Investigating student understanding in intermediate mechanics: Identifying the need for a tutorial approach to instruction

B. A.

Thacker

, “,” (), – ();

E.

Cataloglu

and

R. W.

Robinett

, “,” (), – ();

M. C.

Wittmann

,

R. N.

Steinberg

, and

E. F.

Redish

, “,” (), – ();

L.

Bao

and

E. F.

Redish

, “,” (), – ();

C.

Singh

, “,” (), – ();

B. S.

Ambrose

,

P. S.

Shaffer

,

R. N.

Steinberg

, and

L. C.

McDermott

, “,” (), – ();

R. N.

Steinberg

,

G. E.

Oberem

, and

L. C.

McDermott

, “,” (), – ();

H.

Fischer

and

M.

Lichtfeldt

, “,” (), – ().

R. E.

Scherr

,

P. S.

Shaffer

, and

S.

Vokos

, “,” , – ().

M. E.

Loverude

,

C. H.

Kautz

, and

P. R. L.

Heron

, “,” (), – ();

M. E.

Loverude

,

C. H.

Kautz

, and

P. R. L.

Heron

, “,” (), – ().

L. G. Ortiz, P. R. L. Heron, and L. C. McDermott, “An investigation of student understanding of the equilibrium of rigid bodies” (unpublished).

P. S. Shaffer, “Research as a guide for improving instruction in introductory physics,” Ph.D. dissertation, Department of Physics, University of Washington, 1993 (unpublished).

For research on the learning of the work-energy theorem and impulse-momentum theorems among physics graduate students and advanced undergraduates see

T.

O’Brien Pride

,

S.

Vokos

, and

L. C.

McDermott

, “,” (), – ().

Qualitative questions have frequently been used in empirical investigations of student understanding of introductory-level physics. For specific examples, see

L. C.

McDermott

and

E. F.

Redish

, “,” (), – ().

D. E.

Trowbridge

and

L. C.

McDermott

, “,” (), – ();

D. E.

Trowbridge

and

L. C.

McDermott

, “,” (), – ().

One of these additional pretests is based in part on the research presented in the articles listed in Ref. 8 and accompanies one of the tutorials included in Ref. 15.

For examples of such difficulties identified by research, see R. Allain, “Investigating the relationship between student difficulties with the concept of electric potential and the concept of rate of change,” Ph.D. dissertation, Department of Physics, North Carolina State University, 2001;

D. P.

Maloney

,

T. L.

O’Kuma

,

C. J.

Hieggelke

, and

A.

Van Heuvelen

, “,” , – ();

S. E. Kanim, “An investigation of student difficulties in qualitative and quantitative problem solving: Examples from electric circuits and electrostatics,” Ph.D. dissertation, Department of Physics, University of Washington, 1999 (unpublished);

R. R. Harrington, “An investigation of student understanding of electric concepts in the introductory university physics course,” Ph.D. dissertation, Department of Physics, University of Washington, 1995 (unpublished);

S.

Törnkvist

,

K.-A.

Pettersson

, and

G.

Tranströmer

, “,” (), – ().

See the first, second, and fourth items in Ref. 10. For instance, the first reference (Allain) details the results obtained from a diagnostic test that probes understanding of the electric field as the spatial rate of change of electric potential. The test was administered to both introductory and advanced students after instruction in electricity and magnetism. Also, in the second reference (Maloney et al.), item #18 on the Conceptual Survey of Electricity and Magnetism is designed to be roughly equivalent to part B of the equipotentials problem, although the contour maps given to the students on the CSEM were much simpler. Both references provide strong evidence suggesting a critical failure among students to distinguish between electric potential and electric field.

L. C.

McDermott

,

M. L.

Rosenquist

, and

E. H.

van Zee

, “,” (), – ().

Some of the examples used on the Vector curl pretest were taken from H. M. Schey, Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (Norton, New York, 1997), 3rd ed.

Among the correct explanations described here, another, more visual, approach, is described in Ref. 13, pp. 87–90. Using this approach, one can imagine a paddlewheel placed at a particular location in the $x–y$ plane such that its axis of rotation is perpendicular to this plane. If, by inspection of the force vectors in the vicinity of the paddlewheel, the net torque on the paddles is nonzero, then so must be the curl of the field at the location of the paddlewheel. The direction of the net torque is the same as the direction of the (z component of the) curl.

L. C. McDermott, P. S. Shaffer, and the Physics Education Group at the University of Washington, Tutorials in Introductory Physics (Prentice–Hall, Upper Saddle River, NJ, 2002).

For details on how tutorials have been adapted or developed for courses outside the introductory calculus-based sequence, see

R. E.

Scherr

,

P. S.

Shaffer

, and

S.

Vokos

, “,” (), – ();

B. S.

Ambrose

, “,” (), ();

G. E.

Francis

,

J. P.

Adams

, and

E. J.

Noonan

, “,” (), – ().

L. C.

McDermott

, “,” (), – ().

For research underlying these tutorials, see Refs. 5 and 8, as well as

L. C.

McDermott

,

P. S.

Shaffer

, and

M. D.

Somers

, “,” (), – ().

The graduate students mentioned here attempted the research task on two-dimensional motion as part of a graduate teaching seminar at the University of Washington or while taking a graduate qualifying examination at the University of Washington or Montana State University. For details, see Ref. 5.

For detailed discussion of difficulties that arise in the context of two-dimensional kinematics, see Ref. 5 as well as

F.

Reif

and

S.

Allen

, “,” (), – ().