| 
  • If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.

View
 

Engineering Education Project

Page history last edited by erickuo 7 years, 11 months ago

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]

 

Awards

 

  • Mike Hull, Graduate Student Travel Award for The Conference on Transforming Research on Undergraduate STEM Education, Maine, June 2010.
  • Eric Kuo, Graduate Student Travel Award for The Conference on Transforming Research on Undergraduate STEM Education, Maine, June 2010. 

 

Publications: Peer-reviewed Journal and Conference Proceedings 

  1. Danielak, B. A., Gupta, A., & Elby, A. (Under Review). The Marginalized Identities of Sense-makers: Reframing Engineering Student Retention. Journal of Engineering Education.
  2. Hull, M., Kuo, E., Gupta, A., & Elby, A. (2013) Problematizing problem-solving rubrics: Enhancing assessments to include blended mathematical and physical reasoning throughout the solution. Physical Review Special Topics - Physics Education Research, 9(1), 010105.
  3. Kuo, E., Hull, M., Gupta, A., & Elby, A. (2013) How Students Blend Conceptual and Formal Mathematical Reasoning in Solving Physics Problems. Science Education, 97(1), 32-57.
  4. Gupta, A., & Elby, A. (2011). Beyond Epistemological Deficits: Dynamic Explanations of Engineering Students' Difficulties with Mathematical Sense-making.  International Journal of Science Education, 33(18), pp. 2463-2488.. (Email ayush@umd.edu for PDF.)
  5. Gupta, A., Danielak, B. A., & Elby, A. (2010). Understanding Students' Difficulties in Terms of Coupled Epistemological and Affective Dynamics.  Proceedings of the 2010 Frontiers in Education Conference (ASEE/IEEE). [PDF]
  6. Danielak, B. A., Gupta, A., & Elby, A. (2010). The Marginalized Identities of Sense-makers: Reframing Engineering Student Retention. Proceedings of the 2010 Frontiers in Education Conference (ASEE/IEEE). [PDF]
  7. Gupta, A., & Elby, A. (2010). Beyond Epistemological Deficits: Incorporating flexible epistemological views into fine-grained cognitive dynamics. Proceedings of the International Conference of the Learning Sciences 2010. [PDF] 
  8. Danielak, B., Gupta, A., & Elby, A. (2010). Incorporating Affect in Engineering Students’ Epistemological Dynamics. Proceedings of the International Conference of the Learning Sciences 2010. [PDF]
  9.   Redish, E. F. & Gupta, A. (2010). Making Meaning with Math in Physics: A Semantic Analysis, GIREP Conf. Proc., Leicester, UK, August 20, 2009 [PDF]  

     

 

Invited Talks

  1. Gupta, A., Stevens, R., Elby, A., and Hammer, D. Video Analysis Workshop: Reconciling Cognitivist and Interaction analysis methodologies, Invited Workshop presented at the AAPT 2012 Summer Meeting, Philadelphia, PA. 
  2. Danielak, B. A. (2012, March 20). Using fine-grained code and fine-grained interviews to understand how students learn to program. Invited Talk, University of New Mexico - Department of Computer Science Colloquium. 
  3. "Analyzing Interviews Suggests Patterns of Reasoning with Math in Physics," Kuo, E., Hull, M., Elby, A., & Gupta, A., Invited Poster, FFPER, Bar Harbor, ME. 
  4. "Integrating Emotions with Fine Grained Dynamics of Students' Reasoning" Gupta, A., & Elby, A., Invited Poster, Foundations and Frontiers in Physics Education Research Conference, Bar Harbor, ME, June, 2011 
  5. Cognitive Dynamics of Mathematical Sense-making, Ayush Gupta, Invited Talk at the Center for Engineering Education and Outreach, Tufts University, Boston, MA, March, 2011.
  6. Cognitive Dynamics of Mathematical Sense-making, Ayush Gupta, Invited Talk at the Winter Meeting 2011 of the American Association of Physics Teachers, Jacksonville, Fl, January 2011 (Session on Making Meaning with Mathematics; Organizer: Elizabeth Gire) 
  7. Incorporating Emotions in Fine-Grained Cognitive Dynamics, Ayush Gupta, Invited talk at the The Conference on Transforming Research on Undergraduate STEM Education, Maine, June 2010. 
  8. '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
  9. 'The Dynamics of Constructing Meaning in Physics', Ayush Gupta, Invited Talk at University of Colorado, Boulder (Physics Education Group), March, 2009.
  10. 'Students' Intellectual Resources for Understanding Science', Ayush Gupta, Invited Talk at Northup Grumman (Classroom Readiness for STEM Volunteers Program), Baltimore, MD, March, 2009.

  11. '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)

 

 

Contributed Talks/Posters

  1. Kuo, E. (2013). Not Just “Plug-and-Chug”: How Physics Students Make Sense with Equations.  Contributed poster at the Foundations and Frontiers in Physics Education Research (FFPER) Conference 2013, Bar Harbor, ME.
  2. Gupta, A., & Elby, A. Coupling Identity and Epistemology to Understand Differences in Students' Learning Experiences. Contributed Talk presented at the AAPT 2012 Summer Meeting, Philadelphia, PA. 
  3. Kuo, E., Gupta, A., and Elby, A. (2012). When do I use symbolic forms? Contributed talk at AAPT summer 2012, Philadelphia, PA. 
  4. "Linking the Dynamics of Student Reasoning to Epistemology," Kuo, E., Hull, M., & Gupta, A., Contributed Talk, Jean Piaget Society Annual Meeting, Berkeley, CA, June, 2011.
  5. "Integrating Emotions with Fine Grained Dynamics of Students' Reasoning" Gupta, A., & Elby, A., Contributed Poster, Jean Piaget Society Annual Meeting, Berkeley, CA, June, 2011.
  6. "Toward Expert Problem Solving: Blending Conceptual and Symbolic Reasoning," Kuo, E., Hull, M., Elby, A., & Gupta, A., Contributed Poster, 2010 Conference on Transforming Research in Undergraduate STEM Education (TRUSE), Orono, ME,  
  7. "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]
  8. "Explaining Student Expertise with Mathematical Sense-Making", E. Kuo, M.M. Hull, A. Gupta, and A. Elby, Contributed Talk, AAPT National Meeting, Washington, DC February 16, 2010. [PDF]
  9. "I'm doing what my teacher says, why aren't I expert-like?", M.M. Hull, E. Kuo, A. Gupta, and A. Elby, Contributed Talk, AAPT National Meeting, Washington, DC February 16, 2010.
  10. "The Role of Affect in Stabilizing Judy's Approach Toward Circuits", A. Gupta, B.A. Danielak, and A. Elby, Contributed Talk, AAPT National Meeting, Washington, DC February 16, 2010.[SLIDESHOW IN QUICKTIME]
  11. "Affect and Identity in Engineering Students' Approaches to Learning, Problem Solving", B.A. Danielak, A. Gupta, and A. Elby, Contributed Talk, AAPT National Meeting, Washington, DC February 16, 2010.
  12. '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]

 

 

Current Activities

  • Data Analysis
  • Interviews with students 
    • Students who took two or more semesters of physics with us, and then took ENEE204; with the focus on investigating if and how the reformed physics effort contributes to their approaches to learning in other "regular" engineering courses
    • Phys161 students on how they make sense of mathematics in their physics course

 

Past Activities

  • Teaching Introductory Physics courses for Engineering majors with special emphasis on mathematical sensemaking (AE, AG, DH, EK, MH)
  • Conducting and analyzing clinical interviews (AE, AG, BD, EK, MH)
    • 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
    • Survey validation interviews with engineering students in the circuits course.
  • Designing and administering surveys (AE & AG)
    • 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 (AE, AG, DH, WL)
    • 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
  • Analyzing math-sense making in exams (AE, DH, AG, BD, EK, MH)
    • comparison of traditional versus reformed physics classes on students' mathematical sense-making in specific questions (final exams for Phys161 and Phys260).
  • Collecting Video data (EK & MH)
    • (Spring 2010) Videotaping students engaged in discussions and problem-solving in small groups for Phys270
    • (Spring 2010) Videotaping discussion sessions for ENEE204 (Basic Circuit Theory)
    • (Fall 2009) Videotaping students engaged in discussions and problem-solving in small groups for Phys260
    • (Spring 2009) Videotaping students engaged in discussions and problem-solving in small groups for Phys161
    • (Spring 2009) Videotaping discussion sessions for ENEE204 (Basic Circuit Theory)
    • (Spring 2009) Videotaped 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

 

NAME AFFILIATION PHONE (301-40+) OFFICE EMAIL
Andy Elby (PI) Physics, Education
-55983   elby@umd.edu
David Bigio (Co-PI) Mechanical Engineering -55258 Martin 2184 dbigio@umd.edu
David Hammer (Co-PI) Education, Tufts University
** **
**
Wes Lawson (Co-PI) Electrical and Computer Engineering -54972 AVW 2325 lawson@eng.umd.edu
Edward F. Redish (Co-PI) Physics, Education
-56120 Toll 1308 redish@umd.edu
Ayush Gupta (PD) Physics -51669 Toll 1320 ayush@umd.edu
Mike Hull (GRA) Physics -56185 Toll 1322 mhull12@umd.edu
Eric Kuo (GRA) Physics -56185 Toll 1322 erickuo@umd.edu
Brian Danielak (GRA) Education
    briandk@umd.edu

 

Mailing Address

Ayush Gupta

Room 1320, Physics Building

University of Maryland

College Park, MD  20742-4111

Fax: 301-314-9531

Ph: 301-405-1669

 

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

Comments (0)

You don't have permission to comment on this page.