ABSTRACT

We report data from ten years of teaching with Peer Instruction (PI) in the calculus- and algebra-based introductory physics courses for nonmajors; our results indicate increased student mastery of both conceptual reasoning and quantitative problem solving upon implementing PI. We also discuss ways we have improved our implementation of PI since introducing it in 1991. Most notably, we have replaced in-class reading quizzes with pre-class written responses to the reading, introduced a research-based mechanics textbook for portions of the course, and incorporated cooperative learning into the discussion sections as well as the lectures. These improvements are intended to help students learn more from pre-class reading and to increase student engagement in the discussion sections, and are accompanied by further increases in student understanding.

- 1. For example, see I. Hallounand D. Hestenes, “The initial knowledge state of college physics students,” Am. J. Phys.
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L. C. McDermott, “Millikan Lecture 1990: What we teach and what is learned—Closing the gap,” Am. J. Phys.**59**, 301–315 (1991); ,**Google Scholar****Scitation**,**ISI**

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**(1), 64–74 (1998). ,**Google Scholar****Scitation** - 2. D. W. Johnson, R. T. Johnson, and K. A. Smith,
*Active Learning: Cooperation in the College Classroom*(Interaction Book Company, Edina, MN, 1991);**Google Scholar**

R. T. Johnson and D. W. Johnson, “Cooperative learning and the Achievement and Socialization Crises in Science and Mathematics Classrooms,” from*Students and Science Learning: Papers from the 1987 National Forum for School Science*(AAAS, Washington, DC, 1987), and references therein.**Google Scholar** - 3. Examples include L. C. McDermott, P. S. Schaffer, and the University of Washington PERG,
*Tutorials in Introductory Physics*(Prentice–Hall, Upper Saddle River, NJ, 1998);**Google Scholar***Workshop Physics*(developed by P. W. Laws, R. Thornton, D. Sokoloff, and co-workers, and published by John Wiley);**Google Scholar***Active Learning Problem Solving Sheets*(developed by A. van Heuvelen, Ohio State University);**Google Scholar**

and numerous forms of Socratic dialogue, as in R. R. Hake, “Socratic Pedagogy in the Introductory Physics Lab,” Phys. Teach.**30**, 546–552 (1992),**Google Scholar****Scitation**

or group problem solving, as in Patricia Heller, Ronald Keith, and Scott Anderson, “Teaching problem solving through cooperative grouping. Group versus individual problem solving,” Am. J. Phys.**60**(7), 627–636 (1992), ,**Google Scholar****Scitation**

and Patricia Hellerand Mark Hollabaugh, “Teaching problem solving through cooperative grouping. 2. Designing problems and structuring groups,” Am. J. Phys.**60**(7), 637–644 (1992). ,**Google Scholar****Scitation**

Materials for these innovations are available by contacting the publishers or the developers; information on several innovations is also available at http://galileo.harvard.edu. ,**Google Scholar** - 4. Eric Mazur,
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Additional information and resources for PI can be found at http://galileo.harvard.edu.**Google Scholar** - 5. Catherine H. Crouch, “Peer Instruction: An Interactive Approach for Large Classes,” Opt. Photonics News
**9**(9), 37–41 (September 1998).**Google Scholar****Crossref** - 6. Adam P. Fagen, Catherine H. Crouch, Tun-Kai Yang, and Eric Mazur, “Factors That Make Peer Instruction Work: A 700-User Survey,” talk given at the 2000 AAPT Winter Meeting, Kissimmee, FL, January 2000;
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and “Peer Instruction: Results From a Range of Classrooms” (unpublished).**Google Scholar** - 7. Gregor Novak, Evelyn Patterson, Andrew Gavrin, and Wolfgang Christian,
*Just-in-Time Teaching: Blending Active Learning and Web Technology*(Prentice–Hall, Upper Saddle River, NJ, 1999), and http://webphysics.iupui.edu/jitt/jitt.html.**Google Scholar** - 8. Since 1995, we have replaced textbook readings on one-dimensional mechanics with a draft text written by Eric Mazur, in which concepts are introduced prior to the mathematical formalism, and many research findings of typical student difficulties are directly addressed in the text. In 1998 and 2000 this text was used for all topics in mechanics in the algebra-based course.
**Google Scholar** - 9. Methods for polling for student answers include a show of hands or flashcards, classroom network systems, and scanning forms. A discussion of the pros and cons of each of these methods is given in Ref. 4; we used scanning forms combined with a show of hands in 1991 and classroom network systems thereafter. We did not see any significant changes in student learning on introducing the classroom network system, and find the main advantages of the network are anonymity of student responses and data collection; our experience indicates that the success of Peer Instruction does not depend on a particular feedback method.
**Google Scholar** - 10. Exam questions are free-response and graded primarily on the quality of the student’s explanation of the answer. In class, we typically use multiple-choice ConcepTests, for ease of polling students for their answers.
**Google Scholar** - 11. The “algebra-based” course involves a very small amount of single-variable calculus, primarily derivatives and an occasional integral, in the second semester (electricity & magnetism). The students in this course have less facility with mathematical problem solving than in the calculus-based course.
**Google Scholar** - 12. The FCI is a test of conceptual understanding of mechanics, written in ordinary language so that it can be given before as well as after mechanics instruction.
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The original version is published in D. Hestenes, M. Wells, and G. Swackhammer, “Force Concept Inventory,” Phys. Teach.**30**(3), 141–151 (1992).**Google Scholar****Scitation**

The test was revised in 1995 by I. Halloun, R. R. Hake, E. Mosca, and D. Hestenes; the revised version is printed in*Peer Instruction: A User’s Manual*and can also be obtained from Professor Hestenes at Arizona State University. For nationwide data that have been gathered on student performance on the test, see Hake (Ref. 1). To maintain the validity of the tests, we do not use materials in class that duplicate FCI questions. ,**Google Scholar** - 13. D. Hestenesand M. Wells, “A Mechanics Baseline Test,” Phys. Teach.
**30**(3), 159–166 (1992). This test is available from the same sources as the FCI (Ref. 12).**Google Scholar****Scitation** - 14. In 1990, 1993, and 1994, the calculus-based course was co-taught by Eric Mazur and William Paul; in 1995, the course was taught by Eric Mazur; in 1991 and 1996, the course was co-taught by Michael J. Aziz and Eric Mazur; and in 1997, the year in which the highest FCI gains were obtained, the course was co-taught by Michael J. Aziz, Catherine H. Crouch, and Costas Papaliolios. Leadership of class periods was divided equally among co-instructors, with each instructor taking charge of the same number of classes. All instructors used Peer Instruction beginning in 1991.
**Google Scholar** - 15. In 1994 we changed from the original (29-question) version of the FCI to the revised (30-question) version. An informal e-mail survey on the listserv PhysLrnR found that at institutions which have given the FCI for a number of years, instructors typically see both pretest and posttest scores drop by roughly 3% on changing to the revised version. We saw this drop in our pretest but not in our posttest scores. We thank Professor Laura McCullough of the University of Wisconsin-Stout for telling us about this survey.
**Google Scholar** - 16. A
*t*-test (two-tailed) was performed to determine the likelihood that the difference in average pretest scores is due to real differences between the populations of students rather than simply variation within the population of students. The*p*value was 0.26; a*p*value of 0.05 or less is generally agreed to indicate a statistically significant difference.**Google Scholar** - 17. The questions we identified as significantly quantitative are numbers 9, 11, 12, 17, 18, 23, 24, and 25 (eight in all).
**Google Scholar** - 18. The exam distributions are published in Fig. 2.8 of Mazur (Ref. 4, p. 17). A
*t*-test was performed to determine the likelihood that this increase in mean score was simply due to variation within the population of students rather than genuine improvement in understanding. The*p*value was 0.001, well below the threshold of 0.05 for statistical significance, indicating a statistically significant increase in mean score.**Google Scholar** - 19. B. Thacker, E. Kim, K. Trefz, and S. M. Lent, “Comparing problem solving performance of physics students in inquiry-based and traditional introductory physics courses,” Am. J. Phys.
**62**, 627–633 (1994).**Google Scholar****Scitation**,**ISI** - 20. Catherine H. Crouch, John Paul Callan, Nan Shen, and Eric Mazur, “ConcepTests in Introductory Physics: What Do Students Get Out of Them?,” American Association of Physics Teachers Winter 2000 Meeting, Kissimmee, FL, January 2000;
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“Student Retention of ConceptTests” (unpub-lished); for transparencies and preprints consult http://mazur-www.harvard.edu.**Google Scholar** - 21. To minimize grading work, the Web utility we have developed automatically assigns full credit to every completed answer, and a grader spot-checks answers via a Web interface, which takes relatively little time.
**Google Scholar** - 22. Stephen Kanim, “An investigation of student difficulties in qualitative and quantitative problem solving: Examples from electric circuits and electrostatics,” Ph.D. thesis, University of Washington, 1999, and references therein.
**Google Scholar** - 23. Guidelines for effective group work are found in Heller and Hollabaugh and Heller, Keith, and Anderson (Ref. 3), as well as Johnson, Johnson, and Smith (Ref. 2).
**Google Scholar** - 24. Philip M. Sadler, “Psychometric Models of Student Conceptions in Science: Reconciling Qualitative Studies and Distractor-Driven Assessment Instruments,” J. Res. Sci. Teach.
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“How students respond to innovation,” seminar at the 1998 NSF Faculty Enhancement Conference “Teaching Physics, Conservation Laws First” (audio available at http://galileo.harvard.edu/conference/program.html). The tennis instructor illustration is also courtesy of Professor Sadler (private communication). ,**Google Scholar** - 25. Richard M. Felderand Rebecca Brent, “Navigating the Bumpy Road to Student-Centered Instruction,” College Teaching
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Felder and Brent (Ref. 25). ,**Google Scholar** - 27. Students were asked to give their opinion of the statement “The professor was an effective instructor overall” on a five-point scale ($\text{1=}\mathrm{strongly}$ disagree; $\text{2=}\mathrm{disagree};$ $\text{3=}\mathrm{neutral};$ $\text{4=}\mathrm{agree};$ $\text{5=}\mathrm{strongly}$ agree). EM’s average score in the calculus-based course for both traditional lecturing (one semester) and teaching with PI (six semesters) was 4.5, with standard deviations of 0.6 (traditional, $\text{N=125}$) and 0.8 (PI, $\text{N=789}$).
**Google Scholar** - 28. Over three semesters in the algebra-based course (Fall 1998, Spring 2000, and Fall 2000; Spring 2000 was the electricity and magnetism semester of the course), which was taught only with PI, EM’s average score was 3.5, standard deviation 1.2 $\text{(N=229).}$
**Google Scholar** - 29. Edward F. Redish, Jeffery M. Saul, and Richard N. Steinberg, “Student Expectations in Introductory Physics,” Am. J. Phys.
**66**(3), 212–224 (1998).**Google Scholar****Scitation**,**ISI** - 30. Linda R. Jones, J. Fred Watts, and Andrew G. Miller, “Case Study of Peer Instruction in Introductory Physics Classes at the College of Charleston,” Proceedings of Charleston Connections: Innovations in Higher Education, 2000 (submitted).
**Google Scholar** - 31. Nalini Ambadyand Robert Rosenthal, “Half a Minute: Predicting Teacher Evaluations From Thin Slices of Nonverbal Behavior and Physical Attractiveness,” J. Personality Soc. Psych.
**64**(3), 431–441 (1993).**Google Scholar****Crossref** - 32. Students do not necessarily remember equations in class, especially if they are not required to memorize equations. (Examinations in our course are open-book.)
**Google Scholar** - 33. Lecture schedules for our courses are available online at http://galileo.harvard.edu/galileo/course/ in the “Lectures” area.
**Google Scholar** - 34. Wendell Potter and collaborators at the University of California, Davis have developed an entire program of training teaching assistants in interactive teaching strategies, as reported at the AAPT Winter 2000 meeting.
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