New Physics: Sae Mulli (The Korean Physical Society), Volume 60, Number 9, , pp

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1 New Physics: Sae Mulli (The Korean Physical Society), Volume 60, Number 9, , pp DOI: /NPSM , 1 כ, ( , , ),., כ,, 1 5,. 9 5,, 4, 3, ,,,, כ., כ כ. :,,,,,,,, An Analysis of Physics Textbooks and of Teachers Representations of Sound Waves in Pipes from the Views of Concrete vs. Abstract and Microscopic vs. Macroscopic Jeongwoo Park Junehee Yoo Department of Physics Education, Seoul National University, Seoul (Received 3 August, 2010 : revised 26 August, 2010 : accepted 14 September, 2010) According to previous research, many students seem to have difficulties in understanding and explaining scientifically the movement of air particles in longitudinal wave displacements of air particles. In this study, nine high-school physics textbooks and five teachers explanations for sound waves in pipes were analyzed to determine the sources of students difficulties and to obtain the -960-

2 , implications for teaching sound waves. For this, the illustrations of air particles vibrations and of standing waves in the physics I textbooks of the 7th National Curriculum and the explanations of teachers who taught physics were analysed from the viewpoints of the levels of representations, microscopic vs. macroscopic, the ways of representing the entity, concrete vs. abstract, and the connections and the transfers between levels and representations. All nine textbooks and five teachers used graphs to explain entities on a microscopic level through abstract representations. Also, they used wave equations to explain entities on a macroscopic level through abstract representations. On the other hand, four textbooks and three teachers used concrete representations to explain entities on a microscopic level, and only one teacher used concrete representations to explain entities on a macroscopic level. There were no connections between concrete and abstract representations in the textbooks, but one teacher tried to connect concrete and abstract representations. Applying the views of analysis to the 7th grade students, we found that students seemed to be unable to connect concrete and abstract representations or they made connections between the representations in the wrong ways or they just seemed to recite the representations of the textbooks or they interpreted abstract representations as concrete ones. To clarify the views of illustrations and explanations, such as microscopic vs. macroscopic, and concrete vs. abstract, would be a step to improving students understandings of sound waves in pipes. PACS numbers: Ej Keywords: Air-particles vibrational motion, Longitudinal wave, Diagrams, Concrete, Abstract, Macroscopic level, Microscopic level, Textbook, Standing wave I. כ,,., כ [1]. כ..,. [2 5]. [2],,. 104 Wittmann [3] 24 %, 40 %. pjw1006@snu.ac.kr 22 %. Hrepic [4,5]., כ כ.. כ [6 12]. כ [13 20]. כ.,,, כ כ [13]. Noss [14] כ,,,, כ,,, כ.

3 -962-, Volume 60, Number 9, Hazzan [13] 3.,.,. - כ. [15].., כ, כ. כ [16] 1. Roth [17],,,,,.,,,,,.,,,. Roth [18],., כ, כ [17, 18]. Roth,. Noss [14], [19]. כ. כ 1 [17] Table 1. Definitions of Concrete and Abstract Representations. Concrete Abstract Noss Particular General Context-bounded Decontextualized Intellectually trivial Intellectually demanding Hazzan Familiar Unfamiliar Process conception Object conception Less complex More complex Roth Locality Compatibility Particularity Standardization Materiality Text Multiplicity Calculation Continuity Universality This article Intellectually trivial Intellectually demanding Less complex More complex Materiality Calculation. Noss [14] כ,, Hazzan [13],, Roth [17], Table 1 כ., Johnstone [22] (submicroscopic), (macroscopic), (symbolic) 30 [22 26]. Johnstone [22] (concrete), (imaginary), (abstract),,,, ( ) [22,24]. Treagust [23], כ.,,,,,,,.,,.,

4 , Table 2. Definitions of Microscopic and Macroscopic Levels. Microscopic Macroscopic Johnstone Imaginary Concrete Treagust Electrons, molecules, atoms Experiments and experiences Fazio Agent, particles, pieces of string Behaviour of a whole system This Article Local movement of particles Behaviour of a whole system,, כ [23]. [22,23], [24, 26]. כ. Fazio [27] 7 72 כ כ. Fazio [27],, כ.,, כ כ., 13 %, 83 %, 4 % 7 %, 35 %, 58 %.,,., כ. Table 2 כ. Table 2,.., [28,29]. Johnstone [30],,. Ivowi [31] Helm [32]. [33], כ. (illustration) (typography), (symbolism) (picture) [34]. כ,,,,,, [35].,,,,,, [36]. כ. כ,, כ.,,.. 1. כ?

5 -964-, Volume 60, Number 9, ,? 3.,? II. 5. Table , Table (A), (B), (C), (D), (E), (F), (G), (H), (I) 9. Table 3.. A, D, H, I 4, , (D) (A, B, C, E, F), 4 2 (H, I), 3, 2. G 3. 2 כ 1 (I), 1 כ 3 (A, B, D), 1 כ 5 (C, E, F, G, H). כ, כ.. 5, Table ), 2., כ,,, כ.,, כ, כ. כ כ, כ כ., כ כ, כ כ כ. Table 6. 1 כ, 5. Table 6 2. III.

6 , Table 3. Numbers of Diagrams and Pages for Explanations in Physics Textbooks. A B C D E F G H I Numbers of diagrams Everyday contexts Pipe contexts Numbers of pages for explanations 1 1 1/2 1 1/2 2/3 1/4 3/5 2 Table 4. Questionnaires for Textbook Editors and Teachers. Questions for Editors Questions for Teachers 1. What does each element in diagram of standing 1. What kinds of textbook do you use in school? wave in a pipe represent? 2. Do you mostly use textbook diagrams when 1. 1 Dotted lines you teach standing waves in a pipe? 1. 2 Solid lines If you don t use textbook diagrams, What is your intention to use two kinds of lines? where do you get substitute diagrams? Color What kinds of diagrams do you use? What are meanings of gradation? 3. What is the most difficult thing when you What is your intention to color the teach standing waves in a pipe? area between two lines? 4. In your opinion, what is the most difficult Solid line arrows thing for students when they learn standing Dotted line arrows waves in a pipe? What is your intention to use two kinds of arrows? 5. When you teach standing waves in a pipe, Explain relationships between solid what is your emphasis? lines and solid line arrows. 6. Do you explain relationships between air What is your intention to use two particles displacements and standing wave graphs? kinds of arrows instead of double arrows? 7. Do you explain meaning of standing wave graphs? Which element represents air particles? What is your intention not to use any Additional Question element representing air particles? 1. Do you explain wave length equations when 2. What is your intention to draw one diagram you teach standing waves in a pipe? including two kinds of lines and two kinds of arrows? 2. Do you explain air pressures when you teach 3. What is your intention not to explain elements in diagrams? standing waves in a pipe? 4. Introduce your reference for diagrams Table 5. Physics Teacher Participants. A B C D E Gender Female Male Female Male Male Work experience(years) כ? כ כ כ כ Table 7. 1 כ,,. A Table 7 כ. Table 7 כ,. כ., כ. Table 7.

7 -966-, Volume 60, Number 9, Table 6. Analysis Framework. Representation Microscopic Macroscopic Ways of levels (Movement of air particles) (Behaviour of a whole system) representing entity Concrete Symbolism b c Abstract Graph c c Equation b These diagrams are taken from ref. 37. c These diagrams are taken from ref y t 2 = c 2 2 y λ x 2 n = 4l, (n = 1, 2, 3, ) 2n 1, (n = 1, 2, 3, ) y = n Cn sin(ωnt + φn) sin knx 2l λn = n כ. כ.,.,., כ, , כ Fig. 1. Transverse Standing Wave of rope. This diagram is taken from textbook I. כ (A), 1 (H).,. כ כ 2 (A, F), כ 5 (B, C, E, G, H), 2 (D, I)

8 , Table 7. Analysis of Illustration Elements in 9 Korean High Physics School Textbook Diagrams. Color Line One Kind of Line Two Kinds of Line No Line Total The whole area of a pipe is colored. 2 (22.2 %) The area between 5 (55.6 %) lines is colored. No area 2 (22.2 %) is colored. Total 4 (44.4 %) 4 (44.4 %) 1 (11.1 %) 9 Bold lines around boxes represent diagrams that use arrow elements.. 2 כ כ כ. כ כ. 5 2 (B, G) 3 (C, E, H). 3 1 (H), 1 (C), 1 (E) 6. 2 Fig (C) 2 Fig

9 -968-, Volume 60, Number 9, Fig. 2. Advisable Representation of Pressure Distributions in a Pipe by Using Gradation. This Diagram is taken from Ref , כ. כ.,, כ.,, כ Fig. 2,,.. 1 2, כ. 2.,? כ 7 Table , 3,. 9,. Fig. 3. Textbook Diagrams for Wave Propagation from Microscopic-Abstract View. Fig. 4. Textbook Diagrams from the Microscopic- Concrete and Abstract Mixed View. 4 1 (H), 2 (F, I), 1 (A). 2 (A, H) כ. 3 (A, F, I).. Fig. 3,. 1, כ. כ, כ כ. 9,, כ

10 , Table 8. Analysis of Textbooks Diagrams and Explanations. Representation Ways of levels Microscopic Macroscopic representing entity Concrete Symbolism A, H, F, I Abstract Graph A, B, C, D, E, F, G, H, I Equation A, B, C, D, E, F, G, H, I כ.. כ. 9. Fig (H), 1 (A),., כ,. כ 9, כ., כ 9 A, B, F, G (A, F, I). 2 (D, G).. 4 (B, C, E, H),. [28] 43 Table (41.9 %) (a). (a) (18, 41.9 %) כ כ כ. 8 (18.6 %) (b). 1 (2.3 %) (g). (b) (g) (9, 20.9 %) כ כ. 16 (37. 2 %) (c) 2, (d) 5, (e) 7, (f) 2. (c) (d) 7 (16.3 %) כ. (e) 7 (16.3 %) כ כ כ כ. (f) 2 (4.7 %) כ.

11 -970-, Volume 60, Number 9, Fig. 5. Advisable Example of Representations Which connected Microscopic-Concrete views and Macroscopic- Concrete views.,,. כ, כ,. כ. כ, כ, כ, כ. 3.,? כ 5 Table 10. 1, 3. 5, 5. b, c, d c, d Table 11, b.,. 5 2 (c, d) (c) כ. (d)., כ כ. Fazio [27]. Fig. 5 [40]. 7 כ. כ כ כ כ. [23]. כ כ , Table 11.. Table 12. (a, e) (b, c), (d)., כ,, כ כ. כ - כ (b, c, d, e),

12 , Table 9. Students Ideas of Air Particles Movement in a Pipe (N=43). Representation Ways of levels Microscopic Macroscopic representing entity Students Ideas Forward Motion Other Oscillations No Transverse Explanation On The Line Up Others Oscillations Longitudinal Oscillations No Motion (a) (b) (c) (d) (e) (f) (g) Concrete Symbolism O O O O O O Abstract Graph O O O O O Equation Number of Students 18 8 (41.9 %) (18.6 %) (4.7 %) (11.6 %) (16.3%) (4.7 %) 16 (37.2 %) 1 (2.3 %) Table 10. Analysis of Physics Teachers Diagrams and Explanations in Teaching Standing Waves in a Pipe. Representation Ways of levels Microscopic Macroscopic representing entity Concrete Symbolism b, c, d b Abstract Graph a, b, c, d, e Equation a, b, c, d, e כ (a), כ (c), כ (d). כ (a, b, c, d, e),, (b), (b), (d), (d), (e) כ. - כ 5 4 (a, b, c, d). - Table 11. Diagrams Drawn by Physics Teachers. Teachers Diagrams a, b c, d e כ - כ. 5 1 (b)

13 -972-, Volume 60, Number 9, Table 12. Analysis of Physics Teachers Diagrams and Explanations. Representation Ways of levels Microscopic Macroscopic representing entity Concrete Symbolism Use arrows to explain air particles vibration (c, d) Air pressures are changed Explain nodes and anti-nodes with amplitudes of air at anti-nodes (b) particles vibrations (b, c, d) Emphases on air particles movements (d) Abstract Graph Draw diagrams that represent standing waves (a, b, c, d, e) Explain nodes and anti-nodes with a free-end reflection and a fixed-end reflection (a, c, d) Longitudinal standing waves are similar to transverse standing wave (e) Emphases on the meanings of standing wave (b, c) Equation Use equations of wavelength with diagrams (a, b, c, d, e) Emphasis on calculations of wavelengths (a, e).. 1 (a).. 2 (c, d), 1 (e)., כ כ כ.,, כ כ כ , כ Roth [17,18]. - כ כ. - כ, כ. - כ. - כ כ כ. IV. 7 כ,, 2. כ,, , 4. כ

14 , כ כ 2, כ 2, כ 3, 2., כ כ. כ , 1. כ כ כ. כ כ כ ,, 1., 1., 6. כ כ. כ [23]. כ כ. כ כ ,. [28] - 43, כ 18 (41.9 %), 9 (20.9 %), 7 (16.3 %), כ 7 (16.3 %), כ 2 (4.7 %).,,, כ. כ. ( 3, 1 ), ( 2, 1 ), (, 2 ), ( 4, 1 ). כ כ, כ - כ,, כ. - כ כ. - כ, כ - כ. 9 - כ. - כ. - כ כ. - כ כ.

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