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Some preconceptions brought to the study of sound by students in grade eight Aspden, William E. 1992

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We accept t s thesis as conforming to the required standardSOME PRECONCEPTIONS BROUGHT TO THE STUDY OF SOUND BYSTUDENTS IN GRADE EIGHT.byWILLIAM ERNEST ASPDENB.Ed., The University of British Columbia, 1982.A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THEREQUIREMENTS FOR THE DEGREE OFMASTER OF ARTSinTHE FACULTY OF GRADUATE STUDIESDepartment of Mathematics and Science EducationFaculty of EducationTHE UNIVERSITY OF BRITISH COLUMBIAApril 1992© William Ernest AspdenIn presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of  ,S c. c NC& t:-., t) v...c..#411% t...1The University of British ColumbiaVancouver, CanadaDate ^I s7s712.DE-6 (2/88)AbstractThis study is a natural history of ideas brought to the study ofsound by a sample of Grade Eight students. The topic of soundwas chosen partly because of the technical background of theresearcher and partly because of the lack of previous researchcombining sound and Junior-Secondary students. The researchtechnique used was a Piaget-style interview lastingapproximately fifteen minutes in which the students wereencouraged to physically explore various apparatus and toexplain why that apparatus made sounds. The interviews wererecorded on audiotape and the tapes were then transcribed.The typescripts were then analysed to create a set ofconceptual profiles. The analyses were then considered interms of de Bono's Levels of Understanding. Furthermore,certain difficulties, particularly with concepts related towaves and difficulties related to language, were discussed.Suggestions were made for further research.TABLE OF CONTENTSABSTRACT^ iiTABLE OF CONTENTS^ i i iLIST OF FIGURES i xACKNOWLEDGEMENTS^ xCHAPTER ONE . THE PROBLEM AND ITS CONTEXT1.00 OVERVIEW of CHAPTER ONE 11.10 REASONS FOR DOING THIS STUDY 11.20 EDUCATIONAL SIGNIFICANCE OF THIS STUDY 31.30 STATEMENT OF THE PROBLEM 51.40 SPECIFIC RESEARCH QUESTIONS 61.50 METHOD OF STUDY 81.60 LIMITATIONS OF THE STUDY 1 11.70 SUMMARY OF CHAPTER ONE 1 2CHAPTER TWO. THEORETICAL AND PRACTICAL PERSPECTIVES2.00 INTRODUCTION^ 1 42.01 Two Theoretical Frameworks^142.02 Subject-Oriented^ 152.03 Student-Oriented 24iv2.10 THE PIAGETIAN VIEW^ 282.11 Background 282.12 Piaget's Interview^ 3 22.13 Piaget's Precautions 342.14^Piaget's Classification ofStudent Reactions^ 3 52.20 THE RESEARCHERS' PERSPECTIVES^3 62.21This Researcher's Training in Acousticsand Ultrasonics^ 3 72.22 Concepts from the Science Probe EightTeachers Resource Guide^3 82.23 de Bono's Levels of Understanding^3 82.24 A Model of Mental Organisation^3 92.30 CONSTRUCTIVISM IN PRACTICE^ 412.31 Johnson Abercrombie's Findings^412.32 Bruner's Autobiography^452.33 Gustafson's Findings 472.34 Linder's Findings^ 492.40 SUMMARY OF CHAPTER TWO 5 0CHAPTER THREE. METHODS OF STUDY3.00 INTRODUCTION^533.10 PURPOSE 53V3.10.1 Researcher's Profile of Topics^533.10.2 Profile of Topics fromTeacher's Guide^ 543.20 THE STUDENT SAMPLE 5 83.30 THE CLINICAL INTERVIEW^ 593.40 THE INTERVIEW METHOD 613.50 DESCRIPTION OF TASKS^ 633.51 Researcher's Subsequent Actions^703.60 LIMITATIONS OF THE DATA.^ 72CHAPTER FOUR. RESULTS OF THE STUDY4.00 OVERVIEW OF THE CHAPTER^734.10 USE OF PROFILES^ 744.11. A Conceptual Profile of StudentUnderstanding of Sound^7 54.20 ANALYSIS OF DATA^ 7 51. Human Sound Perception^772. The Energy of Sound 783. Pitch versus Loudness^ 814. Perception of Pitch 8 45. Audible Range of Frequencies^8 86. Vibration^ 897. Responses to Vibration Frequency^9 48. Frequency and Musical Instruments^97105107109112113113114vi9. Air as Transmission Medium^10110. Echoes^ 10311. Waves Without Oscilloscope; Compressionsand Rarefactions12. Student Perception of OscilloscopeTrace4.30 SUMMARY OF CHAPTER FOURCHAPTER FIVE. CONCLUSIONS AND DISCUSSION5.00 INTRODUCTION5.10 SUMMARY OF THE STUDY5.20 CONCLUSIONS OF THE STUDY5.21 Broad Patterns of Belief about Sound1. Know that sound is a kind of energy2. Know the difference between pitch andloudness3. Realize that only certain frequencies areaudible4. Know what frequency means5. Appreciate how different frequencysounds are produced in musicalinstruments6. Understand the nature of sound transmission--realize that sound requires a medium in which totravel, and will not travel through a vacuum 1157. Know what an echo is^ 1168. Realize that sound is carried by wave motion,and that sound waves consist of compressionand rarefactions in the particles making up themedium carrying the sound^1169. Be familiar with the display of several kindsof sound on an oscilloscope screen^11710 Key Ideas^ 117Summary of Section 5.21^ 1185.22 Conclusions of the Study - General^1185.30 EDUCATIONAL IMPLICATIONS OF THE STUDY 1215.31. Implications by Category^1211. Know that sound is a kind of energy^1212. Know the difference between pitchand loudness^ 1223. Realize that only certain frequencies areaudible^ 1234. Know what frequency means^1245. Appreciate how different frequencysounds are produced in musical instruments 124viiviii6. Understand the nature of soundtransmission - realize that sound requiresa medium in which to travel, and will nottravel through a vacuum^ 1 257. Know what an echo is 1 258. Realize that sound is carried by wave motionand that sound waves consist of compressions andrarefactions in the particles making up the mediumcarrying the sound^ 1269. Be familiar with the display of severalkinds of sound on an oscilloscope screen.^1 275.32. Commonalities with Gustafson^1 285.33. Commonalities with Linder 1 285.34. Thoughts with de Bono in Mind^1 285.35. Apparatus.^ 1305.40 SUGGESTIONS FOR FURTHER RESEARCH^1315.50 A LAST WORD^ 133REFERENCE LIST^ 1 35ixAPPENDIX 1:-^The Typescript of an Interview^141LIST OF FIGURES:-1. Equipment Set Up for First Setof Interviews^ 652. Door Harp Used in Later Interviews^67ACKNOWLEDGEMENTSI wish to express my deep appreciation to Dr J. Aguirre ,Dr R. Carlisle and Dr G. Erickson for agreeing to act asmembers of the thesis committee.I wish to thank Dr. J. Aguirre, Dr. R. Carlisle, Dr G.Erickson, Mr L. Exter, Ms P. Galinski, Dr. J. Gaskell, Dr. G. Hill,Mr T. McCune, Mr. D. Pugh , Mr J. Rever, Dr. P. Wesson and Mr D.Yare for their advice and help.I wish to thank Captain M. Shaffer and Mr. M. Stubbs fortheir generosity and hospitality.I wish to thank the Trustees and administrators of theMiltown School District for permission to use Seaside Schooland its equipment for this research.I wish to thank Mr. J. Treen of Seaside School for buildingthe click wheel.I wish to thank my wife, Lynne, for her unstintingsupport in difficult times.I wish to thank the Miltown District Teachers'Association for its financial assistance in the early researchand for the computing assistance during the writing phase.A huge debt of gratitude is owed to Dr Erickson and toDr Gaskell for the tremendous work they did to help me throughan administrative difficulty.xCHAPTER ONETHE PROBLEM AND ITS CONTEXT1.00 OVERVIEW OF CHAPTER ONE This chapter is concerned with this researcher's reasonsfor attempting this study, both personal and professional. Thenit moves to a review of possible problems created, in part, bycurricular needs for a standard product as opposed todifferences in the perceptions of students tackling thatcurriculum. The chapter goes over difficulties in finding andin formulating research questions and the research techniquesnecessitated by those difficulties. Finally it reviews somelimitations of the study.1.10 REASONS FOR DOING THIS STUDYThis researcher chose this topic for these reasons:1.^The researcher had had a very strong background inthe interactions of sound and persons. This stemmed from histraining and experiences as an electronics technician, rangingfrom VHF radio-telephony to ultrasonic detection and locationof hostile submarines (Royal Air Force 1983);122. During that time the researcher had becomeinterested in differences in conceptual ecologies, exemplifiedby curiosity as to why a well-trained wireless mechanic hadcleared a small aircraft to fly from Scotland to Norwaydespite a defective radio compass;3. As a student of Bronowski (1973), Kuhn (1970),Popper (Magee 1974) and Toulmin (1977), this researcher wasaware of the importance of social and societal factors in thedevelopment of physics instruction and learning;4. This researcher sees physics as an act of theimagination and the understanding of sound requires theexercise of imagination; even something as simple as Kundt'stube needs the hypothesis of waves to relate the stroking ofthe rod to the resultant positions of the grains of powder;5. As a classroom teacher, the researcher is aware ofat least two current paradoxes stemming from Chapter 9 ofScience Probe Eight, the current science text. One paradox isthat the approach to understanding sound in the text appears torequire reasoning characteristic of Piaget's Formal Operations;yet it is reasonable to expect most students in Grade Eight tobe in the Concrete Operations stage (e.g. Cowan, 1978, p. 278).The other paradox is that sound, a longitudinally-wavedphenomenon, is usually represented on an oscilloscope as atransverse-waved display.1.20 EDUCATIONAL SIGNIFICANCE OF THE STUDYProfessor Jeff Thompson was the chairman of theScience Task Group on Testing, reporting to the Department ofEducation in London, England. He stated that a paper deliveredby Rosalind Driver to the annual conference of the Associationfor Science Education had left him with a "humdinger" of aproblem. Driver's research shows that children do not acquirescientific knowledge and understanding in a "straight line" asit were. Sometimes they move sideways or even backwards, asexperimental work and new concepts illuminate each other(Sunday Times, 17/1/88, page not known).Traditionally, the student who did not repeat on theyear-end examination just what the teacher had said to himduring the year was said to have failed science. This gradingmade certain assumptions about relationships between thestudent and the material. One of those assumptions is thatstudents receiving the same teaching should produce similarresults; in turn this assumes that all students bring the sameinputs to the course. This researcher is doubtful that ateenager who spends vacations commercial fishing in the Gulfof Alaska has the same ideas about waves as the peer whospends vacations in the Chilcotin. A few days ago, students ata Miltown school were taken to the theatre for a live show;3when his view of the stage was blocked, a Kindergarten boycomplained that he could not see the T.V. (M.L. Aspden,personal communication, Fall 1991).This kind of misapprehension is not limited to children;recently a highly intelligent, well-trained shops teacher toldthe staff room that: "Fishing in winter is the pits! Thosealuminum boats really pull the cold out of the sea!" ( Langley,personal communication, 1988). On an English examination amature student was asked a question about Higgins inPygmalion. Even though that student had played Pickering inmany performances of that comedy, he could not clear his mindof the Higgins of My Fair Lady and so produced an answer whichneeded a very understanding examiner (W.E. Aspden, personalexperience, 1965).The above examples demonstrate that students--even students with successful previous training--do notalways bring the same or even the expected ideas to academicwork. Thus the assumption that all students bring the sameinputs to the course is blatantly false. With that falsehoodmade overt, it becomes necessary to find out more about theinputs those students really bring to the academic study ofsound, in the hope that the teacher can either build on thestudents' present knowledge or arrange, perhaps,4demonstrations which will encourage the students to considerthe possibility that their beliefs are erroneous.Therefore, by exploring and airing some of the beliefsbrought by Grade 8 students to the academic study of sound, itis hoped that this study might help learning become clearerand more efficient.1.30 STATEMENT OF THE PROBLEM The purpose of this study is to expose some of thepreconceptions which students bring the study of sound.On reviewing the literature available on the topic in1987, this researcher found nothing relevant to the expectedcourse of this study. Still in 1987, this researchercommissioned a search by a professional UBC librarian; thissearch turned up nothing relevant to the study of sound bystudents in the intermediate or junior-secondary grades. In1989 a research assistant in the Education Faculty of UBCsearched the literature; again, nothing relevant was found.Faced with such a paucity of research data, theresearcher had to create his own study of the field of sound.He started by taking the relevant concepts from a variety ofphysics texts and created a number of concept maps in thestyle of Novak (1984). From those maps, he synthesised six5major parts of the topic; those parts are: Perception;Vibration; Frequency; Pitch; Transmission and Echoes.1.40 SPECIFIC RESEARCH QUESTIONSIn the absence of published previous research, thisresearcher could find no specific hypotheses to be studied. Infact the researcher suspected that formulating suchhypotheses from the researcher's knowledge of formal physicsmight taint students' answers with the researcher'spreconceptions, expressed unconsciously in such ways as toneof voice and body language.By combining the researcher's understanding of thescientist's perception of sound with the requirements of theprovincial curriculum and the researcher's experiences inteaching that subject, this general question arose:How do students conceptualise sound phenomena ?In turn, this question can lead to several others. Theyinclude:As the students come into the grade eight sound course, whatare their ideas about human hearing, sound as energy,relationships between pitch and loudness, vibration, how werespond to frequencies, how musical instruments work, therole of air as a transmission medium and the formation of6echoes? Do the students "read" an oscilloscope trace in thesame way as does the teacher? Does the port-dwellingstudents' understanding of sea waves affect their perceptionsof sound waves?Therefore the researcher chose to create an exploratorystudy. The most obvious problem in a verbal study is thetendency of students to shade their answers to what they thinkthe teacher wants. This has been attested to in publicationsranging from Goldsmith's Deserted Village: " ... to trace theday's disasters in his (the school master's) morning face" tothe insurance salesman's technique of nodding and of askingquestions requiring a "yes" answer in order to train thecustomer to agree that the latter should sign the contract.To reduce the researcher's effects on the student'sexplanations, the researcher chose to have the studentphysically explore various apparatus--some from a sciencedepartment, some specially-made, some store purchased--andvocalise what the student was thinking. In turn, thesecomments and actions led the researcher to ask questions ofclarification and extension. Therefore the specific researchquestions depended on the individual student's responses to theequipment.7However, a completely unstructured conversation couldgo anywhere; to keep the interview on track, the interviewerused the six major topics from his understanding of thephysics of sound (Perception, Vibration, Frequency, Pitch,Transmission and Echoes) as waypoints in the interview.Therefore, the research questions were developed toelicit students' mental constructs on these six major topicsand to explore the students' elaborations of their answers.1.50 METHOD OF STUDYThe researcher chose the individual interview as thetechnique for gathering data on student preconceptions.The interview was guided in outline by the researcher'ssense of the parts of the study of sound and in detail bystudent actions, comments and responses.Interviewees were self-selected. Students at a junior-secondary school were offered the opportunity to earn a dollarfor about twenty minutes' work during the noon hour. Asstudents came, they were interviewed.During the early seven interviews, a table in theresearcher's laboratory had various sound-producing apparatusput on it. Three interviews did not use any apparatus. Fourinterviews used a door harp as the stimulus.8The interview was usually in three parts, Introduction,Research, Closure. The Introduction by the researcher ensuredthat the student was aware that the interview was intended tohelp the researcher with a university course; that theinterview was absolutely voluntary and that the student hadthe right to leave any time; that the interview would haveabsolutely no effect on the student's future at the junior-secondary school or at university; that the interview wasbeing taped. If the student accepted those conditions, theinterview was continued.The early interviews started with the interviewee beingshown the apparatus on the table, being asked to try out theitems of equipment and to tell the interviewer about them.Sometimes it was necessary to start by asking the studentclose-ended questions about a specific piece of apparatus, inorder to get the student to speak freely.The later interviews used a door harp. This apparatuswas chosen because, at the time, few students had seen oneand so student exploration was more likely to be influenced bystudent concepts of sound than by previous experiences withsimilar items. The particular shape of door harp was chosenbecause it seemed most dissimilar to many stringed musicalinstruments such as guitars.9The final part of the interview consisted of thanking thestudents for their efforts, by informing them that theresearcher's findings would be published as a book and byasking if they had any questions.Because the interviews were carried out during thethirty-five minute noon break, they were limited in time toabout fifteen minutes each. Some interviews were shorterthan others because the student had run out of ideas and one ortwo interviews took almost thirty minutes because both thestudent and the interviewer became fascinated by the topic.Many more interviews were carried out than are cited;five were lost during a transfer of documents from one site toanother; three were carried out with Grade Nine students aspractice for the interviewer; three had to be aborted forvarious reasons, such as excessive interruption from theschool PA system.1.60 LIMITATIONS OF THE STUDYThe researcher cannot be certain that the sample ofstudents was quite random, for he deliberately refrained fromasking interviewees why they had volunteered.Miltown is isolated; one cannot leave the districtwithout riding a ferry or a plane. Suburbs of Miltown are10parochial; for example a student in the suburb of Berrypatchhas told this researcher that students in the suburb ofFerryview (less than a kilometre away) are snobs (Gr. 6student, personal communication, 1985).Miltown's industry is the oldest pulp mill on the coast;this researcher was informed that until recently the MiltownMill took about two hundred employees to do what Cariboo Pulpdid with twelve employees (M. Stubbs, personalcommunication, 1978). Therefore it could be argued that manysocial perceptions in Miltown are more appropriate to anagriculturally-based, rather than to a technically-based,culture.This community has a very strong musical tradition; thechildrens' chorus and orchestra have toured Europe and theSoviet Union. Miltown hosts an international music festivalevery other summer. Therefore, if any preconceptions of soundexist, then they might well stem from experiences of music.Miltown is dominated by the sea. Few students have nothad their perceptions of wave phenomena affected by ferryrides and salmon fishing.The interviews noted represent about five percent of theGrade Eight population of one school in an isolated community.Given this context, the researcher cannot claim that thesample studied represents the Grade Eight population of11British Columbia. However, this research might provide asource of testable hypotheses.1.70 SUMMARY OF CHAPTER ONEThis chapter has explored some of the researcher'sreasons for choosing this topic, outlining some of theresearcher's relevant experiences. The purpose of the study isto learn more about the ideas about sound which students bringto the academic topic of Sound in the Grade Eight Curriculum.Because of the dearth of published research on theinteractions of students and sound at the time this thesis wasstarted, there were few obvious hypotheses to test. Thereforethis research became a type of natural history, trying to getsome idea of how students think of sound. The technique forresearch was to invite volunteer students to look at variousitems of equipment, to have a student manipulate theequipment and to have the student verbalise, spontaneously orby open-ended questioning, what the student was thinking.Although the interviews were exploratory, they were focussedaround six key ideas.The interviews were audio taped and the tapestranscribed to typescript. The researcher then reviewed the12typescripts en masse, looking for consistencies, anomalies andpatterns.It is far from certain that this research can begeneralised to a population of grade eight students, since itwas carried out in one school in an isolated community whichhas an international reputation for music.13CHAPTER TWOTHEORETICAL AND PRACTICAL PERSPECTIVES2.00 INTRODUCTION There seems to be a dearth of research into theinteractions of Junior Secondary students with the academicstudy of Sound. Therefore, to find an academic context for thisresearch, it was necessary to review the historic backgroundof this kind of research. However, during the same period thatthis research was being carried out, two others wereresearching similar fields, one for elementary students andthe other for university students. Some findings are noted atthe end of this chapter.In this chapter the related literature will be reviewed inthree frameworks, two theoretical and the othermethodological.2.01 Two Theoretical FrameworksThis research is about how students reason about sound.One way to describe the interactions of people and the naturalworld is to look at systems of belief. One system is that theUniverse is, and that humans must try to understand it (the14subject-oriented perspective). The other system is that theuniverse is a product of human thought (the student-orientedperspective). This part of the paper first looks at thesubject-oriented perpective historically from the AhmesPapyrus to Heisenberg's Uncertainty Principle and exposesserious problems with that perspective. Then it looks at thestudent-oriented perspective historically from Adelard of Bathto Linder, and exposes some technicalities of this study.2.02 A Subject-oriented FrameworkAlthough the student-oriented view, known as"Constructivism" in science instruction is not perfectlyidentical with that view in mathematics instruction, thisresearcher found that, to understand traditional reasoning inphysics, one must go into mathematics, for as Feynmanwrites:The strange thing about physics is that for thefundamental laws we need mathematics. (1965, p. 36)and Bronowski writes:The exact fit of the numbers describes the exact lawsthat bind the Universe (p. 161).Herodotus (quoted in Turnbull, p. 1) suggests thatmathematics as we know it originated in Egypt, where floodingof the Nile changed the sizes of individual farmer's fields and15so changed the amount of tax the farmer had to pay. Thereforethe King's overseers had to devise means to measure theamount of land each farmer had. Aristotle claims thatmathematics originated with the leisure class of Egyptianpriests; his view was confirmed by the Ahmes papyrus(Turnbull, p. 2).According to Turnbull (p. 4), a Greek merchant, Thales,transferred Egyptian rules of earth-measuring (geometry) toGreece and abstracted the concept of a space. The study ofspaces seemed to be the study of the Universe, for an object isa space filled with matter and a vacuum is a space devoid ofmatter. By further abstraction the Greeks classifiedgeometric ideas by points. A place could be defined as a singlepoint, a line as the connection of two points, a plane as therelationship of three points and the simplest solid, thetetrahedron, as the relationship of four points.Since a point has position but no dimension, the Greekstudy of geometry became more and more idealised until theredeveloped the idea, ascribed to Plato, that a figure such as acircle drawn by an earthling was a tawdry attempt to mimic aperfect circle in existence beyond human experience. Turnbullquotes (p. 27, 28) that to the question "What does God do? "Plato replied, "God always geometrizes." Therefore geometrybecame a search for perfection.16Bronowski (p. 156) reminds us that another Greek,Pythagoras, discovered that by dividing a vibrating string intointeger numbers of lengths, the harmonics of the ground notecould be produced; a non-integer division produced discord.This practicality confirmed the theoretical view thatgeometry was the way to understanding the Universe.The view that the Universe had a static, geometricperfection persisted until the time of the Renaissance, whenperspective painting developed. To quote Bronowski :The perspective painter has a different intention. Hedeliberately makes us step away from any absolute andabstract view. Not so much a place as a moment is fixedfor us ... ; a point of view in time more than in space(p. 180).The intention of these painters was to create a sense ofmovement in space (Bronowski, p.179); this movement becamescientifically important when Kepler, using the more precisemeasurements of Brahe, found that the position of Mars wastoo far off the position expected (by about eight minutes ofarc) (Feynman, p. 16). Therefore Mars did not go in a perfectcircle, but in an ellipse. Newton used geometry to learn moreabout the paths of planets but found that the stasis ofgeometry prevented further analysis. Newton developed a newanalysis based on rates of change; this new analysis, calculus,17became the most important mathematical tool for exploringboth astronomical and terrestrial phenomena in scientificterms (Bronowski, p. 184-6).Newton's development of calculus stemmed from hisassumptions that space and time were absolute, rectangularand passing immutably (Bronowski, p. 241). These assumptionsbecame rules to live by; the work of the next couple ofcenturies was to develop knowledge for economic benefit; theparadigm of the geographer hacking his way through the jungleto learn everything about, say, Africa, was matched by that ofthe scientist in his laboratory hacking his way into learningeverything about, say, heat. However, those explorations wereto ruin the very assumptions on which they were based.Celestial navigation was vital to reliable maritimetransport. Creating the tables of numbers needed to guidereliable navigation required a colossal number of repetitivearithmetical operations. Pascal had demonstrated thatnumbers and operations could form patterns (Turnbull, p. 90);the power loom performed dozens of repetitive movementsevery minute and the embroidery on the cloth could be changedby changing the loom control cards in the Jacquard system.Babbage tried to develop a Pascal design into a machine whichgenerated tables of numbers much as a loom generates cloth;the numbers generated would depend on the human's choice of18Jacquard-type cards. Babbage never got the machine to workas he wanted it to, but he created a mechanical system which,apparently, could take a load of axioms and data and figure outevery possible combination.Babbage's machines raised questions at the overlaps ofmathematics and philosophy; those questions included:a) Could every statement in mathematics beproven or disproven?b) Was mathematics consistent, in that the sameaxioms could not generate both a = b and a # b ?c)^Was there some machine-capable method todecide the truth or falsity of a mathematicalstatement?(Taken from Hodge, p. 91)In exploring these questions, Kurt Godel demonstrated that:... any such precise mathematical systems of rules andprocedures whatever, provided that it is broad enough tocontain descriptions of simple arithmetic propositionsand provided that it is free from contradiction, mustcontain some statements that are neither provable nordisprovable by the means allowed within the system(Penrose, p. 133).19Thus Godel, in 1931, by showing that a reasoningtechnique as simple as arithmetic could contain statementswhich were impossible to classify as true or false byaxiomatic means, showed that the perfection envisaged by theGreeks and searched for through millennia by philosophers andscientists, was a chimera.Since physics needs mathematics for fundamental laws(Feynman, 1965, p. 36), then clearly Godel had shown a seriousflaw in scientific reasoning. Was it then possible to be guidedby the Bronowski quotation (p. 161) and find the exact fit forthe numbers in order to find the exact laws of the Universe?Alas, no.In 1881 Michelson and Morely tried to find the speed ofthe Earth through the ether (a hypothetical fluid whichaccounted for the propagation of light). Instead, they foundthat, in normal dimensions:It appears to be impossible to alter the speed of light inspace by sending it in different directions. In fact thespeed of light in space is found to be the same by allmethods of measuring it, even if the observer and thelig h t source are in relative motion with constantvelocity^ (Buesche, p. 27).20This conclusion seems to be absurd. To illustrate itsabsurdity, consider this example. An observer is driving thefreeway at 80 km/h. Car A is travelling in the same directionat 50 km/h; the observer, perhaps using Doppler, will sensehimself to be passing car A at a relative speed of 30 km/h.Meanwhile, car B is travelling in the same direction as theobserver at 100 km/h; the observer will sense a relative speedof 20 km/h. Car C is in the opposite lane going in the oppositedirection at 90 km/h; the observer will sense a relative speedof 170 km/h. The above makes sense and is experienced inreality. Yet if cars A, B and C are replaced by flashes oflight, then the observer will experience them all at the samerelative speed, that of light, according to Michelson andMorely.To overcome this absurdity, Lorenz suggested that anobject shrinks in the direction of motion (Feynman, 1977, p.1:15:5). This contradicts one assumption at the heart of post-Newtonian physics, that space is absolute (see previousquotation), for it means that an object such as a metre stickfilling that space will change its length according to itsdirection of travel. Therefore, no measurement of distance canbe taken at face value.In an attempt to deal with the above absurdities it wassuggested that time itself depends on relative speeds. This21has been tried; when two identical, very accurate, clocks weresynchronised and one kept stationary whilst the other wasflown round the earth on a commercial jetliner, the clockswere found to be out of synchronisation after the flight. Thustime cannot be held to be absolute. Therefore no timemeasures can be taken at face value. Both the length and timeabsurdities can be handled mathematically; yet Godel haddemonstrated that mathematics is badly flawed.What, then, of microscopic dimensions? To quoteFeynman:(Heisenberg's Uncertainty Principle) says that if we tryto pin down a particle by forcing it to be at aparticular place, it ends up by having high speed. Or ifwe try to force it to go very slowly, or at a precisevelocity, it "spreads out" so that we do not know verywell just where it is^ (1977, p. 6.10).Thus the Greek ambition to find an objective, perfectstructure of the Universe by the use of reason and ofmeasurement was doomed by the imperfections of reason foundby Godel and by the impossibilities of perfect measurementfound by Michelson and Morely and by Heisenberg.Therefore, it is fallacious to believe that there is aperfect truth in the natural world, both independent of humans22and intelligible to them. On a more practical level, manyscientists and mathematicians regard the DifferentialCalculus as the key to post-Newtonian physics:In (the differential calculus) mathematics becomes adynamic mode of thought, and that is a major mental stepin the ascent of man(Bronowski, p. 187).Once the basic ideas of differential calculus have beengrasped, a whole new range of problems can be graspedwithout great difficulty. For two hundred years after thediscovery of the differential calculus, the mainadvantages lay in applications of it (Sawyer, p. 121).If we go back to our chequer game (physics) thefundamental laws are the rules by which the chequersmove^ (Feynman,1965, p. 36)... the Newtonian scheme translates to a precise anddeterminate system of dynamic equations. ... This form ofdeterminism, as satisfied by the world of Newtonianmechanics, had (and still has) a profound influence onphilosophic thought^(Penrose, p. 217).23The curious point about this most valuable mathematicaltool and philosophic viewpoint is that it is inexact. The key tocalculus is to have the term dx*2 which has a magnitude,albeit tiny, equated to zero (Dakin and Porter, p. 42).Therefore this profoundly influential technique is based oninexactitude, that is, imperfection. Therefore any structure ofthe world perceptible to man must come from man himself.The view that mathematical entities exist only if theyhave been (mentally) constructed by man is the core belief ofthe philosophy of constructivism (Flew, 1979). Thisresearcher would argue that one can substitute "physics" for"mathematics" in the above statement.2.03 The Student-oriented Perspective This thesis has already referred to Thompson's referenceto Driver's research. That research indicated that children donot acquire scientific knowledge and understanding in a"straight line" as it were. Sometimes they move sideways oreven backwards as new work and new concepts illuminate eachother (Sunday Times, 17/1/88).To understand how such research can surprise one of theeminences of science education in England, it is appropriate tolook at a history of the viewpoint which stimulated thatresearch.24The earliest reference this researcher has been able tofind which hints at a personally constructed universe is thatof Adelard of Bath, who, in the twelfth century, said that:It is through reason that we are men, for if we turn ourbacks on the amazing rational beauty of the universe welive in we should indeed deserve to be driven therefrom.(Goldstein, p. 88).A more recent quote comes indirectly from Feynman:If one cannot see gravitation acting here, he has no soul(Marion, p. 94).William Shakespeare wrote that :there is nothing either good or bad but thinking makes itso ...^ (Hamlet, II,ii,250).B.L. Whorf wrote that:We dissect nature along lines laid down by our nativelanguages. The categories and types that we isolatefrom the world of phenomena we do not find therebecause they stare every observer in the face: on thecontrary, the world is presented in a Kaleidoscopic fluxof impressions which has to be organised in our minds....We cut nature up, organize it into concepts, and ascribe25significances as we do, largely because we are parties toan agreement to organise it this way--an agreementthat holds throughout our speech community and iscodified in the patterns of our language(quoted in Rheingold,1988, p. 5).Davis and Hersh (1981) state that:The constructivist's argument ... is that mathematicaltruth is time-dependent and is subjective, although itdoes not depend on the consciousness of any particularlive mathematician^ (p. 373).Intuitive means lacking in rigor, and yet the concept ofrigor is defined intuitively rather than rigorously (p. 39).A related meaning of "intuitive" is what one might expectto be true in this kind of situation^(p. 391).Intuitive means relying on some physical model or onsome leading examples^ (p. 392).Kant claimed that:there must be some forms of all possible experience or,as he called them, the forms of intuition, which weimpose on everything that we are in contact with; andthat, since we are capable of attaining organised and26intelligible information about the world, we must havewithin ourselves the organising principles. Our mindsstructure and interpret the observations of our senses.(Popkin and Stroll, p. 135)That so many disparate thinkers have produced ideas assimilar as those quoted above strongly suggests to thisresearcher that there might well be considerable truth in theidea that the apparent organisation of the outside universecomes, in reality, from the organisation of our senses; if thatis so, then the outside world does not "impact upon our senses"but our senses and the outside world interact. However, aconsideration of the anthropic principles of cosmology wouldbe beyond the scope of this study.However John Locke stated that our knowledge comes tous through our senses and we have no innate ideas. He believedthat a neonate's brain was a "white paper, void of allcharacters, devoid of all ideas". Locke thought that we get ourideas of objects because several simple ideas constantlyappear together and always seem conjoined, so we presumethat these ideas belong to one thing (Popkin and Stroll, p. 193).Key ideas of present day constructivism appear to stemfrom Kant's view that there must be principles or concepts bywhich we organise the general content of any possibleexperience in order to reorganise it as a coherent datum.27Jean Piaget is credited with developing the technique forexploring an individual's principles and concepts. He wasoriginally a biologist who had worked on standardising tests ofchildren's abilities with Theodore Simon in the laboratory ofAlfred Binet (Piaget 1977 preface; Thomas 1979, p. 289). Hedescribed his work as Genetic Epistemology, which means thatthe central question guiding his investigations is not, "whatare children like?" but, "How does knowledge develop inhumans?" Or, more precisely, "How does the relationshipbetween the knower and the known change with the passage oftime?" (Thomas, p. 289).2.10 THE PIAGETIAN VIEW2.11 Background According to Piaget himself, the subject of hisinvestigation is:What conceptions of the world does the child naturallyform at the different stages of his development?(Piaget, 1982, p13).In turn, the above becomes two questions:What is the scheme of reality which prompts thisthought?28and:What use does he make of the whims of cause and oflaw? ... (What is) the child's notion of causality?Piaget points out that:the content may or may not be apparent and varies withthe child and the things of which it is speaking. It is asystem of ultimate beliefs and it requires a specialtechnique to bring them to the light of day(Piaget, 1982, p. 13).If Piaget is right in stating that the contentvaries with the child, then he contradicts the "tabula rasa", thebelief of Locke that:at birth a child's mind is a void, an unmarked page ortabula rasa on which the contents of the mind aresketched by the child's experiences as she grows up.(Thomas, p. 32)The relative merits of these views are very importantindeed to the subject teacher, because the key assumption of aprovincial, state or national curriculum to be tested at the endof the year assumes that the same experiences will generatethe same products; in turn this assumes that the inputmaterials--the students--are homogeneous. That is likesaying that if a workshop puts wood through a chair-making29machine, the end-product will be the same whether the woodput in is teak or is balsa. This possibility requires that thesubject teacher investigate whether or not all his studentsthink alike on a certain topic and whether or not the studentsthink in the ways expected by the curriculum designers.One example of how students bring different ideas toscience courses is demonstrated by my experience as scienceteacher in a coastal town who found my students were wellaware of the semi-diurnal nature of the tides, neaps, springs,full and half moons, tidal currents and, in particular, tidaleffects on the locations of salmon. I took my niece (of aboutthe same age as my students) from Quesnel to look at theSmall Boat Harbour in Miltown. It was low tide. The childlooked at the ramp and asked: "What's this for?" "So people canwalk down to the boats." When she asked, "Is it always thissteep?" I said, "No, sometimes it's almost horizontal." "Thenwhy do people walk on it when they will fall off the end?"Clearly I had included a factor, the change of the sealevel, of which the child was not aware and I, and my students,were too familiar; therefore the assumption that children frominterior communities bring the same concepts of tide to classas do students from coastal communities is clearly dubious.Indeed Haggerty has found that a student can have twoconflicting beliefs about a phenomenon and change from30behaviour appropriate to one belief to behaviour appropriate tothe other according to the social situation (Haggerty, personalcommunication, 1986).Piaget's view of knowledge is that it is:A process of acting--physically and/or mentally--onobjects, images and symbols that the child's perceptuallens has cast into patterns that are somewhat familiarto him.... The objects are found in the world of directexperience, whilst the images and symbols can bederived not only from the "real world" but from memoryas well^ (Thomas, p. 294).From the above quotation it is clear that if the teacherwishes to produce predictable results from the objects,images and symbols that the curriculum imposes on the child,the teacher must be aware of the "perceptual lens" which thestudent brings to the course. A synonym for "perceptual lens"might be "preconceptions brought to the course".A key concept in Piaget's writings is the scheme:A scheme is the structure or organisation of actions asthey are transferred or generalised by repetition insimilar or analogous circumstances(Piaget and Inhelder (1969) in Thomas, p. 295).31The child reshapes events of the world somewhat to fitthe pattern of her existing schemes (Thomas, p. 298).Therefore, to match the student and the curriculum moreexactly, the teacher should be aware of what schemes thestudent brings to his studies. Such is the purpose of this study.2.12 Piaget's Interview The clearest statement of the relevant technique is givenby Thomas:During the adolescent years, children are more oftengiven verbal problems and asked about how they arrivedat their conclusion.Piaget has not limited himself to asking each child apreconceived set of questions. Rather, after beginningthe interview with a standard question or two, he hasfelt free to create, on the spot, additional questions forthe child, designed to probe the thought processes thatproduced the initial answer^(Thomas, p. 290).An example of the technique comes from Piaget himself.A child is given two rulers, each about six inches long andshown that they are of the same length. One ruler is then slidabout three inches along and the child is asked if the length of32the moved stick is still equal to that of the other. Only 15% ofchildren aged 5 years believe it is; 70% of eight-year-oldsbelieve it is; 100% of eleven-year-olds think it is. Yet thesame sticks' lengths, if they are placed obliquely to eachother, are more accurately estimated by younger children thanby older (Piaget, 1977, p. 76-9).Such evidence belies the idea that children are littleadults; children have ways of perceiving appropriate to theirages and their experiences.^Constructivist researchers havefound and published many examples of children's surprisingconcepts in physics; just one text (Driver, Guesne, Tiberghien(1985), subsequently abbreviated to DGT) shows students'"unscientific" conceptual understandings of such "scientific"material as:Various models of a simple electrical circuit (p. 36);students who think that mixing water at temperature awith water at temperature b will increase the mixture'stemperature to (a+b) (p. 62);students who think that objects will fall off the Earth ifdropped in the Southern Hemisphere (p. 180).It is not adequate to assume that a successful idea willbe held by the student forever more; for instance Strauss(1981) (cited in DGT, figure 4.2 right) suggests that a student33can hold an idea about the temperature of mixtures at age 4,lose it at age 6 and have it again at age 9.2.13 Piaget's PrecautionsHowever, this method of obtaining insights into students'thinking is not without difficulties. The content of theirthinking may or may not be apparent and varies with the childand the things of which it is speaking. "The method is difficultand tedious and needs one or two years' full training"(Piaget, 1982, p. 14).The researcher should vary the questions, make countersuggestions and respond to student answers rather than to theresearcher's schedule. The form of the question can influencethe answer; if the researcher were to ask, "What makes the sunmove?" this might well indicate to the child that some sort ofmachine or animal is required for the answer.Open ended questions are intended to bring out thechild's ideas, no matter how unexpected those ideas may seem.The researcher's unconscious body language can stop thechild in midanswer or even give the child clues about the kindof answer the researcher wants (p. 16). The validity of theanswer should be assessed by reviewing the spontaneousquestions of children of the interviewed age or younger.34The child might well think of itself as immature and itsideas unworthy of serious discussion. One way of handling thispossible issue is to treat the student as a peer and to assurethe child that answers will not be attributed to him or her.Self-censorship can appear when the child is jolted into self-conciousness; therefore the researcher must consciously workto keep the conversation smooth (p. 19).Recognizing patterns of response is certainly animportant aspect of research, but mere summaries of the type"x children mentioned phenomenon y" are misrepresentative.Instead the researcher should note and perhaps publish theactual phrases used by the child (p. 20).It is dangerous to assume that a child's answers will beon the same level throughout the interview. A student mightbe deeply engaged intellectually by one question and amused bythe triviality of another (p. 21).2.13 Piaget's Classification of Student Reactions An uninterested child might reply to a question with thefirst thing that comes into its head; Piaget describes this as arandom answer (Piaget,1982, p. 21).Sometimes a child might give an answer in which it doesnot really believe; such is romancing (p. 21).35When the child gives an answer suggested by thequestion, or to please the questioner, such is called suggested conviction (p. 22).When the child draws the answer from his or her ownschemata after reflection, such is called liberated conviction.Although it is from the child, it is very possible that thisanswer is fine-tuned to fit the child's perception of thequestion.When the child produces an answer from his or her ownreflections which, in turn, have resulted from previouscogitations in the same mental area, such is said to bespontaneous conviction. It must be noted that liberated andspontaneous convictions can masquerade as each other (p. 22).2.20 THE RESEARCHERS' PERSPECTIVESAs Piaget wrote (Piaget,1982, p.16, 21), there is somedanger that the child's answers will be influenced by theresearcher's schemata; therefore it is vitally important thatthe researcher endeavour to keep his conceptual ecologyhidden. However, if the researcher has no mental structureswith which to guide the interviews and their analysis, he willbe like the proverbial horseman, galloping off in all directions.36This researcher's mental structures stemmed from fivesources. They were first his training in sonics phenomena asan apprentice at Number One Radio School, Royal Air Force,Locking. The next influence was the content of the ScienceTeacher's Course at the College of Education of the Universityof Hull. The third influence was the Teacher's Guide To GradeEight Science. The fourth influence was de Bono's Levels ofUnderstanding. The fifth influence was the paper by Posner,Strike, Hewson and Gertzog (1982) (subsequently abbreviatedto PSHG), on the conceptual ecologies of the typical person.2.21 This Researcher's Training in Acoustics and Ultrasonics This researcher was trained as an electronics technicianby the Royal Air Force. The relevant parts of the courseincluded: microphones and telephones, aircraftintercommunication equipment, testing and servicingcomponents, VHF equipment, UHF equipment, HFcommunications equipment, beacon location, sound,introduction to wireless communication, amplifiers.Additionally, he was trained by RAF Yatesbury in the use andservicing of equipment used to locate submarines by sound. Asa serviceman with Coastal Command, he was introduced tosonobuoys and spent some time as an observer onantisubmarine patrols, practices and research flights.37The researcher used this background, and that from hiscoursework at Hull, to organise the topic of Sound into six keyideas, Perception, Vibration, Frequency, Pitch, Transmissionand Echoes.2.22 Concepts from Science Probe Eight. Teachers' ResourceGuidePage 9-3 of this Guide gives the lists of goals and ofkey ideas with which Grade Eight students of sound would befaced.This researcher reviewed the typescripts of theinterviews with those goals and key ideas in mind, to get anidea of the relevant schemas used when the child thought hewas engaged with the questions developed from the six-topiclist.2.21_ jie jaQnj2'a  Levels of UnderstandingOne example of a Piagetian task and its products comesfrom Edward de Bono. He showed a thousand people a blackcylinder standing alone on a white table. Suddenly, withoutwarning or apparent reason, the cylinder fell over. Eachmember of the audience was asked to try to understand whathad happened and to write down his or her explanation on a filecard. Ten minutes later, the cards were collected(de Bono, p. 18).38de Bono then reviewed the cards and found that theanswers displayed five levels of understanding. They were(summarised from chapter 3):Simple Description:- for example, it changed positionsuddenly..Porridge Words:- for example, the cylinder had a mechanism init that made it fall over after a certain time; here the namesare used to mark unknowns.Give it a Name:- for example, it fell over. Reason? Gravity.Here the word is chosen which is seen as the most appropriate.The Way It Works:- for example, Overbalanced due to a slowshifting of contents.Full Details:- A combination of "Give it a Name" and "The WayIt Works". For example, "The tube was unstable but was stuckto the table by adhesive which eventually gave way"(taken from p. 31).This researcher found de Bono's categories very helpfulindeed when thinking about the children's comments during theinterviews.2.24 A Model of Mental Organisation PSHG (1982) produced a model for a conceptual ecologywhich this researcher bore in mind during the reviews of theinterviews. Features of the model include:39Analogies and Metaphors:- parallels and similaritieswith other ideas which reinforce and stabilise thepresent mental structure;Anomalies:- weaknesses in an idea's structure of whichthe person is aware;Explanatory Ideals:- the criteria the person believes areneeded for a satisfactory explanation;Epistemological Views:- criteria such as elegance,economy and permanence of knowledge;Metaphysical Beliefs:- such as in the orderliness ofnature;Metaphysical Concepts:- such as the stability of timeand distance;Knowledge from other fields.The authors had demonstrated that for a concept to beaccepted into a person's conceptual ecology, it must beintelligible to that person, it must be plausible and verifiableby that person's standards, it must appear fruitful to thatperson and the idea's competition must be shown to havestrange or unacceptable results.402.30 CONSTRUCTIVISM IN PRACTICEThe above has been strongly oriented towards academia.What evidence is there that such material is relevant in reallife teaching? In this section this researcher looks at M.L.Johnson Abercrombie's experiences of teaching at theUniversities of London and Birmingham. Her book, Anatomy ofJudgement, clearly displays the effects of personal schemataon the perception of "objective truth".In addition, this section will look at some research onsound in the recent science education literature.2.31 Johnson Abercrombie's FindingsM.L. Johnson Abercrombie (subsequently abbreviated toJA) taught anatomy and zoology at the Universities ofBirmingham and of London.She found that scientific ways of thinking did not stemautomatically from learning the facts of science.Consequently she started teaching by discussion so that herstudents would become aware of some of the factors that hadaffected their judgement in scientific matters. JA regardedjudgement as ignoring some of the bombardment ofinformation, seizing on the rest and interpreting it in the light41of past experience (p. 14). More to the point of this research,she wrote that:during discussion, students were mutually testing andmodifying their schemata and as a result of reorganisingtheir store of experience were able later to make morevalid interpretations^(p. 21).JA's essential message is:We are unaware of the extent of our personalinvolvement in the act (of forming judgements aboutreceived information), tending to regard the informationas given (p. 172).She cites as examples of the effects of past experiencethe chimpanzee who had been born blind then had its sightrestored; it could not recognise a feeding bottle by sight, butrecognised the bottle when it touched the chimpanzee's cheek(p. 47). Another example was of the human adult whose sightwas restored surgically several years after being born blind;even after thirteen days' training the person could notdifferentiate between a square and a triangle without countingthe corners (p. 46-7).She found that the earlier a schema had formed, theharder it was to verbalise (p. 95) and that the student was notaware of using (such early schema); because the student was42not aware of them he did not question the validity of usingthem on a particular occasion, and therefore tended to usethem inappropriately and so failed to gain information ofpredictive value (p. 95).Those of her students who were told that a Breughelpainting was of a wedding saw joy and musical instruments;those who were told it was of a fight saw anger and weapons(p. 38). She refers to the schematic assumptions involved incertain optical illusions. It might be assumed that suchschemata as health, disease and x-rays are relatively stable;yet JA found that in an experiment involving the reading ofx-ray pictures, radiologists were found to disagree with themselves in twenty percent of their cases. In thatexperiment, a radiologist was shown an x-ray and made adiagnosis. Some weeks later, the doctor was shown the samepicture and asked to make a diagnosis, unaware that he or shehad done so previously. Several such pairs of diagnoses werethen compared (p. 108).JA studied the reactions of several groups of students tovarious topics; amongst other things, she found that what wasa fact to some students was an inference to others (p. 103);that a fact was relevant to some and a red herring to others (p.103); the name given to an object affected its perception (p.104), and even burette readings tended towards the expected43values (p. 105). She found that students tended to think thatthings that were alike in some respects would be alike in allrespects (p. 141). She found that expectation controlledinferences; for example larger cards were thought of asnearer; expanding balloons were seen as approaching;radiograms of human hands were assumed to have been takenat the same distance, so that a larger image was thought to bethat of a larger hand; larger and smaller sizes of hands' imageswere ascribed to age differences; few students looked at thewrist cartilages to verify those inferences (p. 102-3).Students were astonished to learn that their conceptualecologies affected how they viewed documents. The factorsinvolved were:the status of the writer,the repute of the journal,the student's knowledge of the writer's background,the student's level of scepticism (p. 145).Students were surprised to learn that they had so many,and so different, meanings of the word "normal". Manystudents were disturbed to find such "objective" measures asconsistency, suitability and agreement were, in fact,subjective (p. 147). JA summed up her influence on this thesisthus:44Everything we are trying to teach can be learned only ifit is compatible with the student's present attitude, orif his attitude can be so modified as to incorporate it(p. 159).2.32 Bruner's AutobiographyBruner cited research done by "Smitty Stevens" but gaveno citations by which this researcher could find the originalresearch papers. Therefore these notes come directly fromBruner (1983).The purpose of the research was "to find out how the . ..ear ... represented the world of impinging stimulation." (p. 72).The research claimed that there were four basic attributes oftone:- pitch, loudness, density and volume. There are only twophysical properties of pure tones: the amplitude and thefrequency of the simple sound wave which produces them.However, there is also a reference to Fourier's Analysis (p. 73)and a reference to resonance (p. 74).According to Stevens, pitch is produced by resonance at aspecific place in the cochlea. Changing the amplitude, whilstholding the frequency constant, can slightly shift the peak ofresonance. Loudness can be described as the number of neuralfibres in the cochlea that can be fired around the peaking point.Density is related to the concentration of neural fibres near45the resonance site which fire. Volume is related to the numberof fibres in the cochlea which fire (p. 74).Bruner writes that, "(The above) may be totallyirrelevant with respect to how sounds are actuallyexperienced:" (p. 74). Yet he writes of how a colleaguecompressed the tune of "Yankee Doodle". At first, thecompressed version sounded like the repetition of one note, butafter a few sessions, "Yankee Doodle was coming through loudand clear." Indeed the real Yankee Doodle sounded gross!(P. 75 ).In the estimation of physical magnitudes, both thephysical and time separations were found to beimportant^ (p. 75).Bruner also wrote that:We discovered what "primitive" painters had known formany centuries: significant objects in a picture becomeaccentuated in appearance--in size, colour, saturation,clarity--however^ (p. 75).He further wrote that:The psychophysics of sensory attributes is much toowinding a road into the study of perceptual filtering(p. 75).462.33 Gustafson's Findings Gustafson carried out research into the teaching ofsound involving five students in a Grade Four classroom inAlberta. As part of her research she asked students for theirideas about sound prior to the course being taught. Therelevant views are summarised below.Children perceive a difference between learning andunderstanding. Understanding means self-constructed, self-satisfying explanations (p. 109), whilst learning appears torefer to "only memorisation or the ability to repeatterminology or observations" (p. 124).The struggle for personal understanding is not linearlyprogressive; instead, children display many reversals ofdirection, make surprising observations and construct webs ofideas which are intelligent and personal (p. 109). Replies tothe question of how sound is made included:All five said that things must move to make a sound.Some things, for example timers, stereos, photocopiersand airconditioning systems make sound without moving.Four children recognised that sound could be made louderby putting more energy into the sound maker.47Some children recognised that different keys on musicalinstruments produced different notes.One student noted that higher notes sounded louder.Replies to the question of how sound travelled included:Sound can travel through a solid if it is not too thick;Sound can be heard through liquids;We hear better in air than in water;Echoes used big spaces with walls for your voice tobounce back to you.Two children spoke of sound travelling in waves or vibrations,but one had taken the idea from cartoons.Reasons why we hear things included:48We hear things because they are close;Sound is attracted to ears like one magnet to another;Sound waves are invisible and can't be felt; theirexistence is proved by the fact that we hear them.Discussing the reception of sound, most of Gustafson'sstudents knew that ears are involved:that some people have difficulty hearing, so must useaids or have people speak up;that some animals hear better than others, and there issome disagreement on effects of ear size.2.34 Linder's Findings Linder (1989) worked with ten physics graduates from aphysics teacher education program to find out how theythought about and made sense of the phenomena of sound (p.43)He found four qualitatively different ways of thinkingabout sound: one as an entity which is carried by individualmolecules through a medium and the other as an entity whichis transferred from one molecule to another through a medium(p. 45). He referred to the above two views as "microscopic".The two "macroscopic" views were that: sound is a travellingbounded substance with impetus, usually in the form of49flowing air; sound is a bounded substance in the form of atravelling pattern (p. 51).The concept of sound formed by blending microscopicwith macroscopic perspectives became:the concept of sound is linked to the concept of waves,as part of some universal, mathematically abstract,physics modelling system^(p. 146).In reference to the speed of sound, student conceptualisationsincluded:The speed of sound is a function of the physicalobstruction which molecules present to sound as itnavigates its way through a medium.The speed of sound is a function of molecular separation(the closer molecules are to each other in a medium, thefaster the propagation, and vice-versa).The speed of sound is a function of the compressibilityof a medium (the more compressible a medium is, thefaster sound can travel through it, and vice-versa)(p. 146).2.40 SUMMARY OF CHAPTER TWOThis chapter looked at the literature guiding the ideasbehind this research.50The historical study went from the practical problemscaused by the flooding of the Nile to the Greek search for theperfection of the Universe. This search dominated physicsuntil the twentieth century, when Bohr, Einstein, Godel,Heisenberg and Michelson and Morely demonstrated that even ifsuch exists, no person cannot comprehend so perfect aUniverse; consequently, any comprehensible structure mustcome from the human mind. The other part of the historicalstudy moved from Adelard of Bath in the twelfth century to theproblems, exposed by Rosalind Driver, to be faced by theMinistry of Education of England in the 1990's. Driverdemonstrated that students neither conceptualise nor mentallyoperate in ways predicted by scientists' analyses of scientifictopics. The idea that students are "blank sheets" on which theteacher "paints" the scientific topic is the idea from which aprovince-wide curriculum stems. Yet glances at medicalstudents' optical illusions show that what we think we see isoften not, in fact, what is there. Many experiments havedemonstrated that what we think we see is governed by whatwe expect to see--that is our memories and mental habits.Jean Piaget created a technique by which a learner'sunderlying concepts could be brought to consciousness andlooked at by the student, the teacher and, perhaps, by thelearner's classmates. This chapter explored techniques and51pitfalls of the Piagetian interview and looked at examplesaired in texts such as Children's Ideas In Science and Anatomyof Judgement.This chapter looked at some concepts held by thisresearcher, and their sources. It looked at previous work inthe study of student preconceptions about sound; one set offindings from Grade Four and the other from post-graduates.Therefore it is hoped that the historical review has laid thetheoretical framework; that the work on Piaget, de Bono,Gustafson and Linder has laid the methodological framework ofthe research which follows.52CHAPTER THREEMETHODS OF STUDY3.00 INTRODUCTIONThis chapter deals with the technique of data collection.The reasons for, and some limitations of, the data collectiontechniques are given. It relates the data to the provincialcurriculum. It describes the tasks, techniques and apparatusused in the interview. It describes the analytical proceduresused by the researcher to make sense of the data.3.10 PURPOSEThe purpose of this research was to find out what, if any,preconceptions students in Grade 8 brought to the study ofsound.3.10.1 Researcher's Profile of Topics in Sound From the scientific study of sound and the researcher'sexperience, one profile of topics in sound includedPERCEPTIONVIBRATION53FREQUENCYPITCHTRANSMISSIONECHOES3.10.2 Profile of topics from the Teachers' GuideFrom: Bullard et. al. (1985) p. 9-3, another set of topicsin sound included:ENERGYPITCHLOUDNESSAUDIBLE FREQUENCIESFREQUENCIESAIR AS TRANSMISSION MEDIUMECHOESWAVE MOTIONCOMPRESSIONS AND RAREFACTIONSUSE OF OSCILLOSCOPEYet another set of topics comes from the the B.C.Ministry of Education's optional learning outcomes from thecurrent science curriculum:C70: Understand the nature of sound transmission;C90: Understand common applications of light and sound.Possible activities suggested by the curriculumguide include the following:54have students use an oscilloscope to observevarious musical instruments and note wavepatterns;Use slinkies and/or Kuntz's tube to demonstrate thecompressional wave patterns of sound;Have students explain how sound is used in echo-location.The Ministry has prescribed the use of the text ScienceProbe 8 as one means of assisting students to achieve theabove learning outcomes. The goals of the Chapter on Soundinclude:1. Know that sound is a form of energy;2. Know the difference between pitch and loudness;3. Realise that only certain frequencies are audible;4. Know what frequency means;5. Appreciate how different frequency sounds areproduced in musical instruments;6. Understand the nature of sound transmission--realise that sound requires a medium in which totravel, and will not travel through a vacuum;7. Know what an echo is;8. Realise that sound is carried by wave motion, andthat sound waves consist of compressions and55rarefactions in the particles making up the mediumcarrying the sound;9.^Be familiar with the display of several differentkinds of sound on an oscilloscope screen.(Bullard, Baumann, Deschner, Gore, McKinnon andSieben, 1985)As well as goals, the chapter has key ideas (KI). Theyinclude:1. All sounds result form vibrations of some sort;2. Sound is a form of energy;3. The frequency of a vibration is the number ofvibrations completed in one second;4. One vibration per second is called a Hertz;5. Pitch depends on frequency of a sound. The pitchof a sound is your brain's subjective interpretationof frequency;6. Every object that can vibrate has a naturalfrequency at which it will vibrate;7. Musical instruments depend on natural frequencies;8. Audible frequencies range from 15Hz-20 KHz foryoung people with good hearing;9.^Infrasonic sounds have frequencies below theaudible range;5610. Sound requires a medium in which to travel; unlikelight it cannot travel through a vacuum;11. Sound travels in a form of wave motion. The typeof waves is called compressional;12. Sound travels at different speeds in differentmedia;13. An echo results from sound waves reflecting froma barrier near the source of the sound;14. The oscilloscope can be used to display soundcharacteristics such as frequency, loudness andquality.^(Bullard et. al.,1985)Since this thesis is concerned with preconceptions basedon previous experience and thinking, the researcher removedfrom consideration goals 3 and 9 and key ideas 4, 8, 9, 12, 14;consequently, the remaining goals and ideas were organisedinto these topic areas:1. Human Sound Perception ;2. The Energy of Sound;3. Pitch versus Loudness;4. Perception of Pitch;5. Audible Range of Frequencies;6. Vibration;7. Responses to Vibration Frequency;8. Frequency and Musical Instruments;57589. Air as Transmission Medium;10. Echoes;11. Waves Without Oscilloscope; Compressions andRarefactions;12. Student Perception of Oscilloscope Trace.The only relevant research on these aspects of sound ofwhich this researcher was aware of in 1987 was that quotedin Bruner (1984, p. 73-4).3.20 THE STUDENT SAMPLEInterviewees were self-chosen. The researcher and theother science teacher asked their Grade 8 science classes forvolunteers who wished to earn a dollar for an interview duringthe Noon Hour. Usually a half-dozen children per yearvolunteered, from about ninety students. A colleague hassuggested that so few volunteered because word got round thestudent body that a student would be asked questions to whichhe did not know the answer, and the dollar was small rewardfor such discomfort. Eventually approximately twenty studentswere interviewed.The volunteer pool was from Grade 8 of a three-gradeJunior Secondary school in Miltown. It is difficult to classifythe students; the school is in the wealthy suburb, yet drawssome students from the remnants of a 1960-70's hippycommune. Levels of achievement were not studied; neitherwere innate academic abilities.The school is located in an old mill town. The city isgeographically isolated; although the loom of Vancouver'slights can often be seen from this city, a minimum of fivehours' surface travel separate the two. The next adjacent cityis two hours away by ferry. This city has a very strong choraltradition. A childrens' choir toured Poland and the SovietUnion a couple of years ago, and the city hosts an internationalsummer choral festival.3.30 THE CLINICAL INTERVIEWThe interviews were developed and carried out much inthe style of Piaget and de Bono, in that unusual apparatus waspresented for the interviewee's exploration and questions andanswers were developed from that exploration.In the early interviews, apparatus from school stockwas used (see list in section 3.50); however an unusualapparatus was found by chance and used in the laterinterviews. The apparatus used was a Door Harp (see figure 2),made by Langen's Laminations of Victoria B.C. The researcher59had thought that the apparatus was relatively unknown inMiltown, yet in late November and December 1988 a local storesold about 100 units. The shape, the whale, was chosen by theresearcher because it was unusual and did not give the sort ofclues an interviewee might gain from a familiar shape such asthat of a guitar or a piano.Since the interviews were, in some sense, affected bythe apparatus used, it was thought appropriate to carry out afew interviews without apparatus.A conceptual profile for the Science Probe 8 chapter onSound was developed and questions were based on thatprofile. The questions were intended to be open-ended in ordernot to restrict the range of answers. In turn, the researcherfelt free to explore any line of answers which appearedpotentially fruitful. Since no video camera was available, theinterviews were recorded on audiotape. As there was littleresearch on Grade 8 students' understanding of sound itbecame an exploratory study.The interviews were carried out in a Science Room of aJunior Secondary School during the noon hour. This time waschosen so as to avoid interference with instructional time,pre-school help to individual students and the need to catchbuses immediately after school. Interviews were frequently60interrupted by PA announcements, but, since the PA was themedium by which fire and earthquake warnings were given, itwas thought unwise to switch it off.3.40 INTERVIEW METHODThe key condition for permission to carry out thisresearch in the school was that the research in no way affectthe operation of the school; therefore, the usual technique oftaking students from classes for prolonged interviews wasimpossible. Because of the limitations imposed by the schoolbus schedules, interviews had to take place during a thirty-five minute noon hour, including time for administrivia,bathrooms, lunch and gossip. Therefore the interviews werelimited to about fifteen minutes each.The research topic was restricted to grade 8 students soboth science teachers called for volunteers from their classes.Appointments were made with the volunteers, with theresearcher making absolutely clear that the interview wasentirely voluntary and that it, or withdrawal, would have noeffect on the student's program or grades. The student wasinformed that the interviewer was studying at UBC and had thehomework assignment of finding out what students knew about61sound; the student was told that the researcher and theprofessor would publish the results as a book in a year's time.Appointments for noon-hour interviews were made with thosestudents who wanted to go on. No attempt was made to selectstudents; so few volunteered that the researcher wasconcerned to garner enough data within the three yearsavailable. In all, about twenty usable interviews were carriedout.When the student came to Science Room III for theresearch interview, the student was asked to sit at the benchwith the equipment on it. The student was shown therecording equipment and reminded that the interview wascompletely voluntary and that he or she had the right to leaveat any time.When the researcher felt that the student wascomfortable with the situation, the interview was startedwith a statement and question along the lines of, "I'd like tofind out what you think about sound. Just what do we mean bythe word 'Sound'?" The student was then introduced to theequipment and asked to tell the researcher about it. Theresearcher might ask the student questions for clarificationand/or to lead to other points. The researcher asked as manyopen-ended questions as possible; however he sometimes had62to ask a close-ended question to encourage a response.Appendix (1) shows the typescript of a typical interview.When the researcher felt that the student had toldeverything, or the student was getting tired or timeintervened, he closed the interview by thanking the student,asking if the student had any questions, stating that theinterview would be typed up in a way so that no one would beable to recognise who had said what, and handing over theinterview fee.The interview tapes were sent en masse to a Vancouversecretarial company where they were transcribed intoMicrosoft Word 3.0, on 3 1/2 inch disks. After some problemswith the combination of program and computer the researcherreviewed the transcripts and tried to use the computer tocreate a glossary of statements for each of the key concepts.In turn, each glossary was to be scrutinised for importantevidence and patterns of student conceptualisations aboutsound.3.50 DESCRIPTION OF TASKS A sound exists for a relatively short time and so itcannot be studied at leisure as can, say, the forces involved intwo weights pulling a mass. During the early interviews, an63array of sound equipment was laid out and the interviewee wasasked what s/he thought and predicted as the equipment wasmanipulated by the interviewer. The key items of equipmentwere as follows:1. Click Wheel, locally manufactured, intended toprobe student understanding of frequency;2. three tuning forks of differing sizes, to explore anyeffects of source dimensions on sound;3. A ping-pong ball on a thread, to look at forces fromthe tuning forks;4. Metrestick and clamps, to explore effects of lengthon predicted notes;5. Sonometer to explore effects of force and length onpredicted note;6. Oscilloscope to explore student perceptions ofamplitude and pitch.64Figure 1. Two views of apparatus used in the earlierinterviews65During a subsequent conversation with the thesissupervisor, it was agreed to concentrate on one apparatus andexplore the student perceptions of that. A Newton's cradlewas used in an informal exploration but did not produceworthwhile results.By chance, the researcher came across an apparatuscalled a DOOR HARP. The middle of this instrument looks like aguitar, with a wooden box, a hole and three strings of differentlengths and sizes, across it. However, it does not have a neckand frets as does a guitar; instead it has three similar woodenballs hanging by threads, which strike the strings as the harpis shaken normal to both the strings and the threads. Thus itlooks like a strummed instrument such as a guitar, but is infact a percussion instrument like a piano. Sound came notfrom striking keys or plucking strings but from moving thewhole instrument. About 100 door harps had been sold inMiltown (conversation with store owner). Only one intervieweehad seen a door harp.It was felt that the unusual nature of the harp and itsrarity would be a fertile sources of student ideas about sound.66Figure 2. Photographs of the Door Harp used for this Study67The interviewee was led to each apparatus in turn andasked about it. The interviewer tried to give as few verbalclues as possible--often referring, for example, to the doorharp as a "gizmo"--as to the real use of the apparatus, so thatthe student's perceptions would be less likely to be tainted bythose of the interviewer. The interviewer felt that the mostdifficult part of the interview lay in avoiding teaching.As stated previously, this is a naturalistic form ofresearch and it is the only research with Junior Secondarystudents in the field of Sound of which the researcher wasaware. Therefore there were no specific hypotheses to betested. Consequently, the exploration was more like aconversation than a formal interview. The interviewer usedopen-ended questions and interrogative paraphrases to explorethese questions:What do we mean by sound?How does sound travel?How do we hear things?What do we mean by vibration?How do the dimensions of an object affect its sound?How is sound produced?How are echoes produced?The interviewer had a list of appropriate topics duringthe interview and tried to keep to that list. However he felt68free to explore promising lines and cut off others; for examplehe had a long interview with a student clarinettist on how reedinstruments work, and the interviewer shut down oneinterview when he began to suspect that the interviewee wasdeliberately giving answers that the student thought theteacher wanted.In quoting from interviews, "I" refers to the interviewer;"S" refers to the student.An example of a student trying to please the teacher:i^I^Can we make sound point like that?S Yes.I^We can?S NoThis researcher felt some difficulty in shifting from onetopic to another without telling too much about either. Hereare examples of such shifts:i i^I...^How do we hear things?S With our ears.I^Tell me more about what your ears do.I^How do you know when you are hearingsomething?S I don't know.69Examples of circularity in descriptions:iii^I^Let's see. The drawing on the board, are youhearing that drawing?S.^you can hear the different sounds.i v^I^Great. What I want to ask you is this: What dowe mean by the word "sound"?I^How do you recognise what is a high note and whatis a low note?S High notes are pitched a lot higher. They are shrill.Low notes are like a trombone or something.I^How do you recognise high notes?S The pitch. You can tell high notes because they arelike a shriek. They are higher-pitched. It would belike a woman screaming.I^How do you recognise a woman shrieking asopposed to a man bellowing?S Your ears just pick it up.3.51 Researcher's Subsequent Actions Interviewing took place from May 1987 to February 1989.Interviewing ceased at that time because the biology teacherneeded to teach 'Sound' in order to enhance his students' study70of the human ear, and because the time available to completethis thesis was running out.During Summer 1989, the Supervisor and the researcheragreed to computerise the thesis. The interviews' audiotapeswere sent to a firm in Vancouver to be transcribed on to 3 1/2"discs. The researcher intended to take questions and answersfrom the disc and assemble them in the appropriate blocks.Unfortunately, a computer glitch developed in September 1989which wasted five months.The data was finally sorted out when the researcher tookthe typescript of the interviews into isolation and spent threeweeks in Summer 1990 reading the data base, classifying thecomments and entering relevant comments on 8x5 file cards.All the questions and comments about a particular topic wereplaced on one card then that card was reviewed using theconceptual profile from Bullard et. al. (1985).When the research had been sorted, it was reviewedusing de Bono's criteria to get a feel for the depth of studentunderstanding of the topic of sound.713.60 LIMITATIONS OF THE DATAOnly one field researcher was involved and so the studymight well have been coloured by the unusual nature of theresearcher's knowledge of sound and related phenomena.The research apparatus were those commonly available inthe school; for example, the oscilloscope was the onlyelectronic item explored. The sample was drawn from only onecommunity, one which is rather isolated. The community'sindustry has been primitive, requiring an unskilled labourforce. The community has a very strong tradition of music,with international ramifications. The sample was drawn fromonly one school. No attempts were made to discover students'motivations for volunteering. The interviews took place in onlyone room and at only one time of day. The interviews had to berushed. No attempt was made to measure or even to estimatethe effects of fatigue on the participants.72CHAPTER FOURRESULTS OF THE STUDY4.00: OVERVIEW OF THIS CHAPTERThe purpose of this study is to identify some of thebeliefs that children bring to the study of sound. Theinterview scripts were analysed to look for common responsesto interview questions.The analysis was organised around the majorconcepts of perception, vibration, frequency, pitch,transmission and echoes. These concepts formed theframework of the exploratory interviews.When the researcher analysed the students' responses, hefound that their classifications did not quite match either ofthe two profiles discussed in section 3.10. Therefore, he puttogether the findings in a profile based on studentunderstandings; that profile, along with illustrativecomponents, forms Section 4.20.734.10 USE OF PROFILES From a scrutiny of Science Probe 8, supplemented byhis own academic studies in the field, this researcher arrivedat a list of six topic areas which provided a basic frameworkfor use in each interview. The six-topic list is located inSection 3.10.1 of this thesis.During the interviews, the researcher had a paper withthe topic areas before him, to be used as the framework foreach interview. In practice, the actual substantive issuesraised in each interview depended on what equipment was inuse. With that in mind, there were three interview types: theearly one in which students explored apparatus ranging from aball on a thread to an oscilloscope; the middle, veryproductive, interviews in which the researcher and the studentjust talked about sound; the third interviews based on the doorharp.Because the research was about what students thought,the subconcepts of the above profiles came from the students'answers. The sum of the responses in the thesis would not bethe same as the number of responses on tape, because manyresponses overlapped categories, so that one response couldinvolve two or more subconcepts.744.11 A Conceptual Profile of Students' Understanding of Sound1. Human Sound Perception2. The Energy of Sound3. Pitch versus Loudness4. Perception of Pitch5. Audible Range of Frequencies6. Vibration7. Responses to Vibration Frequency8. Frequency and Musical Instruments9. Air as Transmission Medium10. Echoes11. Waves Without Oscilloscope; Compressions andRarefactions12. Student Perception of Oscilloscope Trace.4.20 ANALYSIS OF DATASince this appeared to be the the first research in thefield of Junior Secondary students' perceptions of sound, theresearcher tried to keep his perceptions out of the interviewsand, particularly, out of the interpretations of interview data.A key problem, of course is that despite what John Locke (andsome of the researcher's friends) have said, the researcher'sbrain is not a blank slate. One of the key problems of75measurement is that the instrument affects the measurement;therefore one can only minimise such an effect, not obliterateit. To reduce the effects of the researcher's input, he tried toisolate the comment by the student and to include theinterviewer's question or comment only where it was neededto clarify the student's comment.Therefore the database of interview typescripts wasregarded as a source of student statements about sound ratherthan as a record of conversations.Subsequent to the interviews, the researcher reviewedthe database and copied each student statement about, say,"pitch" onto an eight-by-five card dedicated to "pitch";eventually he had 148 statements about "pitch" on elevencards. Each statement on the card was coded with the student,the apparatus in use and the page of the database where thestatement was to be found. This procedure was carried out foreach topic on list 3.10.2.When the cards had been made up, each card or set ofcards dedicated to a topic was reviewed again to find patternsor consistencies among the statements. These categoriesbecame the topic list noted as 4.11. Once this topic list hadbeen assembled, the statements associated with each topicwere scrutinised for key beliefs about that aspect of sound.76When the researcher had found patterns from thestudents' topic profile, he reorganised them into the profilenoted as 3.10.2.The symbols in brackets after each quotation e.g "(123)"gives the page of the database where the quotation is to befound.1. Human Sound Perception. Major Research Question: How do students think wehear?Subconcepts: (A) Air as Medium(B) The Role of the Ear.A.^Air as MediumOf the thirty-three relevant responses, onlytwo describe sound as a property of air. Most other responsesindicated that sound travels from source to receptor withoutinvolving the air between them. Examples of this kind ofresponse include:i^I: How do you think sound is getting from the(tuning) fork to your ear?S: By the hit of the two ends which make itvibrate.I: Did you say something vibrates betweenthe fork and the ear?77S: The vibration of the two ends.I: And how does the vibration get from thereto our ears? Any ideas?S: No.^ (30)ii^I: How does sound travel?S: I'm not sure. Probably, once you make thenoise,it travels in sound waves. I don't knowhow to explain that.^(14A)B.^Knowledge of the role of the ear.There was a wide range of knowledge rangingfrom:I: Tell me more about what our ears do.S: I don't know.^ (6A)to:S: The noise goes into your ears. It goes in theinner ear, the eardrums, and there are bonesin your ear. They vibrate.^(9A)2 The energy of sound.Major Research Question: Do students recognisethat sound is a form of energy ?78A child recognises energy merely as movement. Therefore, inexploring students' ideas about sound as energy, thisresearcher looked for links between sound and movement.Subconcepts: (A) Local movement, as in thetines of a tuning fork.(B) Translational movement, asin how far a sound isaudible.A. Local MovementOf approximately eighty responses relevant both tosound and to movement, thirty said that sound was caused byhitting; tines hitting air, balls hitting wires and so on.Examples of this kind of response include:i^I: What could that ( the differences in soundof two differently-sized tuning forks) be dueto?S: The longer one is hitting more of the air.(2)i i^I: How do they make music?S: They hit the metal.79(4A)80iii^S: Kind of things like that, wires and hittingthem.^ (45A)B. Translational MovementThirteen responses related sound and distance; theyinclude:i^I: What do you notice when I pull the(sonometer) string quite a long way down,compared with when I pull it a tiny waydown?S: It's a lot louder when you pull it all theway down.(6)i i^S: Higher notes have higher speeds.(3)i i i^S: Loud noise has a larger volume.(52)i v^I: ... with the ping-pong ball. What do youthink should happen when we hit it with the320E tuning fork?S: It shouldn't go as far.I: What's happening?S: It goes further.I Why do you think that is?S: Because it goes slower so they can makemore distance. (27)3. Pitch versus Loudness.Major Research Question: Do students perceive theamplitude and the pitch of sound as two separate factors, orare those two factors perceived as one?Subconcepts: (A) Frequency(B) Amplitude(C) TogetherA. FrequencyOnly one comment mentioned frequencyspontaneously; therefore the researcher looked for synonyms.Examples of relevant comments include:i^S: Smaller fork can give out a higher notebecause the tines move faster.^(5A)ii^I: What do you mean by tone?S: Whether it is a high or low tone. Itsvolume is another way I recognise(sound)8182iii^I: What do you mean by higher and lower?S: Well it does not have any effect on howloud it is.I: Give me an example of a high sound.S: A piano. If you go further up the scale itgets higher.I: Can you make a high sound then a lowsound?(Student demonstrates properly)(9A)i v^I: When some thing is vibrating fast, howdoes that sound to us?S: High-pitched and it hurts your ears a bit.Hard to listen to.^ (46A)B. AmplitudeFew comments mention amplitude inisolation; examples include:i^S: The noise gets louder when the wire ispulled a lot.^ (22)i i^S: As the working length of the string isreduced, the noise gets louder.^(36)83i i i^S: If we made the click wheel go faster, thesound would be louder.^(23)C.^Many comments integrated amplitude andfrequency; examples include:i^S: The note (from the sonometer wire) ishigher when you pull it a little bit comparedwith when you pull it a big amount. Thenoise gets louder when the wire is pulled alot.^ (22)i i^S: Smaller fork can give out a higher notebecause the tines move faster. When thesonometer wire goes quickly, the sound getslouder.^ (5A)iii^S: The lower the note, the more power itshould have.^ (27)i v^Whilst observing the oscilloscope:S: The higher the note, the longer the lines go.I: Try this.S: They are much shorter.I: Shorter up and down or shorter across?S: Up and down. They seem longer.I: Longer up and down or longer across?S: Longer across. Shorter up and down.(33)v^^S: The waves seem to widen as you bring thetuning fork closer.I: Wider across or wider up and down?S: Up and down.(35A)v i^I: What would you say about the width of thewaves?S: As they go up, they increase up and down.They seem to get wider.I: They seem to get wider across the screen?S: Yes.(25A,26A)4. Perception of Pitch. Major Research Question: Do students perceive pitchstrictly as a phenomenon of frequency?Subconcepts: (A) High notes(B) Low notes(C) Causes84Of the over 140 comments about pitch, only a fewrelated the phenomena of high and low notes to rapidity ofvibration. Most students recognised high notes by analogy withanother phenomenon, such as a shriek. In addition somecomments, particularly those relating to pull, force and pitchseemed paradoxical; for example one would expect the strengthof the pull on a sonometer string to have an effect on theamplitude of the note rather than its pitch. Examples of thiskind of response include:A.^High NotesA surprising feature of replies in thiscategory was the number of circular descriptions; examplesinclude:a. Recognitioni^S: High notes are high-pitched, like a shriek.(39)i i^^S: High notes are pitched a lot higher. Theyare shrill.(39)i i i^S: High pitch is squeakier.(2A)b. CharacteristicsS: High notes travel at high speeds.^(3)8586i i^S: Higher note lasts less time.(27)i i i^S: High sound vibrates quickly.^(quoted byfour students)i v^S: Small fork or ruler gives high note. (quotedby seven students)v^S: High-pitched sound is like choppy water.(55)v i^S: A twang is a high note.^(40)B. Low Notesa. Recognitioni^S: Sound is low. I can't really explain it.(26)i i^S: Voice and ocean are both calleddeep,because both are low down.^(2A)87i i i^S: Low notes are like a trombone.b. Characteristicsi^S: Deeper notes take longer to stop.i i^S: Deeper note has further-apart waves.(28)iii^S: Lower-pitched note has more stretched-outwaves.^ (29A)i v^S: Low notes have a space.(10A)v^S: Deeper notes have more power.(27)C. Causesi^S: Recognise a flute in a dark room by highnotes.^ (39)i i^S: High note caused by tines hitting harder.(3)(38)(21)88ii^S: Tone higher because less wire vibrating.(6)i v^S: Long fork makes different sound because itneeds more space to vibrate in.^(17)v^S: Smaller pull on sonometer wire causeshigher note.^ (22)v i^S: Clarinet's low pitch is caused by lettingless air inside.(45)vii^S: Longer clarinet tube gives longer note.(51)5. Audible Range of Frequencies.Major Research Question: Are students aware that somesounds are inaudible?Subconcepts (A) Audible amplitude(B) Audible FrequencyExamples of this kind of response include:A. Audible amplitude89i^I: (looking at oscilloscope) is there a timewhen you cannot hear the tuning fork but youcan still see a wave?S: Yes, right now.I: What does that suggest about the way wehear things?S: Our ears don't pick up all the sounds.(28)B. Audible Frequencyi^S: Some animals, like dogs, can hear pitchesthat people cannot hear.^(9)i i^S: The high note can pierce a dog's ear. Mosthumans can't get up that high.^(60)6.VibrationsMajor Research Question: what factors, of whichstudents are aware, control the frequency of a vibration?Subconcepts: (A) Longer vibrator gives lowernotes(B) Tine thickness affectsvibration rate(C) The vibration rate of astring is controlled by itsdimensions(D) Cavity ResonanceA. Longer vibrator gave lower noteFourteen of the seventy or so relevant statementsgenerated agreed with this. They included:i^S: Tine length lowers sound because it needsmore room to vibrate.^(17)i i^I: Suppose you had several tuning forks.How could you predict what notes theywould give out?S: By the thickness and length of them.^(18)i i i^S: (With ruler overhang extended from 60cmto 70cm) the note is way lower and wayslower.^ (35)B . Tine Thickness is important in controlling the rate ofvibration.Four responses agreed. They included:i^S: Thickness of tine does not let fork vibrateslowly enough.^ (18)9091i i^S: Thinner tine gives deeper note.(25)i i i^S: Shorter fork gave out deeper sound becausethe handles were longer.^(28A)C . The vibrations of a wire are controlled by itsdimensions.Eight responses agreed with this statement. Theyincluded:i^S: Sonometer tone is higher with closerbridges, because less of the wire is vibrating.(6)i i^S: because (the string) is not as long, theycan't vibrate as much so it is higher.(12A)iii^I: Why do you think (a thick wire) would giveout a deep note?S: Because it would make it vibrate slower.I: Why do you think it might vibrate slower?S: Because it is thicker and not so easy tobend.^ (45A)D Cavity ResonanceAlthough only a couple of students referred tothis, their comments suggest some difficulties withperceiving air as an oscillator; examples of such include:i^^I: Tell me how a clarinet works... what do theholes do?S: They cut off air to certain keys. Every keyyou put your finger on makes the note lowerand lower...I: How does this make the note lower?S: Less air is getting inside.^(45)i i^I: What does opening and closing the hole doto the length of the clarinet?S: Nothing.^ (47)iii^S: You need a vibration to get a note.I: ... if you get different notes fromblocking different holes,you must getdifferent notes from different holes. Is thattrue?S: I am not sure. I don't think so. ...92I: The longer the tube the longer the note. Isthat what you are saying?S: Yes....I: How do you think that changing the lengthof the tube in the clarinet changes thevibrations?S: When you blow into it, it vibrates from thereed, it vibrates through the tube, and itvibrates out and it spreads.^(51)i v^I: Is it possible to have two flutes the sameshape and size but blow different notes?S: Yes, ... by making the tube longer orshorter.(28)v^I: What is in the tube?S: Air.I: What do you think the tube is doing to theair to make the sound more concentrated?S: I don't know.^ (47A)v i^I: How does a clarinet have those vibrations?93S: As its travelling through the air,travelling through, it's blowing against itand the keys that made it.^(59)7. Responses to Vibration Frequency.Major research question: Of four ways to look atfrequency (rate of change of field intensity, tally of cyclescompleted every second, as the cause of pitch orcharacteristic of vibration) which do students perceive?CAVEAT Since only one student used the word "frequency"spontaneously in about four hours of interviews, thisresearcher looked for synonyms, such as vibration, pitch andtone.Subconcepts: (A) vibration(B) pitch(C) toneA. Vibration.a.^It is clear that vibration is a familiar concept,94since many students mentioned it spontaneously. Examples ofthis kind of response include:i^I: What do you notice about the overhangingruler?S: It vibrates.^ (22A)ii^S: The harp vibrates when (the ball) hits it.(36A)i i i^S: When a person speaks, the vocal cordsvibrate.^ (41A)b. When asked to define vibration, students' conceptsseemed to agree with with those of the science textsconsulted by the researcher. Although the texts did not definevibration per se, they implied that vibration is a movementabout a point, regular both in distance and in time. Examplesof student concepts include:S: Motion going back and forth.^(40-41)S: A movement, basically side-to-side, or up anddown^ (54)9596c . Some responses gave the researcher the feeling thatstudents perceive sound as something carried by the vibrationbut not produced by it, much like a surfboard carried by a wave.Examples include:i^S: It makes sound because of two forksvibrating.^ (17)i i^S: (a guitar) creates sound from vibration onthe strings..^ (40)i i i^S: A little vibration would hit the otherstrings and and make a sound.^(40-41)i v^S: Speech and noise create sound.^(37)B. Vibration and PitchVibration was frequently used as a cause of pitch,particularly that a higher pitch was a consequence of fastervibrations. Examples include:i^S: (The sound of the clickwheel) will get ahigher pitch as the wheel goes faster.^(24)i i^S: It would go higher...because it vibratesmore.^ (37A)However, many descriptions seemed almostcircular:i^I: How do you recognise a high-pitched note?S: It is pitched a lot higher.^(39)i i^S: Sound is the noise something makes.^(60)I: What do you mean by higher and lower(pitches)?S: Higher is, well, it does not have any effecton how loud it is. It is a higher sound. (9A)C. Only two students referred to tone, one as pitch (54)and the other as loudness (29A-30A)8. Frequency and Musical Instruments.Major Research Question: What do students know of theproduction of sound by musical instruments?Subconcepts:(A) Sonometer(B) Door Harp(C) Clarinet97Only five of the fourteen interviewees had worked with98musical instruments.^Instruments included clarinet, flute,guitar, piano and voicebox. A megaphone was mentioned byone student. Each student mentioned vibrations in explaininghow the instrument worked.A. SonometerSome ideas unexpected by the researcher wererelated by students. Examples include:I: Why do you think the tone sounds higherwhen the distance between the bridges isshorter?S: Less of the wire is vibrating.(6)i i^S: You pull (the sonometer string) a tiny bitand the note is higher than if you pull it a bigamount.iii^I: Which part of the wire would you say isvibrating the most?S: The part of the wire on the far side of thebridge from the finger.^(36)99i v^I: ... ( the pitch of the note) seems to go upwhen?S: When you pull the bridges apart, the pitchgoes up.I: So what happens when I bring them in?S: They go lower.(25)v^I: Which instrument does the sonometerremind you of?S: The oboe.(32A)B. Door HarpAlthough this instrument was new to manystudents, they seemed to recognise that it worked bypercussion. Examples include:i^I: And what do the balls do as they hit thestring?S: They make music.(4A)i i^I: What do you mean by vibrate?S: It goes through the whole piece of metal.I: What does?S: When it hits, it goes straight through.(4A)iii^S: If you turned them (the keys) you couldtighten the strings or loosen them andprobably change the pitch.^(11A)i v^^I: What do you think the tightness does to thewire to make it give off this noise?S: It stretches it.I: How does stretching make it give off noise?S: I don't know.(36A)C. Students who play the Clarinet or the Flute.The wind instrumentalists produced somevariations which surprised this researcher. The first twoexamples appear to demonstrate inconsistent ideas:i^I: Is it possible to to have two flutes thesame shape and size but blow differentnotes?S: Yes.I: How would you do that?By making the tube longer or shorter.(28A)100101i i^I: What does opening and closing the hole doto the length of the clarinet?S: Nothing.(47)i i i^I : How does (covering the holes) make thenotes lower?S: Less air can get inside.(45)9. Air as a Transmission Medium.Major Research Question: Do students recognisethat, in everyday life, air is needed for the transmission ofsound?Subconcepts: (A) Air must vibrate to transmitsound.(B) Sound cannot usually betransmitted in the absence of air.A. Air must vibrate to transmit sound.Many students recognise the need for vibration inthe air. Examples of this kind of response include:1 02i^The longer (tuning fork) is hitting more ofthe air.^ (2)i i^S: Vocal cords make sound in air byvibrating.^ (42A)iii^S: It is important that the clarinet reedvibrate the air.(42A)B. No air means no transmission of sound.Some students, however, do not recognise that theabsence of air causes the absence of sound. Examples include:i^I: Why is there no sound in space?S: Can't hear in space because it is too faraway.^ (34A)i i^I: Could two people sitting a metre apart inspace hear each other?S: Probably.I: How?S: The same way.I: Explain it to me.S: if someone is talking you canhear him down here and you couldprobably hear him in space. (35A)i i i^I: Tell me. If we were in space would webe able to talk like this?S: Not unless we were in an enclosed room.I: What would that do for us?S: It would probably make the sound echolouder.(16A)10. Echoes.Major Research Question: How do students think ofechoes?Subconcepts: (A) Sound can bounce off objects(B) Some effects of those bounces.A. Sound can bounce off objects.Most students were aware that an object is neededto bounce a sound back. Examples of this kind of responseincluded:1 03104i^S: Echoes come from mountains when soundbounces off something and comes backto you.(13A)i i^S: An echo is where you make a noise and itwould hit somewhere, the noise wouldprobably bounce off something and it wouldcome back to you and you would hear itagain.(18A)B. Some effects of these bouncesSome students recognised that the time for whicha note was heard might involve echoes. Examplesinclude:i^S: Sound bounces back and repeats itself as itgets louder.(13A)i i^^S: Noise of the door harp string could hit theend (stops?) and bounce back.(18A)iii^I: Do you know anything of the wood of thedoor harp ?S: It's hollow. It gives a better sound ...because the sound goes through it and backout ... the box echoes the sound.(40A)i v^S: The echo box is like an amplifier.(40A)11. Waves. Compressions. Rarefactions. Major Research Question: How can the teacher inMiltown expect his students to think of sound waves?Subconcepts: (A) Sound travels in waves(B) Sound waves are alternate zonesof compression and refraction(C) Ocean surface waves as a modelfor sound waves.A . Sound travels in waves;This seemed to be well understood. Examplesinclude:i^S: Vibration is caused by sound waves in theair.(7A)105106i i^S: Vibration and waves are linked, becauseboth help sound travel.(16A)i i i^S: Sound waves carry sound to our ears. Whennoises are made, they go off. I guess they gointo the air or wherever and you can hearthem.(56)B. Sound waves are alternate zones of compression andrarefaction.No student described sound waves as alternatezones of compression and rarefaction. There were however,student perceptions which could be developed from the idea ofhitting into that model. Such perceptions include:i^S: Sound is made as nails hit paper.(1)i i^S: Continuous clicking would make a musicalnote.(1)i i i^S: Sound gets from fork to ear by hit of twoends.(30)C. Ocean surface waves as a model for sound wavesOnly two students compared sound waves withocean waves. Examples include:i^S: Sound is like waves in the ocean.(55)i i^S: Sound is soft and wavy.(55)iii^S: If it is high pitch, it will go like choppywater.^ (55)i v^I: You said (ocean) waves travel in ripples.S: The sound waves would travel inindividual lines. Any kind of motion thatwould make the sound travel towards theearth. (15A)12 Student Perceptions of Oscilloscope Trace.Major Research Question: Does a student read anoscilloscope in the same way as does the science teacher?Subconcepts: (A) Do students recognise the heightof the waveform as proportionalto the amplitude of the sound?107(B) Do students recognise the widthof the individual wave asproportional to the pitch of thenote?A. Do students recognise the height of the waveform asproportional to the amplitude of the sound?There are few clear examples where the height ofthe waveform is ascribed to amplitude. Examples include:i^S: Harder strike produces waves of the samehorizontal distance apart but higher.(22)i i^S: The louder the talk, the taller the wavesget.^ (31)i i i S: Waves seem to widen up and down astuning fork brought closer.(25A)B. Do students recognise the width of the individual waveas proportional to the pitch of the note?There were only two examples :i^S: Wave crests are closer with a higher-pitched note.108(5)1 09i i^S: Lower frequency gives wider-acrosswaves.^ (26A)4.30 SUMMARY OF CHAPTER FOURThis chapter has reviewed the topic lists involved in theresearch and has organised student comments about thosetopics so that the researcher has been able to deduce possiblepatterns of preconceptions held by students about sound.The results are discussed more thoroughly in chapterfive.CHAPTER 5CONCLUSIONS AND DISCUSSION5.00: INTRODUCTIONThis chapter summarises the study, states its generalconclusions, draws educational implications from thoseconclusions, suggest further research and attempts to put thestudy into a perspective from a classroom.5.10 SUMMARY OF THE STUDYThe purpose of the study was to attempt to obtain abetter understanding of the beliefs about sound held bystudents in grade eight prior to formal instruction. Theliterature of science education was searched extensively formaterial on sound; in 1987, when this study was started, norelevant literature was found, and so this study became anatural history of student perceptions about sound. Details ofthe techniques and the findings of the study were given inchapters three and four. As this study was being carried out,studies by Gustafson (1988) and Linder (1989) were published;110these studies were reviewed to seek commonalities with thisstudy.5.20 CONCLUSIONS OF THE STUDY5.21 Broad Patterns of Student Beliefs about SoundSince this study is intended to be for the use ofclassroom teachers, it is appropriate to arrange the broadpatterns of belief in the format of the topic list from Bullard,Baumann, Deschner, Gore, McKinnon and Sieben, (1985).Using the goals and key ideas of Chapter Nine, Sound,from Science Probe Eight, presented in section 3.10 of thisstudy, the following broad patterns of student belief aboutsound were identified:z1. Know that sound is a form of energy.Thirty responses in eighty suggested that soundwas caused by hitting; tines hitting air, balls hitting wire andso on.Thirteen responses related sound and distance. Highernotes had more energy and were ear-piercing, travelled fasterand were caused by the tuning-fork tines going faster.No student mentioned the Kinetic Molecular Theory.111That no student cited the Kinetic Molecular Theory inconnection with sound strongly suggests that students eitherhave not been introduced to the theory or do not relate it tosound. Both suggestions are surprising, since the theory hasbeen introduced to the students and sound is a product ofmolecular motion.2. Know the difference between pitch and loudness.In breaking this topic down to its subconcepts, itappears that most students think of pitch and amplitude as onephenomenon. Few considered pitch and amplitude separately.When the oscilloscope was used, there was considerableconfusion about the terms "height " and "width". Many studentsseemed to think that "width" referred to the verticalmagnitude of the display, whilst other students described thesame separation as "height". Students seemed to have muchmental difficulty in isolating a particular cycle from thosedisplayed.It seems, therefore, that there are semantic difficultiesin this field which should be addressed when students areattempting to learn about sound; it seems, also, that there aredifficulties in student observation of the typical laboratoryoscilloscope. Stevens (Bruner,1984,p. 74) found that changingthe amplitude, whilst holding the frequency constant, could112slightly shift the peak of resonance; in short, that frequencyis not independent of amplitude. This, in turn, leads to thepossibly heretical conclusion that children's perceptions ofsound might be more in tune with reality than are scientists'.If this is true in other fields of science, then the thrust ofConstructivism might have to be reversed, so that scientists'preconceptions are brought into line with those of children.3. Realise that only certain frequencies are audible.Students were aware that some animals can hear pitchesinaudible to humans. However, in the absence of an appropriatesignal generator, the researcher was unable to explore thisknowledge further. Some students realised that a sound can beinaudible because its amplitude is too low, yet still be visibleon the oscilloscope display. One can conclude, therefore, that(in the terms of Gustafson's students) an oscilloscope couldbe used to develop "learning" about inaudible sound into"knowledge".4. Know what "frequency" means.Only one student used the term "frequency"spontaneously. However if that term is changed to vibration,then many students appear well-acquainted with thephenomenon, since many students used the term without113prompting. Of the seventy or so relevant responses, fourteenindicated that longer vibrators gave out lower notes. Fourresponses indicated that the thickness of tines partiallycontrolled the rate of vibration. Some students were awarethat the length, thickness and tension of a wire controlled thenote it gave out.If "pitch" is substituted for "frequency", thenfaster-moving tines or wires cause higher pitches. In manycomments, pitch and amplitude were either integrated orconfused. High notes were described circularly, for example,"Higher notes are higher-pitched" and low notes weredescribed as having more power or harder to stop. Vibrationwas frequently described as the cause of pitch.A rather more serious conclusion might be drawnfrom the contrast that, whilst "frequency" was usedextensively by the text authors, it was used only once bystudents; the conclusion is that some curriculum designers andwriters are not in touch with student thinking.5. Appreciate how different frequency sounds are produced in musical instruments. The musically-experienced students thought of amusical instrument as a rod with holes. Each student regardedvibration as the cause of the notes. This researcher could not114elicit the student view of an instrument as a tuned resonantcavity. Students did not explain why changing the holeconfiguration changed the output note.If the sonometer is accepted as a paradigm ofstringed musical instruments, then one can conclude thatstudents are aware that the dimensions of the string affectthe note given out. Comments about the door harp suggest thatstudents are aware that the box of the instrument can affectthe note given off.6. Understand the nature of sound transmission--realisethat sound requires a medium in which to travel. and will not travel through a vacuum. In describing the act of hearing, only two responsesof more than thirty described sound as a property of air. Asstated previously, no student invoked the concept of air as amolecular material. Most other responses indicated that soundtravels from source to receptor without involving the airitself.Many students recognised the need for vibration in,not of, the air in sound transmission. Indeed, no student whohad been asked thought that air was needed for soundtransmission.1157. Know What an Echo Is.Most students were aware that a transmitted soundcan bounce off a large object and be received by the sender.Some students recognised that sound can bounce off the endsof a sonometer wire and thus prolong the wire's reverbrationtime. Students who looked at the door harp were aware of therole of the echo chamber in enhancing the harp's sound.Indeed, one student compared the chamber to an amplifier.8. Realise that sound is carried by wave motion. and thatsound waves consist of compressions and rarefactions in the particles making up the medium carrying the sound One can conclude that the idea that sound travels inwaves seems to be well learned, if not well understood;however, few students seemed to have a clear idea of thestructure of a sound wave. One student compared sound wavesto ocean waves, with high pitches being like choppy water.No student referred to compressions orrarefactions, although many referred to oscillators "hitting"the air.This researcher felt that a student's conception of soundwaves is that they pass through the air without affecting it,just as a light ray goes through a piece of glass without,apparently, changing the glass.1169. Be familiar with the display of several different kindsof sound on an oscilloscope screen. As stated previously, there seem to be some semanticdifficulties with terms such as "high', "wide" and "deep" todescribe the appearance of the traced part of the screen. Therewas considerable difficulty, perhaps because of thefluctuating nature of the display, in drawing the form of aparticular wavelength to the attention of the student; thus onecan conclude that the popular oscilloscope needs to be re-designed in order to ease the student's observational tasks.10. Key Ideas.As well as goals, the chapter has key ideas listed insection 3.10.2. They need no repetition here.Notes on Key Ideas Most key ideas are parts of the patterns alreadymentioned in this section. However, this researcherdeliberately refrained from using terms such as "Hertz" and"Infrasound".There was no opportunity to compare speeds ofsound in different materials; however one student suggestedthat high notes travel faster.117Students demonstrated awareness of naturalfrequency in such statements as "shorter tines vibrate faster",but no attempt was made to generalise that awareness.Summary of Section 5.21 In this researcher's opinion, the most troubling ofthe students' preconceptions (not in any particular order) are:Students use the term "wave" to describe sound yet fewhave an image of a wave.Students imagine sound travelling through airbut not involving that air.Students do not invoke the idea of air being in particleform.Students perceive pitch and amplitude as onephenomenon.There is considerable semantic confusion about phrasessuch as "a high note"; it is unclear whether the height refersto the frequency or to the amplitude.5.22 Conclusions of the study - General In considering the merits and otherwise of thetechniques used for gathering data in a natural history, itseems that the Piagetian interview, with its open-endedquestions, is a technique preferable to a formal, paper-pencil118questionnaire. This is so partly because the latter is both toodeeply organised by the researcher's conceptual ecology and socan taint the student's mental processes by encouraging--ifnot demanding--both answers at random and suggestedconviction (Piaget,1982, p. 21-2). The Piagetian interviewavoids the complications of the student's possible reading andwriting difficulties, and can give information to theinterviewer by body language. However, as Piaget himselfpointed out, it takes at least a couple of years for theinterviewer to become reliably perceptive, for many signs aresubjective and difficult to put into a form available to outsidescrutiny. This researcher did not feel confident enough in hisobservational skills to include them in this study.The analysis of the typescripts yielded much data;however the validity of that data is open to question, sincethis was a first study and there is little or no comparable datato inform one of researcher bias, effects of musical training,ideation specific to this isolated coastal community or even ifsome subtle condition, to which the researcher was oblivious,was controlling the sample self-selection.In view of the commonalities found by three differentinvestigators of student perceptions of sound (mentioned insections 5.32 and 5.33), in widely different locations and age119cohorts, it is reasonable to accept, for the time being, that theinterviewing and analysis techniques carried out in Miltownwere appropriate.The most relevant of the student perceptions found bythis research include:1. Sound travels through air, but is independent of it.2. Students use scientific words with some fluency, butwith little clear ideas of their meanings (de Bono mightrefer to these terms as "porridge" or"give-it-a-name" levels).3. Waves are seen as surface phenomena; little structureis implied.4. Words are used ambiguously, for example "high" canrefer to frequency or to amplitude.5. Students appear unaware of inconsistencies of beliefabout the same phenomenon, such as bringing asonometer's bridges closer will make the note lower--afew minutes later the same student says the same actionwill make the note higher.6. Students did not spontaneously relate the phenomenaof sound to the Kinetic Molecular Theory.7. Few students recognised cavity resonance; thisimplies that they perceive the wood of the clarinet asmatter, but not the air inside it as matter.1 208. Some students seemed unaware of the circularity oftheir descriptions.9. Many students did not relate the compressibility of airto the phenomena of sound.10. Students were able to make sense of anoscilloscope trace, although there was the expectedsemantic confusion about, for example, the word "high".No attempt was made to find out if students were awareof the effects of timebase selection on the display.5.30 EDUCATIONAL IMPLICATIONS5.31 Implications By Category 1. Know That Sound is a Kind of Energy.Student lack of awareness of the Kinetic MolecularTheory suggests that greater efforts should be made to ensurethat students are well aware of the theory before they embarkon the study of sound. One way in which to do this might be toregard sound as heat made coherent; this would imply that ateacher should attempt to tie the study of sound in with thestudy of heat rather than, as is traditional, with the study oflight.Another problem is that "energy" is not taught untilGrade Nine on the " Science Probe " scheme; therefore, in121calling sound a form of energy, the teacher might well berelating the unknown of sound to the unknown of energy! Thefuzziness of such a relationship might go far to explain whysome students, even at university, confuse motion with energy(recall that even kinetic energy needs mass!).?. Know the difference between pitch and loudness.Although many students recognised a high (frequency)note, and several students were well aware of vibration, only afew students related the two. Instead, several descriptions ofhigh pitch resorted to analogy, such as "like a shreik"; thismight tie in with Johnson Abercrombie's finding that theearlier a concept forms the harder it is to bring toconsciousness. If children form their ideas of pitch whilstlearning to speak, then those ideas might well be too hard (oreven too far separated in time) to relate with ease to suchrelatively new concepts as vibration.Many students seemed to think of amplitude and pitch asan integrated phenomenon. This researcher can think of atleast four hypotheses why that should be:1. Steven's finding that resonant frequency can beshifted by amplitude change (Bruner,1984, p.74);2. they are, in fact, part of the same phenomenon ineveryday life, for example, the phrase, "come here, you1 22little monster" will be phrased differently, both in pitchand in amplitude, depending on whether the teacher isspeaking to a student or to a lover;3. it might be an example of the difficulty somestudents have in the late concrete operational stage inmanipulating two variables simultaneously;4. it might be semantic confusion over the use of thewords "high" and "low" , as in, " Lower your voice whenyou talk to me", and, "Sopranoes, try to sing a semi-tonelower".One way to deal with the confusion might be to use anoscillator set to a certain frequency and change the amplitudeof its output, then set the amplitude and change the frequency.Of course this assumes that the human ear has a linearresponse to frequency changes and a linear response toamplitude changes. This researcher's recollection from histraining at Locking is that the ear does not have a linearresponse to amplitude.3. Realise that only certain frequencies are audibleIf this concept is to be developed "scientifically" thenthe most likely technique will involve both a variableoscillator and an oscilloscope. The oscillator is likely to be a1 23" black box", with its workings taken on trust, and the studentperception of the oscilloscope ( as was seen in category 9) isnot quite as simple as could be expected.4. Know What "Frequency" Means.As stated previously, the term has at least fourmeanings. Only one student used the word spontaneously.There was some difficulty in having the student concentrate onone waveform among the many on a rapidly-changing display.It has been suggested that the latter problem could beovercome with the development of an oscilloscope with aliquid crystal display; however, such a machine would berestricted to audio frequency, since the minimum reverse timefor its elements is one millisecond.The term "vibration" is more familiar to thesestudents than is the term "frequency" and so it might be moreproductive to use the former term in discussing the phenomenaof sound.5. Appreciate how different frequency sounds are produced in musical instruments The students who were familiar with musicalinstruments were aware that changing the hole configurationschanged the notes produced. None of those students thought of1 24the air in the instrument oscillating on its own, yet werehappy with the idea of the wood vibrating; this researcherfeels this could be a product of a possible student belief that,whilst wood is matter, air is not. This implies that the teachershould be careful to ensure, perhaps by demonstration, thatstudents know that air is matter.6. Understand the nature of sound transmission--realisethat sound requires a medium in which to travel. and willnot travel through a vacuum.Since no student described air as a molecular material,it appears that this is a point to be emphasised when startingthe unit on sound. Aspden's interviewees echoed Linder's inregarding sound as a phenomenon which passes through air butis not a phenomenon of air itself. This would appear to demandthat the teacher demonstrate that air is needed for sound to beheard.7 .Know what an echo is.Since most students seem to be aware that an echo canbe created when sound bounces off a large object, this topic, initself, needs no unusual emphasis. However, some studentsperceived sound as bouncing off the ends of the sonometer1 25wire; this might prove a fruitful way in which to introduce theconcept of cavity resonance, needed to describe how musicalinstruments work.8. Realise that sound is carried by wave motion. and thatsound waves consist of compressions and rarefactions in the particles making up the medium carrying the sound.The idea that sound travels in waves seems to be wellknown. What is not so clear is the student's mental picture of awave. A couple of students mentioned waves on the surface ofthe ocean; yet such waves are transverse, whilst sound wavesare longitudinal. It would seem appropriate, therefore, toinclude a lesson on the various kinds of wave, based, perhapson the demonstration in the chapter on earthquakes in ScienceProbe 10. No student referred to compressions and rarefactions,although the idea of tines hitting the air might be a useful leadin. Newton's cradle might be another lead; however, theremight be some difficulty in persuading a student that steelballs are elastic.1269. Be familiar with the display of several different kindsof sound on an oscilloscope screen.As stated previously, when observing and describing thetrace, and relating it to heard sound, there is some ambiguityabout ideas such as "high" or "wide". Such ambiguities mightbe resolved by science people agreeing to a convention aboutthe use of such words; as an interim measure, science teachersmight seek the advice of English teachers on such language.This researcher feels that much of the problem stems from thefact that an oscilloscope trace is visually unstable when itdisplays sound in real time; consequently, it is very difficultto draw a student's attention to an aspect of the display suchas the shape of a particular wave. One suggestion to overcomethis difficulty is that an oscilloscope strictly for sounddemonstrations should be designed; such an instrument mighthave a liquid-crystal display, fed from a digital sampler andmemory of the input signal. One problem with such displays isthat an element takes approximately a millisecond to cut in orout; however, elements of the human eye take more than acentisecond to change, and so the display change time wouldbe imperceptible to the human eye. Such a design would let theteacher select and manipulate a specific waveform, simply bymanipulating the input memories.1 275.32 Commonalities with Gustafson's StudyBoth Gustafson's and Aspden's students thought thatmovement was needed for sound. Some students in each grouprelated the loudness of a sound to the energy going into it.Some students in each group recognised that manipulating thekeys of a musical instrument manipulates the notes given offby that instrument. Students in both groups recognised thatechoes need big walls and large spaces. Some of Gustafson'sstudents and many of Aspden's stated that sound travels inwaves.5.33 Commonalities with Linder's StudyBoth Linder's and Aspden's studies found students whothought of sound as travelling through, but not an organisedmovement of, air. Linder's subjects recognised thecompressions of air needed for sound, but Aspden's subjectsdid not.5.34 Thoughts with de Bono in MindWhen this researcher used de Bono's Levels ofUnderstanding to estimate depths of student understanding, hebecame aware that many expressions seemed to be used glibly,with little understanding on the part of the student. Thisimplies that far more probing should be done of students'128answers; such seems obvious to most teachers but somecurricula seem to base much of their contents on dictionary-type definitions.Use of such strictly lexical material would go far inexplaining why many descriptions tend to be circular, such as"High notes are pitched a lot higher" and why students appearto be unaware when they contradict themselves whenexplaining how an apparatus works. It might also go far inexplaining why a student can hold a belief in one situation andcontradict it in another. One way to move away from thedictionary and to make students aware of their standards andof their inconsistencies might be to move towards the kind ofcourse exemplified by Johnson Abercrombie. However, hercourse was taken by adults and introducing students totechniques of civilised disputation might cost more time thanthe science curriculum can spend. However, in clarifyingobservations, definitions, theories unifying disparatephenomena and matters of fact, inference and opinion, JohnsonAbercrombie's techniques of group discussion might well beimplemented. In turn, this might be objected to by those whoregard scientific theories as divine truths to be heard inreverential silence; in turn this view ignores the practicalitythat "scientific" information doubles every few years, so no1 29lecture series can be expected to cover the next several years'discoveries.5.35 Apparatus From the curriculum planner's point of view, there mightbe another reason for the confusion of words in reference toamplitude and frequency.Perhaps the semantic confusion stems from the student'sdifficulty in ascribing a quality such as "high" to twosimultaneous presentations, such as amplitude and frequency.If it is important that students be able to differentiatebetween frequency and amplitude, then equipment which canbe used to produce such differentiation should be available inschools.^At the least, audio-frequency oscillators, amplifiersand transducers and oscilloscopes will be needed. However,such equipment is likely to be complex and, consequently,expensive. For example, the current oscilloscope which willdemonstrate "the display of several different kinds of sound","sound quality" and overcome the visual difficulties mentionedpreviously in observing rapidly-changing waveforms is TheFast Fourier Transform Analyser made by Bruell and Kjaer ata price of about forty thousand dollars each (Dow,130personal communication, April 23 1992, Powell River). Fewschools would be able to afford a class set of those!Even the digital oscilloscope mentioned in section 5.31.9would not be inexpensive.Therefore it is unlikely that individual students wouldbe able to explore such phenomena as amplitude and frequencyseparate from each other. Without opportunities to generatepersonal knowledge, the science classroom becomes merely aplace to paint students with facts, rather than a communityintended to encourage them to construct their own knowledge.5.40 SUGGESTIONS FOR FURTHER RESEARCH With such a dearth of research in the field of studentperceptions about sound, the field is wide open. It might befruitful to fill the gaps in the Gustafson-Aspden-Linder agespectrum in order to find out how age-specific is thedevelopment of the concepts associated with sound. Gustafsonworked with Grade Four students; Aspden worked with GradeEights and Linder worked with physics post- graduates. Suchresearch could be commercially important, for communicationseems to be getting more personal. For example, Plato's idealcity had a population of 5040, the crowd he felt could be131addressed by one speaker; in the nineteenth century,newspapers were tailored to particular segments of society; inthis century, T.V. has addressed groups of one or two; thetelephone and the personal camcorder have madecommunication one-to-one. A major use for personalcommunication is, of course, commercial advertising; so anything, such as a deeper knowledge of people's responses tosound, which makes communication more successful is likelyto be financially rewarding.More work needs to be done on word usage in scienceinstruction. One has only to compare the different meanings ofwords such as "significant" and "integrated" in physics and inother fields to recognise that word usage is often a barrier tocommunication. The study of sound might be a fruitful way inwhich to look at such ambiguities formally; in fact, ratherthan restrict the study of sound to Kundt's tubes, waves andthe like, the study could be used as the core of a course on"communication by sound", ranging from rhetoric to music toelectronics to psychodynamics to noise pollution.It might be worthwhile to use the apparent ambiguitiesof description of amplitude and pitch to explore brainfunctions at a biological level. One might consider that bothFreudian Analysis and Genetic Epistemology have much incommon, with conversation exposing deeper mental structures,1 32parallels between concepts such as "schemata" and "complex",and "ego-defences" and "classifications of student responses".A group instrument could be created to measure boththe strengths and frequencies of concepts needed for theacademic understanding of sound phenomena; this would givethe teacher a far tighter grasp of instructional requirements--and of irrelevancies.The digital oscilloscope might be worth developing forschool use.5.50 A LAST WORDWhen this researcher looks back at his cited reasons forundertaking this study and asks himself what he has found, hecan now say that he has found that the mechanic was quitenormal; the fault lay in the assumption that a person'sconceptual ecology is always perfectly consistent and logicalto another person.Comparing ideas for the Literature Review has convincedthis researcher that the physics of sound stretches theimagination--perhaps in relating the person's voice to thedisplay on the oscilloscope--just as much as does the poetwho relates "my love" and the "red, red, rose". Both are waysto develop and extend persons' knowledge of both themselvesand their environments.133As Storr put it so aptly:. .. in discovering more about our environment wecreate internal patterns or schema. By doing so, wereduce the need to pay equal attention to every impingingstimulus, and only need to take notice of those stimuliwhich are novel . . .^( Storr, 1990, p. 170)This researcher's suspicions about the confusing aspectsof an oscilloscope display appear to have been confirmed.Whether this research, done primarily from theresearcher's private library and using local students, isadequate is not for this writer to say.The ideas behind this thesis can be summed up thus:Mystery and disorder spur man to discovery, to thecreation of new hypotheses, which bring order andpattern to the maze of phenomena. But mystery anddisorder pertain to our own natures as well as to theexternal world. I venture to suggest that, just as it isinconceivable that all the laws of Nature will ever bediscovered, so it is equally impossible to believe thatthe complexities of human nature can ever be grasped intheir entirety.^ (Storr, 1990, p.172-3).134Reference ListAspden, L. (Fall 1991) . Personal Communication.de Bono, E. (1976). Practical Thinking. London: Pelican.Bronowski, J. (1973). Ascent of Man. Toronto: Little, Brown.Bruner, J. (1984). In Search of Mind: Essays in Autobiography.New York: McGraw Hill.Buesche, F. (1969). Introduction to Physics for Scientists andEngineers. New York: McGraw Hill.Bullard, J., Baumann, F; Deschner, D., Gore, G., McKinnon, B., andSieben, G. (1985). Science Probe Eight Teachers ResourceGuide. Toronto: John Wiley.Bullard, J., Baumann, F., Deschner, D., Gore,G., McKinnon, B. andSieben,G.(1986). Science Probe Eight Toronto: Wiley.Bullard et. al.,(1984), Science Probe 10. Toronto: Wiley.Cowan, P. A. (1978) . Piaget With Feeling. New York: Holt,Rinehart and Wilson.135Dakin, A. and Porter, R. (1962). Elementary Analysis. London:Bell.Davis, P. and Hersche, R. (1981). The Mathematical Experience.Boston: Birkhauser.Dow, S.,(1992). Personal Communication, April 23 1992.Dreyer, J. (1977). Dictionary of Psychology. London: Penguin.Driver, R., Guesne, E. and Tiberghien, A. (1985). Children'sIdeas in Science. Milton Keynes: Open University.Feynman, R.P. (1965) Character of Physical Law. London:British Broadcasting Corp.Feynman, R.P., Leighton, R.B., and Sands, M.(1977).Feynman's Lectures in Physics. Los Angeles: Addison-Wesley.136Flew, A. (1979). Dictionary of Philosophy. London: Pan.Gleitman, J. (1981). Psychology. New York: Norton.Goldstein, T. (1988). Dawn of Modern Science. Boston:Houghton Mifflin.Gustafson, B. (1988). Children's Learning in Science: ACollaborative Study. (Ph.D. Thesis University of Alberta,Edmonton).Haggerty, S. (Summer,1986). Personal Communication.Hodges, A. (1983). Alan Turing. The Enigma. New York:Touchstone.Inhelder, B. and Piaget, J. (1958). The Growth of Logical Thinking from Childhood to Adolescence. New York: Basic.Johnson Abercrombie, M. (1969). Anatomy of Judgement.London: Pelican.Kuhn, T. (1970). Structure of Scientific Revolutions. (2nd Ed.).Chicago: Chicago University.137Langley, I. (Spring,1988). Personal Communication.Lincoln, Y. and Guba, E. (1985). Naturalistic Inquiry. BeverlyHills: Sage.Linder, C. (1989). A Case Study of University Physics Students'Conceptualisations of Sound. (D.Ed. Thesis: University of BC).Lovell, K. (1962). Educational Psychology and Children. (5thEd.). London: University of London.Magee, B. (1974). Popper. London: Fontana.Marion, J.B. (1980). Physics and the Physical Universe. NewYork: Wiley.Novak, J. and Gowin, J. (1984). Learning How to Learn.Cambridge: Cambridge University Press.Penrose, R. (1990). The Emperor's New Mind. London: Vintage.Piaget, J. (1976). To Understand is to Invent. London: Penguin.Piaget, J. (1977). Psychology and Epistemology. London:1 38Penguin.Piaget, J. (1982). The Child's Concept of the World. London:Penguin.Piaget, J. and Inhelder, B. (1969). The Psychology of the Child.New York: Basic Books.Popkin, R. and Stroll A. (1972). Philosophy Made Simple.London: Allen.Posner,G., Strike, K., Hewson, P. and Gertzog, W. (1982).Accommodation of a Scientific Conception: Towards a Theoryof Conceptual Change. Science Education. 66. (2). 211-227.Rheingold, H. (1988). They Have a Word For It. Los Angeles:Torcher.Royal Air Force (1983). Synopsis of the Three-Year Royal AirForce Apprentice Air Radio Fitter Course Followed by W.E. Aspden.  Royal Air Force: #1 Radio School.Sawyer, W. (1962). Mathematician's Delight. London: Pelican.Singh, J.J. (1972). Mathematical Ideas. Their Nature and Use.London: Hutchinson.1 39St. John-Brooks, C. (1988/1/17). Whitehall Testing Time.Sunday Times. page not known.Storr, A. (1990). Churchill's Black Dog. Kafka's Mice and OtherPhenomena of the Human Mind. New York: Ballantine.Strauss,S. (1981). U-shaped Behavioural Growth. AcademicPress: Orlando. In R. Driver, E. Guesne and A. Tiberghien, (Eds.)Children's Ideas in Science. Milton Keynes: Open University.Stubbs, M. (1978) Personal CommunicationThomas, R. M. (1979).  Comparing Theories of ChildDevelopment. Belmont: Wadsworth.Toulmin, S. (1977).  Human Understanding. Use and Evaluationof Concepts. Princeton: University Press Paperbacks.Turnbull, H.W. (1962). The Great Mathematicians. London:Methuen.140141Appendix 1.^(Interview with a student ) I:^I would like to interview you, (student's name) as to howwe hear things. Now suppose you tell me as loudly as you can,how do we hear things?S:^With our ears.I:^Tell me more about what your ears do.S:^I don't know.I:^How can you tell when something is making a noise?S:^You just hear it.I:^How do you know that you are hearing something?S:^I don't know.I:^Let's see. The drawing on the chalkboard, are you hearingthat drawing?1 42S:^No.I:^How do you know what is on it?S:^I can see it.I^There is some air blowing in the room. Do you hear it?S:^Yes.I:^How do you know that you can hear it? That you are notseeing it? Tell me, if you saw a man standing by a woman,what differences would you expect in their voices?S:^The man would be deeper.I:^In what way would those voices be different?S:^The pitch would be different.I:^What would you notice about the pitch of the man's voicefrom the pitch of the woman's voice? Which would be which?S:^The woman's would be higher.1 43I:^How would you know that the pitch was higher?S:^You can hear it.I:^What do you mean by a high pitch? Which of these is ahigh pitch and which is a low pitch?S:^The first one.I:^How can you tell it was a high pitch? How did it sound?S:^It sounded squeakier.I:^OK. How could you tell this was a low pitch?S:^It goes deeper.I:^Why do we use the word deep? What else do we calldeep?S:^The ocean is deep.I:^Why do we say that the ocean and the voice are bothdeep?S:^Lower down, I guess.1 44I:^Why do we think of a voice like this as down from a voicelike this (high)? Why do you think that one is downer than theother?S:^Because it sounds lower.I:^It sounds lower? OK. Give me a high pitched sound. Justdo it as if you were singing. Come on, we are friends here, Iwon't bite you. I have just had lunch.S:^I can't.I:^OK. Can you imitate the sound of a foghorn? Come on,give it a try.S:^(No response).I:^You are a bit embarrassed eh? OK. Next question. Whatdo you call it when you hear a sound then you hear it a secondtime? I clapped my hands, and could you hear other clapscoming off the walls? What do we call that?S:^Echoes.1 45I:^What causes echoes?S:^When you are closed in a space, or something.I:^Those are pretty good answers. Let me just show yousomething. Have you seen one of these things before?S:^Yes.I^I call it a gizmo. What is its real name?S:^A door harp.I:^Do you have a door harp at home?S:^Yes.I:^Can you tell me how this thing works. Just talk and tellme how this thing works. First of all, what do you noticeabout its shape? How would you describe its shape?S:^Like a C.1 46I:^What material is it made of?S:^Wood.I:^I tell you what. You play with it and tell me what you aredoing and see if you can get it to work. That's pretty good. OK.Now what is happening, what is going through your mind whenyou tried to make it work?S:^This hit the strings.I:^What hit the strings?S:^The balls.I:^And what do those balls do when they hit the string?S:^They make music.I^How do they make music?S:^They hit the metal.1 47I:^OK. When they hit the metal what do the balls do to themetal?S:^(No response)I:^Let's see. Why not touch one of these metal pieces verygently and see what happens when the ball bangs into them.S:^It vibrates.I:^How can you tell it is vibrating?S:^I can feel it.I^What do you mean by the word vibrate?S:^It goes through the whole piece of metal.I:^What does?S:^When it hits, it just goes right through.I:^How can you tell that it is going right through?S:^By the bell.1 48I:^How can you tell that the vibration or whatever it is, isgoing right through to the other end?S:^If you put your hand there.I:^Which vibration do you think is greatest? The vibrationat the end or the vibration in the middle?S:^In the middle.I:^How would you check? Can you try touching it?S:^By the back of it?I:^You are just about at the middle. Try the top one, it'seasy.S:^At the ends, I guess.I:^OK. Let's see. If I hit this pencil, it moves away in onedirection, doesn't it? When the ball hits the wire, does thewire just go in one direction?S:^It goes back and forth.1 49I:^OK. Can you tell me anything about how quickly it goesback and forth compared with the sound it makes?S:^When it goes really quickly it gets louder.I:^Anything else?S:^There is more vibration.I:^What do we mean by more vibration?S:^You can feel it more.I:^Does it make more vibration in the wire moving back andforth, or is there more vibration in the wire going quicker?Which do you think?S:^Going back and forth.I:^Yes, but going back and forth slowly, or quickly, or a longdistance or a short distance?S:^(No response).1 50I:^OK. I think that is too difficult a question. Suppose wehit the string with the wire but really hard, what do you thinkis happening to the wire?S:^The vibrations keep getting longer.I:^How can you tell?S:^Because it's less time.I:^OK. Suppose I hit it very gently like that?S^They would be quicker then.I:^It dies away quicker. OK. What do you notice about thepitch of the wire? The note, if you like, in the wire? That onethere, or that one here?S:^The second one is softer.I:^Do you mean higher or lower? Or louder or softer?Which?S:^Lower and softer.151I:^OK. Now we will have to go now, so let me thank you foryour efforts. I really enjoyed working with you. I'll be usingyour interview but I will change the names around and add it toother interviews. Thank you for your efforts and here is yourdollar.

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