Decades of effort on quantitative education for undergraduate life scientists have led to hosts of instructional methods to integrate quantitative conceptual and skill development with biological concepts. Now available are a diverse set of textbooks, modules and on-line materials with a biological bent to assist instruction on mathematical topics common to undergraduate curricula, from algebraic ideas covered in high schools to introductory calculus, differential equations, probability and computation. The plethora of biostatistics instructional materials are supplemented by growing biological data science offerings,
with connection to data sets at organismal and ecological levels that are readily understood, in that students can comprehend how the data were collected, and perhaps collect similar data themselves. The growth of data science courses offers the potential to provide a more integrative quantitative perspective, while enhancing comprehension of ecological concepts and methods, yet the vast majority of undergraduate biology curricula include courses that offer little of an integrative view (e.g. separate pre-calculus, calculus and basic statistics courses) and are typically completely divorced from the basic biology courses
required of undergraduates. Key to the 4DEE challenge is how to modify this separation of quantitative methods while broadening and attracting students to ecological fields.
Results/Conclusions
Motivation for this arises from discarding the "pipeline" metaphor and enhancing the "watershed" perspective that encourages and allows for diverse students with different backgrounds to be drawn into ecological fields. An objective is to provide feasible pathways to science-connected degrees that includes those who may have been very successful in their K-12 quantitative education, and those for whom this was a challenge. As a modification of the traditional approach to undergraduate life science quantitative training, in which calculus has primacy, a movement towards the "rule of five" focuses initially on biological data and descriptive statistics, discrete mathematical topics, computational methods, and then moves on to continuous mathematics. This expands on lessons from mathematics education that accounts for alternative perspectives (verbal, numerical, symbolic and graphical) to incorporate field and lab data that connects students directly to biological questions. The argument is that this approach is beneficial for all students across the spectrum of physical, natural and social science. The impact of incorporating biological examples in a data-centric manner along with core continuous mathematical concepts has been assessed through an instrument focused on comparisons of alternative instructional modes, partitioning conceptual difficulties across the graphical, modeling and calculus concepts.