Investigating Trajectories of Learning & Transfer Of Problem Solving Expertise from Mathematics to Physics to Engineering

Principal Investigator: 
Project Overview
Background & Purpose: 
  • Q 1. How does students’ expertise to solve problems of increasing complexity evolve over time? How can we enable learners to solve problems of increasing complexity?
  • Q 2. In what ways does representational form, organization and sequencing affect students’ problem solving expertise? How can we facilitate learners’ development of representational competence?
  • Q 3. How does the trajectory of acquiring problem solving expertise vary with context and domain? How can we facilitate transfer of problem solving expertise across contexts and domains?
  • Q 4. What are the differences between the trajectories of students’ acquiring problem solving expertise? How do these trajectories change over time? Can students be classified based on their trajectories? How can we individualize learning tools to adapt to different students?

Large Midwestern research university.

Research Design: 

The research design for this project is both longitudinal and cross-sectional, is intended to generate evidence which is descriptive [phenomenological]  and associative/correlational [quasi-experimental]. Tutorials (paper and pencil and online) to improve learning and problem solving in physics and mathematics will be compared with standard instruction in the classroom

This project collects original data using assessments of learning/achievement tests, and survey research including self completion questionnaires [both paper and pencil, and online], structured interviewer-administered questionnaires [both face-to-face, and computer assisted telephone interviews (CATI), as well as face-to-face semi-structured teaching/learning interviews with individual students and online assessments of learning.

The interview data will be analyzed using a phenomenographic approach. Categories will be collapsed into emergent themes. The online data will be analyzed using statistical analysis techniques.


The main finding is that most students are able to successfully learn mathematical procedures to succeed in their mathematics classes. However, when they enter their physics and engineering classes they struggle to interpret problems in these classes to create a mathematical model that would enable them to solve these problems. The tutorials and online materials that we have been developing in this project have shown some promise in improving student problem solving performance.

Publications & Presentations: 

Dong-Hai Nguyen and N. Sanjay Rebello. (2011). “Students’ Difficulties with Integration in Electricity.” Physical Review Special Topics - Physics Education Research 7, 010113.

Dong-Hai Nguyen and N. Sanjay Rebello. (2011). “Students’ Understanding and Application of the Area Under the Curve Concept in Physics Problems.” Physical Review Special Topics - Physics Education Research 7, 010112.

For more papers, please see:

Other Products: 

Tutorials to facilitate transfer of problem solving from mathematics to physics and engineering.