_Pools_Surveys/Question_Types/Calculated_Formula_Questions
Brightspace	Arithmetic	https://documentation.brightspace.com/EN/le/question_library/instructor/create_arithmetic.htm
Canvas (New Quizzes)	Formula	https://community.canvaslms.com/t5/Instructor-Guide/How-do-I-create-a-Formula-question-in-New-Quizzes/ta-p/956
Moodle	Formula	https://docs.moodle.org/29/en/Formulas_question_type
Sakai	Calculated	https://sakai.screenstepslive.com/s/sakai_help/m/81161/l/954698-how-do-i-create-a-calculated-question
Scholar LMS	Calculated or simple calculated	https://scholarlms.net/Calculated-question-type/

PROCEDURE

Safety concerns

There are no safety concerns because this is an online activity.

Set the stage for success

Potential stumbling points for students when working with formula questions include inconsistent formatting of answers and lack of familiarity with spreadsheets and computational software. We find it worthwhile to explicitly review these topics at the beginning of the semester, usually as part of our syllabus quiz or in a low-value introductory module focused on the use of basic mathematics in a microbiology laboratory. This modest investment of time sets the stage for success and significantly decreases frustration for students and instructors due to logistical and technological issues. We recommend that the following three topics be considered.

First, it is important to explain the idiosyncrasies of the LMS so students will understand how to format their answers. The LMS cannot give partial credit for incorrect rounding or for answers entered in the wrong format or in the wrong units. We typically use this LMS discussion as an opportunity to review the general rules for rounding, significant figures, and scientific notation, which are important topics that students often struggle with. For example, students could be asked to calculate the original abundance of bacteria in a sample if 53 CFU grow on a plate spread using a 10−7 dilution. Correctly answering this question requires the students to not only understand the concepts of dilution and spread plating but also appreciate what format the LMS uses for scientific notation (e.g., 5.30 * 10^−7 in Canvas versus 5.30e−7 in Blackboard) and what level of rounding is expected.

Second, we review syntax and order of operations. Many students understand these principles when they write the math out on paper but do not appreciate the need to include additional parentheses when coding the information in a calculator or spreadsheet (Fig. 2).

FIG 2

Students are often unaware that extra steps are necessary to ensure that calculators and software like Excel follow the intended order of operations. For example, mistakes are common when the vinculum, a horizontal bar, must be conveyed using the forward slash for division. Going over the difference is important when introducing students to software commonly used in science.

Third, we go over how to use spreadsheets (e.g., Excel or Google Sheets) to solve math problems. Very few students appreciate that complex, multistep math problems can be easily solved using these sorts of programs and instead rely on their graphing calculators. Students who do the calculations manually with a calculator tend to round off after each step, occasionally generating a final answer that is different from what one would obtain without rounding. This can create issues with the automatic grading since the LMS does not round until the final step. Using spreadsheets makes it easy for students to share their work with the instructor and get feedback, and asking that everyone use the same spreadsheet software avoids frustration due to differences in nomenclature and performance. More broadly, teaching with spreadsheets helps prepare students to organize, calculate, graph, and analyze data later in the course, all of which are transferable skills with value outside the microbiology laboratory. Teaching with spreadsheets is akin to working with simulations. Once students have set up their spreadsheet formulas, it becomes easy for them to see how changing the input values affects the final outcome. This expands the depth and breadth of questions we can ask students and broadens their understanding.

Practice, practice, practice!

With these foundations in place, formula questions can be effectively integrated throughout the semester to increase student quantitative learning (Fig. 1). Because the LMS can generate multiple versions of the same question using different random numbers, the students can practice a concept or problem set as much and as often as necessary and get real-time feedback thanks to automated grading. Over the course of the semester, the formula questions become more challenging and require the integration of multiple concepts. For example, prelab assignments could focus on preparing reagents for an experiment with all contextual information provided (e.g., volume and molecular weight). During the lab, students may be given a different compound and asked to independently obtain those parameters prior to performing the calculations. Postlabs offer an opportunity for student reflection and interpretation of the data they generated, and summative assessments, such as an exam, provide an opportunity to assess the learning outcome. Part of the power of formula questions is they allow one to repeatedly call on the same set of quantitative skills in different biological contexts. Learning outcomes related to dilutions and exponential growth also lend themselves well to this synergistic approach. Example questions showing the application of formula questions in several biological contexts are provided in Appendix 1 and 2 in the supplemental material.

CONCLUSIONS

We have had great success using formula questions in Microbiology Lab, Medical Microbiology Lab, and Microbiology Lecture to provide instruction for over 3,000 students during the past 5 years. While not directly quantified, informal discussions with students indicate the word problems are appropriately challenging. Moreover, the types of questions the students ask us during exam reviews and individual meetings indicate they are learning successfully. Laboratory courses provide hands-on collaborative engagement with quantitative content, which increases student interest. This reinforces the message that math is important to biologists.