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1. 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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2. A Classroom Observation Tool for Equity-Oriented Teaching of Mathematical Modeling in the Elementary Grades

   Turner, E. E. (January 2022, North American Chapter for the Psychology of Mathematics Education)

   A. Lischka, E. Dyer (Ed.)

   Mathematical modeling can be a lever for equity in the elementary math classroom, as it empowers teachers to build on the knowledge and cultural resources that children bring to the classroom and empowers students to draw on their experiences and identities to inform their mathematical work. To better support this transformative synergy between mathematical modeling and equity-oriented practices, we need a tool to deepen our understanding of variations and potential trajectories of teacher practice. In this report, we briefly describe our process for developing an equity-oriented mathematical modeling classroom observation protocol. We then discuss two sample dimensions from our tool to illustrate our integrated attention to equity-focused and mathematical modeling-specific teaching practices. 

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3. Physical Physics – Getting students Active in Learning Materials Science

   https://doi.org/10.1557/adv.2017.61  

   Kavanagh, Yvonne; O’Hara, Noel; Palmer, Ross; Lowe, Peter; Raftery, Damien (January 2017, MRS Advances)

   ABSTRACT Physics forms the core of any Materials Science Programme at undergraduate level. Knowing the properties of materials is fundamental to developing and designing new materials and new applications for known materials. “Physical Physics” is a physics education approach which is an innovative and promising instruction model that integrates physical activity with mechanics and material properties. It aims to significantly enhance the learning experience and to illustrate how physics works, while allowing students to be active participants and take ownership of the learning process. It has been successfully piloted with undergraduate students studying mechanics on a Games Development Programme. It is a structured guided learning approach which provides a scaffold for learners to develop their problem solving skills. The objective of having applied physics on a programme is to introduce students to the mathematical world. Today students view the world through smart devices. By incorporating student recorded videos into the laboratory experience the student can visualise the mathematical world. Sitting in a classroom learning about material properties does not easily facilitate an understanding of mathematical equations as mapping to a physical reality. In order to get the students motivated and immersed in the real mathematical and physical world, an approach which makes them think about the cause and effect of actions is used. Incorporating physical action with physics enables students to assimilate knowledge and adopt an action problem solving approach to the physics concept. This is an integrated approach that requires synthesis of information from various sources in order to accomplish the task. As a transferable skill, this will ensure that the material scientists will be visionary in their approach to real life problems. 

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4. 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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5. 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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