Joint Mathematics Meetings 2020 MAA Contributed Paper Session
Modeling-First Inquiry-Based Course Activities
We offer up the material from the Contributed Paper session. The actual files are found in Sopporting Docs.
Wednesday January 15, 2020, 8:00 a.m.-10:55 a.m.
MAA Contributed Paper Session on Modeling-First Inquiry-Based Course Activities, I
Room 502, Meeting Room Level, Colorado Convention Center
Ben Galluzzo, Clarkson University
Brian Winkel, SIMIODE
Corban Harwood, George Fox University
(1A) 8:00 a.m.
Using Modeling in Introductory Differential Equations to Motivate Relevance, Positive Attitudes Toward Mathematics and the Transfer of Knowledge to Other Courses.
Bonnie S Moon*, Brigham Young University-Idaho
Paul Cox, Brigham Young University-Idaho
Abstract: We have redesigned our introduction to ordinary differential equations course using modeling scenarios to provide context for the content. We have incorporated a Modeling, then Visualizing and finally Solving pattern in all elements of the course. The course has been divided into smaller modules which begin with students studying a modeling scenario. They work on modeling the scenario both individually and in groups. After the groups determine a model, they then apply visualizing and solving techniques in the context of the scenario. We are studying the impact this redesign has on student attitudes toward mathematics and on their ability to transfer understanding to courses in other disciplines.
(1B) 8:20 a.m.
What does the X-Mean? Thinking about statistics, not just hearing about statistics: Getting students to engage in the process of learning and doing statistics.
John Z. Hossler*, Seattle Pacific University
Abstract: Drawing students into the material is important! Simply telling students about a model or statistical fact is not the best way to foster a long-term learning environment. Instead, students should be actively engaged in creating models and thinking through the underlying concepts. A focus on the big picture and reasoning behind the formulas helps develop statistical intuition. This talk will discuss examples of how I get my undergraduate introductory statistics students involved in the process of thinking about concepts and developing statistical tools, rather than simply hearing me talk about them.
(1C) 8:40 a.m.
Two Inquiry Based Learning Modeling Activities: The Warming of Cold Water in a Bottle and Using Phase Models to Describing Oscillating Populations.
Eli E Goldwyn*, University of Portland
Abstract: We start by introducing a modeling scenario that should be appropriate for the first week of an introductory undergraduate differential equations course. This scenario steps through the creation and understanding of a differential equation by describing how fluid in a water bottle will change temperature and what factors influence the rate of temperature change. The second modeling scenario walks the student through the process of modeling and analyzing equilibria behavior of an oscillatory system through the use of phase variables with a focus on predator-prey oscillators.
(1D) 9:00 a.m.
SIR and Beyond: An Inquiry Based Approach to Modeling the Spread of Disease in an Introductory Differential Equations Course.
Jennifer L. Garbett*, Lenoir-Rhyne University
Abstract: In this talk, we will discuss an inquiry based modeling activity I have used in my introductory Differential Equations course. First, with some guidance, students develop an SIR (susceptible, infected, recovered) model to model the potential spread of the measles virus at Lenoir-Rhyne University. Students are then asked to consider assumptions they have made and to come up with possible modifications to their basic SIR model which could be used to improve the model. Finally, the activity culminates with a project where each student is asked to choose and implement an appropriate addition or modification to the basic model from class in order to model the spread of a disease of the student’s choice among a population of the student’s choice and to analyze the predictions made by their model as well as its limitations. Students present their work to the class. I will also address where this activity fits in my course and the response from students to this and other inquiry based modeling activities I have used, and I will share lessons I have learned.
(1E) 9:20 a.m.
Dynamic Groundwater Flow Modeling Investigations with Excel.
Michael A. Karls*, Ball State University
Abstract: We provide an example of a groundwater flow model that can be investigated dynamically with Excel. This illustrates a means to study differential equations in a fashion similar to using commands such as Mathematica’s Manipulate to vary parameters in a model.
(1F) 9:40 a.m.
Stability of random Perturbed Logistic Model.
Reza R Ahangar*, Texas A& M University - Kingsville, Texas 78363
Abstract: We are going to study a model that represents the rate of changes of the population with a limited environmental resources described by, p’(t)=p(a-b*p)+g(t,p) where a measures the growth rate in the absence of the restriction force and a/b represents the carrying capacity of the environment and b represent restricted factor b. The random perturbation g(t,p) is generated by random changes in the environment. The behavior of the solution of this model for continuous and discrete case when g(t,p)=r*p with a random change factor r will be studied. The stability and the behavior of the equilibrium point will also be investigated. A computational approach to simulate the solution of this random differential equation and also a regression method will be developed.
(1G) 10:00 a.m.
Teaching Differential Equations with Modeling First.
Arati Nanda Pati*, University of St. Thomas
Abstract: Teaching methodology is evolving with modern time. Gone are those days when students were learning procedural differential equations from the analytical prospective. There is a great need to update the pedagogies to introduce modeling first to appreciate the differential equations techniques. Inspired by MINDE workshop, I introduced the modeling first approach in my classroom teaching to welcome inquiry oriented learning. Data collection, data visualization, and parameter estimation using technology has gained better understanding of math modeling using differential equations not only for Math major but also all STEM students who take differential equations as a core course. In this talk, I will present my effort to incorporate SIMIODE modeling scenarios in my differential equations and mathematical modeling classes
(1H) 10:20 a.m.
Comparing Symmetrical, Asymmetrical, and Parallel Modeling Projects.
Corban Harwood*, George Fox University
Abstract: In this talk, we compare the implementation, group dynamics, and student learning benefits for symmetrical, asymmetrical, and parallel modeling projects. For symmetrical projects, each group investigates the same problem but arrives at independent conclusions, whereas with parallel projects each group investigates a different problem. We define asymmetrical projects as having each group investigate a different problem in a common theme where each perspective is needed to finish the project. These comparisons will be fleshed out with example projects from courses in liberal arts mathematics, differential equations, numerical analysis, linear algebra, and partial differential equations. We will share best practices on implementation in the curriculum, supporting group dynamics, and benefiting student learning which come through pedagogical experiences, assessments, and student evaluations from these courses.
(1I) 10:40 a.m.
Empirical Models for Tropical Storm Windspeeds After Landfall--A Modeling Activity using Separable Equations.
Terrance L Pendleton*, Drake University
Abstract: We model the decay of tropical cyclone winds once a storm makes landfall. We use data from two recent storms from the National Hurricane Center to estimate parameters emanating from a differential equation using a first order exponential decay model.
Wednesday January 15, 2020, 2:15 p.m.-3:10 p.m.
MAA Contributed Paper Session on Modeling-First Inquiry-Based Course Activities, II
Room 502, Meeting Room Level, Colorado Convention Center
(2A) 2:15 p.m.
Using SIMIODE Scenarios to Drive a Differential Equations Course.
Carl Lienert*, Fort Lewis College
Abstract: On the first day of my Differential Equations course in Fall 2019 I presented students with a SIMIODE scenario, i.e. an open ended “story problem.” This scenario and subsequent ones, and their solutions, determined the trajectory of the course. Rather than follow a standard textbook curriculum, we discussed and developed in class the tools needed to model and solve the problems. I’ll discuss the results:
• Did students have a better idea of the value of differential equations?
• Were they confused by the non-textbook path?
• Were standard DE curricular goals compromised?
• Could the students propose models on their own?
• Did my colleagues in Engineering notice?
(2B) 2:35 p.m.
Throwing a ball can be such a drag.
Chris McCarthy*, Borough of Manhattan Community College City University of New York
Abstract: If a tennis ball is thrown through the air it will eventually hit the ground due to gravity. It is common and fairly easy to model this if we neglect drag (air resistance). In this talk we discuss how to include drag. The resulting model is solved using Euler’s method for higher order differential equations. This talk is based on work done at the 2019 SIMIODE DEMARC summer workshop.
(2C) 2:55 p.m.
Be sure to step out of the room -- good advice for teaching modeling.
Brian J Winkel*, Director, SIMIODE, Cornwall NY USA
Abstract: When teaching modeling to students it is important to stand aside, to get out of the way so students can explore and let their minds wander, dream, and inquire. To be sure this happens it is appropriate to leave the room or at the very least stop “professing” and be quite, perhaps just to listen. It is also important to be accepting, never saying, “Yes, but . . .", and be ever ready to go on a long strange trip with student ideas as they wander, perhaps (almost certainly) far off the track YOU thought they would take. It is also important to know what to do AND what not to do when strange things happen in class and to be prepared to come out of class tired, very tired, almost exhausted at times. We give examples from our 40+ years of getting out of the way of students doing modeling in the classroom. Indeed, modeling is the ultimate inquiry-based mathematics experience if we but let it happen more often in our classrooms.
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