Improving students' mathematical sense-making in engineering:  Research and development

Abstract

For engineers, effective use of mathematics is more than manipulating equations and applying algorithms; it involves mathematical sense-making, looking for coherence and meaning partly by translating between symbolic relations on the page and relations (causal and functional) in the world.  Mathematical sense-making is central to students’ success with modeling and design.  Yet, many engineering students have trouble with it. 

Typical engineering students first grapple extensively with mathematical descriptions of the world in the introductory physics courses they take as prerequisites for their majors.  This project, a collaboration among the University of Maryland Departments of Physics, Mechanical Engineering, and Electrical & Computer Engineering, addresses two research questions:

1. What factors contribute to students’ difficulties with mathematical sense-making?
2. Can redesigned introductory physics courses improve students’ mathematical sense-making — and overall performance — in their later engineering courses?

Previous research suggests that, to address (1), we must probe not just for mathematical skill deficiencies but also for students’ lack of understanding of the relevant physics/engineering concepts, lack of ability or propensity to translate between formalism and real-world relations, and naïve beliefs about how to learn and apply math.  We tease these factors apart and explore interactions among them using multiple methods, including analysis of video of students solving challenging problems.

To address (2), we draw on our previous work in the algebra-based introductory physics sequence for life science majors.  There, we developed materials and teaching techniques focused on changing students’ beliefs about how to learn and apply conceptual and mathematical knowledge.  The courses produced substantially improved conceptual learning and mathematical sense-making.

We plan to follow students from the redesigned as well as unchanged (control group) introductory physics courses, into the Basic Circuit Theory course in Electrical & Computer Engineering and a Fluid Mechanics course in Mechanical Engineering.  To see if the redesigned physics courses lead to better mathematical sense-making and overall performance in those engineering classes, we will analyze students’ exam answers and scores, survey responses, and course grades.

Read the entire proposal [Click here to download]

Papers and Publications

1. Gupta, A. & Elby, A. E. (in preparation). Understanding Engineering Students' Difficulties in Sensemaking with Mathematics: A Case Study. To be submitted.

Talks/Posters

1. "Beyond epistemological deficits:  Incorporating flexible epistemological views into fine-grained cognitive dynamics", Gupta, A., & Elby, A., Contributed Poster, International Conference of the Learning Sciences 2010, Chicago, IL. [PDF]
2. 'Undergraduate Engineers' Sense-making of Math'', Mike Hull, Eric Kuo, Ayush Gupta, & Andy Elby, Contributed Poster, 2009 Physics Education Research Conference, Ann Arbor, MI, July 2009. [PDF] [PPT]
3. 'The Role of Epistemology in Explaining Students' Troubles with Math in Science and Engineering Courses', Ayush Gupta and Andy Elby, Invited Talk at Mathematics Education Colloquim Series, EDCI, University of Maryland (College Park), May, 2009
4. 'The Dynamics of Constructing Meaning in Physics', Ayush Gupta, Invited Talk at University of Colorado, Boulder (Physics Education Group), March, 2009.
5. 'Students' Intellectual Resources for Understanding Science', Ayush Gupta, Invited Talk at Northup Grumman (Classroom Readiness for STEM Volunteers Program), Baltimore, MD, March, 2009.
6. 'Improving Engineering Students' Mathematical Sense-making', Ayush Gupta and Andy Elby, 2009 NSF-Engineering Education Centers PI Meeting (Poster), Feb. 2009 (click to download PDF)

Current Activities

• Teaching Introductory Physics courses for Engineering majors with special emphasis on mathematical sensemaking
  • Phys260 (General Physics: Oscillations, Waves, Heat, Electricity and Magnetism) (Fall 2009)
  • Phys161 (General Physics: Mechanics and Particle Dynamics) (Spring 2009)
• Conducting and analyzing clinical interviews
  • with engineering majors in introductory physics courses - focusing on diagnosing student difficulties with mathematical sensemaking in the context of physics problems and possible interventions to prompt sense-making in those contexts
  • with engineering majors in ENEE204 (Basic Circuit Theory) - focusing on how they make sense of mathematics in the context of circuits and exploring their epistemology around sense-making in engineering contexts
• Designing and administering surveys
  • to determine students' attitudes and expectations towards sense-making in physics and in engineering contexts (modified from MPEXII, and EBAPS).
  • Surveys have been administered to about 350 students in Phys161 (Spring 2009) and 52 students in ENEE204 (Spring2009)
• Designing curriculum materials
  • for introductory physics courses for engineering majors -- with emphasis on mathematical sense-making
  • for ENEE 204 (Basic Circuits Theory), providing opportunities for mathematical sensemaking and conceptual reasoning
• Collecting Video data
  • Videotaping students engaged in discussions and problem-solving in small groups for Phys161
  • Videotaping discussion sessions for ENEE204 (Basic Circuit Theory)
  • Videotaping lecture sessions of Phys161 (General Physics: Mechanics and Particle Dynamics) to document how engaging students in mathematical sensemaking can be made an integral part of a large classroom lecture

Personnel Contact Information

Mailing Address

Ayush Gupta

Room 1320, Physics Building

University of Maryland

College Park, MD  20742-4111

Fax: 301-314-9531

Work supported in part by a grant from the US National Science Foundation.