Undergraduate Quantitative Biology Impact on Biology Preservice Teachers

Abstract

Quantitative biology is a rapidly advancing field in the biological sciences, particularly given the rise of large datasets and computer processing capabilities that have continually expanded over the past 50 years. Thus, the question arises, How should K-12 biology teachers incorporate quantitative biology skills into their biology curriculum? The teaching of quantitative biology has not been readily integrated into undergraduate biology curricula that impact preservice teachers. This has potential to cascade effects downward into the quality of learning about quantitative biology that can be expected in K-12 contexts. In this paper, we present the perspectives of a mathematics educator, a science educator, and two biologists, and discuss how we have personally incorporated aspects of quantitative reasoning into our courses. We identify some common challenges relevant to expanding implementation of quantitative reasoning in undergraduate biology courses in order to serve the needs of preservice teachers—both in their disciplinary courses and methods courses. For example, time constraints, math pedagogical content knowledge, and personal views about the relevance of quantitative principles in biology teaching and learning can impact how and to what extent they become implemented in curricula. In addition, although national standards at the K-12 level do address quantitative reasoning, the emphasis and guidance provided are sparser than for other content standards. We predict that both K-12 standards and guidelines for undergraduate education will only increase in their emphasis on quantitative skills as computation, “big data,” and statistical modeling are increasingly becoming requisite skills for biologists.

Appendix

Quantitative reasoning learning progression framework

Achievement level	QR progress variable
	Quantification act	Quantitative interpretation	Quantitative modeling
Level 4 (Upper Anchor)	4a Variation: reasons about covariation of 2 or more variables; comparing, contrasting, relating variables in the context of problem 4b Quantitative Literacy: reasons with quantities to explain relationships between variables; proportional reasoning, numerical reasoning; extend to algebraic and higher math reasoning (MAA) 4c Context: situative view of QR within a community of practice (Shavelson); solves ill-defined problems in socio-political contexts using ad hoc methods; informal reasoning within science context (Steen and Madison; Sadler and Zeidler) 4d Variable: mental construct for object within context including both attributes and measure (Thompson); capacity to communicate quantitative account of solution, decision, course of action within context	4a Trends: determine multiple types of trends including linear, power, and exponential trends; recognize and provide quantitative explanations of trends in model representation within context of problem 4b Predictions: makes predictions using covariation and provides a quantitative account which is applied within context of problem 4c Translation: translates between models; challenges quantitative variation between models as estimates or due to measurement error; identifies best model representing a context 4d Revision: revise models theoretically without data, evaluate competing models for possible combination (Schwarz)	4a Create Model: ability to create a model representing a context and apply it within context; use variety of quantitative methods to construct model including least squares, linearization, normal distribution, logarithmic, logistic growth, multivariate, simulation models 4b Refine Model: extend model to new situation; test and refine a model for internal consistency and coherence to evaluate scientific evidence, explanations, and results; (Duschl) 4c Model Reasoning: construct and use models spontaneously to assist own thinking, predict behavior in real-world, generate new questions about phenomena (Schwarz) 4d Statistical: conduct statistical inference to test hypothesis (Duschl)
Level 3	3a Variation: recognizes correlation between two variables without assuming causation, but provides a qualitative or isolated case account; lacks covariation 3b Quantitative Literacy: manipulates quantities to discover relationships; applies measure, numeracy, proportions, descriptive statistics 3c Context: display confidence with and cultural appreciation of mathematics within context; practical computation skills within context (Steen); lacks situative view 3d Variable: object within context is conceptualized so that the object has attributes, but weak measure (Thompson); capacity to communicate qualitative account of solution, decision, course of action within context, but weak quantitative account	3a Trends: recognize difference between linear versus curvilinear growth; discuss both variables, providing a quantitative account 3b Predictions: makes predictions based on two variables, but relies on qualitative account; uses correlation but not covariation. 3c Translation: attempts to translate between models but struggles with comparison of quantitative elements; questions quantitative differences between models but provides erroneous qualitative accounts for differences 3d Revision: revise model to better fit evidence and improve explanatory power (Schwarz)	3a Create Model: create models for covariation situations that lack quantitative accounts; struggle to apply model within context or provide quantitative account 3b Refine Model: extend model based on supposition about data; do not fully verify fit to new situation 3c Model Reasoning: construct and use multiple models to explain phenomena, view models as tools supporting thinking, consider alternatives in constructing models (Schwarz) 3d Statistical: use descriptive statistics for central tendency and variation; make informal comparisons to address hypothesis
Level 2	2a Variation: sees dependence in relationship between two variables, provides only a qualitative account; lacks correlation, erroneously assumes causation 2b Quantitative Literacy: poor arithmetic ability interferes with manipulation of variables; struggle to compare or operate with variables 2c Context: lack confidence with or cultural appreciation of math within context; practical computation skills are not related to context 2d Variable: object within context is identified, but not fully conceptualized with attributes that are measurable; fails to communicate solution, decision, course of action within context; qualitative account without quantitative elements (Thompson)	2a Trends: identify and explain single case in model; recognize increasing/decreasing trends but rely on qualitative account or change in only one variable 2b Predictions: makes predictions for models based on only one variable, provides only qualitative arguments supporting prediction 2c Translation: indicate preference for one model over another but do not translate between models; acknowledge quantitative differences in models but do not compare 2d Revision: revise model based on authority rather than evidence, modify to improve clarity not explanatory power (Schwarz)	2a Create Model: constructs a table or data plot to organize two dimensional data; create visual models to represent single variable data, such as statistical displays (pie charts, histograms) 2b Refine Model: extends a given model to account for dynamic change in model parameters; provides only a qualitative account 2c Model Reasoning: construct and use model to explain phenomena, means of communication rather than support for own thinking (Schwarz) 2d Statistical: calculates descriptive statistics for central tendency and variation but does not use to make informal comparisons to address hypothesis
Level 1 (Lower Anchor)	1a Variation: does not compare variables; works with only one variable when discussing trends, 1b Quantitative Literacy: fails to manipulate and calculate with variables to answer questions of change, discover patterns, and draw conclusions; 1c Context: does not relate quantities to context or exhibit computational skills 1d Variable, fail to relate model to context by identifying objects no attempt to conceptualize attributes that are measurable; discourse is force-dynamic; avoids quantitative account, provides weak qualitative account	1a Trends: do not identify trends in models 1b Predictions: avoids making predictions from models 1c Translation: fail to acknowledge two models can represent the same context 1d Revision: view models as fixed, test to see if good or bad replicas of phenomena (Schwarz)	1a Create Model: does not view science as model building and refining so does not attempt to construct models 1b Refine Model: accepts authority of model, does not see as needing refinement 1c Model Reasoning: construct and use models that are literal illustrations, model demonstrates for others not tool to generate new knowledge (Schwarz) 1d Statistical: does not use statistics; no calculation of even descriptive statistics