Jerry Becker (2007) recently copied into the open Math-Teach archives
<http://mathforum.org/kb/forum.jspa?forumID=206> a New York Times
article by Claudia Dreifus (2007) titled "A Conversation With Eric
Mazur: Using the 'Beauties of Physics' to Conquer Science Illiteracy."
A telling portion of the exchange between Dreifus (Q) and Mazur (A)
is [bracketed by lines
"Q&A-Q&A-Q&A. . . . ."; my insert at ". . . . .[insert]. . . . .", my CAPS]
Q&A-Q&A-Q&A-Q&A-Q&A-Q&A-Q&A-Q&A-Q&A-Q&A-Q&A-Q&A
Q. Do you think you're better than the instructors you experienced as
a student?
A. When I first started teaching here in the 1980s, I didn't ask
myself such questions. I DID WHAT EVERYONE ELSE DID: LECTURES. And
the feedback was positive. The students did well on what I considered
difficult exams.
Around 1990, I learned of the work of David Hestenes. . . . .[Halloun
& Hestenes (1985a,b)]. . . . ., an Arizona State physicist studying
how abysmally students in his region did in science. He'd given
hundreds of undergraduates a test in concept comprehension before and
after they'd taken their physics classes. The tests showed that even
with a term of instruction, their understanding hadn't improved very
much.
I felt challenged by this. I then tested my own Harvard students
similarly. We had discussed Newtonian mechanics earlier in the
semester, and the students had already solved some difficult
problems. Yet, when I gave them a new "concept-based" exam, ABOUT
HALF HAD NO CLUE AS TO WHAT NEWTONIAN MECHANICS WERE ABOUT.
Q. Perhaps this concept-based test was flawed?
A. No. But it was different. It measured their knowledge of physics
forces in daily life. If they'd really understood Newtonian
mechanics, they would have aced it. One student asked me: "How should
I answer these questions? According to what you taught me? Or
according to the way I usually think about these things?"
THAT WAS THE MOMENT I FELL OUT OF MY IVORY TOWER. It was then that I
began to consider new ways of teaching. . . . . .[see e.g., Crouch &
Mazur (2000), Fagen et al. (2002), Lorenzo et al. (2006), Rosenberg
et al. (2006), Crouch et al. (2007)] . . . . .
Q&A-Q&A-Q&A-Q&A-Q&A-Q&A-Q&A-Q&A-Q&A-Q&A-Q&A-Q&A
It's interesting that Math-Teach's mathematically correct
<http://www.mathematicallycorrect.com/> math warriors, who
continually berate all forms of pedagogy other than direct
instruction, choose not to comment on Mazur's statements:
"I did what everyone else did: lectures. And the feedback was
positive.. . . . when I gave them. . . [the Halloun-Hestenes (1985a)
concept-based exam]. . . about half had no clue as to what Newtonian
mechanics were about."
I shall forego enumerating the research that is consistent with
Mazur's experience and with a nearly two-standard deviation
superiority [Hake (1998a,b; 2002a,b] in normalized conceptual gains
of interactive engagement pedagogy over traditional direct
instruction: Redish, Saul, & Steinberg, 1997; Saul, 1998; Francis,
Adams, & Noonan, 1998; Heller, 1999; Redish & Steinberg, 1999;
Redish, 1999; Beichner et al., 1999; Cummings, Marx, Thornton, &
Kuhl, 1999; Novak, Patterson, Gavrin, & Christian, 1999; Bernhard,
2000; Crouch & Mazur, 2001; Johnson, 2001; Meltzer, 2002a, 2002b;
Meltzer & Manivannan, 2002; Savinainen & Scott, 2002a, 2002b);
Steinberg & Donnelly, 2002; Fagan, Crouch, & Mazur, 2002; Van Domelen
& Van Heuvelen, 2002;, and Belcher, 2003; Dori & Belcher, 2004;
Hoellwarth, Moelter, & Knight, 2005; Lorenzo, Crouch, & Mazur, 2006;
& Rosenberg, Lorenzo, & Mazur, 2006. [For the references see Hake
(2007).]
Is there a mathematics test comparable to the Halloun-Hestenes or
the Force Concept Inventory that might be used to test the
superiority claimed by the Mathematically Correct crowd for direct
instruction? Yes, the "Calculus Concept Inventory" [Epstein (2007)].
Contact Jerry Epstein <jepstein@duke.poly.edu> for the details.
Epstein, J. 2006. "The Calculus Concept Inventory," abstract online
at "2006 Conference on Research in Undergraduate Mathematics
Education, online at
<http://mathed.asu.edu/CRUME2006/Abstracts.html>, scroll down about
one third of the way to the bottom.
Fagen, A.P., C.H. Crouch, & E. Mazur. 2002. "Peer Instruction:
Results from a Range of
Classrooms," Physics Teacher 40, 206-209; online at
<http://tinyurl.com/sbys4>.
Hake, R.R. 2007. "Design-Based Research in Physics Education
Research: A Review," in A.E. Kelly, R.A. Lesh, & J.Y. Baek (in
press), "Handbook of Design Research Methods in
Mathematics, Science, and Technology Education." Lawrence Erlbaum. Online at
<http://www.physics.indiana.edu/~hake/DBR-Physics3.pdf >(1.1MB)
Halloun, I. & D. Hestenes. 1985a. "The initial knowledge state of
college physics students." Am. J. Phys. 53:1043-1055; online at
<http://modeling.asu.edu/R&E/Research.html>. Contains the "Mechanics
Diagnostic" test, precursor to the "Force Concept Inventory"
[Hestenes et al. (1992)].
Hestenes, D., M. Wells, & G. Swackhamer. 1992. "Force Concept
Inventory," Phys. Teach. 30:
141-158; online (except for the test itself) at
<http://modeling.asu.edu/R&E/Research.html>.
The 1995 revision by Halloun, Hake, Mosca, & Hestenes is online
(password protected) at the
same URL, and is available in English, Spanish, German, Malaysian,
Chinese, Finnish, French,
Turkish, Swedish, and Russian.
Rosenberg, J., Lorenzo, M., & Mazur, E. (2006). Peer instruction:
Making science engaging. In
J. J. Mintzes and W. H. Leonard (Eds.) Handbook of College Science
Teaching (pp. 77-85).
Arlington, VA: NSTA Press. Retrieved on 5 March 2007 from
<http://mazur-www.harvard.edu/sentFiles/Mazur_22532.pdf>.