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Utilizing theme demonstrations and concept maps to
integrate electrostatics teaching
Wheijen Chang
Feng-Chia Unviersity, Taiwan
[email protected]
Abstract
Teaching electrostatics is a challenging task due to its complexity and degree of
abstraction. To help students meaningfully grasp the whole picture of the topic, this
study (1) analyzed students’ learning difficulties in electrostatics, (2) developed
demonstrations using a plasma globe and other equipment, (3) designed questions for
students to participate in small group discussion, and (4) guided students to draw
concept maps. The program has been implemented and modified by the author in
Taiwan, involving both university and high school students, for three consecutive
years. Both affective outcomes and academic performance were evaluated. The results
suggest that the combination of theme demonstration, group discussion based on the
worksheets, and concept mapping is effective in (1) clarifying the meanings of the
terminology and concepts, (2) integrating related terms/theories into a global picture,
and (3) engaging students’ participation in the learning process.
Introduction
Teachers may find it challenging to teach electrostatics for three reasons: (1)
Electrostatics involves a large amount of terminology, the meanings of which are
mostly abstract. Key terms, such as electric fields, electric flux and electric potential
are not commonly adopted in everyday life. The novelty and complexity of the
terminology may impede students’ comprehension of their meanings, and thus they
may refrain from adopting these key tools when reasoning in electrostatics (Furio &
Guisasola, 1998; Viennot & Rainson, 1992). (2) The relations amongst these terms are
not independent, but rather are closely related. The links amongst each pair of terms
involve important conceptions, which can be represented by formulae. In addition,
each quantity may be derived in multiple ways, depending on the given conditions.
v
For example, electric field ( E ) can be derived from source of charges (q), electric
v
flux (ΦE), electric force ( Fe ), or electric potential (ΔV). The selection of appropriate
1
formulae may be challenging but critical for students when solving problems in
electrostatics. (3) In order to facilitate students to grasp the meanings and functions of
each term/formula, and to connect the links amongst these conceptions, the provision
of abundant contextualized problems is required. However, the real-life
examples/demonstrations provided by the current literature seem to be insufficient,
and appear to be far fewer in electrostatics than in other topics such as mechanics and
optics. (4) Meanwhile, the content structure of most textbooks is in linear form for all
topics, including electrostatics. Although the linear structure shows conciseness in
introducing each term and formula systematically, the unique direction of instruction
deprives the students of opportunities to compare the meanings and usages amongst
related terms and formulae. After studying electrostatics, students may be able to
recite several “hot formulae”, but fail to grasp the framework of the whole idea.
In responding to the existing challenges described above, the author has designed
a teaching sequence and evaluated its outcomes. The study included four steps: (1) an
investigation of the students’ difficulties in learning electrostatics in high school, (2)
the design of a teaching sequence, including development of demonstrations of a
plasma globe and other equipment, the design of conceptual-oriented questions for
in-class dialogues, and concept mapping, all of which were incorporated with the
lecturing, (3) the implementation of the teaching program, and (4) an evaluation of the
outcomes of the teaching sequence, and further modifications of the program. The
teaching sequence introduced in this paper is the outcome of three years of
implementation and modifications.
Literature
The literature has reported on the difficulties of learning electrostatics. First,
concepts of electricity are more abstract than other topics such as mechanics, and the
required mathematics is very sophisticated (Chabay & Sherwood, 2006). Second,
students are unable to grasp the meanings of the representation tools of field lines and
equipotential lines. Electric field lines are found to be confused with the line of
trajectory, and most students are found to fail to reflect the density of field lines to the
magnitude of electric force (Maloney, O’Kuma, Hieggelke, & Van Heuvelen, 2001;
Tornkvist, Pettersson & Transtromer, 1993). Meanwhile, most students are incapable
of deriving either energy differences or electric fields from the distribution of
equipotential lines (Maloney et. al., 2001). Third, Furio & Guisasola (1998) found
that university students have epistemological and ontological difficulties in using the
idea of field. When dealing with problems of electrostatics, students tend to adopt the
Coulumbian model and ignore Faraday’s idea of the field model, which may be due to
the epistemological similarity between the Coulumbian and Newtonian models (Galili,
2
1995). Fourth, Viennot & Rainson (1992) found that university students tend to
inappropriately adopt the superposition law of Gauss’ Law and Coulumb’s Law,
disregarding the fact that the given charge density of the conductor surface has been
influenced by an outside charge.
In sum, the literature has highlighted the difficulties of grasping the key ideas
of electric fields, force, potential and energy. The existing barriers in comprehending
electrostatics seem not only due to the abstraction and complexity of the related
terminology/concepts, but also to the lack of recognition of the functions/values of the
tools.
In order to facilitate students’ learning in electrostatics, several studies have
reported on their strategies, including (1) adopting oriented-research to enhance the
idea of the electric field (Furio, Guisasola, Almudi & Ceberio, 2003). By means of
problem-based learning, students are guided to bridge the gap between theories, to
appreciate the needs for shifting from Coulumb’s towards electric field models, and to
construct a comprehensive knowledge framework; (2) teaching content incorporated
with the science history of the development of electromagnetism (Pocivi, 2007). Both
projects incorporated the “invention” of the electric field, which aimed to reinforce
the students’ recognition and appreciation of the critical tool of the electric field.
In addition, the strategy of using theme demonstrations to integrate the related
knowledge of a broad topic has been recognized in the literature (Buncick, Betts &
Horgan, 2001). The purposes of using theme demonstrations to integrate related
knowledge include (1) illustrating the meanings of terminology/principles via real-life
examples, (2) providing multiple times for practicing is required, especially for
becoming acquainted with complex principles, and (3) allowing comparison of related
principles with their meanings, function and limitations (Aron, 1994; Buncick, et. al.,
2001). Observing and discussing real-life questions may not only facilitate students to
visualize the meanings of the related terms or concepts, but may also provide
opportunities to integrate multiple concepts (Crouch, Fagen, Callan & Mazur, 2004).
For example, Buncick, et. al. (2001) incorporated demonstrations and concept
questions to guide students to integrate their conceptual framework in mechanics.
The incorporation of demonstrations, discussion and concept mapping seems to
have gradually become popular in “physics teaching innovation” programs. However,
the rationale behind these strategies needs to be addressed to highlight the foci. First,
the introduction of real-life examples/demonstrations is not merely for affective
reasons, acting as a tool for entertainment to liven up a tedious physics class. Contexts
of everyday life are required to illustrate the meaning of the corresponding concepts,
3
which is essential for conceptual development (Posner, Strike, Hewson & Gertzog,
1982). With respect to the epistemological aspect, adopting everyday life examples
can highlight the relevance between real life phenomena and physics theories, and
demonstrate the compact structure amongst physics theories (Hammer, 1995;
Gunstone & White, 1981). The task of integrating related conceptions is even more
critical for topics with more complexity. In order to facilitate students to perceive its
unity, concept mapping may be an effective strategy (White, 1994).
Second, providing questions to stimulate discussion and reasoning has been
highly recommended by many innovation programs, as it allows students to practice
in class (e.g., Beichner, et. al., 2000; Chang & Bell, 2002; Crouch & Mazur, 2001).
However, teachers need to be aware that providing information (lecturing) and
stimulating thinking are both essential to facilitate effective learning (Driver, et. al.,
1994). Psychological tools such as words, mathematics and diagrams are essential for
mediating higher levels of mental functions to extend the students’ zone of proximal
development (Wertsch, 1991; Carter, Westbrook & Thompkins, 1999). The sequences
and foci between tackling unfavorable conceptions and introducing new tools may
vary amongst different topics (White, 1994). For example, ideas of mechanics are
closer to everyday life experiences than those of electricity. Students have therefore
been found to have more confidence in answering questions in mechanics than those
concerning DC circuit problems (Planinic, et al., 2006). Despite their acquaintance,
however, they have been found to possess stronger alternative conceptions in
mechanics as well. Therefore, when teaching electricity, it is suggested to start by
introducing key terms and their relations, followed by examining and amending the
students’ understandings of these tools.
In addition, introducing conceptual tools should facilitate students to (1)
recognize the meanings and functions of the key tools/terms, which may be novel to
their everyday life experiences, (2) become acquainted with the regulations of
adopting the related tools, and (3) appreciate the value of the related tools in
enhancing scientific arguments/reasoning (Roth & McGinn, 1998).
In sum, the combination of theme demonstrations, lecturing, in-class discussion
and concept mapping is expected to benefit the students in that it will (1) stimulate
their learning motivation, (2) allow them to notice, visualize and become acquainted
with the meanings of the key terms and formulae, and appreciate the functions/values
of scientific arguments, (3) provide opportunities for them to construct/amend their
understandings of the concepts, and (4) allow them to integrate related knowledge
into a meaningful and robust unity.
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Methodology
This study has been conducted over a period of three years, which has allowed
for ongoing modifications of the teaching of the intervention program to best suit the
students’ needs. To investigate the students’ existing knowledge, both university and
high school students answered written examinations designed by the author, and the
backgrounds of the participants were analyzed based on their scores in the University
Entrance Examination.
During the three years of implementation and modifications, the researcher has
taught the topic six times in first year university physics courses, and twice in high
school workshops. This paper reports the design and outcomes of the last year of
implementation. In the university classes, the teaching time is normally distributed as
70% lecturing, 10% assessment and 20% discussion, which includes observation,
whole class conversation and small group discussion. The teaching style was the same
as that usually adopted by the author in the university physics course (Chang, 2005)
throughout the entire academic year, so that the students may feel that learning
electrostatics was similar to learning other topics. The topic of electrostatics took
about 12 teaching hours (4 weeks) for the university classes.
Evaluation of the intervention program included the students’ academic
performance and their comments about how they learnt, as well as the teaching
design/performance. Only the academic performance of the university students was
evaluated, based on written examinations, which were given to two classes taught by
the author and two classes by two other instructors (both of whom have taught the
course for over 20 years). The two classes of the control group and the experimental
group have the same major, and have a homogeneous background. Details of the
subjects are listed as follows.
Table 1: Physics background and numbers of both
experimental and control groups with different majors
Subject’s major
(background)
Major A
(72%±11.5%)1
Major B
(57%±16.7%)
Experimental group
Control group
n = 60
n = 83
n = 58
n = 68
Both the university and high school students participating in the intervention
teaching filled in an open-ended questionnaire to express their opinions about the
design.
1
The percentages superior to other candidates who studied physics, i.e. a higher % means a stronger
background.
5
The questions for the high school students were:
By participating in the workshop, (1) what have you learned? (2) how do you
feel about the program? (3) any suggestions for improving the program? (4) further
questions regarding the topic. The questionnaire completed by the university students
included the above four questions and one more question asking them to (5) compare
their learning experiences/achievements in electricity between university and high
school.
Four weeks after studying the topic, sixteen university students in the
experimental group were interviewed by the researcher (their instructor) to examine
their understanding of electrostatics, and to let them express their opinions about the
teaching,.
Findings of existing learning difficulties
The teaching sequence includes 7 key terms in electrostatics, i.e. electric charge,
force, field, flux, energy and potential. Understanding the definitions of these terms
and the links amongst them is the key task of learning electrostatics. The terms and
formulae are:
z
z
z
electric force due to point charges (Fe = kq1q2/r2) --------------------------- (1)
v
v
relation between electric field and electric force ( F = qE ) ---------------- (2)
v v
q
relations amongst charges, flux, and fields ( ∫ E ⋅ dA = ∫ Φ E = in ) -------(3)
εo
z
v v
v v
definition of electric potential energy ( ΔU e = − ∫ Fe ⋅ dr = − qE ⋅ dr ) -------(4)
z
relation between electric potential and energy ( ΔU = q ⋅ ΔV ) ------------- (5)
z
electric potential due to point charges (V = kq/r) ---------------------------- (6)
v v
relation between electric field and potential ( ΔV = − ∫ E ⋅ dr )-------------- (7)
z
Learning tasks include not only figuring out the meanings of the individual terms,
but also distinguishing the multiple routes of deriving each unknown, which greatly
reinforces the complexity of the topic. For example, to calculate electric field,
students need to select one of the four formulae of (Eq. 1, 2, 3, 7), and one of three
options (Eq. 5, 6, 7) for deriving electric potential.
The results of the written examinations indicated that electrostatics remains very
challenging even to the top 16% of high school students2, right after studying the
2
In Taiwan, by means of senior-high school entrance examinations, only one third of the students enter
regular senior-high schools, most of whom will move forward to university afterwards. Due to the high
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topic. Students were found to face a variety of difficulties when answering the
questions encompassing definitions/concepts. Major difficulties included: (1) failure
to grasp the relations between electric potential and energy (ΔU = q⋅ΔV) (App. #1,
#2); (2) failure to grasp the relations between electric potential and electric field
(including the direction) (ΔV = E ⋅ Δr; E = ΔV/Δr ) (App. #1, #2, #3, #4), where (3)
omitting the idea of difference (Δ) was found to retard the adoption of the formula (E
= ΔV/Δx ≠ V/x) (App. #6); (4) failure to grasp the relations between electric field
v
v
and force ( F = qE )(App. #7) (5) confusing the representations of equipotential lines
and electric field lines (App. #2, #5), (6) a tendency to plug-in the “hot formula”
(E=kq/r2) inappropriately in contexts where either the conditions are beyond the
limitations (App. #8) or where the required variables are absent (App. #9), and (7)
confusion about the vector/scalar properties of electric field and electric potential
(App. #10). Therefore, the key concepts/theories of electrostatics have mostly
remained unlearnt.
Design of the teaching sequence
Based on the prevalent learning difficulties found in this study and the literature,
the teaching sequence was designed with the aim of providing more real-life
examples/demonstrations to introduce each term and illustrate their meanings and
functions. Also, abundant questions were provided to help the students to grasp an
overall understanding of the knowledge framework. Outlines of the designed
questions, demonstrated phenomena and the corresponding theories of the teaching
sequence are given below:
The first demonstration utilizes “the charge generator” to introduce the four ideas of
electric charges (q), electric potential (V), electric field (E), electric force (F) and
electric energy (U), and the relations amongst them. The questions and answers are as
follows:
【Example 1】Question 1-1: Why does “the charge generator” (Fig. 1) spark when the
wheel is rotated?
Answer: Rotating the wheel allows the two materials to
rub together, separating the ± charges (charging process). The
charges gradually accumulate and result in intensive electric
fields between the two poles.
Question 1-2: Where does the energy that produces the Fig.1: Charge generator
university entrance rate (> 90%), the percentage (top 16%) of high school graduates who studied
physics can reflect the level of university entrants.
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sparks come from?
Answer: The energy is transformed by the work done by the rotation of the
wheel.
Question 1-3: If the sparks do not appear after rotating, which method can trigger
them? Why can sparks appear then?
Answer: (1) Reducing the distance (Δr) between the two poles can intensify the
electric field (E), because E=ΔV/Δr; E ∝ 1/Δr, when ΔV is fixed. (2) Since potential
V depends only on the amount of charges accumulated on each pole (±V=kQ/r), the
ΔV is fixed when the charges of the two poles are fixed; (3) The electric force exerted
v
)
on the ions within the two poles increases when the electric field increases ( F = qE ),
which can trigger sparks when the field is up to the threshold of turning air into a
conductor.
When teaching, the term “dielectric strength” is defined as the required minimum
electric field to make dielectrics conductive. For dry air, the breakdown threshold is
3.0 MN/C.
Question 1- 4: When sparks do not yet appear, the electric potential remains very
high. How could an object carry high electric potential without transferring electric
energy? What’s the relation between electric potential and energy? Which entity plays
the role of transportation to transfer energy from electric potential difference?
Answer: High potential does not transfer energy because it lacks charge (sparks
indicate current) to act as the vehicle to transport energy. Based on the definition of
electric potential from energy ΔV = ΔU/q, the energy transferred is ΔU = q⋅ΔV.
The didactic functions of this demonstration-questioning sequence include (1)
electric potential as a function of charge, (2) the role of distance (Δr) in linking E and
ΔV, (3) the relations between E and F, (4) the significance of electric field as the
threshold to trigger sparks (dielectric strength), and (5) the relation between potential
and energy.
After providing a brief outline of the related terms: charges, fields, force, energy
and potential, the instructor gave a lecture based on the conventional textbook
sequence, i.e. defining the key terms and the related formulae, i.e. Eqs (1)−(7), along
with several exercises which are mostly de-contextualized from everyday life. A
contextualized example from the textbook is the Cathode Ray Tube (CRT) from a
television, which is stated below:
【Example 2】Question 2-1: TV CRT (without demonstration) (a) calculate the kinetic
8
energy of the electrons when accelerated by a given
potential difference of 5.0 kV.
Answer: Ek = ΔU = e⋅ΔV
Question 2-2: Derive the equation of the path of an
electron moving perpendicular into a uniform electric
Fig. 2: Path of electrons moving
field (Fig. 2).
Answer: Fe= e⋅E=me⋅ay;
⎛ − 1 eE ⎞
⎟
2 ⎜
y＝x ⎜⎝ 2 mυi 2 ⎟⎠
within uniform electric field
Then, two demonstrations with questions were added, mainly to highlight the
significance of electric field and the relation between electric field and potential.
Electric field and potential are two terms which are very abstract but critical, and thus
need more examples for students to be able to comprehend their meanings.
【Example 3】Question 3-1: Why does the electric
stunner (Fig. 3) produce sparks?
Answer: The threshold of creating lightning is
that the electric field needs to be big. Since the
electric potential of the stunner is very high, the
electric field between poles is big(ΔV = E· d).
Fig. 3: Utilising the electric stunner
linking electric field and potential
Question 3-2: To estimate the range of the
electric potential of the stunner, which quantity of the stunner should be measured,
and how can you calculate the range of the electric potential?
Answer: The distance between the two poles needs to be measured (d =3.6 cm), and
then you need to utilize the data of the dielectric strength of dry air (E ≥ 3.0 MV/m) to
estimate the minimum electric potential of the equipment.
ΔV ≥ E· d = 3.0×106 ×0.036 =1.08×105 V
【Example 4】Question 4-1: An electric insect-catcher (Fig. 4)
provides the potential difference of a few kV between
neighboring gates, which can eliminate insects. Explain why
high potential can eliminate insects. Why can’t an electric
insect-catcher produce sparks in the same way a stunner does?
How can we trigger sparks between gates without them being
connected by conductors?
Fig. 4: Electric
insect-catcher
Answer: The high electric potential between gates, when
touched by insects which behave as conductors with small resistance, delivers electric
power (P=V2/R) which is fatal to the insects. However, the potential difference of a
9
few kV is still smaller than that of the stunner. The key to triggering sparks is the
strength of the electric fields (E) (for dry air, E ≥ 3.0 ×106 V/m), which can be
increased by shortening the distance between neighboring gates. (E =ΔV /d; ∴E ∝ 1/d
when ΔV is fixed).
Question 4-2: If the potential difference between the neighboring gates is 5000V,
estimate how close they should be in order to trigger sparks?
Answer: Based on E ≥ 3 × 106 V/m; and E = ΔV/d, the gap between gates is
d ≤ ΔV /E = 1.7 × 10-3 m.
Then, the instructor guides the students to draw a concept map (Fig. 5) using the
following steps (1) locate the four terms E, ΔV, F, ΔU in the corners, (2) add the
formulae to connect each corner, (3) modify the formulae to improve the precision,
e.g. negative sign, vector form, integration, divergent, etc., (4) clarify the causality of
the formulae, and distinguish the differences of the same symbol in different formulae,
e.g. “q” means the source of or the detector of E, and (5) add the formulae to reverse
the derivations.
v v
F = E ⋅q
Fe
E
ΔV = E ⋅ Δr
ΔU = F ⋅ Δr
ΔU
ΔU = ΔV ⋅ q
ΔV
Fig. 5: Concept map linking the four terminologies and four formulae
After the task of drawing a concept map is accomplished, more questions are
needed to help the students to further comprehend the conceptions entailed in the
concept map. Inspired by Guilbert’s (1999) article, a theme demonstration of a
plasma globe, along with a series of questions, were then included in the lesson..
【Example 5】 Question 5-1: The technology required to
make a plasma globe glow (Fig. 6) is as follows: (1) the
center provides high electric potential to enable the globe
to become conducting, and (2) the globe contains low gas
pressure (of Ne or Ar) to allow glowing.
Select
appropriate electrostatics formulae to explain the above
technology.
Fig. 6: Electric principles
incorporating a plasma
globe
10
Answer: (1) Based on E = ΔV/Δr, since Δr of the globe is not big, high ΔV
allows strong E, which reaches the breakdown threshold (dielectric strength) and thus
makes the plasma conducting. (2) Low gas pressure indicates low density in the gas
molecules, which allows longer distances for accelerating between collisions. During
the “free” accelerating region (Δr), ions can release enough potential energy (ΔU =
F⋅Δr) and transform it into kinetic energy, which is sufficient to stimulate photons
within visible light (ΔU = Ek > Uphoton).
Question 5-2: The shape of the blaze indicates the path of the ions, which implies the
pattern of the “electric flux (ΦE)” in the globe. (1) Derive the electric field as a
function of the radius in the globe. (2) According to the distribution of the electric
field, explain the colors of the blaze: why is the inner part purple and the outer part
red (Fig. 6)?
Answer: (1) The path of the ions is determined by the electric force, which is
parallel with the direction of the electric fields (when initial velocity is comparatively
small).
v
v
1 v
v 1v
∵ r = at 2 = ( Fe / m)t 2 , Fe = qE ;
2
2
v
v v
v
∴ r (path )// a // Fe // E (electric filed)
(2) The pattern of the blaze shows radial direction, thus the intensity of the
electric field gradually weakens (E↘) along the radial direction (r↗).
v
v
∵ r↗⇒E↘, and Fe =q E ; ∴ r↗⇒Fe↘
The blaze within the globe is called “stimulated light”, based on photon theory
Uphoton = hf (h: Plank constant, and f: frequency). Uphoton is transferred from the energy
accumulated on the ions due to acceleration by electric force. Thus,
v
v
Uphoton ≤ ⎢ΔU⎪ = Fe ⋅ Δr ( Δr ` : free path = constant) ; From the above
∵ r↗⇒Fe↘ ∴ r↗⇒ ⎢ΔU ⎪↘⇒ Uphoton↘
⇒ colors change from purple (inner) to red (outer).
Question 5-3: When handling the globe, (1) why can
we see the intensive glow “being attracted” by the hand
(Fig. 7)? (2) Since there is a high potential difference
across the body, why is the globe not harmful to the person
(as an insect-catcher is to an insect)?
Answer: (1) When handling the globe, the blaze Fig. 7: Touching with a
hand can attract the blaze
tends to concentrate through the hand because the
resistance (R) of a human body is lower than that of the air, so more current goes
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through the hand (I=V/R, ∵R↘and V↗⇒ I↗). (2) Whether the assembly is harmful
or not depends on the amount of electric energy delivered (ΔU). According to ΔU =
q⋅ΔV, a high potential difference (ΔV) may still be safe, but only if the charge (q)
transferred is very small. Therefore, although the globe shows an intensive beam
passing through the hand, the current transmitted to the hand should be rather low
(q=I ⋅Δt).
Question 5-4: How can a plasma globe (1) light up a
fluorescent tube (Fig. 8), but (2) fail to light up a bulb? (3)
Can the bulb eventually be lit up if you wait longer?
Answer: (1) A fluorescent tube emits stimulated light Fig. 8: Electric principles
which applies to the photon theory (Uphoton = hf). The
incorporating a plasma
threshold of lighting up the tube is that the electric field
needs to be large enough to make the material (mercury vapor) conducting. The high
potential difference provided by the plasma globe is sufficient to provide the required
electric field. (2) The light of the bulb is due to thermal radiation of the filament,
which needs to be heated to more than 500℃. (3) The filament of a bulb is normally
manufactured with a large surface area to allow optimum illumination. This increases
the rate of energy leak by heat conduction. Therefore, the filament of the bulb
normally reaches its terminal temperature shortly after being connected with electric
potential. Thus, extending the duration of the connection will not help light up the
bulb.
Question 5-5: How can one extinguish the tube
without moving the tube away (task A)?
Answer: Reducing the potential difference is an option
to extinguish the tube. This can be approached by touching
the globe with the other hand, i.e., increase the potential of Fig. 9: Extinguish the tube
by reducing potential
the end to reduce the potential difference of the two hands
differences
(Fig. 9). This task may highlight the significance of potential difference over that of
absolute potential value (reflecting difficulty 3).
Question 5-6: Now, if the tube is not touching
the globe, but is being held by two people, where the
person on the right is touching the globe (Fig. 10),
which strategies can help light up the tube (task B)?
What are the principles (formulae) underlying the
strategies?
Fig. 10: How to light up the tube
indirectly?
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Answer: In order to directly light up the tube, the trick is to increase the electric
field between the two hands on the tube. Possible strategies include (1) shortening the
gap between the two hands (E = ΔV/d, let d↘⇒E↗) (Fig. 11), or (2) increasing the
ΔV of the two hands by “isolating (anti-grounded)” the person touching the globe.
The method of “isolating” is jumping. In addition to the correct reasoning, it is very
common for students to come up with the invalid strategy of “letting the other hand of
the second (left) person touch the globe in order
to form a “closed loop”. Although the assertion is
in accordance with the scientific notion of
“current appears in close circuit only”, the
instructor can take this opportunity to encourage
the opposing opinion of the result of zero Fig. 11: Shortening the distance can
potential difference (ΔV=0) between the two ends
light up the tube successfully
to show the violation of the strategy in science.
With careful trialing of the equipment (including selection of appropriate shoes),
strategies (1) and (2) can both be effective. This question has been found to be very
challenging but inspiring for the students. Based on previous implementation,
normally a few groups are able to propose effective solutions. While the results
appear to fulfill what they have already predicted, the students usually cheer out loud
at their success, providing a thrilling climax to the end of the class!
Outcomes of the teaching sequence
The outcomes of the teaching sequence have been found to be promising in
terms of (1) comments about learning achievements and teaching performance, (2)
academic achievement in electrostatics, and (3) students questioning and reflecting on
their cognitive engagement, and making suggestions for further modifications.
¾
Comments from the participating students
The results of the student questionnaire survey show that most of the students
agreed with the teaching design, and the results appear to be consistent across both
university and high school students. The students noted that the strengths of the
teaching include:
(1) stimulating their interest and curiosity in thinking about the answers;
(2) helping to illustrate the meanings of the terminology and reinforce the
conceptions;
(3) appreciating the links of demonstration equipment and physics principles;
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(4) demonstration, discussion and concept mapping were all beneficial to
helping them construct an overall picture of the topic;
(5) when the relationships amongst the terms are clarified, the topic is no
longer complicated; and
(6) feeling satisfied with the outcome of being able to comprehend such a
difficult topic.
In addition to the positive comments summarized above, a few students
expressed a desire to receive more hints/guidance to facilitate effective thinking.
Extracts from the students’ comments are provided below:
z
High school workshops
1. The major difference (of this workshop) from other lectures is that it involves lots of
interaction and reasoning, and the content is relevant to what we are currently studying. The
level is just right for high school students.
2. The physics class is not filled with boring formulae anymore; instead, there are many
interesting mini labs and more space for thinking. (Suggestions) This program is perfectly
suited to 3rd grade (senior high), but if presented to lower grades, I suggest that more simple
labs be added.
3. I have grasped the effects of E and V. Before this, I never knew what the functions of
electric potential and electric field were. Utilizing a lab to guide thinking is indeed very
interesting, and the group discussion inspired me a lot. Very good ways of thinking…fantastic
program. Wish there were more (workshops) like this.
4. I used to feel that learning about electricity was very abstract. After attending this program,
I feel the ideas (of electricity) have become more concrete and acceptable.
5. Although there are plenty of formulae in electricity, we no longer feel that they are
complicated when figuring out the relationships amongst them. If time is available, I hope that
the time for experiment and discussion can be extended, allowing us to complete the
prediction and thinking.
6. (Through this program), I have figured out the relations amongst potential, electric field
and current. I used to recite the formulae without knowing what was going on. I am so glad
that their relations have been clarified and linked by means of playing games. Looking
forward to more programs!
z
University physics classes (experimental group)
1. (I) realize that Fe, E, △U and △V can explain many phenomena. University physics
allows us to think about how to explain the problems. Some phenomena look complicated, but
can be explained with simple formulae.
2. Everyone tried so hard to think about and discuss how to (indirectly) light up the tube.
Every group was highly engaged in the discussion. During the break time, many of us
crowded around the equipment to try out our methods. That was really fun!
3. With regards to how to light up and extinguish the tube, everyone put much effort into it,
even “breaking our heads” to figure out possible solutions.
4. Super! Exploring the (plasma globe) experiment can help us understand many concepts in
electricity and learn to apply the 4 key formulae.
5. I wish that the questions can provide more hints, because, for students like me with less
14
imagination, we often don’t know in which direction to start thinking.
6. Amazing equipment, which engaged everyone deeply. But I feel regret that there is only
one set (of the plasma globe), so that I can’t explore it myself first-hand.
7. It was fun to learn so many things that we did not know before. It is amazing that the
application of electric field in everyday life can be so special.
8. Finally, I have understood the reasons for and logic behind those formulae leant in high
school. Learning physics in high school is just keeping reciting formulae and practicing
problems. There is such a huge difference between that and the style in university.
9. (University physics) lets me realize how limited the knowledge is that I learnt from high
school, which is much less than what I have learnt now. Gradually I can appreciate the power
and sophistication of electricity, and start to recognize the significance of learning. Hope that
the conventional education style can be adjusted.
10. (I have) understood the reasons and rationality of many formulae, grasped more methods
for solving problems, and have been able to link with everyday life phenomena. I learnt a lot
in high school, but I only knew how to deal with problems which seem to be irrelevant to
daily life. The current teaching incorporates real stuff which makes me like physics.
11. Compared with high school, (university physics) is no more suffering with lots of cold
formulae, rather, (I have) come to understand electricity step by step.
While the students praised the program, many of them also expressed their hopes
to be able to attend similar programs in other topics. Meanwhile, some students
described their prior learning experiences in electrostatics as “suffering from the cold
formulae”, or “reciting the formulae without knowing their meanings”, reflecting the
need for modification to the conventional teaching of electricity.
¾
Comparison of academic performance
In addition to the affective outcomes discussed above, the intervention teaching
seemed to guide the students to learn in a more meaningful way. Based on the
examinations of the students’ understanding after studying the topic, the intervention
group was found to perform better than their counterparts in terms of most theories of
the topic. Examples of the questions and the percentages of correct answers are listed
in Appendix A. The intervention group was found to have a better grasp of the
knowledge regarding (1) the relationship between potential and energy (App #1b, #2b,
#11)3, (2) meanings of electric fields and force (App #3b. #7b), (3) derivation from
electric field to electric potential (App #2c, #3a, #4) and vice versa (App #1c), and (4)
distinguishing the scalar/vector properties of the electric potential/electric field (App
#10).
¾
Students’ questioning
The learning outcomes of the program were not only found by the evaluation of
3
Not all of the problems for evaluating the students’ academic performance were taught in the classes
for both experimental and control groups.
15
how students understood the content, but were also indicated by the questions raised
by the students after the program. Examples of students’ questioning are given below:
1.
2.
If the globe is filled with different gas, will the colors of the lights change?
Is it possible to light the bulb up, if the globe keeps in contact with the bulb?
3.
Why can some globes make people’s hair stand on end? What’s the difference between the
two kinds of globe?
4.
If the globe is not spherical, what would the beam pattern be?
5.
How can gas be ionized? Once the tube is lit up, why is it hard to extinguish even when the
electric field is reduced?
6.
Why could the globe be conducting when shielded by a layer of glass?
7.
What is the relation between electric field and potential?
Students’ questioning provided information indicating that (1) they can actively
link with other phenomena, #3, #4; (2) they are aware of what has been learnt and
what has not, # 5, (3) questions had been discussed, but were not thoroughly clarified,
#1, #2, #5, #6, #7. Therefore, the post-teaching questioning by the students provides
valuable information for the instructor to (1) be aware of those ideas which need
further clarification, (2) modify the questions to better suit the students’ background,
e.g. providing more information before discussion, and (3) provide more examples
and questions. The strategy of post teaching questioning, i.e. 1-minute reflection, has
been addressed in the literature (Wilson, 1986), but it may be unfruitful if the teaching
lacks learning engagement. The abundance of students’ questions indicated that the
teaching design of incorporating demonstration and questioning is beneficial in
inspiring students’ thinking, which is consistent with Buncick et. al.’s (2001) study in
mechanics.
Discussion and Conclusion
The teaching program has been found to be beneficial in confronting the
challenges of teaching and learning electrostatics. The ingredients for the success of
this program are summarized to provide guidance for developing teaching sequences
in other topics.
First, the combination of demonstration and lecturing helps to illustrate the
meanings and functions of key terms and major formulae. These formulae play the
role of linking the relationships between terms. Therefore, adopting demonstration in
class not only serves as a tool for entertainment but also facilitates cognition.
Second, while introducing the multiple strategies/content which are labeled as
16
“innovative”, including demonstration, discussion and concept mapping 4 , this
program does not ignore the value and function of the foci and activity of
conventional teaching, such as adoption of formulae, mathematics derivation and
lecturing. In order to enhance learning comprehension, multiple strategies and media
are suggested (White, 1994). Therefore, this program merged both innovative and
conventional notions of teaching, including (1) exploring physics principles
embedded in everyday life applications, (2) switching flexibly from lecturing to
discussing, and (3) reasoning the phenomena by means of words, formulae,
mathematics and images. The usage of multiple tools in reasoning is found to enhance
learning not only in solving traditional problems, but also in promoting the students’
capability in scientific arguments.
While adopting qualitative verbal explanations of everyday life phenomena, the
teaching sequence does not sacrifice the standard and precision of the course in terms
of quantitative manipulations. Most real-life phenomena contain interactions amongst
multivariables, but common verbal explanations tend to be limited to a single variable
(Viennot & Rozier, 1994). Thus, verbal explanations based on appropriate formulae
may help to highlight all the related variables, and to ensure the thoroughness of the
reasoning. On the other hand, while adopting traditional activities such as lecturing on
mathematical derivations, the current program has enhanced the sophistication and
visualization by explaining the demonstration phenomena. While merging
demonstrations and concept mapping, the program was found not only to help
illustrate the meanings of the key tools, connecting the relations amongst them, but
also to highlight the functions/value of these tools. The last purpose can enhance
students’ appreciation of the significance of these artificial conceptual tools, and thus
they can actively adopt these tools when necessary (Roth & McGinn, 1998), which
relates to the domain of belief rather than cognition.
Third, in reflecting on Aron’s (1994) notion, the spiral structure of the content
which provides students with several opportunities to practice the related concepts is
beneficial to grasping the complete knowledge. The four formulae constructing the
concept map were adopted repeatedly through the questions about the demonstrations.
For example, the relation between electric field and potential (E = ΔV/d) was adopted
three times in the questions about the “electrical insect-catcher”, the electric stunner
and indirectly lighting up the tube using the globe. For a complicated topic with many
terms and formulae such as electricity, the combination of repeated questioning and
4
According to student interviews, concept mapping was found to be absent in regular schools, but
commonly adopted in cram-schools. However, demonstration and discussion are rarely seen in either
kinds of schools. In Taiwan, the majority of students (>80%) attend cram-school classes after regular
school hours.
17
concept mapping seems to be effective in facilitating students to construct and
strengthen their conceptual framework.
Fourth, a balance between the tasks of stimulating thinking and providing
information needs to be addressed. In reflecting on Vygotsky’s notion (Wertsch, 1991),
psychological tools are essential to proceed to higher levels of cognition. For
electricity, many terms are abstract and novel to everyday life usage, and thus the
definitions, meanings and regulations of these tools need to be thoroughly introduced
to the students prior to the task of questioning to provoke thinking. Reflecting on the
three years of developing this teaching sequence, modifications to the worksheets
were mainly made to supply more information. The drawback of lacking support still
remains, according to a few students’ comments. While providing questions to tackle
alternative conceptions has gradually been adopted by many physics innovation
programs, this study recognizes the importance of providing sufficient information
before questioning, and the balance between lecturing and dialogue (Driver, et. al.,
1994).
Although the adoption of combining demonstrations and questions in teaching
physics has gradually drawn the interest of many physics instructors as it is promising
both to cognitive and affective outcomes, the expected outcomes may not necessarily
be easily obtained if the design does not deeply engage students. This study suggests
several strategies for improving the outcomes of implementing the design. First,
popular demonstration examples tend to present “valid” phenomena only, while this
study showed that the comparison of “valid” and “null” phenomena may become
powerful in integrating related theories (e.g. to distinguish the dual properties of light
by comparing the effects of lighting up the tube and the bulb). Second, while
conventional questions may be limited to observing, predicting and explaining (OPE)
the demonstration phenomena, this study found that questions which are task-oriented,
e.g. extinguishing and indirectly lighting up the tube, seem to be beneficial to
engaging students’ participation. In reflecting on the students’ responses, when
providing the task-oriented questions, providing equipment for each group to allow
hands-on trialing is suggested, if the time constraint is not tight 5 . Third, when
designing questions, the grasp of reasonable difficulties is crucial and very
challenging to instructors. The major reason that students are reluctant to participate
in discussion is that they have no idea in which direction to go to resolve the puzzles.
Therefore, continuous modifications based on the evaluations of prior
implementations, including students’ comments, are necessary. Thus, a mature design
5
In high school workshops, each group was equipped with one set of plasma globe and lights, while in
university classes only one set of the equipment was used by the instructor.
18
of teaching sequence may not be obtained until after several years of implementation
and modifications.
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Appendix A
1. A uniform electric field pointing to the left, as shown in
the figure on the right. If the electric potential difference
between point a and point c is 5000Volt, (a) while
shifting the electron from point a to c, what is the change
of the kinetic energy of the electron? 8×10-16 J ；(b)
What is the electric field in the space? 1.25×105 V/m
subjects
High school
(N=66, background 84%)
Experimental B (N=58,
background 57%)
Control B (N=68, background
57%)
a3
48.5%
b3
30.3%
31.0%
41.4%
1.5%
8.9%
2. As shown in the figure, a proton is located at the center of a capacitor, initially at rest. (a) What
would be the kinetic energy of the proton, when colliding with one plate of the capacitor? 25 eV; (b)
What is the magnitude of the electric force exerted on the proton during the acceleration process?
2.67×10-15 N
subjects
(a)3
(b) 3
High school
30.3%
24.3%
(N=66, background 84%)
Experimental A (N=60,
40.0%
63.3%
background 72%)
Control A (N=83, background
9.6%
12.0%
72%)
3. Unit of electric field: (a) Volt ÷ m=(b) N ÷ coul
a3
High school
24.3%
(N=66, background 84%)
Experimental A (N=60,
88.3%
background 72%)
Control A (N=83, background
50.6%
72%)
b3
Not applicable
75.0%
44.6%
20
4. According to the equip-potential lines, shown as dashed lines, evaluate the
magnitude (including unit) and direction of the electric field at the dot position.
ΔV
E=
= 20000 V/m (↙)
Δl
subjects
High school
(N=175, background 84%)
Experimental A (N=60,
background 72%)
Control A (N=83, background
72%)
magnitude3
24.0%
unit3
30.3%
direction3
30.8%
All3
22.3%
60.6%
73.4%
78.3%
56.7%
30.1%
33.7%
44.6%
24.1%
5. According to the figure shown on the right,
(a)compare the magnitude of work done by
external force when shifting a charge from
point a to point b; (b) compare the
magnitudes of the electric fields at point B in
each of the three situations; (c) Explain the
reasons for your answers.
subjects
(a)3
(b)
High school
(N=241,
background 84%)
67.6%
75.1%
(c) 3
(c) ×
imply to field
lines
13.6%
(N=66)
18.2%
(N=66)
(c) × imply to
E=
kQ
r2
20.7%
(Exp. B)
6. The distribution of electric potential (V) as function of
position (x) is shown in the figure on the right. At x =
3.0 cm, find the (a) magnitude of electric potential 20V,
(b) electric field 0
subjects
(a)3
79.4%
(b) 3
E=ΔV/Δx
33.7%
(b) × E=V/x
=20/0.03
22.9%
High school
(N=66, background 84%)
Experimental B
(N=58, background 57%)
Control B
(N=68, background 57%)
84.5%
19.0%
53.4%
72.1%
7.4%
23.5%
7. As shown in the figure on the right, a charged particle of m = 3.0×10－6 g, q=25 nC is
hung up reacted by uniform electric field and gravitational field. The particle is in the
state of equilibrium when the inclined angle to the vertical axis isθ= 30∘. Evaluate
the electric field of the space E = Fe = mg = 0 .679 N / C
q
subjects
High school
(N=66, background 84%)
Experimental A
(N=60, background 72%)
Control A
(N=83, background 72%)
3q
3adopted “Fe=qE” or
“E=Fe/q”
53.1%
2others
blank
16.7%
28.8%
70.0%
16.7%
13.3%
33.7%
21.7%
44.6%
21
8. A solid cylinder with total charge of Q is uniformly distributed in the cylinder. The radius of the
cylinder is R, and the height is h (where h>> R), Calculate the electric field at the distance of 2R from
the axis of the cylinder. E=ΦE/A= Q/εo(4πRh)
subjects
1
1
3E ∝
2E ∝ 2
R
R
University students
(N=72, background 73%)
(Gauss’ Law)
16.7%
(Coulumb’s Law)
45.8%
9. Two Styrofoam balls carry the same sign and amount of charge, are hung up and expel
each other at an angle of 30o inclined to the vertical axis (as shown in the figure on the
30o
right). If the mass of each ball is 0.15 g, and the charge is +20 nC each (1nC = 10-9C),
evaluate (a) the magnitude of electric force exerted on each ball 8.5×10-4 N ; (b) the
magnitude of the electric field reacted in each ball? E= Fe/q=4.25×104 N/C
subjects
(a)3
(b) 3
1
2Fe or E ∝ 2
Force
E= Fe/q
R
equilibrium
(Coulumb’s Law)
High School
58.3%
46.7%
13.2%
(N=175, background 84%)
10. Two point charges ±Q are separated at the two ends,
as shown in the right figure. If point a is located at the
center between the two charges,
is the electric field at point a zero? No ;
Is the electric potential at point a zero? Yes
× Ea = 0
Subjects
3Both
High school
58.3%
23.9%
(N=175, background 84%)
Experimental A
58.3%
21.6%
(N=60, background 72%)
Control A
50.6%
47.0%
(N=83, background 72%)
Experimental B
51.7%
34.4%
(N=58, background 57%)
Control B
36.8%
47.0%
(N=68, background 57%)
×
–Q
+Q
a
× Va ≠ 0
37.5%
26.6%
33.7%
29.3%
39.7%
y
11. A ring with radius r, is uniformly distributed with charge,
shown in the figure on the right. If the electric potential at point P is
Vp, how would the electric energy change when an electron what
is shifted from infinite to point P? eVp
Subjects
Experimental A
(N=60, background 72%)
Control A
(N=83, background 72%)
3
30.0%
× Vp
15.0%
× blank
10.0%
7.2%
14.5%
57.8%
22