 ¹ Å] k ùX ì Ä V ê s½ Û ; c" e8 ý  ¹ ÅM > Hz º ~ ¿} º; c å ¾ ˔ X ¢

R

 ¹ Å] k ùX ì Ä V ê s½ Û
; c" e8 ý  ¹ ÅM  > Hz º ~ ¿} º; c å ¾ ˔ X ¢

€

¾Ž Ö «] K ¡t  ô p §8 ý ß Ã ÅÅ k Ä

T

+ ä \ 8 ; · 4 w Hõ i ;) Ö < ·  ™ »€ Ða : @ ·  ™ »^ ï B õ i ;

^∗

ô

 Dz D G “ §" é ¶ @ /† < Ɠ § Ó ü t o “ §¹ ¢ ¤ õ , Ø  æ· ¡ ¤ 363-791 (2009¸   1 Z 4 7{ 9  ~ à Î6 £ §, þ j7 á x‘ : r 2009¸   1 Z 4 13{ 9  ~ à Î6 £ §)

„

 l   r– Ð\  › ' a ô  Ç q „  + þ A& h   © œ S ! \ " f „  l   r– Ð כ ¹™ è x 9   r– Ð\  @ /ô  Ç œ í1 p x † < ÆÒ q t[ þ t _  “  d ” `  ¦ › ¸  

%

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½

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@

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&

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• ¸ ß ¼l   8 ß ¼€   „  ½ ¨  8 µ 1 ß “ ¦ “  d ”    H † < ÆÒ q t[ þ t s  ´ ú §€ Œ ¤ . € 9  F ' pà Ô = å S # Q”    © œ S ! \  @ /K 

"

f  H @ / Òì  r _  † < ÆÒ q ts   Ø Ô>  “  d ”  “ ¦ e ” % 3 Ü ¼
, Ä »o ½ ¨ L :”   „  ½ ¨  H Ô  ¦ s  & t t  · ú §  H  “ ¦ “  d ” 

  H † < ÆÒ q t[ þ t s  B Ä º ´ ú §€ Œ ¤Ü ¼ 9 5† < Ƹ  _   â Ä º  H ] X @ /& h Ü ¼– Ð ´ ú §“ É r † < ÆÒ q ts  Õ ªX O >  “  d ”  “ ¦ e ” % 3  . „  

‚

 “ É r U  ´s ü < [ O u   ) a — ¸€ ª œ\     „  ½ ¨_  µ 1 ßl  ² ú ˜ ”   “ ¦ “  d ”    H † < ÆÒ q t[ þ t s  ´ ú §€ Œ ¤ .  r– Ð\ " f „  

½

¨_  0 Au  µ 1 ßl \  % ò † ¾ Ó`  ¦ Šғ ¦, „  ½ ¨ „  t ˜ Ð   © œ@ /& h Ü ¼– Ð Z  }“ É r / B M \  0 Au ½ + É  â Ä º Ô  ¦ s  & t t 

· ú

§  H   1 p x _   € ª œô  Ç † < ÆÒ q t[ þ t _  “  d ” s  ³ ðØ  ¦ ÷ &% 3  .

PACS numbers: 01.40.Ej, 01.40.Jp

Keywords: „lr–Ð כ¹™è, š¸>h¥Æ, †<ÆÒqt >h¥Æ, œí1px†<Ɠ§ õ†<Æ

I. " e  ] Ø

2007¸   > h& ñ õ † < Æõ  “ §¹ ¢ ¤ õ & ñ _  † < Ƹ  Z >  ? /6   x \ " f œ í 1

p

x † < Ɠ § 5† < Ƹ  _  ‘(7)„  l  r– Ð’   H “„  l  r– Ð\  ¦ Ë ¨p   H ~ ½ Ó Z O

`  ¦ [ O " î ½ + É Ã º e ”  ” “ ¦ " î r  “ ¦ [„ à н ¨  Ö ¸1 l x] Ü ¼– Ð" f

„

 t , „  ½ ¨, „  ‚   1 p x`  ¦ ƒ     # Œ „  ½ ¨\  Ô  ¦ & l \  ¦ : Ÿ x K 

‘„  À Ó’    H 6   x # Q\  ¦ • ¸{ 9  # Œ „  ½ ¨\  Ô  ¦ s  & t   H  â Ä º\ 



 H „  l   r– Ð\  „  À Ó â ìØ Ô“ ¦ e ” 6 £ §`  ¦ · ú ˜• ¸2 Ÿ ¤ % i   [1, 2]. „  À Ó\  @ /ô  Ç > h¥ Æ “ É r œ í1 p x † < Ɠ § ‘õ † < Æ’õ 3 l q Ü ¼– РÒ'  @ /

†

< Æ_  ‘{ 9 ì ø Í Ó ü t o † < Æ’\  s Ø Ôl  t  — ¸Ž  H é ß –> \ " f ì ø Í4 Ÿ ¤& h  Ü

¼– Ð Ø Ô5 g”   . s  Qô  Ç “ §¹ ¢ ¤ õ & ñ `  ¦ : Ÿ x # Œ C Ø  ¦ ) a “ §



 Ø Ô' ¬ I6 £ § \ • ¸ Ô  ¦ ½ ¨ “ ¦ „  À Ó > h¥ Æ \  @ /ô  Ç  1 l x[ þ t _

 > h¥ Æ  Ä »+ þ As   € ª œ   [3–5]. Õ ªo “ ¦ õ † < Æ& h “   „  À Ó

>

h¥ Æ Ü ¼– Ð    or v  9  H à º\ O  t • ¸ ~ ½ Óî ß –\  @ /ô  Ç ƒ  ½ ¨

>

5 Å q ”  ' Ÿ ÷ &“ ¦ e ”   [6–8]. Ó ü t o _  y Œ • ì  r  \ " f † < ÆÒ q t[ þ t s 

 ? /  H @ /î ß – > h¥ Æ \  › ' a ô  Ç ƒ  ½ ¨  H t è ß – 20# Œ¸   1 l x î ß –  Ö ¸ µ

1 Ï >  ”  ' Ÿ ÷ &# Q M ® o  . Õ ª  X < s X O >  † < ÆÒ q t[ þ t _  @ /î ß – > h

¥ Æ

\  › ' a ô  Ç ƒ  ½ ¨  Ö ¸ µ 1 Ïô  Ç X < q K  “ § [ þ t s  s \  › ' aº   ) a

∗E-mail: [email protected]

ë

 H ] j\  @ /% ƒ l  0 AK  ‰ & ³ © œ\ " f s 6   x ½ + É Ã º e ”   H ½ ¨^ ‰& h 

“

   « Ñ, ¢ ¸  H t g Ë >\  @ /ô  Ç ƒ  ½ ¨  H p q ô  Ç ¼ # s   [9]. „   l

† < Æ\ " f• ¸ „  À Ó\  › ' a ô  Ç # Œ Q + þ AI _  š ¸> h¥ Æ  — ¸+ þ As  ì  r

$

3 ÷ &% 3 “ ¦  € ª œô  Ç † < Æ_ þ v — ¸+ þ A_  & h 6   x`  ¦ : Ÿ x K  † < ÆÒ q t[ þ t _  õ 

†

< Æ& h  > h¥ Æ Ü ¼– Ð_     o\  ¦ — ¸Ò  o % i Ü ¼
 [10, 11], † < ÆÒ q t[ þ t s

 „  À Ó\  ¦ s K    H X < l ‘ : r כ ¹™ è ÷ &  H „  t , „  ½ ¨, „  

‚

 , „  l  r– Ð\  › ' a ô  Ç “  d ” s  # Q* ‹ô  Çt  ì  r$ 3  ) a ƒ  ½ ¨ p  q

  . 2007¸   > h& ñ õ † < Æõ  “ §¹ ¢ ¤ õ & ñ \ " f÷  r ë ß –  m   t

è ß – 7 ü < 6  “ §¹ ¢ ¤ õ & ñ \ " f• ¸ „  l  r– Ðü < „  À Ó > h¥ Æ 



s \  y © œô  Ç ƒ  > $ í `  ¦ ° ú • ¸2 Ÿ ¤ ½ ¨$ í ÷ &# Q e ”   [9,12]. t  è

ß – 6  “ §¹ ¢ ¤ õ & ñ \ " f ^ ” ”  ¸ n q õ   Ý ¶$ í l  [13]  H œ í1 p x † < ÆÒ q t _

 „  l  r– Ð > h¥ Æ `  ¦ › ¸  “ ¦ 1 l x r \  „  À Ó > h¥ Æ `  ¦ › ¸ 

# Œ ¿ º > h¥ Æ _  › ' a > \  ¦ ì  r$ 3 ô  Ç   õ , „  l  r– Ð > h¥ Æ `  ¦ õ 

†

< Æ& h Ü ¼– Ð + þ A$ í ô  Ç   H  כ s  „  À Ó > h¥ Æ `  ¦ õ † < Æ& h Ü ¼– Ð + þ A

$ í

  H X < ×  æ כ ¹ô  Ç כ ¹“  s  H † d`  ¦ µ 1 ß+ À I . † < ÆÒ q t[ þ t÷  r ë ß –  m 



 \ Vq  õ † < Ɠ § , \ Vq  œ í1 p x “ § [ þ t _  „  À Ó\  @ /ô  Ç š ¸> h

¥ Æ

s  ´ ú §   H ƒ  ½ ¨[ þ t s  Ê ê5 Å q ƒ  ½ ¨– Ð" f ] jî ß – “ ¦ e ”   H  כ

“ É

r õ † < Æ& h  > h¥ Æ `  ¦ µ 1 ϲ ú ˜r ~  ´ à º e ”   H “ §¹ ¢ ¤ á Ԗ ÐÕ ªÏ þ › > hµ 1 Ï _

 r / å L$ í `  ¦ ƒ  / å L “ ¦ e ”  .

-101-

‘

: r ƒ  ½ ¨\ " f  H · ú ¡‚   ƒ  ½ ¨[ þ t _  @ / Òì  r s  „  + þ A& h “    © œ S !

 7 £ ¤ | „  t ü < „  ‚   x 9  „  ½ ¨\  ¦ ƒ     # Œ „  À Ó > h¥ Æ `  ¦ › ¸



 % i l  M :ë  H \  × ¼ Q
t  · ú §€ Œ ¤~   > h¥ Æ `  ¦ › ¸  l  0 A

# Œ q „  + þ A& h “    © œ S ! `  ¦ t “ ¦ œ í1 p x † < ÆÒ q t[ þ t _  “  d ” `  ¦

›

¸  % i  . q „  + þ A& h “    © œ S ! “ É r „  t _  l  † < Æ& h  ß ¼l , Ä

»o ½ ¨ L :”   „  ½ ¨, € 9  F ' pà Ô = å S # Q”   „  ½ ¨, „  ‚  _  U  ´ s

, ¡ óÔ  ¦ ¡ óÔ  ¦ ô  Ç „  ‚  , „  t _  € ª œF G õ  6 £ §F G \ " f „  ½ ¨ t  _

 „  ‚   U  ´s , „  t ü < „  ½ ¨_   © œ@ /& h  Z  } s  1 p x s  Ÿ í† < Ê÷ &% 3 



. „  + þ A& h “    © œ S ! \ " f š ¸> h¥ Æ _  " é ¶…  ;`  ¦ · ú ˜ à º e ” “ ¦, ¢ ¸ ô

 Ç D h– Ðs  µ 1 ß) €”   š ¸> h¥ Æ `  ¦ K   ½ + É Ã º e ” • ¸2 Ÿ ¤ “ §õ " f


†

< Æ_ þ v  « Ñ\ " f ˜ Ð ¢ - a ~ ½ ӆ ¾ Ó`  ¦ · ú ˜ à º e ”    H & h \ " f _ p 

e ”

 .

II. Ž ì ŏ ŒU ê s0 n É

1. Ž ì ŏ Œ 6 V ê s

œ

í1 p x † < Ɠ § † < ÆÒ q t[ þ t _  „  l   r– Ð l ‘ : r כ ¹™ è\  › ' a ô  Ç “  d ” 

›

¸ \  ¦ 0 Aô  Ç ƒ  ½ ¨ @ / © œ_  ‚  & ñ “ É r œ í1 p x † < Ɠ § 4† < Ƹ  õ  5† < Æ

¸

 _  “ §¹ ¢ ¤ õ & ñ \  „  ½ ¨\  Ô  ¦ & l ü < „  l  r– Ð Ë ¨p l \  @ / ô

 Ç ? /6   x s  ] jr ÷ &# Q e ” 6 £ §`  ¦ “ ¦ 9 # Œ, @ /• ¸r \  ™ èF ô  Ç

œ

í1 p x † < Ɠ § 4† < Ƹ   80" î (z Œ ™ 40, # Œ 40)õ  5† < Ƹ   80" î (z Œ ™ 42,

#

Œ 38)`  ¦ @ / © œÜ ¼– Ð Ù þ ¡ . s  † < ÆÒ q t[ þ t“ É r — ¸¿ º 4† < Ƹ   „  ½ ¨\  Ô

 ¦ & l  é ß –" é ¶ õ  5† < Ƹ   „  l  r– Ð Ë ¨p l  é ß –" é ¶`  ¦ † < Æ_ þ v ô  Ç  © œ I

\ " f [ O ë  H s  s À Ò# Q& ’  .

2. כ r Ç Ã U ØU 

‘

: r ƒ  ½ ¨\ " f œ í1 p x † < Ɠ § † < ÆÒ q t[ þ t _  „  l  r– Ð ½ ¨$ í כ ¹™ è _

 “  d ” `  ¦ › ¸  l  0 A # Œ  6   x ) a [ O ë  H t   H „  t , „  ½ ¨,

„

 ‚  , „  l  r– Ð\  @ /K  8 ú x 7ë  H † ½ ÓÜ ¼– Ð ½ ¨$ í ÷ &# Q e ”  . „   + þ

A& h “   ë  H † ½ Ó`  ¦  À ҍ  H “ §õ " fü < ² ú ˜o   _   À Òt  · ú §  H ë

 H † ½ Ó 7 £ ¤ q „  + þ A& h “   ë  H † ½ Ó[ þ t – Ð > hµ 1 Ï % i  . [ O ë  H t _  y Œ • ë

 H † ½ ӓ É r 6 £ x ² ú š ‚  × þ ˜ Ê ê 6 £ x ² ú š\  @ /ô  Ç s Ä » [ O " î `  ¦ ”  Õ ü t > 

# Œ „  l   r– Ð כ ¹™ è\  @ /ô  Ç & ñ $ í & h  s K \  ¦ › ¸    H X <

Å

Òî ß –& h `  ¦ ¿ º% 3  . [ O ë  H _  ? /6   x“ É r Table 1 õ  ° ú   .

III. + s ÇÊ Ý õ m Í ‚ º8 ý

1.  ¹ ÅU ; c å ¾ ˔ X ¢ à U Ø< g

„

 t \  › ' a ô  Ç „  + þ A& h “   ë  H ] j[ þ t“ É r @ / Òì  r „  t _  f ” § > = õ

 # î § > = ƒ    õ  › ' aº  ô  Ç  כ “  X < ‘ : r ƒ  ½ ¨\ " f  H „  t \  + ‹ e ”

  H Õ ü w   7 £ ¤ „  · ú šõ  l  † < Æ& h  ß ¼l \  ¦ ë  H ] j o # Œ † < ÆÒ q t [

þ

t _  “  d ” `  ¦ › ¸  % i  .

Fig. 1. Problem 1.

Fig. 2. Problem 2.

1.1 „  · ú š_  ß ¼l ü < „  t _  ß ¼l  q Y V t  · ú §  H

 â

Ä º\  @ /ô  Ç 6 £ x ² ú š ë

 H † ½ Ó 1“ É r „  · ú š_  ß ¼l ü < „  t _  ß ¼l  q Y V t  · ú §  H

 â

Ä º „  ½ ¨_  µ 1 ßl \  @ /ô  Ç | 9 ë  H s  . † < ÆÒ q t[ þ t _  6 £ x ² ú š   õ  139" î (86.9 %)_  † < ÆÒ q t[ þ t s  V° ú כs  ß ¼l  M :ë  H \  7 £ ¤ 9 V _ 

„

 t  3 V_  „  t ˜ Ð  „  ½ ¨  8 µ 1 ß “ ¦ % i  . 20" î (12.5 %) _  † < ÆÒ q t[ þ t“ É r „  t  ß ¼l   8 & " f \  -t   8

´ ú

§`  ¦  כ ° ú    3V  8 µ 1 ß “ ¦ 6 £ x ² ú š % i  . ´ ú §“ É r † < ÆÒ q t[ þ t s

 „  · ú šÜ ¼– Ð ³ ðr ÷ &  H Õ ü w    8  H „  t \  ƒ       H „  

½

¨  8 µ 1 ß “ ¦ Ò q ty Œ •   H  כ Ü ¼– Ð
 z Œ ¤ . “„  · ú šs   8

&

" f”    H s Ä »\  ¦ æ ¼l  ˜ Ð   H @ / Òì  r _  † < ÆÒ q t[ þ t s  “V

° ú

כs   8 & " f”  “ ¦   H  כ Ü ¼– Ð s  Qô  Ç Ò q ty Œ •`  ¦ · ú ˜ à º e ” 



.

1.2 „  · ú š_  ß ¼l   H ° ú  Ü ¼
 „  t _  ß ¼l 



 É r  â Ä º

„

 · ú š“ É r 3 V – Ð ° ú  “ ¦ „  t _  ß ¼l    É r  â Ä º\  „  ½ ¨_  µ

1 ßl \  ¦ ¶ n s  H ë  H † ½ Ó\ " f 4† < Ƹ   † < ÆÒ q t[ þ t _  52" î (32.5 %)õ  5 † < Ƹ  _  22" î (13.8 %)s  “V° ú כs  ° ú   ”    H s Ä »– Ð „  

½

¨_  µ 1 ßl  ° ú   “ ¦ 6 £ x ² ú š % i  . 4† < Ƹ   23" î (14.4 %)õ  5 † < Ƹ   53" î (33.1 %)“ É r “V ° ú כ“ É r ° ú  t ë ß – „  t   8 ß ¼€  

„

 l   8 ´ ú §s  [ þ t # Qe ”  ”    H s Ä »– Ð () „  t ü < ƒ    

 )

a „  ½ ¨  8 µ 1 ß “ ¦ 6 £ x ² ú š % i  . 4† < Ƹ   † < ÆÒ q t[ þ t“ É r „  ½ ¨

\

 Ô  ¦ & l  é ß –" é ¶`  ¦ : Ÿ x K  „  t , „  ½ ¨, „  ‚  õ  % ƒ6 £ § ] X  > 

÷

& 9 „  ½ ¨_  ƒ    `  ¦ C î  r  © œI s  . 5† < Ƹ  “ É r „  l  r– Ð Ë ¨

Table 1. Contents of questionnaire.

Categories Contents of questions No. of problems

Not proportional case between voltage and physical size 1 Battery

Not the size of battery but the same voltage 2

Bulb With broken glass or disconnected filament 3

Brightness depending on the wire length 4

Brightness for zigzagging wire 5

Wire Brightness on the length from positive

or negative electrodes 6

Electric circuit Relative height of battery and bulb 7

Table 2. Responses to the problem 1.

Grade Types of responses Reasons of response No. of students The same

( ) Larger physical size 3

4 Larger the numeral value of V 77

(
) Larger V contains more electricity (5) No response

The same

( ) Larger size contains more energy 17

5 Larger the numeral value of V 62

(
)

Larger V contains more electricity (4)

No response 1

p

l \  ¦ : Ÿ x K  „  t _  ƒ    õ  # Œ Q t  „  l  r– Ð\  ¦ † < Æ_ þ v Ù þ

¡t ë ß – µ 1 ßl  ° ú     H 6 £ x ² ú šÖ  ¦ \ " f  H  8 $ › ¸ % i  . 4† < Æ

¸

 õ  5† < Ƹ   † < ÆÒ q t — ¸¿ º „  t   8 9 þ t M : “„  l ”   8 ´ ú § s

 [ þ t # Qe ”      H ³ ð‰ & ³`  ¦  6   x ô  Ç  כ s  : £ ¤f ç “  X < œ í1 p x † < Æ

“

§\ " f „  l \  › ' aº   ) a ¿ º é ß –" é ¶`  ¦ C Ä º€  " f „  l     H 6   x

#

Q\  ¦ & ñ _  t  · ú §6 £ § \ • ¸ Ô  ¦ ½ ¨ “ ¦ † < ÆÒ q t[ þ t“ É r „  t _  ß ¼ l

ü < › ' aº   # Œ “„  l ”    H t g Aõ  † < Êa  „  t _  ß ¼l \  ¦

„

 l _  € ª œÜ ¼– Ð Ò q ty Œ •ô  Ç   H  כ `  ¦ · ú ˜ à º e ”  . „  t \   ã ¶

 [ þ t # Qe ”    H › ' a& h `  ¦ t “ ¦ e ”  .

œ

í1 p x † < Ɠ § “ §¹ ¢ ¤ õ & ñ “ É r „  t  Á º% Á “  t  # Q‹ "  % i ½ + É`  ¦ 



 H  כ “  t \  @ /K   À Òt  · ú §  H  . Õ ª Q
 „  t \  ¦ f ” § > =– Ð

ƒ

    % i `  ¦ M :ü < # î § > =– Ð ƒ     % i `  ¦ M : „  ½ ¨_  µ 1 ßl \ 

› '

a ô  Ç ? /6   x“ É r Ø Ô• 2 ; . „  t  Á º% Á s “ ¦  r– Ð\ " f # Q‹ " 

%

i ½ + É`  ¦   H t  · ú ˜t  3 l w   H  © œI \ " f † < ÆÒ q t[ þ t“ É r f ” § > =õ 

# î

§ > = ƒ    `  ¦ · ú ˜“ ¦ „  ½ ¨_  µ 1 ßl  t  · ú ˜   l  M :ë  H \ 

 

² D G „  t _  ƒ    `  ¦ s K    H  כ s   m   € Œ ™l K   



 H  © œ S ! s  . 1.5 V „  t  ¿ º > h\  ¦ f ” § > = ƒ    ô  Ç  כ õ  3V



o  1> h\  ¦ ƒ    ô  Ç  r– Ð\ " f „  ½ ¨_  µ 1 ßl \  ¦ q “ §K ˜ Ѝ  H

 כ

`  ¦ : Ÿ x # Œ „  · ú š`  ¦ @ /| Ä Ìs  • ¸ Ø Ôu   H  כ `  ¦ “ ¦ 9 

#

Œ ^  ¦ € 9 כ ¹ e ”  . „  t \  ¦ # î § > =– Ð ƒ       H  כ “ É r $  © œ

 )

a „  l  \  -t ü < › ' aº  s  e ” 6 £ §`  ¦ # Q‹ "  d ” Ü ¼– Ў  H ƒ    r  v

  H & h s  € 9 כ ¹  “ ¦ Ò q ty Œ •ô  Ç .

Fig. 3. Problem 3.

2. – ¥P  Œ B Ià à Š ¹ ŏ ŒÑ ÷ ý m Ç Ž Ö ² Ž k E# aà à Å

 ¹

ŏ Œ à U Ø< g

„

 ½ ¨\  › ' a ô  Ç „  + þ A& h “   ë  H ] j[ þ t“ É r =  G t ü < =  G t û Z & h  ] X

 >  ƒ    ÷ &% 3   H t \  ¦ · ú ˜ ˜ Ѝ  H  כ “  X < ì ø Í # Œ ‘ : r ƒ  

½

¨\ " f  H Ä »o ½ ¨ L :”    â Ä ºü < € 9  F ' pà Ô = å S # Q”   q 

„

 + þ A& h “    © œ S ! `  ¦ ë  H ] j o % i  .

„

 ½ ¨_  Ä »o ½ ¨ \ O s  € 9  F ' pà Ô ” ¸Ø  ¦ ÷ &# Q e ”   H ( )



© œ S ! \ " f † < ÆÒ q t[ þ t“ É r “ Ä »o ½ ¨ \ O l  M :ë  H \ ”    H s Ä »

Table 3. Responses to the problem 2.

Grade Types of responses Reasons of response No. of students

The same The same numeral value of V 52

( ) Larger size contains more electricity even the same V 23

4 Smaller size consumes more 2

(
) If V is equal, smaller size is fulfilled with electricity 2

No response 1

The same numeral value of V 22 The same

If V is equal, electricity is the same 1 ( ) Larger size contains more electricity even the same V 53 5 ( ) is not lightening brightly for long time,

(
)

(
) is lightening brightly in short time 1

No response 3

Table 4. Responses to the problem 3 ( ).

Grade Types of responses Reasons of response No. of students

Ë Filament exists even without glass 31

4 × No glass 49

No response 5

Ë Filament exists even without glass 1

5 × No glass 77

No response 3

–

Ð „  ½ ¨\  Ô  ¦ s  & t t  · ú §  H  “ ¦ 6 £ x ² ú šô  Ç † < ÆÒ q t“ É r 4 † < Ƹ  _ 

 â

Ä º 49" î (30.6 %), 5† < Ƹ  “ É r 77" î (48.1 %)s % 3  . ì ø ̀  

\

 “Ä »o ½ ¨ \ O # Q• ¸ € 9  F ' pà Ô e ” # Q" f”    H s Ä »– Ð

„

 ½ ¨\  Ô  ¦ s  & ”   “ ¦ 6 £ x ² ú šô  Ç † < ÆÒ q t[ þ t • ¸ e ”  . 4† < Ƹ   „  

½

¨_  Ô  ¦ & l  é ß –" é ¶`  ¦ : Ÿ x K  # Œ Q t  „  ½ ¨\  ¦ › ' a ¹ 1 Ï €  " f

„

 ½ ¨_  =  G t ü < =  G t û Z  Òì  r“ É r † < Æ_ þ v s  ÷ &t ë ß – „  ½ ¨_  ½ ¨

›

¸\ " f Ä »o ½ ¨_  % i ½ + ɓ É r q ×  æ`  ¦ ¿ º# Q  À Òt  · ú §l  M :ë  H Ü

¼– Ð ^  ¦ à º e ” “ ¦, à º\ O  ×  æ “ §  { 9 Â Ò † < ÆÒ q t_  | 9 ë  H \  @ / K

 Ä »o ½ ¨_  % i ½ + É`  ¦ ƒ  / å L ô  Ç % ò † ¾ Ó\  _ ô  Ç  כ Ü ¼– Ð ˜ Г   .

Õ

ª Q
 „  ½ ¨_  =  G t ü < =  G t û Z „  t _  € ª œF G õ  ƒ    ÷ &

#

Q e ” “ ¦ „  À Ó â ì É r    H  © œ S ! `  ¦ “  d ”    H [ O " î s 
 6 £ x

² ú

š“ É r \ O % 3  . z  ´+ « >& h Ü ¼– Ð ()_   © œ S ! “ É r „  À Ó f  Ë  Q Ô  ¦ s

 & ”   Ê ê\   – Ð  t   H  כ `  ¦ S X ‰ “  ½ + É Ã º e ”   H X < † < ÆÒ q t [

þ

t _  6 £ x ² ú š s Ä » ×  æ s  Qô  Ç  © œ S ! `  ¦ Ò q ty Œ •   H  â Ä º  H \ O % 3 



.

„

 ½ ¨_  Ä »o ½ ¨ e ” t ë ß – € 9  F ' pà Ô = å S # Q4 R e ”   H (  )

\

" f „  ½ ¨_  Ô  ¦ s  & t t  · ú §  H  “ ¦ 6 £ x ² ú šô  Ç † < ÆÒ q ts  4† < Ƹ   õ

 5† < Ƹ   — ¸¿ º ´ ú §€ Œ ¤ . ()\ " f € 9  F ' pà Ô e ” “ ¦ Ä »o ½ ¨

 \ O `  ¦ M : Ô  ¦ s  & t t  · ú §  H  “ ¦ ô  Ç † < ÆÒ q t[ þ t s  ´ ú §“ É r    õ

ü <  H  © œì ø Í÷ &  H   õ – Ð ^  ¦ à º e ”  . ()\ " f € 9  F ' pà Ô

 e ” # Q• ¸ Ä »o ½ ¨ \ O # Q" f Ô  ¦ s  & t t  · ú §  H  “ ¦ @ /² ú š ô

 Ç † < ÆÒ q t[ þ t s  ´ ú §€ Œ ¤t ë ß – ( )\ " f † < ÆÒ q t[ þ t“ É r Ä »o ½ ¨ e ” t  ë

ß – € 9  F ' pà Ô = å S # Q”    כ \   8 | 9 ×  æ % i  . ()\ " f Ä » o

½ ¨\  | 9 ×  æ ô  Ç † < ÆÒ q tõ  ( )\ " f € 9  F ' pà Ô\  | 9 ×  æ ô  Ç 6 £ x ² ú š



_  à º\  ¦ q “ §K  ˜ Ѐ Œ ¤`  ¦ M : † < ÆÒ q t[ þ t“ É r „  ½ ¨ Ô  ¦ s  & t 



 H X < Ä »o ½ ¨ ˜ Ð  € 9  F ' pà Ô\   8 ×  æ כ ¹$ í `  ¦ ¿ º“ ¦ e ” 6 £ §`  ¦

· ú

˜ à º e ”  . q 2 Ÿ ¤ Ä »o ½ ¨\  @ / # Œ Ø Ôu   H  כ s  “ §¹ ¢ ¤ õ & ñ \  \ O t ë ß – „  À Ó â ìØ Ô  H U  ´s  € 9  F ' pà Ô\  ¦ : Ÿ x # Œ {

Œ

—˜ 2 ³  r– Ð ÷ &# Q  ô  Ç   H & h `  ¦  Ø Ô>  Ø Ô} 9  € 9 כ ¹

e ”

`  ¦  כ Ü ¼– Ð Ò q ty Œ •ô  Ç .

3.  ¹ ō Ò Å; c å ¾ ˔ X ¢ à U Ø< g

„

 ‚  \  › ' a ô  Ç ¢ - a„  ô  Ç  r– Ð_  ¢ - a$ í ë  H ] j\ " f „  ‚  `  ¦ # Q b 

G>  ƒ     % i   H \  @ /ô  Ç ë  H ] j[ þ t“ É r e ” t ë ß – „  ‚    ^ ‰

\

 › ' a ô  Ç „  + þ A& h “   ë  H ] j  H Z > – Ð \ O  . ‘ : r ƒ  ½ ¨\ " f  H q 

„

 + þ A& h “   ë  H ] j– Ð „  ‚  _  U  ´s \  ¦ ² ú ˜o  Ù þ ¡`  ¦ M : „  ½ ¨_  µ 1 ß l

, ¡ óÔ  ¦ ¡ óÔ  ¦ ô  Ç „  ‚  `  ¦  6   xÙ þ ¡`  ¦ M :, „  t _  € ª œF G õ  6 £ § F

G  s _  „  ‚   U  ´s \  ¦ ² ú ˜o  Ù þ ¡`  ¦ M : „  ½ ¨_  µ 1 ßl \  ¦ ë  H ]

j o % i  .

3.1 „  ‚  _  U  ´s \    É r „  ½ ¨_  µ 1 ßl 

„

 ‚  _  U  ´s  ² ú ˜ • ¸ „  ½ ¨_  µ 1 ßl  ° ú    “ ¦ 6 £ x ² ú š ô

 Ç † < ÆÒ q t[ þ t“ É r “„  ‚  _  U  ´s ü < „  ½ ¨_  µ 1 ßl   H  © œ › ' a\ O  ,

Table 5. Responses to the problem 3 (  ).

Grade Types of responses Reasons of response No. of students

Ë Bulb is correctly connected to make 2

4 × complete circuit Filament is broken 83

Ë Bulb is correctly connected to make 2

5 × complete circuit Filament is broken 79

Table 6. Responses to the problem 4.

Grade Types of responses Reasons of response No. of students No relation between wire length and brightness 27 The same The same battery (the same electric quantity) 12 a is later on but the same brightness 1

Electricity arrives to bulb earlier

4 Longer wire makes dimmer because of late arrival 20

` Shorter wire

Electric consumption is different 19 a Electricity becomes stronger by going along longer wire 2 No response

No relation bet. wire length and brightness. 14 The same

The same battery (the same electric quantity) 7 Electricity arrives to bulb earlier

Longer wire makes dimmer because of late arrival 26

5 ` Shorter wire

Electricity becomes weaker by going along 29 wire (needs more force to longer wire)

a Longer wire can carries more electricity 1

No response 4

Fig. 4. Problem 4.

„

 t  ° ú  Ü ¼Ù ¼– Ð, „  l _  € ª œs  ° ú  Ü ¼Ù ¼– Д  “ ¦ s Ä »\  ¦

´ ú

˜ % i “ ¦ Ô  ¦ _  µ 1 ßl   H ° ú  “ ¦ „  ‚  s  |    â Ä º 0 p y >  & ”  



“ ¦ ´ ú ˜ô  Ç † < ÆÒ q t• ¸ e ”  . „  ‚  s   ú ª“ É r  â Ä º  8 µ 1 ß “ ¦ 6

£

x ² ú šô  Ç † < ÆÒ q t[ þ t“ É r “„  l   8 À 1 Ïo  „  ½ ¨\  • ¸² ú ˜÷ &Ù ¼– Ð,

„

 ‚  s  U  ´€   Y O # Q" f „  l  0 p y >  „  ² ú ˜÷ &# Q y n Cs  €  •K ”  



” 1 p x Ü ¼– Ð • ¸‚  `  ¦ : Ÿ x K   ã ¶  â ì É r    H ³ ð‰ & ³`  ¦ “ ¦ e ”  Ü

¼ 9 “„  l ”   H 6   x # Q\  ¦  6   x ô  Ç . † < ÆÒ q t[ þ t s  „  ‚  _  : £ ¤

$ í

\  @ /K  Ø  æì  r y  s K  “ ¦ e ” t  3 l w   H X < s p  ƒ    ÷ &

#

Q e ”   H „  ‚  \  ¢ ¸ 
_  „  ‚  s  f ” § > =– Ð  8K t €  , 7 £ ¤

„

 ‚  `  ¦ U  ´>  ë ß –[ þ t€    r– Ð\  ß ¼>  % ò † ¾ Ó`  ¦ p u t  · ú §  H  כ

`

 ¦ ´ ú §“ É r † < ÆÒ q t[ þ t s  z  ´+ « >& h Ü ¼– Ð · ú ˜“ ¦ e ” Ü ¼
  = Õ ª  t  s  K

 “ ¦ e ” t  3 l w ô  Ç G , „  ‚  `  ¦  8   H  כ “ É r # Qb  G>   8 

Ž

 H t   © œ › ' a\ O s   r– Ð\  % ò † ¾ Ó`  ¦ p u t  · ú §  H  כ Ü ¼– Ð { 9 ì ø Í



or v   H  ⠆ ¾ Ós  e ”    H ƒ  ½ ¨ [14]ü <  H   É r   õ \  ¦ ˜ Ð

#

Ε  r  .

3.2 ¡ óÔ  ¦ ¡ óÔ  ¦ ô  Ç „  ‚  \ " f „  ½ ¨_  µ 1 ßl 

„

 ‚  _  ƒ     — ¸€ ª œs    É r ¿ º  r– Ð\ " f „  ½ ¨_  µ 1 ßl \  ¦

¶ n

s  H ë  H † ½ Ó\  „  ½ ¨_  µ 1 ßl  ° ú    “ ¦ 6 £ x ² ú šô  Ç † < ÆÒ q t“ É r 4 † < Æ

¸

 õ  5† < Ƹ   — ¸¿ º 37" î (23.1 %)s % 3  . s  † < ÆÒ q t[ þ t _  6 £ x ² ú š s

Ä »  H U  ´s ü < ¿ ºa  ° ú  “ É r „  ‚  Ü ¼– Ð ƒ    ÷ &% 3 l  M :ë  H s

 “ ¦ % i  . `   „  ‚  s   8 µ 1 ß   “ ¦ 6 £ x ² ú šô  Ç † < ÆÒ q t

Table 7. Responses to the problem 5.

Grade Types of responses Reasons of response No. of students The same The same length and thickness without wiring methods 28

Electricity goes faster in ` because of straight,

and slower in a because of zigzag 4 Electricity passes better in ` because of straight,

4 and more difficult in a because of zigzag 46

(Zigzag may consume electricity completely)

No reason 3

Telephone works fine with zigzag wire 1

a No reason 1

No response 1

The same The same length and thickness 8

Electricity goes faster in ` because of straight,

and slower in a because of zigzag 12

5 `

Electricity passes better in ` because of straight,

and more difficult in a because of zigzag 54

a No reason 1

No response 6

Fig. 5. Problem 5.

[ þ

t s  119" î (74.4 %)s “ ¦ 6 £ x ² ú šs Ä »  H `   „  ‚  s  / B I >  .

á <# Q e ” # Q À 1 Ïo  “ ¦ a   „  ‚  “ É r ¡ ó# Œe ” # Q" f 0 p y >  l  M

:ë  H \ , `   „  ‚  “ É r / B I >  . á <# Q e ” # Q" f „  l  ¸ ú ˜ : Ÿ x 

“

¦ a   „  ‚  “ É r ½ ¨Â Ò Q4 R e ” # Q" f „  l  s 1 l x l  j Ë µ[ þ t l

 M :ë  H \   “ ¦ [ O " î % i  . † < ÆÒ q t[ þ t“ É r „  t ü < „  ½ ¨  s 

\

 ¦ s # QŠҍ  H „  ‚  _  ƒ     — ¸€ ª œ\    " f „  ½ ¨_  µ 1 ßl \ 

% ò

† ¾ Ó`  ¦ p • 2 ; “ ¦ Ò q ty Œ •   H  ⠆ ¾ Ós  y © œ >  × ¼ Qz Œ ™`  ¦ · ú ˜ Ã

º e ”  .

3.3 „  t _  € ª œF G õ  6 £ §F G \ " f „  ½ ¨ t _  „  ‚   U  ´s 

\

   É r µ 1 ßl 

@

/ Òì  r _  „  + þ A& h “    © œ S ! \ " f ë  H ] j[ þ t“ É r „  ½ ¨\  ¦ î  r X <

7

£

¤ € ª œF G \ " f „  ½ ¨ t _  U  ´s ü < 6 £ §F G \ " f „  ½ ¨ t _  U  ´ s

 ° ú  “ É r „  ‚  `  ¦  6   x # Œ > h¥ Æ › ¸ \  ¦ % i  . ‘ : r ƒ  ½ ¨

Fig. 6. Problem 6.

Fig. 7. Problem 7.

\

" f  H € ª œF G õ  6 £ §F G \ " f „  ½ ¨ t _  U  ´s   Ø Ô>  



 H q „  + þ A& h “   ë  H ] j– Ð † < ÆÒ q t[ þ t _  “  d ” `  ¦ › ¸  % i  .

„

 t ü < ƒ     ) a „  ‚  \ " f +F G õ   î  r / B M, −F G õ  



î  r / B M, +F G õ  −F G _  î  r X <\  „  ½ ¨ ƒ    ÷ &# Q e ” `  ¦ M

: „  ½ ¨_  µ 1 ßl \  ¦ ¶ n s  H ë  H † ½ Ós  . „  ½ ¨_  0 Au ü <  © œ › ' a\ O  s

 µ 1 ßl  ° ú     H 6 £ x ² ú š“ É r — ¸¿ º 12" î (7.5 %) s % 3  . (
)

Table 8. Responses to the problem 6.

Grade Types of responses Reasons of response No. of students The same No dependence on locations of the bulb 10

( )

Electricity arrives together from both sides

If the location is one side, 26 4 (
) electricity may not be supplied from electrodes

Because of center of wire (balance) 16

No reason 2

(  ) Nearest position from battery 23

No response 8

The same No dependence on locations of the bulb 2 ( )

Electricity arrives together from both sides,

(
) If the location is one side, 34

5 electricity may not be supplied from electrodes

Because of center of wire (balance) 13

(  ) Nearest position from battery 21

No response 11

Table 9. Responses to the problem 7.

Grade Types of responses Reasons of response No. of students No dependence on relative positions of battery and bulb

The same

(correct complete circuit) 25 Electricity should not flow downward 2 ( ) Electricity cannot pass through the downside bulb 10

4 No reason 4

Electricity can flow well downward 2 (
) Upward electricity is difficult, so no flow 23

No reason 7

No response 12

No dependence on relative positions of battery and bulb The same

(correct complete circuit) 18 Electricity can flow more well upward than downward 12 ( ) Upside bulb is brighter because bulb used to be upside 9

5 No reason 7

Electricity can flow well downward

(
) and Upward electricity may be difficult 30

No reason 3

No response 2

  © œ µ 1 ß “ ¦ ô  Ç † < ÆÒ q t[ þ t“ É r “ € ª œA á ¤ \ " f „  l  ° ú  s  ü <

"

f ë ß –
Ù ¼– Ð, # QÖ ¼ ô  Ç F G \  u Ä º5 g e ” Ü ¼€   −F G s 
 +F G _

 „  l  ¸ ú ˜ / B N/ å L ÷ &t  · ú §Ü ¼Ù ¼– Ð, „  ‚  _  î  r X < e ” Ü ¼Ù ¼

–

Д 1 p x s  . „  À Ó „  t _  # QÖ ¼ ô  ÇF G \ " f
ü <" f   É r ô

 Ç F G Ü ¼– Ð [  t  ç ß – “ ¦ l ˜ Ð   H „  t _  € ª œA á ¤ F G \ " f

 ã

¶  f  Ë  Q
ü <" f „  ½ ¨\ " f  Òv 9 y l  M :ë  H \  „  ½ ¨\  Ô  ¦ s

 [ þ t # Q“ : r  “ ¦ Ò q ty Œ •   H  â Ä º e ”   [15]  H ‚  ' Ÿ  ƒ  ½ ¨ ü

< ° ú  “ É r   õ \  ¦ ˜ Г   . ( )  © œ µ 1 ß “ ¦ ô  Ç † < ÆÒ q t[ þ t“ É r 1

l x{ 9  >  “„  t ü <  © œ ¾ ú šl  M :ë  H \ ”   H 6 £ x ² ú šs Ä »\  ¦

˜

Ð% i   H X < „  t _  +F G`  ¦ “„  t ”  “ ¦ : Ÿ xg Aô  Ç  כ s  . „   t

_  # QÖ ¼ ô  Ç F G s  ×  æ כ ¹  “ ¦ Ò q ty Œ •  9 s   â Ä º @ /Â Ò ì

 r _  † < ÆÒ q t[ þ t s  +F G`  ¦ ×  æ כ ¹ >  Ò q ty Œ •   H  כ Ü ¼– Ð · ú ˜ 94 R e ”

  [16].  r– Ð\     o\  ¦ Å Ò% 3 `  ¦ M : „  À Ó +\ " f Ø  ¦ µ 1 Ï

Ù ¼– Ð    o { 9 # Qè ß –  Òì  r \ " f Ò'  „  t _  +F G  s   H

„

 ) € % ò † ¾ Ó`  ¦ ~ à Ît  · ú §“ ¦ −F G A á ¤ \ ë ß – % ò † ¾ Ós  e ” Ü ¼o  “ ¦ Ò q

ty Œ •   H  â Ä º  H @ /³ ð& h “   \ Vs  . ô  Ç ¼ #  „  ½ ¨ „  t _ 

#

QÖ ¼ ô  Ç F G \ ë ß – ƒ    ÷ &# Q• ¸ Ô  ¦ s  [ þ t # Qš ¸o  “ ¦ Ò q ty Œ • 



 H  â Ä º• ¸ e ”   H X <, s   â Ä º\ • ¸ +F G \  ƒ    ÷ &# Q  ô  Ç 

“

¦ Ò q ty Œ •   H  â Ä º t C & h s   [15,16].

4.  ¹ ÅM > Hz º; c" e  ¹ ÅU Ñ ÷  ¹ ŏ Œ8 ý V ê s6 X ì Ä  Ò ãT ; c



 \ ¥ à U Ø< g

@

/ Òì  r _  „  + þ A& h “   ë  H ] j  H — ¸Ž  H  r– Ð\  ¦ Õ þ ˜ © œ 0 A 7 £ ¤ ° ú  

“ É

r Z  } s \ " f  ê  r  . ‘ : r ƒ  ½ ¨\ " f  H q „  + þ A& h “    © œ S ! Ü ¼

–

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“

 d ” `  ¦ › ¸  % i  .

„

 l  r– Ð\ " f „  t  „ à Ì   A A á ¤ \  Z  ~ # Œe ” “ ¦ „  ½ ¨

„ Ã

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„

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‚

 s   Ø Ô>  ƒ    ÷ &# Q e ” Ü ¼Ù ¼– Ð Ñ ü t   & ”     H 6 £ x ² ú šs  43" î (26.9 %)s  . „  t   A A á ¤ \  e ” “ ¦ „  ½ ¨ 0 A\  Z

 ~ # Œe ”   H  â Ä º“   () & ”   “ ¦ ô  Ç † < ÆÒ q t[ þ t“ É r “„  l 



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%

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 6 £ x ² ú šs Ä »\  ¦ ´ ú ˜ % i  . † < ÆÒ q t[ þ t“ É r „  t \ " f  ã ¶  f  Ë  Q

ü < „  ½ ¨– Ð ç ß –   H Ò q ty Œ •`  ¦
 ? /“ ¦ e ” Ü ¼ 9, „  t  0 A

\

 e ” “ ¦ „  ½ ¨  A A á ¤ \  Z  ~ # Œe ”   H  â Ä º“   (
) & ”  



“ ¦ 6 £ x ² ú šô  Ç † < ÆÒ q t[ þ t“ É r “„  l   A – Ð f  Ë  Q  8 À 1 Ïo   m

 , 0 A\ " f  A – Ð ? / 9m   „  l  ¸ ú ˜ â ì É r  ”   H s

Ä »\  ¦ ´ ú ˜ % i  . • ¸‚  `  ¦ : Ÿ x K   ã ¶  â ì É r    H Ò q ty Œ •`  ¦  l

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Œ

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>

 # Œ|   “ ¦ ^  ¦ à º e ”  .

IV. ~ ¿W d l õ m Í S  X ì È

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Ó\  ¦ s K    H X < l ‘ : r כ ¹™ è ÷ &  H „  t , „  ½ ¨, „  ‚  , „   l

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%

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8  H „  t \  ƒ       H „  ½ ¨  8 µ 1 ß “ ¦ Ò q ty Œ • “ ¦ è  H \ 

˜

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„

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L

:”   „  ½ ¨  H Ô  ¦ s  & t t  · ú §  H  “ ¦ “  d ”    H † < ÆÒ q ts  B  Ä

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š ¸  H  כ % ƒ! 3  ˜ Ðs  l

 M :ë  H“    כ ° ú   . Ä »o ½ ¨ L :4 R• ¸ „  À Ӎ  H â ìØ Ô“ ¦  Œ ™ õ

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Elementary School Students’ Recognition of Electric Circuit Elements in Untypical Situations

Jungsook Lee, BogSoon Won, Soyeon Kim and Jung Bog Kim

^∗

Department of Physics Education, Korea National University of Education, Chungbuk 363-791 (Received 7 January 2009, in final form 13 January 2009)

We have researched elementary students’ recognition of both basic components such as batteries, bulbs, wires, and the circuit itself, in untypical situations in order to develop instructional materials for conceptual understanding. Students were asked about the brightness of an electric bulb in untypical situations, such as a physical size of a battery, an electric bulb with broken glass or a disconnected filament, length of electric wire, zigzag wires, various relative positions of the bulb along the electric wire, and various relative vertical heights between the bulb and the battery.

Eighty students in the 4th grade and in the 5th grade took a designed problem set. They were shown new misconceptions that had not been detected in problems on circuit elements in typical situations. They recognized that a bulb connected to the larger-sized battery was brighter than the smaller-sized battery. They had a scientific concept for the bulb with a disconnected filament;

however, they concluded that the bulb with broken glass would not light. Especially, almost all students in the 5th grade had the wrong conception. Also they recognized that the brightness of the bulb depended on the total length of electric wire, the relative length between the positive electrode and the bulb, and the relative height between the bulb and the battery.

PACS numbers: 01.40.Ej, 01.40.Jp

Keywords: Elements of electric circuit, Misconception, Students conception, Elementary school science

∗E-mail: [email protected]