Many research discoveries in biology and medical applications rely on the use of mathematical models that encapsulate ideas about biological phenomena. These mathematical models allow scientists to harness computers to represent phenomena, test hypothetical scenarios, and make predictions. However, many students in biology are not comfortable using or applying mathematics and have little experience with mathematics beyond solving an equation for the correct answer. Students who fail to make connections between mathematical equations and the represented biology struggle to solve problems that are not the same as covered in the classroom, therefore, as instructors, we need to help students make connections between the mathematics and biology. My research and that of others suggests that there are three aspects of instruction that are important: 1) the activity students are asked to do, 2) working in groups on challenging tasks, and 3) how instructors talk to students as they work in those groups.
My research group analyzes discussions within groups of two or three students who work with mathematical equations representing biological phenomena during one of five activities: 1) developing a mathematical equation, 2) modifying a mathematical equation, 3) comparing two mathematical equations, 4) describing relationships between variables in the mathematical equation, and 5) solving mathematical equations to find a numerical answer. During these activities, students discuss biological as well as mathematical ideas suggesting that working with mathematical equations in biology can help students learn the science. Conversely, students who engage in solving mathematical equations to find a numerical answer tend to focus on how to perform the steps of the equations and the names for the variables. They also make few connections between the biology and mathematics or between different biological ideas and spend longer on the activity.
Students who engage in the other tasks spend more time discussing biological patterns and mechanisms, as well as how the equation is structured to represent those patterns and mechanisms. This additional time spent discussing connections, mechanisms and patterns helps explain findings showing that students who engage in these tasks improve their understanding of the science and their ability to solve mathematical problems, especially those that require application to a new context. While there is a place for teaching and having students practice solving problems to get a numerical answer, the evidence suggests that this should not be the primary activity. Students gain more from other types of instructional activities that treat mathematical equations as representations (or models) of biological phenomena. Moreover, students enjoy this new way of experiencing mathematics and recognize its value. As one student commented: “One strategy that has worked well for me was surprisingly the mathematical models; I typically don't enjoy math that much…. This really helped to understand the concepts behind the model.”
A key component of these activities is having students work in groups on a challenging task to help them gain a deeper understanding of the topic through discussion and team learning. During an analysis on group discussions, our team noted that students would contribute different ideas and then synthesize them later in the process, building connections between their mathematical ideas and science ideas. Students recognize the benefits of working in groups to do these types of challenging activities: “As a group we were working really hard to build this model and through that process we got a better understanding of our individual styles and strengths. It was a really great opportunity for us to synthesize our team.”
How instructors talk to students is also an important component in helping students draw on their resources and make connections while working on tasks involving mathematical equations in biology. In particular, our research analysis found that the types of questions teachers ask can help students connect biological and mathematical ideas. Prompting students with questions to clarify their explanations, think about different contexts relevant to the equation, as well as draw a representation of the biology represented by the equation was helpful. Telling students the answer or negatively evaluating them shut down their exploration and sensemaking. It is just as important for the instructor to know when to walk away. In our studies, much of the productive work occurred after the instructor asked a thought-provoking question and/or offered encouragement and then walked away to allow the group to continue the discussion.
In summary, activities and instructor questions that help students make sense of how mathematical equations represent biological phenomena can foster students’ understanding of biology and their ability to apply these equations to new contexts and solve difficult problems. Such an approach can also better prepare students for careers in research and medicine that are increasingly relying on mathematics to model biology. If you would like to learn more, these articles are a good starting point:
Zhao, F. (Lead Author), Chau, L., & Schuchardt, A. (Corresponding Author) (2021). Blended and more: Instructors organize sensemaking opportunities for mathematical equations in different ways when teaching the same scientific phenomenon. International Journal of STEM Education, 8, 26. doi: https://doi.org/10.1186/s40594-021-00280-5
Zhao, F. (Lead Author), & Schuchardt, A. (Corresponding Author) (2021). Development of the Sci-Math Sensemaking Framework: Categorizing Sensemaking of Mathematical Equations in Science. International Journal of STEM Education, 8(1), 1-18. doi: https://doi.org/10.1186/s40594-020-00264-x
Schuchardt, A. M., & Schunn, C. D. (2016). Modeling Scientific Processes With Mathematics Equations Enhances Student Qualitative Conceptual Understanding and Quantitative Problem Solving. Science Education, 100(2), 290-320. doi: 10.1002/sce.21198
About Dr. Schuchardt
Anita Schuchardt is an associate professor in the Department of Biology Teaching and Learning.
About BTL Insights
Throughout the department’s 10th anniversary year, BTL faculty and staff will share their findings and offer best practices on a range of topics related to biology teaching and learning.