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1. Change in student understanding of modeling during first-year engineering courses

   https://doi.org/10.18260/1-2--34269  

   Marbouti, Farshid; Rodgers, Kelsey J.; Verleger, Matthew A. (June 2020, ASEE Annual Conference proceedings)

   All engineers must be able to apply and create models to be effective problem solvers, critical thinkers, and innovative designers. To be more successful in their studies and careers, students need a foundational knowledge about models. An adaptable approach can help students develop their modeling skills across a variety of modeling types, including physical models, mathematical models, logical models, and computational models. Physical models (e.g., prototypes) are the most common type of models that engineering students identify and discuss during the design process. There is a need to explicitly focus on varying types of models, model application, and model development in the engineering curriculum, especially on mathematical and computational models. This NSF project proposes two approaches to creating a holistic modeling environment for learning at two universities. These universities require different levels of revision to the existing first-year engineering courses or programs. The proposed approaches change to a unified language and discussion around modeling with the intent of contextualizing modeling as a fundamental tool within engineering. To evaluate student learning on modeling in engineering, we conducted pre and post surveys across three different first-year engineering courses at these two universities with different student demographics. The comparison between the pre and post surveys highlighted student learning on engineering modeling based on different teaching and curriculum change approaches. 

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2. Impact of a Modeling Intervention in an Introductory Programming Course

   Rodgers, Kelsey J.; McNeil, Jaqi C.; Verleger, Matthew A.; Marbouti, Farshid (June 2019, American Society for Engineering Education (ASEE) 126th Annual Conference and Exposition)

   This complete research paper describes the impact of a modeling intervention on first-year engineering students’ modeling skills in an introductory computer programming course. Five sections of the first-year engineering introductory programming course at a private, STEM+Business institution were revised to center around modeling concepts. These five sections made up the experimental group for this study. The comparison group consisted of four sections of the course that were not revised. Students in all these sections were given two different versions of a modeling problem two times in the semester to test their progress in gaining modeling skills. Each version required two submissions – a written solution and a coded solution. The assessment of these four submissions based on the three established dimensions of modeling were quantitatively analyzed in this study. The three dimensions within mathematical modeling that were the focus of this study were mathematical model complexity, modifiability, and reusability. Mathematical model complexity is being able to address the complexity of the problem. Modifiability addresses the generalizability of the model solution. Reusability is showing an understanding of the problem and the user. Statistical analysis showed that students in the experimental group had more gains in their demonstrated modeling abilities across all three dimensions than the students in the comparison group. This study demonstrated that intentional and explicit instructional strategies targeting model development resulted in greater gains in students’ demonstrated modeling skills and both their written and coded solutions to a complex modeling problem. 

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3. Comparing Students’ Solutions to an Open-ended Problem in an Introductory Programming Course with and without Explicit Modeling Interventions

   Rodgers, K; Verleger, M; Marbouti, F (January 2020, ASEE Annual Conference proceedings)

   Engineers must understand how to build, apply, and adapt various types of models in order to be successful. Throughout undergraduate engineering education, modeling is fundamental for many core concepts, though it is rarely explicitly taught. There are many benefits to explicitly teaching modeling, particularly in the first years of an engineering program. The research questions that drove this study are: (1) How do students’ solutions to a complex, open-ended problem (both written and coded solutions) develop over the course of multiple submissions? and (2) How do these developments compare across groups of students that did and did not participate in a course centered around modeling?. Students’ solutions to an open-ended problem across multiple sections of an introductory programming course were explored. These sections were all divided across two groups: (1) experimental group - these sections discussed and utilized mathematical and computational models explicitly throughout the course, and (2) comparison group - these sections focused on developing algorithms and writing code with a more traditional approach. All sections required students to complete a common open-ended problem that consisted of two versions of the problem (the first version with smaller data set and the other a larger data set). Each version had two submissions – (1) a mathematical model or algorithm (i.e. students’ written solution potentially with tables and figures) and (2) a computational model or program (i.e. students’ MATLAB code). The students’ solutions were graded by student graders after completing two required training sessions that consisted of assessing multiple sample student solutions using the rubrics to ensure consistency across grading. The resulting assessments of students’ works based on the rubrics were analyzed to identify patterns students’ submissions and comparisons across sections. The results identified differences existing in the mathematical and computational model development between students from the experimental and comparison groups. The students in the experimental group were able to better address the complexity of the problem. Most groups demonstrated similar levels and types of change across the submissions for the other dimensions related to the purpose of model components, addressing the users’ anticipated needs, and communicating their solutions. These findings help inform other researchers and instructors how to help students develop mathematical and computational modeling skills, especially in a programming course. This work is part of a larger NSF study about the impact of varying levels of modeling interventions related to different types of models on students’ awareness of different types of models and their applications, as well as their ability to apply and develop different types of models. 

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4. Comparing students’ solutions to an open-ended problem in an introductory programming course with and without explicit modeling interventions

   https://doi.org/10.18260/1-2--34311  

   Rodgers, Kelsey J.; Verleger, Matthew A.; Marbouti, Farshid (June 2020, ASEE Annual Conference proceedings)

   Engineers must understand how to build, apply, and adapt various types of models in order to be successful. Throughout undergraduate engineering education, modeling is fundamental for many core concepts, though it is rarely explicitly taught. There are many benefits to explicitly teaching modeling, particularly in the first years of an engineering program. The research questions that drove this study are: (1) How do students’ solutions to a complex, open-ended problem (both written and coded solutions) develop over the course of multiple submissions? and (2) How do these developments compare across groups of students that did and did not participate in a course centered around modeling?. Students’ solutions to an open-ended problem across multiple sections of an introductory programming course were explored. These sections were all divided across two groups: (1) experimental group - these sections discussed and utilized mathematical and computational models explicitly throughout the course, and (2) comparison group - these sections focused on developing algorithms and writing code with a more traditional approach. All sections required students to complete a common open-ended problem that consisted of two versions of the problem (the first version with smaller data set and the other a larger data set). Each version had two submissions – (1) a mathematical model or algorithm (i.e. students’ written solution potentially with tables and figures) and (2) a computational model or program (i.e. students’ MATLAB code). The students’ solutions were graded by student graders after completing two required training sessions that consisted of assessing multiple sample student solutions using the rubrics to ensure consistency across grading. The resulting assessments of students’ works based on the rubrics were analyzed to identify patterns students’ submissions and comparisons across sections. The results identified differences existing in the mathematical and computational model development between students from the experimental and comparison groups. The students in the experimental group were able to better address the complexity of the problem. Most groups demonstrated similar levels and types of change across the submissions for the other dimensions related to the purpose of model components, addressing the users’ anticipated needs, and communicating their solutions. These findings help inform other researchers and instructors how to help students develop mathematical and computational modeling skills, especially in a programming course. This work is part of a larger NSF study about the impact of varying levels of modeling interventions related to different types of models on students’ awareness of different types of models and their applications, as well as their ability to apply and develop different types of models. 

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5. Engineering Students’ Perceptions of Mathematical Modeling in a Learning Module Centered on a Hydrologic Design Case Study

   https://doi.org/10.1007/s40753-020-00131-8  

   Merck, Madeline F.; Gallagher, Melissa A.; Habib, Emad; Tarboton, David (July 2021, International Journal of Research in Undergraduate Mathematics Education)

   null (Ed.)

   Abstract Engineering students need to spend time engaging in mathematical modeling tasks to reinforce their learning of mathematics through its application to authentic problems and real world design situations. Technological tools and resources can support this kind of learning engagement. We produced an online module that develops students’ mathematical modeling skills while developing knowledge of the fundamentals of rainfall-runoff processes and engineering design. This study examined how 251 students at two United States universities perceived mathematical modeling as implemented through the online module over a 5-year period. We found, subject to the limitation that these are perceptions from not all students, that: (a) the module allowed students to be a part of the modeling process; (b) using technology, such as modeling software and online databases, in the module helped students to understand what they were doing in mathematical modeling; (c) using the technology in the module helped students to develop their skill set; and (d) difficulties with the technology and/or the modeling decisions they had to make in the module activities were in some cases barriers that interfered with students’ ability to learn. We advocate for instructors to create modules that: (a) are situated within a real-world context, requiring students to model mathematically to solve an authentic problem; (b) take advantage of digital tools used by engineers to support students’ development of the mathematical and engineering skills needed in the workforce; and (c) use student feedback to guide module revisions. 

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