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Ù þ
d # Q: & ñ © , ' a, Ó ü t o §õ " f, ¶ ú o, ¦1 p x < ÆÒ q t
High School Students’ Interpretations and Understandings of Physics Textbooks’ Illustrations of Standing Waves in a Pipe
Jeongwoo Park · Junehee Yoo ∗
Department of Physics Education, Seoul National University, Seoul 151-742 (Received 7 July 2011 : accepted 23 August 2011)
Physics textbooks’ illustrations of standing waves in a pipe are not easy to understand because even a single illustration includes various representations such as the macro level, micro levels, concrete ways and abstract ways with line, arrows and coloring. The purpose of this study was to investigate high school students’ interpretations and understandings of illustrations of standing waves in a pipe. The participants were 145 high school students who learned standing waves in a pipe during the physics 1 course. Their recalled knowledge about standing waves, which was stimulated by one illustration, and their interpretations of the illustration components were surveyed by using questionnaires. The responses were compared with the editor’s intention for that illustration. To investigate tentatively the relations between students’ interpretations and
-862-
understandings of illustrations, participants were asked to explain the movements of eight individual air particles in a pipe. Wave length formulas, an example of macro and abstract representation, were recalled by 67 % of the participants. Only 6 %, 9 %, and 1 % of the participants interpreted the lines, arrows, and coloring in the illustration in accord with the editor’s intent. Students showed a tendency to interpret illustrations on a macro level and in concrete ways rather than on a micro level and in abstract ways. Various models were given when students explained the movements of individual particles. At most 2 % of the participants seem to have scientific models while most of the participants uses mixed models. When students constructed their own models for explaining the movements of individual particles, they seemed to consider one or two illustration components rather than all components. Some students did not seem to consider the given illustration at all, or they constructed their own models, neglecting inconsistencies between the illustration and their own models.
PACS numbers: 01.40.Fk
Keywords: Standing wave, Pipe, Physics textbook, Illustration, High school student
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r$ 3 d ¦` ¦ & h 6 x # èo H ' a î ß _ / B N l 1 l x \ ' a ô Ç
< ÆÒ q t_ 6 £ x ² ú [2]\ ì r$ 3 ô Ç õ , < ÆÒ q t[ þ t É r @ /Â Òì r Æ Ò © & h
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, Æ Ò © & h ³ ð & ³` ¦ ½ ¨^ & h ³ ð & ³ ~ ½ ÓZ O Ü ¼ Ð ¸ ú 3 l w s K
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s
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E-mail: [email protected]
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2. Ó ü t o I §õ " f_ & ñ © ¶ ú o\ í < Ê ) a ¶ ú o כ ¹ è\
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a ô Ç < ÆÒ q t[ þ t _ K $ 3 É r # Q* 9, s H ¼ # | 9 _ _ ¸
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u H ?
3. ¦1 p x < ÆÒ q t_ ' a ? / & ñ © ¶ ú o\ @ /ô Ç K $ 3 õ / B N l { 9
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x < Æ § 3 < Ƹ < ÆÒ q t 79" î s % 3 . ¸ H ë H ½ Ó\ 6 £ x ² ú ` ¦ t
· ú § É r < ÆÒ q t É r 26" î ` ¦ ] jü @ô Ç 8 ú x 145" î _ 6 £ x ² ú s ì r$ 3
÷ &% 3 . ¢ ¸ô Ç ¶ ú o כ ¹ è\ ' a ô Ç ¼ # | 9 _ _ ¸ü < < ÆÒ q t_ K
$ 3 ` ¦ q § l 0 AK : r ½ ¨\ " f 6 x ) a ¶ ú o à º2 ¤
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a §õ " f_ ¼ # | 9 1 ` ¦ @ / © Ü ¼ Ð " f | 9 _ \ ¦ z ´r
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Table 1. Analysis Framework.
Representation levels
Ways of Microscopic Level Macroscopic Level
representing entity (Focused on an individual (Focused on a whole particle’s behavior) system’s behaviour)
Concrete
b cArrows Coloring
Abstract Graph
c cLines Lines
Equation
∂∂t22y= c
2 ∂∂x2y2λ
n=
2n−14l, (n = 1, 2, 3, . . .) y = P
n
C
nsin(ω
nt + φ
n) sin k
nx λ
n=
2ln, (n = 1, 2, 3, . . .)
Formula Formula
b
These diagrams are taken from Ref. 18.
c
These diagrams are taken from Ref. 19.
Table 2. Framework of Students’ Understandings of Air Particles Vibrations in Pipe.
Forward Motion Other Oscillations
Longitudinal
Transverse No Motion
Up On The Line Oscillations
Oscillations Others
Students Understanding Abbreviations of
Students’ Model FM OL LO TO OO NM
2. Ä Z ØV Ä ý u § õ m Í Ä Z ØV Ä U ê s0 n É
: r ½ ¨\ " f H Johnstone [10], Treagust [11], Fazio [12]
_
½ ¨\ ¦ l ì ø ÍÜ ¼ Ð ³ ð © ` ¦ p r & h à ºï r õ r & h à ºï r Ü
¼ Ð ¾ º ¦, Noss [13], Hassan [14], Roth [15]_ ½ ¨\ ¦ l
ì ø ÍÜ ¼ Ð ³ ð & ³ ~ ½ ÓZ O ` ¦ ½ ¨^ & h ³ ð © õ Æ Ò © & h ³ ð © Ü
¼ Ð ì r À Óô Ç ~ Ã Ì& ñ Ä º [1]_ 2 × 2 ì r$ 3 d ¦` ¦ 6 x % i .
³
ð © _ à ºï r õ ~ ½ ÓZ O \ É r y y _ # 3 Å Ò\ @ /ô Ç @ /³ ð& h
³ ð © ` ¦ í < Ê ¦ e H ¶ ú o\ ¦ Table 1 \ ] jr % i .
¶ ú
o\ ¦ ½ ¨$ í H n l : r כ ¹ è [16,17] H , z ´ o
¶ ú
³ ðü < & h o¶ ú ³ ð, G Ò oõ " î 1 p x [1] Ü ¼ Ð ì r À Ó½ + É Ã º e
. Table 1\ " f ] jr ô Ç \ Vr ¶ ú o × æ # Q " ¶ ú o כ ¹ è
y # 3 Å Ò\ K { © H @ /³ ð& h ³ ð © t \ ¦ ¶ ú o A é
ß # Q Ð t & h % i . > hZ > / B N l { 9 _ î r1 l x` ¦ ³ ð & ³ H
o¶ ú ³ ð H p r & h à ºï r _ ½ ¨^ & h ³ ð © Ü ¼ Ð, ' a ? / / B N l _ x 9
¸ ì r í\ ¦ ³ ð & ³ô Ç G Ò oõ " î É r r & h à ºï r _ ½ ¨^
Table 3. Students’ Recalled Representation of Standing Wave in Pipe (n=122).
Microscopic level Macroscopic level
Concrete - Longitudinal vibrations of air particles (1, 0.7 %) - Principles of instruments (2, 1.4 %) ways - Particles movements to the right (1, 0.7 %) - Density of medium (2, 1.4 %)
- Velocity of medium (1, 0.7 %)
3
∗(2.1 %) 4
∗(2.8 %)
Abstract - Formula (97, 66.9 %)
ways - Node and antinode (30, 20.7 %)
- Standing wave (23, 15.9 %) - Reflection of wave (12, 8.3 %)
- Constructive and destructive interference (11, 7.6 %) - Longitudinal wave (5, 3.4 %)
0 (0 %) 122 (84.1 %)
∗
Multiple response
&
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?
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© & h ³ ð © Ü ¼ Ð ì r À Ó % i . ¢ ¸ô Ç ' a ? / / B N l { 9 _ 1 l x ì
r í\ ¦ ³ ð & ³ H © ' aº d É r r & h à ºï r _ Æ Ò © & h
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ð & ³Ü ¼ Ð ì r À Ó % i . > hZ > / B N l { 9 _ î r1 l x ~ ½ Ó& ñ d É r p
r & h à ºï r _ Æ Ò © & h ³ ð © Ü ¼ Ð ì r À Ó % i Ü ¼ ¦1 p x < Æ §
§õ õ & ñ ` ¦ Å # Ql M :ë H \ ì r$ 3 r ] jü @ % i . : r
½
¨\ " f H y # 3 Å Ò\ 6 x ) a ¶ ú o כ ¹ è ¸¿ º í < Ê ) a ¶ ú
o\ ¦ & ñ % i .
< ÆÒ q t_ ' a ? / & ñ © \ @ /ô Ç s K \ ¦ ì r$ 3 H X < H Wittmann [20], Hrepic [21,22] Fazio [12]1 p x _ ½ ¨\ ¦
½ ÓÜ ¼ Ð × æ < Æ § © 0 A Ý ¶ < ÆÒ q t_ ' a ? / / B N l 1 l x _ 6 £ x ² ú
`
¦ ì r$ 3 ô Ç ~ Ã Ì& ñ Ä º [2]_ ½ ¨\ " f 6 x ô Ç ì r$ 3 d ¦` ¦ 6 x
% i . Table 2_ ¢ , aA á ¤ \ " f Ò' í H " f@ / Ð ' a î ß _ / B N l { 9
' a` ¦ ô Ç ~ ½ Ó ¾ ÓÜ ¼ Ð s 1 l x H כ ` ¦ f î r 1
l
x ¸+ þ A(Forward Motion; FM), & ñ © ` ¦ s 1 l x
H כ ` ¦ © î r1 l x ¸+ þ A(On the Line; OL), ' a õ ê ø Í ô
Ç ~ ½ Ó ¾ ÓÜ ¼ Ð 1 l x H כ ` ¦ 7 á x 1 l x ¸+ þ A(Longitudinal Oscillation: LO), ' a` ¦ Ð| 9 Q 1 l x H כ ` ¦ S 1 l x
¸+ þ A(Transverse Oscillation; TO), ~ ½ Ó ¾ Ó$ í \ O H 1 l x
H כ ` ¦ l 1 l x ¸+ þ A(Other Oscillation; OO), ¹ ¡ §f s t
· ú § H כ ` ¦ & ñ t ¸+ þ A(No Motion; NM) s 2 £ § · ¡ s ¦ y
y FM, OL, LO, TO, OO, NM_ \ ¦ 6 x K ³ ðl
% i .
3. ß e È Ã U Ø] §
ë H ½ Ó É r ' a ? / & ñ © ' aº Ó ü t o I §õ " f ¶ ú o × æ \
¶ ú
o כ ¹ è\ ¦ ] j{ 9 ´ ú §s í < Ê ¦ e H H §õ " f [22]_ ¶ ú
o\ ¦ s 6 x # ] j ÷ &% 3 . ë H ½ Ó É r Ä º ¶ ú o\ @ / ô
Ç < ÆÒ q t_ > h F c& h s K ü < y ¶ ú o כ ¹ è\ @ /ô Ç s K ,
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a ? / / B N l 1 l x \ ' a ô Ç < ÆÒ q t_ s K \ ¦ Ðl 0 AK Table 2 ü < ° ú s ¶ ú o\ @ /K H @ / Ð & h # Q Ð H | 9 ë H õ y
¶ ú
o כ ¹ è\ @ /ô Ç | 9 ë H, ' a î ß _ 8> h t & h \ " f / B N l { 9 _
¹ ¡ §f e ` ¦ ¶ n s H | 9 ë H Ü ¼ Ð ½ ¨$ í ÷ &% 3 .
III. ì Å + s ÇÊ Ý
1. w Ö «] K ¡t ô p §T ö n ÚP I w Ê Ý" e8 ý å ¾ Ë 5 X N ËV ê s כ q
×
D õ u § | ºw > HV ê s À W ¥ »V ê s
“ ' a ? / & ñ © ¶ ú o\ ¦ Ð ¦ H @ / Ð @ /² ú ” H | 9 ë
H \ @ /ô Ç < ÆÒ q t[ þ t _ 6 £ x ² ú ì r í H Table 3 õ ° ú . ì r$ 3
@
/ © 145" î × æ 123" î (85 %)s 6 £ x ² ú % i Ü ¼ 9, s [ þ t _ 6 £ x
² ú
` ¦ Table 1 _ ì r$ 3 d ¦` ¦ s 6 x K ì r$ 3 % i . ‘= å Q s {
2 ³ ` ' a s .’ ¦ é ß t ë H ½ Ó\ e H ' a _ : £ ¤f ç ` ¦ F
Õ ü t ô Ç 1" î (15 %)_ 6 £ x ² ú ` ¦ ì r$ 3 \ " f ] jü @ % i Ü ¼ 9,
Qt 122" î (84 %)_ 6 £ x ² ú ` ¦ ì r$ 3 ô Ç õ H Table 3 õ
° ú
. # $ Á " î _ < ÆÒ q ts × æ4 ¤6 £ x ² ú ` ¦ # , 6 £ x ² ú à º H 122" î s ¦ 6 £ x ² ú ¸Ã º H 129 > hs . 6 £ x ² ú × æ ì r$ 3 ] j ü
@ @ / © 1" î ` ¦ ] jü @ô Ç " é ¶ \ K { © H 122" î s d , C ü <
n , & ñ © , 1 l x _ ì ø Í , © Wç ß [ O õ Ðy © ç ß [ O , 7 á x 1
p
x r & h à ºï r _ Æ Ò © & h ³ ð © ` ¦ 6 x # 6 £ x ² ú
%
i Ü ¼ 9, s H 8 ú x 6 £ x ² ú 145" î _ 83 %\ K { © ô Ç . · ú ¡Ü ¼
Ð ¸ H Ñ þ ì rÖ ¦ É r ¸¿ º 145" î \ @ /ô Ç ° ú כs . s [ þ t × æ
l _ " é ¶ o , B | 9 _ x 9 ¸ 1 p x r & h à ºï r _ ½ ¨^ & h
³
ð © ` ¦ × æ4 ¤ # 6 x # 6 £ x ² ú ô Ç 6 £ x ² ú H 4" î (3 %) Ð
z ¤ . / B N l { 9 _ ¹ ¡ §f e , ¸ É rA á ¤ Ü ¼ Ð ¹ ¡ §f s H / B N l
{ 9 , B | 9 ? /\ " f 5 Å q ¸ 1 p x p r & h à ºï r _ ½ ¨^
Table 4. Analysis of Students Answers Who Mentioned Formula(n=97).
Answer Types Number of students
Fundamental mode(λ = 4l, l =
λ4, . . .) 48(33.1 %) Right answers
Normal mode(λ
n=
2n−14l, . . .) 18(12.4 %) 66 (45.5 %) Fundamental mode(λ = 2l, . . .) 11(7.6 %)
Wrong answers Normal mode(λ
n= 4(2n − 1)l, . . .) 7(4.8 %) 31 (21.4 %) Not mention term or use wrong term(4l, P eriod = 4l, . . .) 13(9.0 %)
Fig. 1. (Color online) Test Items.
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h ³ ð © ` ¦ × æ4 ¤ # / å L ô Ç < ÆÒ q t É r 3" î (2 %)s . p r
& h à ºï r _ Æ Ò © ³ ð © ` ¦ 6 x ô Ç < ÆÒ q t É r \ O % 3 .
r & h à ºï r _ Æ Ò © & h ³ ð © ` ¦ / å L ô Ç 6 £ x ² ú 122" î
×
æ 97" î (67 %) É r & ñ © _ © \ ' aº ) a d ` ¦ / å L % i
. C ü < n \ ¦ / å L ô Ç 6 £ x ² ú 30" î (21 %), & ñ © \ ¦
/ å L ô Ç 6 £ x ² ú 23" î (16 %), 1 l x _ ì ø Í \ ¦ / å L ô Ç 6 £ x
² ú
12" î (8 %), Ðy © ç ß [ O õ © W ç ß [ O ` ¦ / å L ô Ç 6 £ x
² ú
11" î (8 %), 7 á x \ ¦ / å L ô Ç 6 £ x ² ú 5" î (3 %)Ü ¼
Ð z ¤ . r & h à ºï r _ ½ ¨^ & h ³ ð © ` ¦ / å L ô Ç 4" î _
< ÆÒ q t × æ 2" î É r z ´Ò q t Ö ¸ õ ' aº ) a l _ " é ¶ o \ ¦, Q t
2" î É r B | 9 _ x 9 ¸\ ¦ / å L % i . p r & h à ºï r _ ½ ¨
^
& h ³ ð © ` ¦ / å L ô Ç 3" î É r / B N l { 9 _ ý aÄ º 1 l x, ¸
É
rA á ¤ Ü ¼ Ð_ ¹ ¡ §f e , B | 9 _ 5 Å q ¸\ ¦ y y 1" î m / å L % i
.
×
æ4 ¤6 £ x ² ú H 8 ú x 6" î (4 %)Ü ¼ Ð p r & h à ºï r _ ½ ¨^ & h
³
ð © õ r & h à ºï r _ Æ Ò © & h ³ ð & ³` ¦ ° ú s / å L ô Ç 6 £ x ² ú
H 2" î (1 %), r & h à ºï r _ ½ ¨^ & h ³ ð © õ r & h à º ï
r _ Æ Ò © & h ³ ð © ` ¦ ° ú s / å L ô Ç 6 £ x ² ú H 3" î (2 %), p r
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r & h à ºï r _ Æ Ò © & h ³ ð © ` ¦ ° ú s / å L ô Ç 6 £ x ² ú H 1" î (1 %)s % 3 . p r & h à ºï r _ ½ ¨^ & h ³ ð © õ r & h Ã
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B
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\
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Æ Ò © & h ³ ð © ` ¦ ° ú s / å L ô Ç < ÆÒ q t É r 3" î × æ 2" î É r l _
" é ¶ o ü < ` É r d , C ü < n \ ¦ / å L Ù þ ¡ ¦, 1" î É r x 9 õ
è, ` É r d , { 9 ü < ì ø Í , C ü < n \ ¦ / å LÙ þ ¡ . p r
& h à ºï r _ ½ ¨^ & h ³ ð © , r & h à ºï r _ ½ ¨^ & h ³ ð © õ
r & h à ºï r _ Æ Ò © & h ³ ð © ` ¦ ° ú s / å L ô Ç 6 £ x ² ú 1" î É r B
| 9 _ 5 Å q§ 4 , B | 9 _ x 9 ¸, ¸ ú 3 l w ) a d ` ¦ / å LÙ þ ¡ .
d
\ @ /K / å L ô Ç 97" î _ 6 £ x ² ú ` ¦ & ñ ² ú õ ¸² ú Ü ¼ Ð ì r
$
3 ô Ç õ H Table 4 ü < ° ú . 6 £ x ² ú × æ 66" î (46 %)s ' a
?
/ & ñ © _ © ` ¦ ½ ¨ H d ` ¦ Ó ü t o & h Ü ¼ Ð ` > / å L Ù þ
¡ . ¸ ú 3 l w ) a d ` ¦ / å L ô Ç 31" î (21 %)× æ 11" î (8 %)_ < Æ Ò q
t É r l : r ¸× ¼_ d × æ > à º\ ¦ ¸ ú 3 l w & h % 3 ¦, { 9 ì ø Í ¸× ¼ _
d ` ¦ / å L ô Ç 7" î (5 %)_ < ÆÒ q t É r > Ã º\ ¦ ¸ ú 3 l w & h ,
¾ º# Q ½ + É ½ Ó` ¦ Y LÙ þ ¡ ¦, Qt 13" î (9 %)_ < ÆÒ q t É r s
_ p H כ s Á º% Á t & h t · ú § Å Òl ü < © ` ¦
D ¥1 l x # Å Òl = 4ls ¦ ¸ ú 3 l w ) a 6 x # Q\ ¦ 6 xÙ þ ¡ . ¸ ú 3
l
w ) a d ` ¦ / å L ô Ç < ÆÒ q ts 8 ¸ 6 x ô Ç d _ + þ AI H `
É r d õ Ä » Ù þ ¡ .
2. ö n ÚP I w Ê Ý" e8 ý å ¾ Ë 5 X N ËV ê s כ q× D; c Ó Þc Ü R כ q
×
D~ ¿} º; c 6 X ¢ ] K ¡t ô p §8 ý A 0V Ä
1) -¶ ú o כ ¹ è ()ü < ( ): & ³F _ 1 l x õ ì ø ÍÅ Òl Ê
ê_ 1 l x vs. { 9 ü < ì ø Í
¼
# | 9 H & ³F _ 1 l x _ ¸_ þ v õ ì ø ÍÅ Òl Ê ê_ 1 l x _
¸_ þ v` ¦ ? /l 0 AK ` ¦ 6 xÙ þ ¡ ¦ 6 £ x ² ú Ù þ ¡ . 7 £ ¤, ¼ #
| 9
H y t & h \ " f B | 9 _ þ j@ / 0 A\ ¦ ³ ð & ³ô Ç Õ ªA á Ô
\
¦ ? /l 0 AK ` ¦ 6 x % i . s Õ ªA á Ô H 7 á x 1 l x
H / B N l { 9 _ î r1 l x` ¦ Õ ªA á Ô Ð · p כ s l M :ë H
\
< ÆÒ q t[ þ t s Õ ªA á Ô K $ 3 ` ¦ : x K / B N l { 9 _ 7 á x 1 l x` ¦ _
p ô Ç ¦ s K ½ + É Ã º ¸ e . s Qô Ç ¼ # | 9 _ _ ¸ H Table 1 \ " f ] jr ô Ç ì r$ 3 d ¦ Ð H p r & h à ºï r _ Æ Ò © & h
³
ð © Ü ¼ Ð K $ 3 ½ + É Ã º e .
^ 6 £ x ² ú × æ 91" î (63 %)s _ _ p \ ' a K 6 £ x ² ú Ù þ
¡Ü ¼ 9 ì r$ 3 ô Ç õ H Table 5 \ " f ] jr ô Ç ü < ° ú .
`
¦ r & h à ºï r _ Æ Ò © & h ³ ð © Ü ¼ Ð K $ 3 ô Ç 6 £ x ² ú H 71" î (49 %), p r & h à ºï r _ ½ ¨^ & h ³ ð © Ü ¼ Ð K $ 3 ô Ç 6 £ x
² ú
H 14" î (10 %), p r & h à ºï r _ Æ Ò © & h ³ ð © Ü ¼ Ð K
$
3 ô Ç 6 £ x ² ú H 6" î (4 %), r & h à ºï r _ ½ ¨^ & h ³ ð © Ü ¼
Ð K $ 3 ô Ç 6 £ x ² ú H 0" î s % 3 .
` ¦ r & h à ºï r _ Æ Ò © & h ³ ð © Ü ¼ Ð K $ 3 ô Ç 6 £ x ² ú 71" î × æ 60" î (41 %) É r s { 9 ü < ì ø Í \ ¦ _ p ô Ç
¦ 6 £ x ² ú % i . ` ¦ & ñ © _ { 9 ü < ì ø Í Ð K
$
3 ô Ç 6 £ x ² ú H 5" î (3 %), À Òü < Y J Ð K $ 3 ô Ç 6 £ x ² ú H 2" î (1 %), · ú ü < Z , Ðy © ç ß [ O , 1 l x, " f Ð ì ø Í@ /
~
½ Ó ¾ ÓÜ ¼ Ð ' H 1 l x 1 p x Ü ¼ Ð K $ 3 ô Ç 6 £ x ² ú y y 1" î (1 %)m Ü ¼ Ð z ¤ .
` ¦ p r & h à ºï r _ ½ ¨^ & h ³ ð © Ü ¼ Ð K $ 3 ô Ç 14" î × æ 9" î (6 %) É r s / B N l { 9 _ S 1 l x` ¦ _ p ô Ç ¦ 6 £ x
² ú
% i . 6 £ x ² ú × æ 3" î (2 %) É r / B N l { 9 _ 7 á x 1 l x` ¦ _
p ô Ç ¦ % i H X < s H ¼ # | 9 _ _ ¸ü < Ä » ¦
½
+ É Ã º e . ¢ ¸ô Ç / B N l { 9 _ î r1 l x â Ð, { 9 ü < ì ø Í
_ / B N l _ ¹ ¡ §f e ` ¦ _ p ô Ç ¦ ô Ç 6 £ x ² ú y y 1" î (1 %)m Ü ¼ Ð z ¤ .
` ¦ p r & h à ºï r _ Æ Ò © & h ³ ð © Ü ¼ Ð K $ 3 ô Ç 6" î (4
%) _ 6 £ x ² ú H ¸¿ º s & ³F _ 1 l x õ ì ø ÍÅ Òl Ê ê_ 1
l
x` ¦ _ p ô Ç ¦ 6 £ x ² ú % i . s Qô Ç 6 £ x ² ú É r ¼ # | 9 _ _
¸ü < { 9 u H כ s . ` ¦ / B N l { 9 _ 0 A Ð K $ 3 ô
Ç 6 £ x ² ú 3" î (2 %)õ < Êa , ¼ # | 9 _ _ ¸ü < { 9 u
Ä » ô Ç ~ ½ ÓZ O Ü ¼ Ð _ _ p \ ¦ K $ 3 ô Ç 6 £ x ² ú H 9" î (6
%) Ü ¼ Ð z ¤ .
2) o¶ ú ³ ð- ¶ ú o כ ¹ è( )ü < ( ): / B N l { 9 _ ¹ ¡ §f e
vs. 1 l x _ ¹ ¡ §f e
¼
# | 9 H / B N l { 9 _ ý aÄ º ¹ ¡ §f e ` ¦ I ? /l 0 AK
o¶ ú ³ ð\ ¦ 6 xÙ þ ¡ ¦ 6 £ x ² ú Ù þ ¡ . 7 £ ¤, ¼ # | 9 H o¶ ú ³ ð\ ¦ p
r & h z ´^ _ ½ ¨^ & h ³ ð & ³ ~ ½ ÓZ O Ü ¼ Ð 6 xÙ þ ¡ . ^ 6
£
x ² ú × æ 59" î (41 %)s o¶ ú ³ ð_ _ p \ ' a K 6 £ x ² ú Ù þ ¡ Ü
¼ 9 ì r$ 3 õ H Table 6 õ ° ú . 5" î _ < ÆÒ q t_ 6 £ x ² ú s Ô
¦ì r" î # ì r$ 3 \ " f ] jü @ % i Ü ¼ 9, 54" î (37 %)_ 6 £ x ² ú s
ì r$ 3 ÷ &% 3 .
o¶ ú ³ ð\ ¦ r & h à ºï r _ ½ ¨^ & h ³ ð © Ü ¼ Ð K $ 3 ô Ç 6 £ x
² ú
41" î (28 %), p r & h à ºï r _ ½ ¨^ & h ³ ð © Ü ¼ Ð K
$
3 ô Ç 6 £ x ² ú 13" î (9 %)Ü ¼ Ð z ¤ . o¶ ú ³ ð\ ¦ r
&
h à ºï r _ ½ ¨^ & h ³ ð © Ü ¼ Ð K $ 3 ô Ç 41" î É r ¸¿ º o¶ ú ³ ð
1 l x _ ¹ ¡ §f e ` ¦ · p ¦ 6 £ x ² ú % i Ü ¼ 9, o¶ ú ³ ð
\
¦ p r & h à ºï r _ ½ ¨^ & h ³ ð © Ü ¼ Ð K $ 3 ô Ç 13" î É r ¸¿ º
Table 5. Students Interpretations of Lines (n=91).
Microscopic level Macroscopic levle Sum
Concrete - Air particles’ transverse Oscillation (9, 6.2 %) way - Air particlesï Longitudinal Oscillation
(3, 2.1 %)
∗- Path of air particles’ movement (1, 0.7 %) - 14 (9.7 %) - Movements of air particles in incident and
reflect wave (1, 0.7 %)
14(9.7 %) 0 (0 %)
Abstract - Present wave and 0.5T after wave - Incident and reflect wave (60, 41.4 %) way (6, 4.1 %)
∗- Incident and reflect of standing wave
(5, 3.4 %)
- Crest and trough (2, 1.4 %)
- Alpha and beta wave (1, 0.7 %) 77 (53.1 %) - Constructive interference (1, 0.7 %)
- Wave (1, 0.7 %)
- Intensity of waves that interact in the opposite direction (1, 0.7 %)
6(4.1 %) 71(49.0 %)
Cumulative sum 20(13.8 %) 71(49.0 %) 91 (62.8 %)
∗
Answers which is similar to the editor’s intention
Table 6. Students’ Interpretations of Arrows (n=59).
Microscopic level Macroscopic levle Sum
Concrete way - Movement of air particles (13, 9.0 %)
∗- Movement of wave (41, 28.3 %) 54 (37.2 %)
Abstract way - - 0 (0.0 %)
Cumulative Sum 13 (9.0 %) 41 (28.3 %) 54 (37.2 %)
etc
∗∗5 (3.4 %)
∗
Answers which is similar to the editor’s intention
∗∗
Answers which can not be analyzed because of ambiguity.
o¶ ú ³ ð / B N l { 9 _ ¹ ¡ §f e ` ¦ · p ¦ 6 £ x ² ú % i .
" f ¼ # | 9 _ _ ¸ü < { 9 u > o¶ ú ³ ð\ ¦ / B N l { 9 _
¹ ¡ §f e Ü ¼ Ð K $ 3 ô Ç < ÆÒ q t É r 13" î (9 %)\ K { © ô Ç .
Figure 2 H ( )\ " f ( ) t _ õ & ñ ` ¦ 5 g S _
&
ñ © ( ) + þ A$ í ÷ & H õ & ñ ` ¦ ? / H ¶ ú os .
s
¶ ú o\ " f z ´ É r { 9 , & h É r ì ø Í , Ï ã T É r É r
½
+ Ë$ í \ ¦ ? / ¦, z ´ o¶ ú ³ ð H { 9 _ ' ~ ½ Ó ¾ Ó,
&
h
o¶ ú ³ ð H ì ø Í _ ' ~ ½ Ó ¾ Ó` ¦ · p . s כ É r
© ´ ú § É r < ÆÒ q t[ þ t _ 6 £ x ² ú s { 9 ü < ì ø Í \ ¦
? / ¦, o¶ ú ³ ð 1 l x _ ¹ ¡ §f e ` ¦ · p H כ õ { 9 u
ô Ç . ¢ ¸ô Ç & ñ © _ + þ A$ í ` ¦ [ O " î H õ & ñ × æ \ { 9
ü < ì ø Í _ 0 A © s ì ø Í@ / © I \ ¦ ? / H ( )
'
a ? / / B N l 1 l x ' aº ¶ ú oü < Õ ª + þ AI Ä » H & h
\
" f ¿ º > h_ ¶ ú o\ ¦ D ¥1 l x ô Ç ¦ K $ 3 ½ + É Ã º e . & ñ © _
+ þ A$ í ' aº ¶ ú o\ " f H y ¶ ú o כ ¹ è _ p H כ s Á
º% Á t \ ¦ ? / H Å Ò$ 3 s ² ú 9 e t ë ß ' a ? / / B N l 1
l
x ' aº ¶ ú o H Õ ªX O t · ú § . " f s o¶ ú ³ ð _ p
H כ s Á º% Á t \ ¦ [ O " î H Å Ò$ 3 s 9 כ ¹ ¦, _
â Ä º H Æ Ò © & h ³ ð & ³s ¦ Õ ªA á Ôs l M :ë H \ Õ ªA á Ô _
» ¡ ¤` ¦ Õ ªo ¦ » ¡ ¤ \ ' a ô Ç [ O " î ` ¦ Æ Ò H כ s < ÆÒ q t [
þ
t _ s K \ ¸¹ ¡ §` ¦ × ¦ à º e ` ¦ כ s .
3) G Ò o- ¶ ú o כ ¹ è( ): C ü < n vs. B | 9 _ èü <
x 9
¼
# | 9 H C  Òì r õ n  Òì r` ¦ y © ¸ l 0 AK G Ò o
`
¦ 6 xÙ þ ¡ ¦ 6 £ x ² ú Ù þ ¡ . 7 £ ¤, ¼ # | 9 H r & h à ºï r _ Æ
Ò © & h ³ ð © Ü ¼ Ð G Ò o` ¦ 6 x ô Ç כ s . ^ 6 £ x ² ú × æ
Table 7. Students Interpretations of Coloring and Gradation (n=84).
Microscopic Macroscopic Sum
Concrete - Air particles vibration and movement - Compression and rarefaction(34, 23.4 %)
(2, 1.4 %) - Area or range of wave, vibration range of 50 (34.5 %) - Air particles that are influenced by wave(10, 6.9 %)
waves (1, 0.7 %) - Intensity of sound(2, 1.4 %) - Movement range of rope(1, 0.7 %)
3 (2.1 %) 47 (32.4 %)
Abstract - Displacement of each point (1, 0.7 %) - Constructive and destructive interference (3, 2.1 %) - Standing wave (2, 1.4 %)
- Node/antinode (1, 0.7 %)
∗- Crest and trough (1, 0.7 %)
- Intensity of composite wave (1, 0.7 %) 14 (9.7 %) - When two waves are close or far (1, 0.7 %)
- Energy (1, 0.7 %) - Period (1, 0.7 %) - Wave length (1, 0.7 %)
- Differentiation of two waves (1, 0.7 %)
1(0.7 %) 13 (9.0 %)
Cumulative Sum 4(2.8 %) 60 (41.4 %) 64 (44.1 %)
etc
∗∗20 (13.8 %)
∗
Answers which is similar to the editor’s intention.
∗∗
