How to measure student learning?


Assessment tools


Normalized Gain (G)

One way to gauge students' improvement over the course of a semester. Think of it as the the fraction of the concepts learned that were not already known at the beginning of the course.

FCI illustration


  • A student with a prescore of 20%, and a postscore of 60% would have a G of 0.50.
  • A student with a prescore of 50% and a postscore of 75% would also have a G of 0.50.



Dick Hake published one of the first analysis of FCI results from colleges & high schools. One of his findings was that "interactive" courses, no matter what techniques were used, yielded higher gains than "traditional" courses.1, 2


Despite the fact that most students in a class show improvements in their understanding of physics concepts, there are often students who struggle to grasp the fundamentals. Even with interactive teaching techniques often a fraction of the class is not able to perform at the expected level.


Within each course there are, of course, variations among the individual student gains. For example, here is an example histogram from one of my recent Introduction to Mechanics courses that shows students' normalized gains on the Force Concept Inventory (FCI):

Dr. Jeff's fci distribution

Despite the fact that the class average gain was 0.48, several students had low gains (below 0.30). In fact, some students had negative "gains"!



  1. R. Hake, "Interactive-engagement vs traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses" American Journal of Physics 66, 64-74 (1998)
  2. Some readers may remember a slightly different distribution of normalized gains that was presented in "Teaching physics: figuring out what works" by E. F. Redish and R. N. Steinberg, Physics Today 52, 24-30 (1999). While the details are different, both distributions clearly show that traditional, passive courses result in less student learning.