Education research: FCI gains (Cuesta College)

Richard R. Hake quantifies gains made by first-year students in taking the Force Concept Inventory (Doug Hestenes, et al.) in terms of the average normalized gain <g>:

<g> = (final FCI class average - initial FCI class average)/(100% - initial FCI class average)

which represents the possible amount that a class can raise their average FCI score from the start of the semester to the end of the semester. E.g., if the initial FCI class average is 40%, then the maximum gain achievable is 60%; thus a final FCI class average of 40% represents a <g> = 0 (no gain), a final FCI class average of 70% represents a <g> = 0.5 (half of the maximum achievable gain), and a final FCI class average of 100% represents a <g> of 1.0.

Hake goes on to classify courses in terms of <g>:

"High-g" courses:         <g> >= 0.7
"Medium-g" courses: 0.7 > <g> >= 0.3
"Low-g" courses:    0.3 > <g>
Interactive engagement courses (48 courses): 
                          <g> = 0.48 +/- 0.14
Traditional courses (14 courses): 
                          <g> = 0.23 +/- 0.04

In Hake's words, interactive engagement courses:

"...promote conceptual understanding through interactive engagement of students in heads-on (always) and hands-on (usually) activities which yield immediate feedback through discussion with peers and/or instructors."

In contrast, traditional courses:

"...make little or no use of IE methods, relying primarily on passive-student lectures, recipe labs, and algorithmic-problem exams."

The FCI was administered to Physics 8A (first-semester of calculus-based physics sequence) students at Cuesta College, San Luis Obispo, CA during the first week of instruction, then on the last week of instruction. The results below are class averages for the initial and final FCI scores (given as percentages, with standard deviations), as well as the Hake normalized gain <g>:

Physics 8A Spring Semester 2007 sections 4909-4911
         N = 27
<initial%> = 41% +/- 17%
  <final%> = 49% +/- 20%
       <g> = 0.14

Physics 8A Fall Semester 2006 sections 0910-0912
         N = 36
<initial%> = 42% +/- 21%
  <final%> = 51% +/- 18%
       <g> = 0.16

Physics 8A Spring Semester 2006 sections 4888-4893
         N = 72
<initial%> = 44% +/- 21%
  <final%> = 53% +/- 20%
       <g> = 0.15

The low <g> for these past three semesters comes as no surprise, as this course was taught using traditional passive lectures and "cookbook" labs.

However, the initial class average FCI scores at Cuesta College are encouragingly high to begin with (ranging from 41% to 44%, N = 135), compared to the colleges (39%, N = 597) and universities (48%, N = 4,832) surveyed by Hake.

It is hoped that at Cuesta College, future use of electronic response systems ("clickers," from einstruction.com) and interactive whiteboards (Ubiquitous Presenter on Tablet PCs) over the next two years will result in better student learning of introductory physics, as reflected in higher <g> values.

• R.R. Hake, "Interactive-engagement vs. traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses," Am. J. Phys. 66, 64 -74 (1998).
  Definition of <g>, and relative comparison of many interactive engagement and traditional courses.


• D. Hestenes, M. Wells, and G. Swackhamer, Arizona State University, "Force Concept Inventory," Phys. Teach. 30, 141-158 (1992).
  Development of the FCI, a 30-question survey of basic Newtonian mechanics concepts.


• Physics Teacher Education Coalition: California Polytechnic State University, San Luis Obispo Project Report: September 2006
  Implementation of interactive engagement methods at Cal Poly, using different assessment tools (Force and Motion Concept Evaluation, and other conceptual tests).