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In the 1990s, physics teachers had a new tool for measuring whether their students understood Newton's laws: the Force Concept Inventory. Richard Hake, a physicist at Indiana University (his 1998 paper lists that affiliation), collected results from courses across the United States and asked a simple question: does the way a course is taught change how much students learn?
What did Hake measure?
Hake's paper in the *American Journal of Physics*, "Interactive-engagement versus traditional methods", gathered pre-test and post-test scores from 62 introductory physics courses in high schools, colleges and universities, with 6,542 students in total. The tests were the Force Concept Inventory or its predecessor, the Mechanics Diagnostic.
Raw post-test scores are unfair to compare, because classes start at different levels. So Hake used the normalized gain, written ⟨g⟩: the actual gain divided by the largest gain that was possible.
⟨g⟩ = (post% − pre%) / (100 − pre%)
He sorted courses by how they were taught. In the paper's own definitions, interactive-engagement (IE) methods are "those designed at least in part to 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". Traditional (T) courses made little or no use of IE methods, "relying primarily on passive-student lectures, recipe labs, and algorithmic-problem exams".
What did the study find?
From the abstract:
14 traditional courses (2,084 students) averaged ⟨g⟩ = 0.23.
48 interactive-engagement courses (4,458 students) averaged ⟨g⟩ = 0.48, almost two standard deviations higher.
On the problem-solving Mechanics Baseline test, results for 30 courses suggested that IE methods improved problem-solving ability too, not only concepts.
The most common IE method in the survey was collaborative peer instruction, used in all 48 IE courses, followed by microcomputer-based labs, concept tests and modelling (Hake 1998).
What are the caveats?
This was a survey, not a randomised experiment: the data came from published accounts and from instructors who sent in their results. Hake says so directly: the study did not try to measure the average effectiveness of mechanics courses, but whether IE methods can raise effectiveness well beyond traditional teaching. He discussed possible systematic errors, such as teaching to the test and differences in student motivation, and argued it was extremely unlikely they explained a gap this large.
He also noticed that some IE courses got low gains. Case studies linked these to implementation problems, including instructors new to the methods without enough training and a lack of grade incentives for taking the activities seriously. Interactive teaching done badly does not deliver.
Later evidence points the same way. A 2014 meta-analysis of 225 studies by Freeman and colleagues found that exam and concept-inventory scores rose by 0.47 standard deviations under active learning, and that students in traditional lecture classes were 1.5 times more likely to fail.
Worked example: calculate your own gain
Try this with any chapter test you take twice, for example before and after revising.
You score 40% on a mixed set of concept questions before revising.
After a week of revision you score 64% on a fresh set of similar questions.
Gain = (64 − 40) / (100 − 40) = 24 / 60 = 0.40.
A second student moves from 70% to 82%. Their gain is (82 − 70) / (100 − 70) = 12 / 30 = 0.40, the same. The normalized gain shows both learned a similar share of what they had left to learn.
How can you get interactive engagement while self-studying?
Hake's definition has three parts: heads-on thinking, discussion and immediate feedback. You can build each into your week.
Predict before you calculate. Write what you expect and why, then solve. A wrong prediction is the feedback.
Explain to someone. Two friends, one concept question each, two minutes to convince each other. Our guide to study groups that work shows how to structure it.
Use concept questions, not only numericals. Ask "what happens if the mass doubles?" before you reach for formulas.
Check fast. Mark your work the same day, while your reasoning is fresh.
For a classroom version of these ideas, read about Eric Mazur and peer instruction.
If you would rather learn in a class with a teacher than only on your own, Fermi Testprep offers live classes for JEE Main and Advanced, alongside an AI tutor and adaptive mocks.
