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In this paper, we present an overview of a series of 1-credit applied problem solving courses. The goal of these courses was to help students develop their oral and written communication skills, ability to work as a team, and general problem solving skills through preparation and participation in the Mathematical Contest in Modeling (MCM) and Interdisciplinary Contest in Modeling (ICM). In the first part of the course series, teams of students worked on past contest problems to simulate the contest experience over a 15-week semester. We provided feedback and guidance at each step of the modeling process, but students were ultimately responsible for all modeling choices. Students were required to write a 20-page report detailing their solutions (as in the contest) and to present their work orally. In the follow-on course, students participated in the MCM/ICM and shared their work in an oral presentation at a local conference or on campus. Here, we provide course details and share student feedback, positive outcomes (including a winning team!), and plans for future iterations of the course. We suggest that this type of experience provides an opportunity for students to engage with open-ended problems similar to those they may face in their careers.

Transforming an observable phenomenon into a tractable model is a challenging process, from determining the appropriate modeling scale to making realistic simplifying assumptions. However, many modeling texts are anchored around problems that have already been synthesized into a digestible format, which inhibits an opportunity to engage students in the decision-making process that leads to a model's design. In this paper, I discuss course elements that provide opportunities for students to participate in the early stages of a model's construction. These include open-ended projects and deconstructed textbook problems, which I explore within the context of an applied mathematical modeling seminar that emphasizes models from the life sciences.

In this paper, we discuss mathematical modeling opportunities that can be included in an introductory Differential Equations course. In particular, we focus on the development of and extensions to the single salty tank model. Typically, salty tank models are included in course materials with matter-of-fact explanations. These explanations miss the opportunity for students to develop rate of change equations for themselves. In this paper, we highlight an open-ended single salty tank task that provides the foundation for more complicated salty tank models that we also detail herein. Furthermore, we discuss instructional implementation techniques that instructors can use in their classes to meet their specific learning goals.

In this paper, we present an overview of a series of 1-credit applied problem solving courses. The goal of these courses was to help students develop their oral and written communication skills, ability to work as a team, and general problem solving skills through preparation and participation in the Mathematical Contest in Modeling (MCM) and Interdisciplinary Contest in Modeling (ICM). In the first part of the course series, teams of students worked on past contest problems to simulate the contest experience over a 15-week semester. We provided feedback and guidance at each step of the modeling process, but students were ultimately responsible for all modeling choices. Students were required to write a 20-page report detailing their solutions (as in the contest) and to present their work orally. In the follow-on course, students participated in the MCM/ICM and shared their work in an oral presentation at a local conference or on campus. Here, we provide course details and share student feedback, positive outcomes (including a winning team!), and plans for future iterations of the course. We suggest that this type of experience provides an opportunity for students to engage with open-ended problems similar to those they may face in their careers. [ABSTRACT FROM AUTHOR]

In this paper, we discuss mathematical modeling opportunities that can be included in an introductory Differential Equations course. In particular, we focus on the development of and extensions to the single salty tank model. Typically, salty tank models are included in course materials with matter-of-fact explanations. These explanations miss the opportunity for students to develop rate of change equations for themselves. In this paper, we highlight an open-ended single salty tank task that provides the foundation for more complicated salty tank models that we also detail herein. Furthermore, we discuss instructional implementation techniques that instructors can use in their classes to meet their specific learning goals. [ABSTRACT FROM AUTHOR]

Transforming an observable phenomenon into a tractable model is a challenging process, from determining the appropriate modeling scale to making realistic simplifying assumptions. However, many modeling texts are anchored around problems that have already been synthesized into a digestible format, which inhibits an opportunity to engage students in the decision-making process that leads to a model's design. In this paper, I discuss course elements that provide opportunities for students to participate in the early stages of a model's construction. These include open-ended projects and deconstructed textbook problems, which I explore within the context of an applied mathematical modeling seminar that emphasizes models from the life sciences. [ABSTRACT FROM AUTHOR]