Since electrical field concepts are usually unfamiliar, abstract, and difficult to visualize, conceptual analogies from familiar gravitational phenomena are valuable for teaching. Such analogies emphasize the underlying continuity of field concepts in physics and support the spiral development of student understanding. We find the following four tables to be helpful in reviewing gravitational and electrical comparisons after students have worked through hands-on activities analyzed via extended student discourse.1

1.
For a compelling vignette demonstrating advanced student discourse in the introductory physics class, see D. Desbien, M. Joshua & K. Falconer, RTOP Video 4 (SUNY-BSC, Buffalo, NY, 2003). Streamed Quick-Time video available from http://physicsed.buffalo-state.edu/rtop/videos/RTOP4/RTOP4play.html.
2.
R. Knight, Physics for Scientists and Engineers with Modern Physics: A Strategic Approach (Pearson Addison-Wesley, San Francisco, 2004), p. 808 develops the r-hat notation. The workbook is an excellent source of PER-inspired activities.
3.
R. Chabay and B. Sherwood, Matter & Interactions Vol. II: Electric and Magnetic Interactions (Wiley, Hoboken, NJ, 2002). This is an outstanding PER-influenced curriculum for studying electricity and magnetism. Section 14.8 is a case study of sparks in air. See the text website, http://www4.ncsu.edu/∼rwchabay/mi, and their paper
R.
Chabay
and
B.
Sherwood
, “
Restructuring the introductory electricity and magnetism course
,”
Am.J. Phys.
74
(
4
),
329
336
(April
2006
).
4.
A. Arons, Teaching Introductory Physics (Wiley, Hoboken, NJ, 1996). See problems 5.11, p. 73 (the charge ferry) and 5.17, p. 76 (parallel plate E field) of Vol. II in this three-section book.
5.
B. S.
Andreck
, “
Using contour maps to teach electric field and potential
,”
Phys. Teach.
28
,
499
(Oct.
1989
).
6.
D.
MacIsaac
and
K. A.
Falconer
, “
Reform your teaching via the Reformed Teacher Observation Protocol (RTOP)
,”
Phys. Teach.
40
,
479
(Oct.
2002
); http://PhysicsEd.BuffaloState.Edu/RTOP.
7.
See Ref. 3.
8.
D. Hestenes, G. Swackhamer, and L. Dukerich, Modeling Physics Curriculum (ASU, Tempe, AZ, 2004); http://modeling.asu.edu/Curriculum.html. See second semester (electricity & magnetism) curricular materials (worksheets, digitized videos and activities), particularly Units E1: Charge and Field and E2: Potential. A freely reproducible HS curricular resource based on physics education research (PER) touchstone curricular activities.
9.
P. Laws, The Workshop Physics Activity Guide Module 4: Electricity & Magnetism (Wiley, Hoboken, NJ, 2004). For a comparative development of E and g fields, see especially Unit 21: Electrical and Gravitational Energy, p. 573–593.
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