Improving the quantitative skills of life science students through General Biology reform (Supported by NSF Award DUE-9752339 to the University of Tennessee)

S. M. Harrell, M. L. Beals, L. J. Gross, B. Mullin, and S. E. Riechert.

Ecological Society of America Meetings. Spokane, WA. August 1999



The quantitative training of undergraduate biology students is generally weaker than that of students in the physical sciences. Quantitative concepts should be integrated into life sciences curriculum, rather than isolated in a few courses focused on mathematical concepts. Student's comprehension of quantitative concepts can be enhanced by incorporating simple mathematical examples into lectures. In addition, brief modules, designed to complement lectures or lab work, can be provided to students. Both lectures and modules should emphasize how quantitative methods can enhance biological understanding. To assess the quantitative skills and needs of biology majors, General Biology students were given a short competency exam covering basic mathematical concepts considered prerequisites for the course. Quantitative examples were included in lectures throughout the semester. Reinforcement of quantitative concepts within the biology curriculum is necessary for im provement of student skills. Ideally, an accessible set of quantitative examples should be available for instructors, and a goal of our project is to produce a Primer of Quantitative Biology containing such examples appropriate for inclusion in a General Biology sequence.



    Biology is becoming increasingly quantitative  
understanding key biological concepts relies on a student's ability to grasp quantitative concepts

quantitative training in areas such as data analysis, probability, and model interpretation is as essential as laboratory training

Quantitative training of undergraduate biology students is typically weak

generally isolated in mathematics courses not linked to biology curriculum

though 79% of life-science programs require some degree of calculus, many quantitative techniques applicable to the life-sciences require broader exposure

quantitative concepts should be integrated into the life-sciences curriculum rather than isolated in math or statistics courses

Quantitative training could be enhanced by integrating quantitative concepts into the life-sciences curriculum through assessment of biology students' quantitative skills

employment of mathematical examples in lectures

addition of modules to complement lectures or lab work


Assess the quantitative skills of General Biology undergraduate students, Spring Semester 1999  
competency exam at the start of the semester

include quantitative examples in lectures and tests throughout the semester

assess student improvement with another competency exam at end of semester

Develop quantitative modules and examples for use in upcoming semesters

Develop a Primer of Quantitative Biology




Competency exam designed for students of Biology 140, Introductory Cell Biology  
covered basic mathematical concepts used in course and labs

assessed student familiarity with these concepts

emphasized the importance of quantitative skills to biology

given at start, January, and end, May, of the 1999 Spring Semester

eleven multiple-choice questions, not requiring a calculator (Table 1)

exam given to students in classes taught by three different professors

 Dr. Mullin's Biology 140 class emphasized mathematical concepts
 throughout the semester when possible   using graphs and quantitative examples in lectures   requiring simple calculations on exams   student improvement from first to second competency exam was assessed with a paired t-test
            Other faculty member's classes were considered as controls, although
            it is not known whether mathematical concepts were emphasized   mean scores from Dr. Mullin's and other classes at the start of the semester were compared with a t-test

Table 1. Topics covered on the competency exam given at the start and conclusion of each semester. Scores for Dr. Mullin's class at the start (January) and end (May) of the semester are given. Scores indicate the percent of students who missed the question.
% who missed in January
% who missed in May
metric conversion
calculation of mean/median
molecular weight
% solution
dilution/metric conversion
graph interpretation
constant rates of reaction
volume of cylinder
graph/ interpolation

  Mean competency exam scores for Mullin's class (143 students, mean = 7.61) and other sections (255 students, mean = 7.36) at the start of the semester were not significantly different (t-test, p = 0.290, Fig. 1)   End of semester scores for Mullin's class (123 students, mean = 10.21) and other sections (96 students, mean = 6.54) were significantly different (t-test, p < 0.0001, Fig. 1). But note that Mullin's students were offered extra credit for taking the exam while other sections were not.   Mullin's students had difficulty with some exam questions, but showed improvement by the end of the semester (Table 1 )   For student's who took Mullin's exam in both January and May, the mean increase in score was 2.44 points and was significant (paired t-test, p < 0.0001, Figure 1)

Figure 1. Frequency distribution of total scores (out of 11 possible points) for Mullin's class (1a), where quantitative concepts were emphasized, and other sections (1b) at the start, January, and end, May, of the spring semester.

Figure 1a. Mullin's Class

Figure 1b. Other Sections


  While student improvement in Mullin's class may be an artifact of the students' knowledge that their scores would count as extra credit, it does indicate that emphasizing quantitative skills may encourage students to review mathematical concepts and acknowledge their importance   Spring Semester 1999 will be a base-line for comparison with upcoming semesters   repeat for Biology 140, Fall Semester, more thoroughly incorporating quantitative examples into lectures   develop similar competency exam and quantitative examples for Biology 130 (Biodiversity) with emphasis on Ecology and Evolution
Develop a database of quantitative examples and modules to integrate into General Biology Courses


One reason for the lack of quantitative exposure within biology courses is the general paucity of quantitative examples designed for undergraduate students

  Quantitative training of undergraduate students could be improved by developing a set of modules for incorporation into General Biology course work   Modules could enhance lectures or lab work (see examples)   designed at a simple mathematical level for introductory biology students   cover the range of general biology topics and mathematical concepts (Module Page)   incorporated into lectures or given as homework   accessible to faculty through a text or the Internet
Quantitative training of students can be improved when instructors emphasize the importance of quantitative concepts   Quantitative concepts should be integrated into the life-sciences curriculum rather than isolated in a few mathematics courses   Ideally, an accessible set of quantitative examples should be available for instructors   A goal of our project is to produce a Primer of Quantitative Biology containing such examples appropriate for inclusion in a General Biology sequence

Flannery, M. C. 1995. Math matters. The American Biology Teacher 57:56-59.

Gross, L. J. 1994. Quantitative training for life-science students. BioScience 44:59.

Levin, S. A., editor. 1992. Mathematics and Biology: The Interface. Lawrence Berkeley Laboratory, University of California. PUB-710.

Marsh, J. F. and N. D. Anderson. 1989. An assessment of the quantitative skills of students taking introductory college biology courses. Journal of Research in Science Teaching 26:757-769.


WWW Resources for Mathematics Training for Biology Students

WWW Links to General Biology Education

General Biology Quantitative Modules

BioQUEST Home Page Richard Hake's Guide to Biology Education Resources on the Web Bioinformatics Courses on the Web Math Archives for the Life Sciences CTI Centre for Learning Technology Use in Biology Education Population Biology, Evolution and Biomath Index of On-Line Courses and Educational Material


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