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1. Work in Progress: Implementing Elements of Engineering Design into Calculus

   Dr. Salvador Mayoral California State University, Fullerton (July 2021, Zone 1 Conference of the American Society for Engineering Education)

   null (Ed.)

   In order to contextualize calculus, first-year engineering students take on a semester-long design project that grounds engineering design as an epistemic practice. The project is designed to motivate students to creatively and collaboratively apply mathematical modeling to design roller coasters. Students are asked to engage as engineers and respond to a hypothetical theme park that has solicited design proposals for a new roller coaster. Students are required to use various mathematical functions such as polynomials and exponentials to create a piece-wise function that models the roller coaster track geometry. The entire project is composed of five modules, each lasting three weeks. Each module is associated with a specific calculus topic and is integrated into the design process in a form of a design constraint or performance metric. The module topics include continuity, smoothness, local maxima and minima, inflection points, and area under the curve. Students are expected to refine their models in each module, resulting in the iteration of the previous design to satisfy a new set of requirements. This paper presents the project organization, assessment methods, and student feedback. This work is part of a multi-year course intervention and professional development NSF project to increase the success of underrepresented and women students in engineering. 

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2. Work in Progress: Implementing Elements of Engineering Design into Calculus

   Mayoral, S.; Linton, A.; Yousefi, H.; Huang, J. (July 2021, Zone 1 Conference of the American Society for Engineering Education)

   null (Ed.)

   n order to contextualize calculus, first-year engineering students take on a semester-long design project that grounds engineering design as an epistemic practice. The project is designed to motivate students to creatively and collaboratively apply mathematical modeling to design roller coasters. Students are asked to engage as engineers and respond to a hypothetical theme park that has solicited design proposals for a new roller coaster. Students are required to use various mathematical functions such as polynomials and exponentials to create a piece-wise function that models the roller coaster track geometry. The entire project is composed of five modules, each lasting three weeks. Each module is associated with a specific calculus topic and is integrated into the design process in a form of a design constraint or performance metric. The module topics include continuity, smoothness, local maxima and minima, inflection points, and area under the curve. Students are expected to refine their models in each module, resulting in the iteration of the previous design to satisfy a new set of requirements. This paper presents the project organization, assessment methods, and student feedback. This work is part of a multi-year course intervention and professional development NSF project to increase the success of underrepresented and women students in engineering. 

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3. Statewide Coalition: Supporting Underrepresented Populations in Precalculus through Organizational Redesign Toward Engineering Diversity (SC:SUPPORTED) Results from Year One

   Gallagher, E.; Brown, C.J.; Brown, D.A.; Frady, K.; Marcanikova, M.; Atamturktur, S.; Ihekweazu, S.; Matthews, M.; Rabb, R.; Roberts, R.; et al (June 2018, ASEE annual conference & exposition proceedings)

   National data indicate that initial mathematics course placement in college is a strong predictor of persistence to degree in engineering, with students placed in calculus persisting at nearly twice the rate of those placed below calculus. Within the state of South Carolina, approximately 95% of engineering-intending students who initially place below calculus are from in-state. The “Statewide Coalition: Supporting Underrepresented Populations in Precalculus through Organizational Redesign Toward Engineering Diversity (SC:SUPPORTED),” a Design and Development Launch Pilot funded under the National Science Foundation INCLUDES program, is a coalition of secondary districts and post-secondary institutions throughout South Carolina, joining together to address the systemic issue of mathematical preparation for engineering-intending students. First year results include an analysis of system-wide data to identify prevalent educational pathways within the state, and the mathematical milestones along those pathways taken by engineering-intending students. Using individual data for all 21,656 first-year students in engineering-related fields enrolled in a public post-secondary institution in the state, we identified specific pathways with high rates of placement in or above calculus, pathways with balanced rates of placement in/below calculus, pathways with high rates of placement below calculus, and ‘missing’ pathways, defined as those which produce disproportionately few engineering-intending students [5]. For example, rates of placement in or above calculus among engineering majors ranged from below 17% in eight counties of origin to nearly 100% in four counties of origin. First-year results also included analysis of qualitative data from focus groups conducted at key points along each pathway category to identify factors that do not readily appear in institutional data (e.g., impact of guidance counselor recommendations in selection of last high school math course taken). Broad themes emerging from the focus groups provided additional insight into potential interventions at multiple points along educational pathways. Focus group data are contributing to the development of a survey to be administered in Year 2 to all post-secondary engineering majors statewide, with the goal of creating structural equation models of the factors leading to placement at or below the calculus level upon entry into an engineering major. These models will then allow us to design targeted interventions at points of maximal potential impact. 

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4. A MATLAB App to Introduce Chemical Engineering Design Concepts to Engineering Freshmen through a Pharmaceutical Dosing Case Study

   C. V. Eastep, G. K. (April 2019, Chemical engineering education)

   Hands-on design experiences to introduce first year students to chemical engineering are limited.[1] The College of Engineering, Architecture and Technology (CEAT) Summer Bridge Program at Oklahoma State University is a three-week camp designed to acclimate first year students to college life while providing calculus and physics preparatory short courses and design experiences from multiple disciplines in CEAT.[2] Since first-year students enjoy and value hands-on experiences,[2] we have developed a hands-on design module on the topic of pharmaceutical dosing for the chemical engineering portion of the Summer Bridge Program. We have taught the design module in nine sessions that were each two hours per day over three days during the 2015 – 2018 offerings of the Summer Bridge Program. The detailed lesson plan for using the design module to introduce mass balance and design concepts and an overview of the initial version of the MATLAB app were discussed in our previous ASEE conference proceedings paper.[2] In the present work, we discuss a redesigned MATLAB app (Figure 1) that has been expanded from two drugs and four cases to five drugs and eight cases. The new version of the MATLAB app is available as SB17CHE.mlappinstall on our GitHub repository.[3] Any future updates to the software will be released to the same archive. Additionally, we include a new section focused on our experiences in teaching chemical engineering design concepts using the MATLAB app and in responding to typical student questions. Our aim is to provide a tutorial for other educators interested in using the MATLAB app in their classroom or outreach activities related to chemical engineering design. For those interested in creating similar computational instructional tools, we have published details regarding the software implementation of the app and its documentation.[4] 

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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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