### Abstract

We investigate introductory physics students' difficulties in translating between mathematical and graphical representations and the effect of scaffolding on students' performance. We gave a typical problem that can be solved using Gauss's law involving a spherically symmetric charge distribution (a conducting sphere concentric with a conducting spherical shell) to 95 calculus-based introductory physics students. We asked students to write a mathematical expression for the electric field in various regions and asked them to graph the electric field. We knew from previous experience that students have great difficulty in graphing the electric field. Therefore, we implemented two scaffolding interventions to help them. Students who received the scaffolding support were either (1) asked to plot the electric field in each region first (before having to plot it as a function of distance from the center of the sphere) or (2) asked to plot the electric field in each region after explicitly evaluating the electric field at the beginning, mid and end points of each region. The comparison group was only asked to plot the electric field at the end of the problem. We found that students benefited the most from intervention (1) and that intervention (2), although intended to aid students, had an adverse effect. Also, recorded interviews were conducted with a few students in order to understand how students were impacted by the aforementioned interventions.

Original language | English |
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Title of host publication | 2012 Physics Education Research Conference |

Editors | N. Sanjay Rebello, Paula V. Engelhardt, Alice D. Churukian |

Publisher | American Institute of Physics Inc. |

Pages | 250-253 |

Number of pages | 4 |

ISBN (Electronic) | 9780735411340 |

DOIs | |

Publication status | Published - 2013 Jan 1 |

Event | 2012 Physics Education Research Conference, PERC 2012 - Philadelphia, United States Duration: 2012 Aug 1 → 2012 Aug 2 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 1513 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Other

Other | 2012 Physics Education Research Conference, PERC 2012 |
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Country | United States |

City | Philadelphia |

Period | 12-08-01 → 12-08-02 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*2012 Physics Education Research Conference*(pp. 250-253). (AIP Conference Proceedings; Vol. 1513). American Institute of Physics Inc.. https://doi.org/10.1063/1.4789699

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*2012 Physics Education Research Conference.*AIP Conference Proceedings, vol. 1513, American Institute of Physics Inc., pp. 250-253, 2012 Physics Education Research Conference, PERC 2012, Philadelphia, United States, 12-08-01. https://doi.org/10.1063/1.4789699

**Student difficulties in translating between mathematical and graphical representations in introductory physics.** / Lin, Shih Yin; Maries, Alexandru; Singh, Chandralekha.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Student difficulties in translating between mathematical and graphical representations in introductory physics

AU - Lin, Shih Yin

AU - Maries, Alexandru

AU - Singh, Chandralekha

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We investigate introductory physics students' difficulties in translating between mathematical and graphical representations and the effect of scaffolding on students' performance. We gave a typical problem that can be solved using Gauss's law involving a spherically symmetric charge distribution (a conducting sphere concentric with a conducting spherical shell) to 95 calculus-based introductory physics students. We asked students to write a mathematical expression for the electric field in various regions and asked them to graph the electric field. We knew from previous experience that students have great difficulty in graphing the electric field. Therefore, we implemented two scaffolding interventions to help them. Students who received the scaffolding support were either (1) asked to plot the electric field in each region first (before having to plot it as a function of distance from the center of the sphere) or (2) asked to plot the electric field in each region after explicitly evaluating the electric field at the beginning, mid and end points of each region. The comparison group was only asked to plot the electric field at the end of the problem. We found that students benefited the most from intervention (1) and that intervention (2), although intended to aid students, had an adverse effect. Also, recorded interviews were conducted with a few students in order to understand how students were impacted by the aforementioned interventions.

AB - We investigate introductory physics students' difficulties in translating between mathematical and graphical representations and the effect of scaffolding on students' performance. We gave a typical problem that can be solved using Gauss's law involving a spherically symmetric charge distribution (a conducting sphere concentric with a conducting spherical shell) to 95 calculus-based introductory physics students. We asked students to write a mathematical expression for the electric field in various regions and asked them to graph the electric field. We knew from previous experience that students have great difficulty in graphing the electric field. Therefore, we implemented two scaffolding interventions to help them. Students who received the scaffolding support were either (1) asked to plot the electric field in each region first (before having to plot it as a function of distance from the center of the sphere) or (2) asked to plot the electric field in each region after explicitly evaluating the electric field at the beginning, mid and end points of each region. The comparison group was only asked to plot the electric field at the end of the problem. We found that students benefited the most from intervention (1) and that intervention (2), although intended to aid students, had an adverse effect. Also, recorded interviews were conducted with a few students in order to understand how students were impacted by the aforementioned interventions.

UR - http://www.scopus.com/inward/record.url?scp=84994770242&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994770242&partnerID=8YFLogxK

U2 - 10.1063/1.4789699

DO - 10.1063/1.4789699

M3 - Conference contribution

AN - SCOPUS:84994770242

T3 - AIP Conference Proceedings

SP - 250

EP - 253

BT - 2012 Physics Education Research Conference

A2 - Rebello, N. Sanjay

A2 - Engelhardt, Paula V.

A2 - Churukian, Alice D.

PB - American Institute of Physics Inc.

ER -