Bridging Abstract Mathematics and Practical Engineering Design: A Pre-Capstone Project to Enhance Learning and Cultivate Entrepreneurship

Mehran Andalibi; Jonathan M Adams

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Conference: 2025 ASEE PSW Conference
Location: California Polytechnic University, California
Publication Date: April 10, 2025
Start Date: April 10, 2025
End Date: April 12, 2025
DOI: 10.18260/1-2--55166
Permanent URL: https://peer.asee.org/55166

Paper Authors

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Mehran Andalibi Embry Riddle Aeronautical University

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Mehran Andalibi has been with Embry Riddle
Aeronautical University, Prescott, AZ as an Associate Professor of Mechanical Engineering and director of robotics and rapid prototyping labs since 2015. He graduated from Oklahoma State University with Ph.D. in Mechanical engineering in 2010. His research interests are engineering education, artificial intelligence, and robotics.

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Jonathan M Adams United States Military Academy

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Dr. Jonathan Adams is an Assistant Professor at The United States Military Academy at Westpoint where he assists in the direction of the writing program. Dr. Adams specializes in rhetorical theories of persuasion, especially as they relate to the fields of engineering and technical communication. His work in business communication and marketing practices in engineering has been used internally by multiple U.S. Universities and he is an active participant in ASEE's push for the integration of writing and rhetoric with engineering.

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Abstract

This abstract will be intended for a full paper. It is a Work in Progress.

The project studied herein aims to develop engineering students’ ability to innovate and design within an entrepreneurial setting. Through integration into a pre-capstone engineering course, a new entrepreneurial approach to instruction tasked engineering students with a comprehensive design experience that mirrors industry practices and equips them for success in their capstone projects. To foster this innovative coursework, students were tasked with creating “physical manipulatives” (demonstrators, games, exemplars, etc.) to make abstract concepts in university-level mathematics courses more accessible and engaging for students. The integration of physical manipulatives into mathematics education has been shown to improve comprehension, retention, and application of abstract concepts. Hands-on learning tools, when effectively designed, enable students to visualize and interact with complex ideas, fostering deeper understanding and engagement. By designing these educational tools that bridge theoretical knowledge and tangible learning, students would seek to use engineering practice to enhance the learning experience and attract students to mathematics in a project that prioritized competitive innovation.

As an overview of the project, students work in teams throughout the semester, engaging in a competitive design process. Faculty members from the Mathematics Department act as clients and judges, selecting only half of the designs for potential funding, manufacturing, and commercialization. This process encourages students to adopt an entrepreneurial mindset, with opportunities to patent and sell their creations as the course progresses.

Coupling the entrepreneurial mindset with design-based learning approaches aligns with national initiatives emphasizing innovation and interdisciplinary skill-building in STEM education. This project addresses gaps in existing educational methods by combining technical design, entrepreneurship, and AI integration to produce scalable and impactful learning tools. It contributes to ongoing efforts to prepare students for real-world problem-solving while enhancing their technical and entrepreneurial competencies.

The key entrepreneurial competencies fostered in this project are as follows: 1) Cost Efficiency and Quality: Teams must create innovative yet practical designs, balancing cost minimization with quality and functionality; 2) Marketing: Students consider marketability and commercialization, fostering an entrepreneurial perspective; and 3) Business and Proposal Writing: Instruction from an expert in the field of rhetoric equips students with essential skills in persuasive proposal writing and business communication.

This project targets seven key areas relevant to higher education, ABET accreditation, and industry expectations: 1) Computer-Aided Design (CAD): Students utilize SolidWorks for advanced design and optimization techniques; 2) AI Integration: AI tools enhance creativity and efficiency throughout the design cycle, from brainstorming to final presentations and reports; 3) Entrepreneurial Mindset: Students simulate a real-world product development cycle, identifying and leveraging market opportunities; 4) Proposal Writing: Lectures on persuasive communication enable students to effectively present their ideas and value propositions; 5) Teamwork: Peer reviews and self-evaluations assess contributions and foster collaboration; 6) Oral and Written Presentations: Students are evaluated on their ability to articulate ideas confidently and produce high-quality technical reports, and 7) Creative Thinking: The project emphasizes problem-solving, risk-taking, and innovative solutions to meet existing needs.

The effectiveness of the project is evaluated through various components: 1) Oral Presentations: Students present their designs to faculty, emphasizing innovation, feasibility, and educational impact; 2) Final Written Technical Report: Teams submit detailed documentation of their design process, technical specifications, and market potential; 3) Teamwork Evaluations: Peer reviews, self-evaluations, and team contracts measure collaboration and individual contributions, and 4) Skill Assessments: A pre- and post-project survey measures progress across the seven learning outcomes using 41 multiple-choice questions on a Likert scale. AACU rubrics are employed for learning outcomes related to teamwork, creative thinking, and communication. A paired t-test will assess whether significant skill improvement occurs through participation in the project.

To evaluate the long-term impact of the manipulatives and as a future work, Mathematics Department faculty will deploy the selected tools in their courses starting in Spring 2025. The goal will be to investigate the effects of these innovative learning aids on students' understanding and mastery of abstract mathematical concepts. This deployment will provide additional data on the effectiveness of the tools and guide future refinements.

This Work-In-Progress (WIP) project explores how integrating industry-inspired design processes into coursework enhances student learning, entrepreneurial readiness, communication, and engagement with abstract mathematical concepts. It provides a blueprint for fostering collaboration, innovation, and technical skills in future engineers.

Citation
Format

Andalibi, M., & Adams, J. M. (2025, April), Bridging Abstract Mathematics and Practical Engineering Design: A Pre-Capstone Project to Enhance Learning and Cultivate Entrepreneurship Paper presented at 2025 ASEE PSW Conference, California Polytechnic University, California. 10.18260/1-2--55166

TY  - CPAPER
AB  - This abstract will be intended for a full paper. It is a Work in Progress. 

The project studied herein aims to develop engineering students’ ability to innovate and design within an entrepreneurial setting. Through integration into a pre-capstone engineering course, a new entrepreneurial approach to instruction tasked engineering students with a comprehensive design experience that mirrors industry practices and equips them for success in their capstone projects. To foster this innovative coursework, students were tasked with creating “physical manipulatives” (demonstrators, games, exemplars, etc.) to make abstract concepts in university-level mathematics courses more accessible and engaging for students. The integration of physical manipulatives into mathematics education has been shown to improve comprehension, retention, and application of abstract concepts. Hands-on learning tools, when effectively designed, enable students to visualize and interact with complex ideas, fostering deeper understanding and engagement. By designing these educational tools that bridge theoretical knowledge and tangible learning, students would seek to use engineering practice to enhance the learning experience and attract students to mathematics in a project that prioritized competitive innovation. 

As an overview of the project, students work in teams throughout the semester, engaging in a competitive design process. Faculty members from the Mathematics Department act as clients and judges, selecting only half of the designs for potential funding, manufacturing, and commercialization. This process encourages students to adopt an entrepreneurial mindset, with opportunities to patent and sell their creations as the course progresses. 

Coupling the entrepreneurial mindset with design-based learning approaches aligns with national initiatives emphasizing innovation and interdisciplinary skill-building in STEM education. This project addresses gaps in existing educational methods by combining technical design, entrepreneurship, and AI integration to produce scalable and impactful learning tools. It contributes to ongoing efforts to prepare students for real-world problem-solving while enhancing their technical and entrepreneurial competencies. 

The key entrepreneurial competencies fostered in this project are as follows: 1) Cost Efficiency and Quality: Teams must create innovative yet practical designs, balancing cost minimization with quality and functionality; 2) Marketing: Students consider marketability and commercialization, fostering an entrepreneurial perspective; and 3) Business and Proposal Writing: Instruction from an expert in the field of rhetoric equips students with essential skills in persuasive proposal writing and business communication. 

This project targets seven key areas relevant to higher education, ABET accreditation, and industry expectations: 1) Computer-Aided Design (CAD): Students utilize SolidWorks for advanced design and optimization techniques; 2) AI Integration: AI tools enhance creativity and efficiency throughout the design cycle, from brainstorming to final presentations and reports; 3) Entrepreneurial Mindset: Students simulate a real-world product development cycle, identifying and leveraging market opportunities; 4) Proposal Writing: Lectures on persuasive communication enable students to effectively present their ideas and value propositions; 5) Teamwork: Peer reviews and self-evaluations assess contributions and foster collaboration; 6) Oral and Written Presentations: Students are evaluated on their ability to articulate ideas confidently and produce high-quality technical reports, and 7) Creative Thinking: The project emphasizes problem-solving, risk-taking, and innovative solutions to meet existing needs. 

The effectiveness of the project is evaluated through various components: 1) Oral Presentations: Students present their designs to faculty, emphasizing innovation, feasibility, and educational impact; 2) Final Written Technical Report: Teams submit detailed documentation of their design process, technical specifications, and market potential; 3) Teamwork Evaluations: Peer reviews, self-evaluations, and team contracts measure collaboration and individual contributions, and 4) Skill Assessments: A pre- and post-project survey measures progress across the seven learning outcomes using 41 multiple-choice questions on a Likert scale. AACU rubrics are employed for learning outcomes related to teamwork, creative thinking, and communication. A paired t-test will assess whether significant skill improvement occurs through participation in the project. 

To evaluate the long-term impact of the manipulatives and as a future work, Mathematics Department faculty will deploy the selected tools in their courses starting in Spring 2025. The goal will be to investigate the effects of these innovative learning aids on students&#39; understanding and mastery of abstract mathematical concepts. This deployment will provide additional data on the effectiveness of the tools and guide future refinements. 

This Work-In-Progress (WIP) project explores how integrating industry-inspired design processes into coursework enhances student learning, entrepreneurial readiness, communication, and engagement with abstract mathematical concepts. It provides a blueprint for fostering collaboration, innovation, and technical skills in future engineers. 
AU  - Mehran Andalibi
AU  - Jonathan M Adams
CY  - California Polytechnic University, California
DA  - 2025/04/10
PB  - ASEE Conferences
TI  - Bridging Abstract Mathematics and Practical Engineering Design: A Pre-Capstone Project to Enhance Learning and Cultivate Entrepreneurship
UR  - https://peer.asee.org/55166
DO  - 10.18260/1-2--55166
ER  -