appendices - university of adelaide...page 829 abbreviations appendix 1 sait (2) south australian...

APPENDICES

APPENDIX I: LIST OF ABBREVIATIONS

AAMT Australian Association of Mathematics Teachers AARE Australian Association for Research in Education AAS Australian Academy of Science ABC Australian Broadcasting Corporation ACE Australian College of Education ACEID Asia-Pacific Centre of Educational Innovation for

Development ACER Australian Council for Educational Research ACME Adelaide Consortium for Mathematics Education ACT Australian Capital Territory AEC Australian Education Council AGPS Australian Government Publishing Service AMP Adelaide Mathematics Project (SA) AMS Australian Mathematical Society ANZAAS Australian and New Zealand Association for the

Advancement of Science ANZHES Australian and New Zealand History of Education Society APMEP Association des Professeurs de Mathématiques de

l‘Enseignement Publique APU Assessment of Performance Unit (England & Wales) ATC Adelaide Teachers’ College (SA) ATM Association of Teachers of Mathematics (UK)

BA Bachelor of Arts BBC British Broadcasting Corporation BC British Columbia (Canada) BCE Before the Common Era (formerly BC) BEd Bachelor of Education BLIPS Basic Learning in Primary Schools (SA) Br Brother BSc Bachelor of Science BSCS Biological Science Curriculum Study (USA/Australia) BSEM Broad-Spectrum Ecological Model

C&EN not known c. Circa (about) CA California (USA) CAC Curriculum Area Committee (of SSABSA) CAE College of Advanced Education CC Curriculum Corporation CDC Curriculum Development Centre/Corporation (Australia) CE Common Era (formerly AD)

Abbreviations Appendix 1

CEDIC not known (a French educational organisation) CEEB College Entrance Examination Board (USA) CEM Colonial Echo Model CIEAEM Commission Internationale pour l’Etude et l’Amélioration

de l’Enseignement des Mathématiques [International Commission for the Study and Improvement of Mathematics Teaching]

CIEM not known (French) CO Colorado (USA) CR Coefficient of Reproducibility CSMP Comprehensive School Mathematics Program (USA) CSMS Concepts in Secondary Mathematics and Science (UK) CUP Cambridge University Press CURASS Curriculum and Assessment Committee

D-FRG Dice-Family Random Generator DAI Dissertation Abstracts International DC District of Columbia (USA) DEET Department of Employment, Education and Training

(Australia) DES Department of Education and Science (and the Welsh

Office) (UK) DETE Department of Education, Training and Employment (SA)

ed./eds editor(s)/edition EdD Doctor of Education EDA Exploratory Data Analysis EDSA Education Department of South Australia; South Australia.

Education Department; &c EEC European Economic Community elem. elementary ERDC Education Research and Development Committee

GB Great Britain GP General practitioner GRG SA Archival Classification. Vide Sources, Archived

Documents.

HEES Higher Education Entrance Score (SA) HESS Higher Education Selection Subject (SA) HMI H[er] Majesty’s Inspector HMSO H[er] Majesty’s Stationery Office

I Interviewer ICME International Congress on Mathematical Education


ICMI International Commission on Mathematical Instruction ICOTS International Conference on Teaching Statistics IDM Institut für Didaktik der Mathematik [Institute for the

Teaching of Mathematics] (Germany) IEA International Association for the Evaluation of Educational

Achievement IL Illinois (USA) IN Indiana (USA) IOS Not stated, possibly Dutch for Institute of Statistics IOWO Instituut voor de Ontwikkeling van het Wiskunde Onder-

wijs [Institute for the Development of Mathematical Education] (Netherlands)

IREM Institut de Recherche sur L’Enseignement des Mathémat-iques [Institute for Research into the Teaching of Mathematics] (France)

ISI International Statistical Institute

JP Justice of the Peace Lt-Col. Lieutenant-Colonel LUDDITE Learning the Unlikely at Distance Delivered as an

Information Technology Enterprise (Australia)

MA Massachusetts (USA) MASA Mathematics Association of South Australia MATs Mathematical Attribute Tiles MAV Mathematical Association of Victoria (Australia) MCTP Mathematics Curriculum and Teaching Program

(Australia) MEd Master of Education MEdAdmin Master of Educational Administration MEdSt Master of Educational Studies MERGA Mathematics Education Research Group of Australasia MMR Minimum Marginal Coefficient of Reproducibility MN Minnesota (USA) MPhil Master of Philosophy MS Manuscript MSc Master of Science MTM Muddling Through Model

na not applicable NAEP National Assessment of Educational Progress NCTM National Council of Teachers of Mathematics (USA) ndp No date of publication NEF New Education Fellowship


NFER National Foundation for Educational Research NIEF National Industry Education Forum NJ New Jersey (USA) No Number np not possible Npd No publication details Npp No place of publication n’r number NSOED New Shorter Oxford English Dictionary NSW New South Wales (Australia) NT Northern Territory (Australia) NY New York (USA) NZ New Zealand NZAMT New Zealand Association of Mathematics Teachers

OCDL Office Central de Librairie (France) OED Oxford English Dictionary OEEC Organisation for European Economic Co-operation OOB Out of Balance (Vide O’Daffer.) OSTP Our Schools and Their Purpose (SA) OUP Oxford University Press

PA Pennsylvania (USA) PEB University of Adelaide. Public Examinations Board or

Public Examinations Board of South Australia PES Publicly Examined Subject (SA) PME [International Group for the] Psychology of Mathematics

Education PMS Primary Mathematics Series PNG Papua-New Guinea

Q Queensland (Australia)

R-D-D Research-development-dissemination (Vide Griffiths & Howson, 1974)

RG Random Generator RIME Reality in Mathematics Education (Vic)

S Subject or Student SA South Australia(n) SACAE South Australian College of Advanced Education SACE South Australian Certificate of Education SACSA South Australian Curriculum, Standards and Accountabil-

ity Framework SAIT (1) South Australian Institute of Teachers


SAIT (2) South Australian Institute of Technology SAS School Assessed Subject (SA) SMP School Mathematics Project (UK) SMRF School Mathematics Research Foundation (Vic) SMSG School Mathematics Study Group (USA) SOLO Structure of Observed Learning Outcomes (Vide Biggs &

Collis) SOSE Studies of Society and Environment (Australia) SPSS Statistical Package for the Social Sciences SSABSA Senior Secondary Assessment Board of South Australia SSC Secondary School Certificate (SA)

TAB Totalizator Agency Board (Australia) TAFE Technical and Further Education Tas Tasmania (Australia) TIMSS Third International Mathematics and Science Study

U University u unknown UICSM University of Illinois Committee on School Mathematics

(USA) UMR Unistructural, Multi-structural and Relational (SOLO

Taxonomy) UK United Kingdom UNESCO United Nations Educational, Scientific and Cultural

Organization UP University Press URL Unique/Universal Resource Locator USA United States of America

VA Virginia (USA) VCE Victorian Certificate of Education Vic Victoria (Australia) VUSEB Victorian Universities Schools and Examination Board

WA Western Australia

APPENDIX II: EXAMPLES OF ARGUMENTS PUT FORWARD FOR STOCHASTICS

This Appendix provides, without comment, extracts from various documents which are too long for comfortable quotation in the main body of the text, but which are referred to in the text where appropriate.

1959—COLLEGE ENTRANCE EXAMINATION BOARD

… the field of probability & statistical inference has been extensively developed in recent years. In this field, too, a research society and research journal have been established in this country: the Institute of Mathematical Statistics, and the Annals of Mathematical Statistics, now in its twenty-ninth year. At least 10 other journals, in English, are entirely devoted to the theory and applications of probability and statistics.1

[discussing recommendation for mathematics in Years 9, 10 & 11] Just as mathematics deals with situations in which the facts can be determined, it also provides ways to study, understand, and control uncertainty. Many of the newer applications of mathematics use probability and statistical reasoning … .2

Statistical thinking is playing more and more of a part in the daily lives of educated men and women. An introduction to statistical thinking is an important supplement to an introduction to deductive thinking.3

[discussing the Year 12 course on Introductory Probability with Statistical Applications] It is not intended that this course be a more elaborate presentation of descriptive statistics than the optional unit in Elementary Mathematics. … This course is a course in mathematics, built around concepts of great importance for our modern technological societythe theory of probability.4

So great is the current scientific and industrial importance of probability and statistical inference that the Commission does not believe valid objections based on theoretical considerations can be offered to its inclusion in the curriculum.5

1 CEEB (1959b, pp. 1–2) 2 CEEB (1959b, p. 29) 3 CEEB (1959b, p. 29) 4 CEEB (1959b, p. 31) 5 CEEB (1959b, p. 32)

Arguments for Stochastics Appendix II

Though no more intricate than some traditional topics in algebra, the theory of probability is tremendously more vital and important, and fully as valuable in developing and keeping alive algebraic skills. Since an appreciation of the ideas involved requires some maturity, we recommend that the study of probability be undertaken in grade 12.6

The theory of probability is an example of a small axiomatic system that has remarkably extensive consequences: it takes its place beside the deductive systems recommended for geometry and for algebra. Moreover, the theory of probability provides a natural use for the important notion of sets … .7

1959—ROYAUMONT SEMINAR

Arguments about Mathematics in General

362. The case for reform in the secondary-school programme is based on the following points:

a) The new developments in graduate and research mathemat-

ics imply a necessary shift in emphasis for secondary school mathematics. New topics such as abstract algebra, vector spaces, theory of sets, etc. will enter the school programme, bringing a changed point of view on what mathematics is today.

b) The new applications of mathematics suggest new problem

material. Probability, statistical inference, finite mathe-matical structure, linear programming, numerical anal-ysisall indicate expansion in useful applications of mathematics.

c) The development of new standards of accuracy and clarity of

statements and the emphasis on mathematical structures indicate a need for reconsideration of the concepts embedded in our classical treatment of mathematics.

d) The tremendous increase in knowledge in the various

branches of mathematics demands a synthesis and broader base for teaching at the pre-university level. To learn math-ematics today requires more efficient and more general approaches.

6 CEEB (1959b, p. 32) 7 CEEB (1959b, p. 32)


e) The changes in cultural, industrial and economic patterns of many nations call for a basic change in educational patterns. More people must be better trained in scientific knowledge. Even laymen must come to understand science; today, knowing mathematics is basic to understanding science.8

Arguments about Stochastics in Particular 407. [Probability and statistical inference], particularly the second, are

recommended as a desirable new field of instruction in the secondary school. While probability, based on a priori con-sideration of the number of possible combinations (and permutations), has sometimes been a part of secondary-school algebra, the use of a posteriori considerations from experiments and the use of confidence limits is new.

408. There is also the possibility of treatment of combinatorial analysis

from the viewpoint of sets, set functions and sample space, thus affording another opportunity to develop the modern symbolism and thinking which is at the base of all the mathematical disciplines.

409. There was general agreement on the method of presenting the sub-

jects. The subject matter should include permutations, combinat-ions, probability, the binomial distribution and statistical infer-ence.* An extension may be made to include correlation, normal distribution, and stochastic processes. It is strongly urged that all countries create and experiment with these courses so that they become a permanent part of the secondary-school curriculum.9

425 The seminar reached the following general conclusions: …

II Elementary probability must be recognised as an appropri-ate part of the mathematics taught in secondary schools.

(a) Statistical inference must be recognised as applied

mathematics which contributes in an essential way to decision processes in the spirit of the “scientific method” basic to some many fields, both in the phys-ical sciences and in the science of human behaviour. Furthermore, it must be recognised that statistical

8 OEEC (1961, p. 107) * This emphasis on starting with permutations and combinations reflected the prevailing

tradition of teaching the topic in tertiary institutions. Vide discussion on Piaget’s work in Chapter 8.

9 OEEC (1961, pp. 117–118)


reasoning is of growing importance in the field of public affairs.

(b) Suitable elementary instruction in probability and

statistics must be introduced into the curricula of secondary schools.

(c) Suitable preparatory courses for teachers of these

subjects must be introduced in normal schools and teacher-training institutions.10

10 OEEC (1961, p. 122)

APPENDIX III: NATIONAL CURRICULUM DOCUMENTS FROM THE 1990s

To assist in reading the text of Chapter 16 this appendix provides the basic structures of all work on probability in

• A National Statement on Mathematics for Australian Schools • Mathematics—a curriculum profile for Australian schools • Attainment Levels

and relevant sections of • Mathematics—Work Samples • Studies of Society and Environment—a curriculum profile for Australian

schools

The pagination of the original documents may be seen as well as the pagination for this thesis. Title pages are provided as introductions to the excerpts from each document.

Appendix III is available in the print copy of this thesis, Barr Smith Library,

Adelaide University.

SOURCES

UNPUBLISHED PRIMARY SOURCES

The Royal Prince was by the King entrusted To my fond care, ere I grew old and crusted; When traitors came to steal his son reputed My own small boy I deftly substituted! The villains fell into the trap completely— I hid the Prince away—still sleeping sweetly; I called him “son” with pardonable slyness— His name, Luiz! Behold his Royal Highness!1

ARCHIVED DOCUMENTS

Australian Council for Educational Research. Archives. Radford Collection Item 357. Documents relating to the 1964 Primary Mathematics Conference.

––– Archives. Vol. 224

Education Department of South Australia. GRG 18/98. Miscellaneous files, probably from the office of the Superintendent of High Schools. Covers 1965–1966. Includes addresses by the Superintendent, memos to and from the Director of Education, circulars to Head Masters, details of in-service courses, inspections, and Matriculation requirements.

––– GRG 18/142. Notebook of J.D. Gunton, Assistant Superintendent of Primary Schools on authorised experimentation in schools from approximately 1965–1968

––– GRS 1049 Primary and Secondary Advisory Curriculum Boards. Minutes of Meetings 1955–present. Three boxes. In Box 1 the minutes from 1952–1960 are badly damaged by water and mud, and very fragile. This box contains a bound booklet listing resolutions of the Primary Schools Advisory Curriculum Board. Box 2 contains bound Minutes of the Primary Advisory Curriculum Board, 1960–1970. Box 3 contains Minutes of the Primary and Secondary Advisory Curriculum Boards.

The Mathematical Association (UK). Archives. Box 544

1 The Gondoliers Gilbert (1889, p. 282) Inez is brought to the court in the closing moments of

the play to declare authoritatively what happened to the heir to the throne who was com-mitted to her care many years previously.

Bibliography

DOCUMENTS IN THE PRIVATE DOMAIN

These documents are held by the author unless otherwise stated.

AAMT/DEET Project in the Teaching and Learning of Chance and Data via Open Learning Typescript (ii + 11 pages) of project submission from AAMT submitted April 1994.

Cooper, Barry (1993) Secondary Mathematics Education in England: recent changes and their historical context

Edwards, Roger (ndp) Teachers’ Ideas about Teachings Statistics Working bibliography for doctoral dissertation at the University of Waikato, NZ which was unfinished because of his untimely death. Document made available by his supervisor, Dr AJC Begg, and a summary was published in Statistics Education Research Newsletter in 2001.

E-mail messages. Messages which have been sent to me personally are treated as correspondence and are listed as Personal Communications. Messages which have been sent via a bulletin board or list server are public documents, but are usually ephemeral. I have therefore treated the copy which I have preserved at a Document in the Private Domain. Such messages are identified as e-mail messages in the text and in the Index and are not usually listed here.

Fourth Assembly of the Bards of the Gorsedd of Cornwall in Australia May 18th, 1991 Moonta Mines SA: no publisher

High School Papers (c. 1975) A collection of miscellaneous tests and handouts found in a drawer at an Adelaide suburban High School some years after the teacher concerned had left. I was allowed to make notes and transcriptions of relevant material but not to make copies. Because of the way in which I gained access to the material, evidence taken from this source is not attributed to any identifiable school or person. The current provenance of this collection of papers is not known. The collection was examined on 20 Aug 1993.

Initial Thoughts on Levels 7 & 8 Chance & Data Notes under this title prepared by one person involved in the construction of the relevant Profiles. A total of three A4 pages of typescript, with some hand-written annotations. The provenance of these notes is uncertain, so it is inappropriate to name the author. This has limited the use made of this typescript to general issues.

Jones, Keith, 28 Nov 97. A report of an article in the Times Educational Supplement posted by Keith Jones, University of Southampton, to the bulletin board of the Association of Mathematics Education Teachers. The document being summarised is Key Stage 2 Mathematics Schemes published by the Qualifications and Curriculum Authority, Newcombe House, 45 Notting Hill Gate, London W11 3JB.

Long, Eleanor (ndp, c. 1990) Some Notes on What is Commonly Known as Process Maths. Introduction of Process Maths in South Australia—Mathematics Project: R–4 Unpublished paper, provenance unknown

Kelly, Dr Robert A., Flinders U of SA. Unpublished lecture notes for the Subject “54902 Language and Education” given in 1989. MacGregor, Dr Mollie. File of papers related to her association with the Australian Mathematics Works Project. Held in the Department of Mathematics and Science Education, and examined and discussed with Dr MacGregor on 8 Dec 1994.

Mack, John (c. 1986) A Rationale for National Mathematics Curriculum Guidelines Unpublished document used by SSABSA Curriculum Area Committee when planning alternative Year 12 courses. Copy sighted by author when examining High School Papers (c. 1975).

Bibliography

Mathematical Association of Tasmania - Education Department (1972) Mathematics Seminar [An unpublished set of duplicated notes on 42 foolscap pages issued for a meeting at Elizabeth Matriculation College on 6–8 Sep 1972]

Probability Theory An undated duplicated document of 15 pages, probably a reprint made c. 1985 of a document made perhaps as early as 1964 at Henley High School, SA., although the use of the term “half-crown” suggests that it has English origins.

School Mathematics Project (1965a). Annotations by author to personal copy made when using the book in a classroom in 1966 or 1967.

Senior Secondary Assessment Board of South Australia. (1985–1990) Minutes and other material relating to the Curriculum Area Committee. The material which I have sighted was not held at SSABSA but was located and shown to me by a third party who was in no way involved in the events covered in the documents. I was allowed to make notes and transcriptions of relevant material but not to make copies. Because of the way in which I gained access to the material, evidence taken from this source is not attributed to any identifiable individual. Because I had access to this source I did not seek access to the official SSABSA archives. The current provenance of this collection of papers is not known. The collection was examined on 20 Aug 1993.

South Australian Institute of Technology. A Submission for the Accreditation of the Course for the Award of the Graduate Certificate of Mathematics Education. October 1989. Similar documents were prepared for all tertiary institutions at this time, and the submissions were accepted and the relevant parts incorporated into the institutions’ Calendars.

Truran, John M. Diary 1964–1968

Why Change School Mathematics Syllabuses? An undated document quoted by Sumner (1969). I have not been able to trace this document.

Bibliography

PERSONAL COMMUNICATIONS

Michael Arnold, a former colleague at Melbourne Grammar School, interview 15 Jun 1994

Nicholas Balacheff, Laboratoire Leibnitz, Grenoble, letter, Apr 1996

Ken Berndt, formerly Adelaide Teachers’ College, interview, May 1993

Professor Manfred Borovcnik, University of Klagenfurt, Austria, letter, Apr 1996

Professor Ken Clements, University of Brunei Darussalam. Discussion, Brisbane, 14 Jul 1993; correspondence, Jan 1994.

Dr Christopher J. Dawson, University of Adelaide, general discussions during writing up of (a) Masters thesis, 1990–1992 and (b) this thesis 2001

Dr Ruhama Even, Weizmann Institute of Science, Israel, letter, 20 Apr 1998.

Dr David Green, University of Loughborough, interview, Aug 1994

Anthony Harradine, Prince Alfred College, Kent Town, SA. Address to Statistical Society of SA, 16 Aug 2000

Dr Peter Holmes, University of Sheffield, discussions at ICME, Adelaide, Aug 1984

Professor Phillip Hughes, Hobart, interview, May 1995

Hartley Hyde, Wirreanda High School SA, telephone discussions, Mar 1993; letter, 2 Aug 1998

John Izard, ACER, Hawthorn Victoria, interview, December 1993

Professor Alan James, University of Adelaide, discussions, 8 Jun 1995

Gordon Jones, a former colleague at Melbourne Grammar School, interview, 13 Jun 1994

Professor John Keeves, Flinders University of South Australia, interview and comments on draft, 10 Aug 1993

Professor Christine Keitel, Free University of Berlin, letter, Apr 1996

Sarah Ketteridge, many medical consultations from 1997 onwards

Dr Jan Lokan, Australian Council for Educational Research, letter, 16 Nov 1994

Robert Lucas, Minister for Education and Children’s Services, South Australia, letter, 20 Aug 1994

Dierdre Maddern, Martyrs School, Popondetta PNG, May 1984

Nancy McConnan, Cambridge University Press, Melbourne, letter, c. Apr 1968, conversation, c. 1976

Revd Peter G. Osborn, conversation, 25 Dec 1993

Dr Andrea Peter-Koop, University of Münster, discussions July 1999

Dr Jane Pitman, University of Adelaide, interview, Nov 1996

Dr Jack Rowell, University of Adelaide, interview, Jul 1993

Dr Paul Scott, University of Adelaide, discussions throughout the writing of this thesis

Dr Brian Sherman, University of Adelaide, discussions, Nov 1993

Kath Truran, University of South Australia, discussions, Apr 1993 and many short conversations

Dr David Tynan, University of Melbourne, correspondence, 10 Nov 1999

Dr J.J. Vonèche, Directeur des Archives Jean Piaget, Geneva, conversations, Aug 1994 while I was working in the Archives.

Dr Geoffrey Watterson, Monash University, interview, 15 Nov 1993

Bibliography

Michael Wheal, formerly Curriculum and Assessment Officer SSABSA, telephone conversation, 4 Apr 2001

Dr Julian Williams, University of Manchester, contribution to Stochastics Discussion Group, PME Conference, Hiroshima, July 2000.

Dr Bernd Wollring, University of Münster, discussions at Münster, Aug 1994

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NEWSPAPERS, JOURNALS AND PERIODICALS Adelaide Teachers’ College Handbook Advertiser Age American Mathematical Monthly Annual Report of Western Teachers’ College

Australian and New Zealand History of Education Society Journal (later History of Education Review)

Australian Broadcasting Commission Education Program Notes. Radio and Television South Australia

Australian Mathematics Teacher Australian Senior Mathematics Journal Australian Way Calendar of the University of Adelaide Current Affairs Bulletin Education Gazette. New South Wales Education Gazette. South Australia

Educational Studies in Mathematics

Guardian Weekly Journal for Research in Mathematics Education New Zealand Mathematics Magazine Mathematics Education Research Journal Mathematics in School Mathematics Teacher Mathematics Teacher Education and Development

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Möbius

National Council of Teachers of Mathematics News Bulletin

New Scientist

Newsletter of the International Study Group for Research on Learning Probability and Statistics

Official Yearbook of the Commonwealth of Australia School Mathematics Journal South Australian Parliamentary Papers 44 South Australian Mathematics Teacher South Australian Teachers’ Journal2

2 formerly South Australian Institute of Teachers Journal

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The other children [followed] in strict order of precedence, those who had the longest names going first.1

“A ‘New’ Syllabus” (1965) Vinculum 2 (1): 8

Ableman, Paul (1989) Dad’s Army. The Defence of a Front Line English Village London: BBC Books

Abraham, D.A. (Tony) (1975) The Development of the Mathematics Syllabus in New South Wales State High Schools, 1883–1962 MEd Thesis: U of Newcastle

Abrahamson, B. (1967) “Tertiary Mathematics Course in South Australia—first-year mathematics at Flinders University” South Australian Mathematics Teacher 1 (1): no pagination

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1 Oscar Wilde The Birthday of the Infanta, 1891. P. 225 in Wilde (1994)

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Amir, Gilead; Williams, Julian (1994) “The Influences of Children’s Culture on their Probabilistic Thinking” Vol. II, pp. 24–31 in da Ponte & Matos Proceedings of the Eighteenth PME Conference

Anderson, Peter; Kempster, Geoffrey; Pegg, John (1985) The Chances Are … a teaching approach to informal probability in the primary school Npp: New England Mathematical Association for the AAMT

Anderson, Peter; Pegg, John (1988) “Informal probability—an investigative teaching approach”. Pp. 92–95 in Pegg, John (ed.) Mathematical Interfaces Proceedings of the 12th Biennial Conference of the Australian Association of Mathematics Teachers, Newcastle, January 1988. Armidale, NSW: New England Mathematical Association for the AAMT

Andrew, David (1993) “Special General Meeting” Möbius 20 (3): 43

Andrewartha, H.G.; Birch, L.C. (1984) The Ecological Web. More on the Distribution and Abundance of Animals Chicago IL: U of Chicago Press

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Andrich, David (1988) Rasch Models for Measurement Newbury Park CA: Sage

Apple, Michael (1988) Teachers and Texts. A Political Economy of Class and Gender Relations in Education NY: Routledge

––– (1992) “Do the Standards Go Far Enough?” Journal for Research in Mathematics Education 23 (5): 412–431

––– (1993) Democratic Education in a Conservative Age NY: Routledge

Archer, Douglas; Hewson, Henny; Cumming, Alan (1993) The Curriculum Development Centre: an assessment Unpublished paper presented to the Annual Conference of the Australian and New Zealand History of Education Society, Melbourne Vic, November, 1993. Copy held by author.

Armstrong, Prince Winston (1972) The Ability of Fifth and Sixth Graders to Learn Selected Topics in Probability EdD Thesis: U of Okalahoma. DAI (1972) 33B: 810

Arnold, Anne; Truran John M. (1999) “Working With Students to Enhance a Statistics Course”. Pp. 113–119 in Fallows, Stephen; Ahmet, Kemel (eds) Inspiring Students—case studies in motivating the learner London: Kogan Page

Arnold, Matthew (1855) Stanzas from the Grande Chartreuse

Arthurs, A.M. (1965) Probability Theory London: Routledge & Kegan Paul

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Askew, Mike; Brown, Margaret; Rhodes, Valerie; Johnson, David; William, Dylan (1997) Effective Teachers of Numeracy. Final Report (Feb 1997). Report of a study carried out for the Teacher Training Agency 1995–96 by the School of Education, King’s College London. London: King’s College, London

Association des Professeurs de Mathématiques de l’Enseignement Publique (1967, 1968) Pour apprendre à conjecturer Npd [Read at U of Bielefeld]

––– (ndp, prob. 1976) Harsardons-nous Brochure de APMEP No 17.

Astill, Brian R. (1998) Influences on the Social Values of Students in Year 12: a South Australian study PhD Thesis: Flinders U of SA

Attainment Levels—Fact, Fear or Fantasy A document of uncertain provenance informally circulating in Australia in the early 1990s. Copy held by author.

Atweh, B.; Flavel, S. (eds) (1995) MERGA 18: Galtha Proceedings of the Eighteenth Annual Conference of the Mathematics Education Research Group of Australasia (MERGA). Darwin NT: MERGA

Bibliography

Atweh, Bill; Kanes, Clive; Carss, Marjorie; Booker, George (eds) (1993) Contexts in Mathematical Education Proceedings of the Sixteenth Annual Conference of the Mathematics Education Research Group of Australasia (MERGA) Brisbane, July 9–13 1993. Npp: MERGA

Aune, David E. (1987) “Oracles” Vol. 11, pp. 81–87 in Eliade The Encyclopedia of Religion

Australian Academy of Science (various dates) Mathematics at Work. Canberra ACT: AAS. Vide principal authors discussed in this thesis: Vaughton & Gaffney (1980); Treilibs & Gaffney (1980).

Australian-American Educational Foundation (1990) Directory of Fulbright Alumni 1950–1990 Canberra ACT: Australian–American Educational Foundation

AAMT/DEET Project in the Teaching and Learning of Chance and Data via Open Learning Npd. Copy held by author.

Australian Association of Mathematics Teachers (1981) Recommendations for Mathematics Teacher Education for Australian Schools [Thirteen page stapled duplicated A4 document. Copy held by author.]

Australian Broadcasting Commission (South Australian Branch) (1963) Educational Television. Infant, Primary and Secondary. 4 (1). Teachers’ Notes, Term 1, 1963

Australian Council for Educational Research (1964) Thirty-fourth Annual Report 1963–64 Hawthorn Vic: ACER

––– (1964a) Primary School Mathematics Report of a Conference of Curriculum Officers of State Education Departments, held in Melbourne 16th–20th March 1964 to Consider a Desirable Course of Study in Mathematics for Australian Primary Schools, The Manner of Intro-duction of Decimal Currency into the Course of Study, and Related Matters such as the Place and Value of Structural Aids. Hawthorn Vic: ACER

––– (1965) Thirty-fifth Annual Report 1964–65 Hawthorn Vic: ACER

––– (1966) Background in Mathematicsa guide-book to elementary mathematics for teachers in primary schools Melbourne Vic: Education Department of Victoria & ACER. [Another printing of this book, by the NSW Government Printer, may have different pagination.]

––– (1972) Background in Mathematicsa guide-book to elementary mathematics for teachers in primary schools Melbourne Vic: Education Department of Victoria & ACER. [This edition contains only minor revisions of the first edition and conversion to metric units.]

Australian Education Council (1989) The Hobart Declaration for Schooling Melbourne Vic: AEC

––– (1991) A National Statement on Mathematics for Australian Schools Carlton Vic: CC for the AEC

––– (1994a) Mathematics—a curriculum profile for Australian schools Carlton Vic: CC for the AEC

––– (1994b) Mathematics—work samples Carlton Vic: CC for the AEC

––– (1994c) A Statement on Studies of Society and Environment for Australian Schools Carlton Vic: CC

––– (1994d) Studies of Society and Environment—a curriculum profile for Australian schools Carlton Vic: CC

Australian Education Council Review Committee (1991) Young People’s Participation in Post-compulsory Education and Training Canberra ACT: AGPS [Finn Report (1991)]

Australian Encyclopaedia Fifth Edition (1988) Terrey Hills NSW: Australian Geographic for Australian Geographic Society

Australian Item Bank Program (1978) Mathematics Item Bank Book 2 Hawthorn Vic: ACER

Bibliography

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Campbell, Bruce; Lack, Elizabeth (eds) (1985) A Dictionary of Birds Calton UK: Poyser

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Carlson, Jerry S. (1969) “Children’s Probability Judgements as Related to Age, Intelligence, Socio-Economic Level, and Sex” Human Development 12: 192–203

Carlson, Jerry S. (1970) “The Development of Probabilistic Thinking in Children: A Comparison of Two Methods of Assessment” Journal of Genetic Psychology 116: 263–269

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Clapp. E.K.H.; Hamann, K.M.; Lang, I.P. (1966) Algebra 1 Adelaide, SA: Rigby

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Clarke, David (1985) “Teaching probability: what chance?” Pp. 286–291 in Sullivan, Peter (ed.) Mathematics—curriculum, teaching and learning Papers presented at the 22nd MAV Annual Conference

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Clarke, David; Hollingsworth, Hilary (1994) “Reconceptualising Teacher Change” Pp. 153–163 in Bell et al. Challenges in Mathematics Education

Clarke, Doug (1996) The Case of the Mystery Bone. A Unit of Work on Measurement for Grades 5 to 8 North Ryde NSW: The Mathematical Association of New South Wales Inc.

Clarkson, Philip C. (ed.) (1996) Technology in Mathematics Education Proceedings of the 19th Annual Conference of the Mathematics Education Research Group of Australasia (MERGA) June 30–July 3, 1996 at the University of Melbourne. Melbourne Vic: MERGA

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Clements, M. A. (Ken) (1978) “Forces Influencing Mathematics Curricula in Australian Secondary Schools—an historical case study”. In Papers Presented to the Second Conference of the M.E.R.G.A. Mathematical Education Research Group of Australia. Sydney NSW: Macquarie U

––– (1999) “Education Policy, Education Research, and the Development of Mathematics Teach-ers” Pp. 70–103 in Ellerton, Nerida F. (ed.) Mathematics Teacher Development. International Perspectives Perth WA: Meridian Press

Clements, M.A. (Ken); Ellerton, Nerida F. (1996) “Standardising the Mathematics Curriculum: some historical and comparative perspectives” Pp. 138–145 in Clarkson Technology in Mathematics Education

––– (1996apr) Mathematics Education Research: past, present and future Bangkok Thailand: UNESCO Principal Regional Office for Asia and the Pacific

Clements, M.A. (Ken); Grimison, Lindsay A.; Ellerton, Nerida F. (1989) “Colonialism and School Mathematics in Australia 1788–1988” Pp. 50–78 in Ellerton & Clements School Mathematics: the challenge to change

Clements, M.A. (Ken); Thomas Jan (1996) “Politics of Mathematics Education: Australian perspectives” Pp. 345–364 in Sullivan et al. Research in Mathematics Education in Australasia 1992–1995

Cleveland, Donald B.; Cleveland Ana D. (1990) Introduction to Indexing and Abstracting Eaglewood CO: Libraries Unlimited

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Cobb, Paul; Wood, Terry; Yackel, Erna; Nicholls, John; Wheatley, Grayson; Trigatti, Beatriz; Perlwitz, Marcela (1991) “Assessment of a Problem-centred Second-Grade Mathematics Project” Journal for Research in Mathematics Education 22 (1):3–29

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Cohen, John (1964) Behaviour in Uncertainty London: George Allen & Unwin

Cohen, John; Hansel, C.E.M. (1955) “The Idea of Independence” British Journal of Psychology 46: 178–190

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Cohen, Steve; Chechile, Richard A. (1997) “Probability Distributions, Assessment and Instructional Software: lessons learned from an evaluation of curricular software” Pp. 253–262 in Gal & Garfield The Assessment Challenge in Statistics Education

Cole, Percival R. (ed.) (1932) Primary School Curriculum in Australia Melbourne Vic: Melbourne UP

Coleridge, Samuel Taylor (1797–98) The Rime of the Ancient Mariner

Colgan, Len (1977) “Markov Chains—a non-static situation” Möbius 4 (2): 22–31. [I have a version of this article, headed Matriculation Mathematics 1. Option (Probability and Statistics) and without any author attribution distributed by J. Baxter as 12 duplicated stapled pages of notes to assist student teachers and perhaps others. Copy held by author.]

––– (1978) “Mathematics IS—some personal comments” Möbius 5 (1): 40–41

Collected (1976cd) “Curriculum Development—a strategy” Educational Studies in Mathematics 7 (3): 351–361

Collected (1976luck) “Look on Luck” Educational Studies in Mathematics 7 (3): 295–307

College Entrance Examination Board. Commission on Mathematics (1957) Introductory Probability and Statistical Inferencean experimental course NY: Commission on Mathematics, CEEB. [Short Reference: CEEB (1957)]

––– (1959a) Introductory Probability and Statistical Inferencean experimental course NY: Commission on Mathematics, CEEB

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Collins, Cherry (ed.) (1993) Competencies—the competencies debate in Australian education and training Deakin ACT: ACE

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Collis, Kevin F. (1974) “Cognitive Development and Mathematics Learning” Paper Presented to the Psychology of Mathematics Education Workshop. Centre for Science Education, Chelsea College, London, 28 June, 1974.

––– (1978) “Operational Thinking in Elementary Mathematics” Pp. 221–248 in Keats, J.A.; Collis, K.F.; Halford, G.S. (eds) Cognitive Development. Research Based on a Neo-Piagetian Approach. Chichester NY: John Wiley

––– (1988) “The ‘Add Up’ or ‘Take Away’ Syndrome”. Pp. 66–75 in Pegg, J. (ed.) Mathematical Interfaces Proceedings of the 12th Biennial Conference of the Australian Association of Mathematics Teachers

Collis, Kevin F.; Biggs, John B. (1991) “Developmental Determinants of Qualitative Aspects of School Learning”. Pp. 185–207 in Evans, G. (ed.) Learning and Teaching Cognitive Skills Melbourne Vic: ACER

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Collis, Kevin F.; Romberg, Thomas (1992) Collis-Romberg Mathematical Problem Solving Profiles Hawthorn Vic: ACER

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Izard, John F. (1977) Construction and Analysis of Classroom Tests Hawthorn Vic: ACER

––– (1992) “Patterns of Development with Probability Concepts: assessment for informative purposes” Pp. 355–367 in Stephens & Izard Reshaping Assessment Practices

––– (1993) “Challenges to the Improvement of Assessment Practice” Pp. 185–184 in Niss Investigat-ions into Assessment in Mathematics Education

Izard, John F.; Drummond, D.J.; Goodger, D.H.; Haig, B.D.; Smith, F.L. (1965, 1970) Individual Mathematics Programme Adelaide SA: Rigby

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Kapadia, Ramesh (1984) Children’s Intuitions and Conceptions of Probability Unpublished Paper delivered at the Fourth ICME, Adelaide SA. Copy held by author.

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––– (1992ar) Annual Report. Senior Secondary Assessment Board of SA for Year ending 31

––– (1992qm) Quantitative Methods. Stage 2 Detailed Syllabus Statement. Board-approved Draft Version November 1992 Adelaide SA: SSABSA


––– (ndp) [A public document from which I have made notes, but have mislaid the title and provenance]

––– (ndpa) Mathematics 1S. 4 Units. Curriculum Area—Mathematics. Year 12. Subject Guide

––– (ndp, ? 1986) Mathematics. Year 12 Detailed Syllabus Statements for Mathematics 1S, Mathematics 1, Mathematics 2 [31 printed loose-leaf pages photocopied from a document of unknown format]

––– (ndp, ? 1987) Year 12 Publicly Examined Mathematics 1 & 2. Report on the Teacher Survey [11 printed, stapled pages]

Shakespeare, William. Quotations come from Shakespeare Complete (1926) NY: World Syndicate Company

Sharma, Sashi Varta (1997) Statistical Ideas of High School Students: some findings from Fiji PhD Thesis: University of Waikato, NZ

Sharma, Sashi; Begg, Andy (1995) Statistics Education Bibliography (partially annotated) Version 20 June, 1995. Hamilton, New Zealand: Centre for Science, Mathematics and Technology Education Research, U of Waikato [Floppy disk available to interested workers. Copy held by author.]

Shaughnessy, J. Michael (1977) “Misconceptions of Probability: an experiment with a small-group, activity-based, model-building approach to introductory probability at the College level” Educational Studies in Mathematics 8: 295–316

––– (1992) “Research in Probability and Statistics: reflections and directions” Pp. 465–494 in Grouws Handbook of Research on Mathematics Teaching and Learning

––– (1993) “Probability and Statistics” Mathematics Teacher 86: (3): 243–248

––– (1997) “Missed Opportunities in Research on the Teaching and Learning of Data and Chance” Pp. 6–22 in Biddulph & Carr People in Mathematics Education

Shaughnessy, J. Michael; Garfield, Joan; Greer, Brian (1996) “Data Handling” Pp. 207–277 in Bishop et al. International Handbook of Mathematics Education

Shaughnessy, J. Michael; Bergman, B. (1993) “Thinking about uncertainty: probability and statistics” Pp. 177–197 in Wilson, P.S. (ed.) Research Ideas for the Classroom: high school mathematics NY: Macmillan

Shaw, George Bernard (1903) Man and Superman. Maxims for Revolutionists: Education Westminster UK: Archibald Constable

––– (1923/1953) Saint Joan Melbourne Vic: Penguin

Shepler, Jack L. (1969) A Study of Parts of the Development of a Unit in Probability and Statistics for the Elementary School Research and Development Center for Cognitive Learning, Technical Report No 105. Madison WI: U of Wisconsin

Bibliography

Sherlock, A.J. (1964) An Introduction to Probability and Statistics London: Edward Arnold [One of the St Dunstan’s College Booklets edited by Geoffrey Matthews and issued under the general heading of Contemporary School Mathematics]

Sherrington, Geoffrey; Petersen, R.C.; Brice Ian (1987) Learning to Lead. A History of Girls’ and Boys’ Corporate secondary Schools in Australia Sydney NSW: Allen & Unwin

Shulman, Lee S. (1987) “Knowledge and teaching: foundations of the new reform” Harvard Educational Review 57 (1): 1–26

Shulte, Albert P.; Smart, James R. (eds) (1981) Teaching Statistics and Probability 1981 Yearbook of the National Council of Teachers of Mathematics. Reston VA: NCTM

Siegel, Sidney (1956) Nonparametric Statistics for the Behavioral Sciences Tokyo, Japan: McGraw-Hill Kogakusha

Siegel, Sidney; Andrews, Julia McMichael (1962) “Magnitude of Reinforcement and Choice Behaviour in Children” Journal of Experimental Psychology 63 (4): 337–341

Siegler, Robert S. (1976) “Three Aspects of Cognitive Development” Cognitive Psychology 8: 481–520

Sierpinska, Anna; Kilpatrick, Jeremy (eds) (1998) Mathematics Education as Research Domain: a search for identity Dordrecht Netherlands: Kluwer

Sierpinska, Anna; Kilpatrick, Jeremy; Balacheff, Nicolas; Howson, A. Geoffrey; Sfard, Anna; Steinbring, Heinz (1993) “What is Research in Mathematics Education, and What are Its Results?” Journal for Research in Mathematics Education 24 (3): 274–278

Siet, Hans-Dieter (1993) “Zum Zufallsbegriff in der Stochastischen Allgemeinbildung” Zentralblatt für Didaktik der Mathematik 25 (2): 84–88

Simpson, J.A.; Weiner, E.S.C. (1989) Oxford English Dictionary 2nd Edition Oxford UK: OUP [OED (1989)]

Singer, J.; Resnick, L. (1992) Representations of Proportional Relationships: are children part-part or part-whole reasoners? Educational Studies in Mathematics 23 : 231–246

Skemp, Richard R. (1971/1986) The Psychology of Learning Mathematics London: Penguin

––– (1976) “Relational Understanding and Instrumental Meaning” Mathematics Teaching 77: 20–26

Smith, Alan G.R. (1972) Science and Society in the Sixteenth and Seventeenth Centuries London: Thames & Hudson

Smith, E.R. (1959) “Teaching Technique with a Mathematics Class” Education Gazette. South Australia 15 May 1959, pp. 184–186

Smith, David L.; Lovat, Terence J. (1991) Curriculum. Action on Reflection Wentworth Falls NSW: Social Science Press

Smith, Ron (1994) “Taking a Chance: songs as starting points” Pp. 305–310 in Beesey & Rasmussen Mathematics without Limits

Smith, Tracey (2000) “Bridging the Research-Practice Gap: developing a pedagogical framework that promotes mathematical thinking and understanding” Mathematics Teacher Education and Development 2: 4–16

Soliman, I.K. (1977) “Interactive Curriculum Development in Secondary School: a phenomenological perspective” Australian Journal of Education 21 (3) : 277–294

Soucek, Victor (1993) “Is there a Need to Redress the Balance Between Systems Goals and Life-World Oriented Goals in Public Education in Australia?’ Pp. 162–181 in Collins Competencies

Bibliography

South Australia. Department of Education, Training and Employment (2001) South Australian Curriculum, Standards and Accountability Framework Adelaide SA: Department of Education, Training and Employment [The SACSA Framework]. Two ring bound volumes—Part A contain the General Introduction, a statement on Accountability, and guidance for the Early Years and Primary Years Bands. Part B contains guidance for the Middle Years and Senior Years Bands and well as some Overviews.

South Australia. Department of Transport (1997) Road Traffic Code Npp: Government of SA

South Australia. Education Department Vide Education Department of South Australia

Southwell, Beth; Eyland, Roger; Cooper, Martin; Conroy, John; Collis, Kevin (eds) (1984) Pro-ceedings of the Eighth International Conference for the Psychology of Mathematics Education Sydney NSW: International Group for the Psychology of Mathematics Education

Southwell, Beth; Perry, Bob; Owens, Kay (eds) (1992) Space—the first and final frontier Proceedings of the Fifteenth Annual Conference of the Mathematics Education Research Group of Australasia (MERGA). Sydney NSW: MERGA

Sowey, Eric R. (1995) “Teaching Statistics: making it memorable” Journal of Statistics Education [Electronic] 3 (2) <http://www.stat.ncsu.edu/info/jse/homepage.html>

––– (1998) “Statistics Teaching and the Textbook—an uneasy alliance” Pp. 151–157 in Pereira-Mendoza et al. Statistical Education

Spiegel, M.R. (1961) Schaum’s Outline of Theory and Problems of Statistics NY: Schaum

Spinolla, Alina Galvão (1997) “Chance Estimates by Young Children: strategies used in an ordering chance task” Vol. 4, pp. 182–189 in Pehkonen Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education

Spode Group, [The] (1986) Enterprising Mathematics Oxford UK: OUP

Stacey, Kaye (1994) “The Curriculum and Standards Framework: new directions for mathematics curriculum” Pp. 113–119 in Beesey & Rasmussen Mathematics without Limits

Stacey, Kaye; Groves, Susie; Bourke, Sid; Doig, Brian (1993) Profiles of Problem Solving Hawthorn Vic: ACER

Standards Association of Australia (1993) Interim Australian Standard. General Conditions for Engagement of Consultants [AS 4122} Homebush, New South Wales: Standards Association of Australia

Starr, Karen (1987) Mathematics Curriculum Material Evaluation Npp: Education Department of South Australia. Directorate of Studies [There are conflicting dates on this document: I have chosen the later one.]

Steedman, Philip H. (1991) “There is No More Safety in Numbers: a new conception of mathemat-ics teaching” Pp. 1–11 in von Glaserfeld Radical Constructivism in Mathematics Education

Steen, Lynn Arthur (1999) Review of Sierpinska & Kilpatrick (1998) in Journal for Research in Mathematics Education 30 (2): 235–241

Steffe, Leslie P. (1991) Epistemological Foundations of Mathematical Experience NY: Springer

Steffe, Leslie P.; Wiegel, Heide G. (1992) “On Reforming Practice in Mathematics Education” Educational Studies in Mathematics 23: 445–465

Stehn, Jan (1997) “Renewing the Curriculum Cycle in South Australia” Ch. 8, pp. 166–194 in Lokan, Jan (ed.) Describing Learning. Implementation of Curriculum profiles in Australian Schools 1986–1996 Camberwell Vic: ACER

Stein, Joseph (1964) Fiddler on the Roof (arranged by Sheldon Harnick) NY: Pocket Books

Bibliography

Steinbring, Heinz (1989) “The Interaction between Teaching Practice and Theoretical Concept-ions” Pp. 202–214 in Morris Studies in Mathematics Education

––– (1991) “The Theoretical Nature of Probability in the Classroom” Pp. 135–167 in Kapadia & Borovcnik Chance Encounters

Steiner, George (1989) Real Presences: is there anything in what we say? London: Faber & Faber

Steiner, Hans-Georg (1987) “Philosophical and Epistemological Aspects of Mathematics and their Interaction with Theory and Practice in Mathematics Education” For the Learning of Mathematics 7 (1): 7–11

Stephens, Max; Izard, John (eds) (1992) Reshaping Assessment Practices: assessment in the mathematical sciences under challenge Proceedings from the First National Conference on Assessment in the Mathematical Sciences Geelong, Victoria, 20–24 November 1991. Hawthorn Vic: ACER

Stephens, Max; Money, Robert (1993) “New development in Senior Secondary Assessment in Australia” Pp. 155–171 in Niss Cases of Assessment in Mathematics Education

Sterling, Richard W.; Scott, William C. (1985) Vide Plato The Republic.

Stevens, J. B. (1979) A Statistical Summary of Education in South Australia Adelaide SA: South Australian Council for Educational Planning and Research

Stevenson, H.W.; Zigler, E.F. (1958) “Probability Learning in Children” Journal of Experimental Psychology 56: 185 –192

Stevenson, R.L. (1885) A Child’s Garden of Verses Npd

Stewart, Ian (1996) “It Could Be You But Here’s Why It Won’t Be Me” Mathematics in School 25 (1): 2–3

Stoppard, Tom (1967) Rosencrantz and Guildenstern are Dead London: Faber & Faber

––– (1993) Arcadia London: Faber & Faber

Stoyanov, Jordan (1986) “The Use of Counterexamples in Learning Probability and Statistics” Pp. 280–286 in Davidson & Swift Proceedings of the Second International Conference on Teaching Statistics

Strachey, Lytton (1923) “The Sad Story of Dr Colbatch” The Nation and the Atheneum XXXIV: 22 Dec 1923. Portraits in Miniature

Strauss, Anselm L.; Corbin, Juliet M. (1990) Basics of Qualitative Research Newbury Park CA: SAGE Publications

Style Manual for Authors, Editors and Printers (4th ed.) (1988) Canberra ACT: AGPS

Sullivan, Peter; Owens, Kay; Atweh, Bill (eds) (1996) Research in Mathematics Education in Australasia 1992–1995 Npp: MERGA

Sumner, Robert J. (1969) The Introduction of Modern Mathematics Courses into the First Four Years of South Australian High Schools Public Examinations Board Streams MEd Qualifying Paper: Flinders U of SA

Sumner, Robert J.; Lafleur, Clayton D. (1972) Bibliography of Educational Research and Innovation in South Australia No 1 September 1972. Npp: EDSA. Research and Planning Branch

Sweeney, Ross (1990) Review of Olssen (1987) in Software Focus 5 (4): no pagination

Swinson, Kevan (1977) Probability Concepts in Elementary School Children and the Development of a Curriculum Programme in Probability for Grades in Junior High School MEd Thesis: U of NSW

––– (1978) “Curriculum Development Concerning the Study of Probability in Australian Junior High Schoolsthe implications of recent research” Research in Mathematics Education in Australia 1978: 306–317

Bibliography

Swinson, Kevan (1993) “Investigating the Methods Used by Queensland Mathematics Teachers to Obtain Curriculum Information” Pp. 537–541 in Atweh et al. Contexts in Mathematics Educ-ation

Szendrei, J. (1990). “Some Aspects of Teaching Stochastics in Hungary” Vol. 2, pp. 262–283 in Wirszup, I.; Stocit, R. (eds) Developments in School Mathematics around the World Reston VA: NCTM

Tamlin, E.A. (1968) “Matriculation Mathematics, Paper I” South Australian Mathematics Teacher 2 (1): no pagination

Tanur, Judith; Mosteller, Frederick; Kruskal, William H.; Link, Richard F.; Pieters, Richard S.; Rising, Gerald, R; Lehmann, Erich L. (eds) (1978) Statistics: a guide to the unknown San Francisco CA: Holden-Day

Tarr, James E.; Jones, Graham A. (1997) “A Framework for Assessing Middle School Students’ Thinking in Conditional Probability and Independence” Mathematics Education Research Journal 9 (1): 39–59

Tasmania. Education Department. Curriculum Centre (1966) A Programme for Primary School Mathematics Hobart. Tas

Tate, Frank (1932) “Curriculum Making” Pp. 92–119 in Cole Primary School Curriculum in Australia

Taylor, Merilyn (1995) “Probability Education: can primary children cope?” Pp. 505–510 in Atweh & Flavel MERGA 18: Galtha

Taylor, Merilyn; Biddulph, Fred (1994) “‘Context’ in Probability Learning at the Primary School Level” In SAME Papers 1994 Hamilton NZ: U of Waikato, Centre for Science and Mathematics Education Research

Taylor, Peter C.S., Fraser, Barry J.; White, Loren R. (1993) “The Revised Constructivist Learning Environment Survey” Pp. 335–342 in Mousley & Rice Mathematics: of primary importance

Teigen, K.H. (1983) “Studies in Subjective Probability I: Prediction of Random Events Scandinavian Journal of Psychology 24: 13–25

Teilhard de Chardin, Pierre (1959/1969) L’avenir de l’homme Translation by Denny, Norman The Future of Man London: Fontana

Teloh, Henry (1986) Socratic Education in Plato’s Early Dialogues Notre Dame IN: U of Notre Dame Press

Temple, William (1930) The Distinctive Excellences of Greek and Latin London: John Murray

Tesch, Renata (1990) Qualitative Research: analysis types and software tools NY: Falmer

The Industry Education Forum (c. 1991) [A typescript of four A4 pages with this heading produced by the Industry Education Forum explaining its aims and listing its members. No contact address is provided. Copy held by author]

Thiele, Colin (1975) Grains of Mustard Seed Adelaide SA: EDSA

Thomas, Jack (ed.) (2001) Australian Prescription Products Guide Hawthorn Vic: Australian Pharmaceutical Publishing Company

Thompson, Michael David (1986) A Philosophical Study of the Value of Mathematical Knowledge and the Place of Mathematics on the Curriculum [sic] MEdSt Thesis: U of Tasmania

Thompson, William (1963) “Some of the Significant Developments in American Secondary Education Since 1956” Education Gazette. South Australia 17 Jun 1963, pp. 191–197

Thoreau, Henry (1850) Journal

Bibliography

Thwaites, Bryan (chairman) (1961) On Teaching Mathematics. A Report on some Present-Day Problems in the Teaching of Mathematics being the Outcome of Discussions and Lectures at the Southampton Mathematical Conference 1961 under the Chairmanship of Bryan Thwaites Oxford UK: Pergamon

––– (1972) The School Mathematics Project. The First Ten Years. being Primarily the Collection of Director’s Reports for the Years 1961–1971 Cambridge UK: CUP

Tims, Joanne E. (1994) “The Development of a Typology for Describing Mathematics Assessment Items” Pp. 615–622 in Bell et al. Challenges in Mathematics Education

Tinbergen, Niko (1953) The Herring Gull’s World: a study of the social behaviour of birds London: Collins

Tirosh, Dina; Dreyfus, Tommy (1998) “Efraim Fischbein, 1920–1998” International Commission on Mathematical Instruction. Bulletin No. 45 December 1998

Tobin, Kenneth G. (1982) Patterns of Reasoning: Probability Paper Presented at the Annual Meeting of the Australian Science Research Association, Macquarie U, Sydney NSW [My copy is in MS form. The Australian Education Index lists an alternative source : Pp. 42–49 in Rattray-Wood, L.; Ferguson, P. (eds) Research in Science Education Volume 12 Papers from 12th Annual Conference Macquarie University May 1982. Melbourne Vic: Australian Science Education Research Association]

Tobin, Kenneth G.; Capie, William (1981) “The Development and Validation of a Test of Logical Thinking Educational and Psychological Measurement 41 (2): 413–423

Tobin, Kenneth; Fraser, Barry J. (1988) “Investigations of Exemplary Teaching in Australian Mathematics Classes” Australian Mathematics Teacher 44 (1): 5–8

Todhunter, I. (1865) A History of the Mathematical Theory of Probability from the Time of Pascal to That of Laplace Cambridge UK: Macmillan

––– (1875) Algebra for the Use of Colleges and Schools London: Macmillan

Tolkein, J.R.R. (1954/1978) The Two Towers [Pagination from 1978 Unwin Paperbacks edition of the trilogy The Lord of the Rings]

Toohey, Philip G. (1995) Adolescent Perceptions of the Concept of Randomness MEd Thesis: U of Melbourne

Toon, Ernest R.; Ellis, George L. (1973) Foundations of Chemistry NY: Holt, Rinehart & Winston

Torok, Rob; Watson, Jane (2000) “Development of the Concept of Statistical Variation: a pilot study” Mathematics Education Research Journal 12 (2): 147–169

Tosh, John (1991) The Pursuit of History Harlow UK: Longman

Treffers, Adrian (1987) Three Dimensions: a model of goal and theory description in mathematics instruction—the Wiskobas Project Dordrecht Netherlands: Kluwer

Treilibs, Vern (1979) Formulation Processes in Mathematical Modelling MPhil Thesis: U of Nottingham

Treilibs, Vern; Gaffney, John (1980) Making the Best of Things Canberra ACT: AAS

Trésor de la langue française. Dictionnaire de la langue du XIXe et du XXe siècles (1789–1960) (1992) Nancy France: Centre National de la Recherche Scientifique, Institut National de la Langue Française, en collaboration avec Gallimard

Truran, John M. (1964) To What Extent Should Ideas from Modern Mathematics be Incorporated in South Australian School Mathematics? [Unpublished essay submitted in partial fulfilment of the requirements of Principles of Secondary Education III, a subject in the Diploma of Education awarded by the University of Adelaide. The essay was submitted to Mr R.W. Close and is not marked. The Bibliography gives some idea of the material which was available in the libraries of the Adelaide Teachers’ College and the University of Adelaide to a practising teacher at this date. Copy held by author.]

Bibliography

Truran, John M. (1972) “The Place of Mathematics in the General School Curriculum” P. 9 in Mathematical Association of Victoria Ninth In-Service Conference for Teachers of Secondary School Mathematics

––– (1973a) Probability Melbourne Vic: Melbourne Church of England Grammar School Copy held by author.

––– (1973b) Probability—Teacher’s Notes Melbourne Vic: Melbourne Church of England Grammar School Copy held by author.

––– (1973fsg) “The Field Studies Group at Melbourne Grammar School” Australian Science Teach-ers' Journal 19 (1): 57–62

––– (1979) The Teaching of Probability and Statistics in Schools Unpublished essay submitted in partial fulfilment of the requirements of the unit “Advanced Curriculum Studies in Mathematics” as part of Bachelor of Education Studies at the University of Adelaide. Copy held by author.

––– (ndp, c. 1980) Mathematics I Melbourne Vic: Melbourne Church of England Grammar School [This includes an anonymous revision of J. Truran (1973a). Copy held by author.]

––– (1983) “One-one Teaching” Unicorn 9 (4): 323–327

––– (1985) “Children’s Understanding of Symmetry” Teaching Statistics 7 (3): 69–74 [Republished as pp. 49–51 in Green (1994)]

––– (1986) "Das Verständnis von Symmetrie bei Kindern" Stochastik in der Schule 6 (2): 31–38

––– (1989) Probability Adelaide SA: Adelaide College of TAFE

––– (1990) “Development of Probabilistic Understanding in Children—results from clinical interviews” [Unpublished paper presented to the 13th Annual Conference of the Mathematics Education Research Group of Australasia, Hobart Tas, July 1990. [Copy held by author.]

––– (1991) Some Aspects of Secondary School Mathematics in South Australia 1870 to 1913. Paper presented to the 14th Annual Conference of the Mathematics Education Research Group of Australasia, St Thomas More College, Perth WA, 30 June–3 July 1991 [Copy held by author.]

––– (1992) The Development of Children’s Understanding of Probability and the Application of Research to Classroom Practice MEd Thesis: U of Adelaide

––– (1992a) “Children’s Understanding of the Independence of Random Generators” Pp. 551–555 in Southwell et al. Space—the first and final frontier

––– (1993anzhes) Forces Influencing the Introduction of Probability into South Australian Schools Unpublished paper presented to the Annual Conference of the Australian and New Zealand History of Education Society, Melbourne, November, 1993. Copy held by author.

––– (1993mav) “Testing Children’s Understanding of Probability” Pp. 441–446 in Mousley & Rice Mathematics: of primary importance

––– (1994amtprob) “What is the Probability of … ?” Australian Mathematics Teacher 50 (3): 28–29

––– (1994icohis) “The Introduction of Probability into South Australian Schools” P. 422 in Proceedings of the Fourth International Conference on Teaching Statistics [Full paper in possession of author]

––– (1994icovar) “Children’s Intuitive Understanding of Variance” P. 85 in Proceedings of the Fourth International Conference on Teaching Statistics. [Full paper in Garfield Research Papers from the Fourth International Conference on Teaching Statistics]

––– (1994mavinf) “Inference—the link between chance and data” Pp. 311–314 in Beesey & Rasmussen Mathematics without Limits

Bibliography

Truran, John M. (1994merga) “Diagnosing Children’s Probabilistic Understanding” Pp. 623–630 in Bell et al. Challenges in Mathematics Education

––– (1994merhis) “Curriculum Innovation and the Teaching of Probability in South Australia—colonial echo, mature development or muddling through?” Pp. 631–640 in Bell et al. Challenges in Mathematics Education

––– (1994mob2) “Chance & Data or Probability & Statistics—are we oversimplifying?” Möbius 21 (1, 2): 46–48

––– (1994pme) “Examination of a Relationship between Children’s Estimation of Probabilities and Their Understanding of Proportion” Vol. IV, pp. 337–344 in da Ponte & Matos Proceedings of the Eighteenth PME Conference

––– (1994solo) Book Review of Collis & Romberg (1992), in Australian Journal of Remedial Education 26 (3): 32

––– (1994voi) “Maths-Teacher Bashing Denies the Need for Vision” Voice 2 (1): 3–4, 22

––– (1995aamtinf) “Statistical Inference—mathematics or emotional feelings” Pp. 377–382 in Richards, Ann (ed.) (1995) FLAIR: Forging Links and Integrating Resources Proceedings of the 15th Biennial Conference of the Australian Association of Mathematics Teachers held at Darwin, Australia, July 1995

––– (1995aare) “Probability and Statistics in Australian Secondary School Curricula Since the 1960s—a tale of uncertainty”. Paper presented to the Annual Conference of the AARE, Hobart November 1995 AARE Conference Papers and Abstracts 1995. Electronically published, ISSN 1324-9339, deposited in Australian National Library, Canberra. Web address <http://www.swin.edu.au/aare/aare95/conf95/trurj95.331>

––– (1995mef) “Mathematics in Environmental Fieldwork” Pp. 735–744 in Hunting et al. Regional Collaboration in Mathematics Education 1995

––– (1996) Links between Mathematics and Science with Some Examples from Fieldwork Done by Secondary Students Unpublished paper presented to Working Group 14 at the Eighth International Congress on Mathematical Education, Sevilla, Spain, July 1996

––– (1996pme) “Children’s Misconceptions about the Independence of Random Generators” Vol. 4, pp. 331–338 in Puig & Gutiérrez Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education

––– (1997anzhes) “Re-interpreting Australian Mathematics Curriculum Development Using a Broad-Spectrum Ecological Model”. Vol. 1, pp. 241– 262 in Old Boundaries and New Frontiers in Histories of Education Proceedings of the Australian and New Zealand History of Education Society Conference, University of Newcastle Australia, 7–10 December 1997

––– (1997merhis) “The Introduction of Probability into Australian Schools Interpreted within a Broad-Spectrum Ecological Framework” Pp. 522–529 in Biddulph & Carr People in Mathe-matics Education

––– (1998iconh) “The Development of the Idea of the Null Hypothesis in Research and Teaching” Pp. 1067–1073 in Pereira-Mendoza et al. Statistical Education

––– (1998pmehab) “Using Research into Children’s Understanding of the Symmetry of Dice in Order to Develop a Model of How they Perceive the Concept of a Random Generator” Vol. 4, pp. 121–128 in Olivier & Newstead Proceedings of the 22nd Conference of PME

––– (1999ausico) The Place of Educational Theory in Evaluating and Improving Statistics Teaching Unpublished paper presented at “AusIcots2” Conference, Swinburne University of Technology, Melbourne Vic, 10 Dec 1999

–––(2000pmehab) “Children’s Learning of Independence: can research help?” Vol. 4, pp. 209–216 in Nakahara & Koyama Proceedings of the 24th Conference for the Psychology of Mathematics Education

Bibliography

Truran, John M. (2000saoa) “The Foundation Period: 1899–1913” Pp. 18–56 in Collier, Roger; Hatch, John; Matheson, Bill; Russell, Tony (eds) Birds, Birders & Birdwatching. 1899–1999. Celebrating One Hundred Years of the South Australian Ornithological Association Adelaide SA: SA Ornithological Association

––– (2001aamtjou) “What is the Value of Professional Journals for Shaping Teacher Devel-opment?” Pp. 255–262 in Mathematics: Shaping Australia. Proceedings of the Eighteenth Biennial Conference of The Australian Association of Mathematics Teachers Inc. 15–19 January 2001. Australian National University Canberra, ACT. Adelaide, South Australia: The Australian Association of Mathematics Teachers Inc. [CD-ROM ISBN 1 875900 47 0]

––– (2001phd) The Teaching and Learning of Probability, with Special Reference to South Australian Schools from 1959–1994 Unpublished MS in possession of author submitted for the award of PhD to the U of Adelaide

––– (2001pmefra) A Framework for Assessing Questions Investigating the Understanding of Probabilistic Concepts Accepted for presentation at the 25th Conference of the International Group for the Psychology of Mathematics Education, Utrecht, Netherlands, July 2001. Publication details not yet available.

––– (in press) “Making Probability Accessible to the Classroom Teacher” In Proceedings of the Mathematics, Science and Environment Education Symposium Deakin U Vic, 5–6 Dec 94 [I was assured in July 1998 that this document was still “in press”!!]

Truran, John M.; Arnold, Anne (2000) “Teaching Consulting: learning to listen and learning to answer”. Unpublished paper presented to AusIcots3, Swinburne University of Technology, December, 2000. Copy held by author.

Truran, John M.; Truran, Kathleen M. (1995) “Linking Researchers, Curricula and Teachers in Australasia—an exploratory case study based on the teaching and learning of stochastics” Pp. 530–536 in Atweh & Flavel MERGA 18: Galtha

––– (1996) “Research into the Learning and Teaching of Stochastics” Pp. 345–364 in Sullivan et al. Research in Mathematics Education in Australasia 1992–1995

––– (1997ind) “Statistical Independence—one concept or two?: implications for research and for classroom practice” Pp. 87–100 in Phillips, Brian (ed.) Papers on Statistical Education Presented at ICME-8, Seville, Spain, July 14-21, 1996 Melbourne Vic: Swinburne U of Technology

––– (1998) “Using Clinical Interviews in Qualitative Research” Pp. 61–83 in Malone, John A.; Atweh, Bill; Northfield, Jeffrey R. (eds) Research and Supervision in Mathematics and Science Education Mahwah NJ: Lawrence Erlbaum

––– (1999pmehab) “Using a Handbook Model to Interpret Findings about Children’s Comparison of Random Generators” Vol. 4, pp. 281–288 in Zaslavsky Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education

––– (eds) (1999mer) Making the Difference Proceedings of the Twenty-second Annual Conference of the Mathematics Education Research Group of Australasia Incorporated, held at Adelaide, South Australia, 4–7 July, 1999. Sydney NSW: MERGA

––– (2000merfai) “Is the MERGA Conference Refereeing Process Fair?” Vol. 2, pp. 596–602 in Bana, Jack; Chapman, Anne (eds) Mathematics Education beyond 2000 Proceedings of the Twenty-third Annual Conference of the Mathematics Education Research Group of Australasia Incorporated, held at Fremantle, Western Australia, 5–9 July, 2000. Sydney NSW: MERGA

Truran, Kathleen M. (1992) “Perceptions of Chance Events among R–7 Children” Pp. 541–550 in Southwell et al. Space—the first and final frontier

––– (1992pma) “Chance & Data—some thoughts & strategies for primary schools” Pp. 1–3 in Primary Mathematics Notes from the Primary Mathematics Association. Discussion Paper No. 16

Bibliography

Truran, Kathleen M. (1993) Report of a P.E.L. Investigation on the Impact of the National Curriculum of England and Wales January–April 1993 Adelaide SA: U of SA, School of Education, Salisbury Campus

––– (1994) “Children’s Understanding of Random Generators” In Garfield Research Papers from the Fourth International Conference on Teaching Statistics

––– (1995) “Animism: a view of probability behaviour” Pp. 537–542 in Atweh & Flavel MERGA 18: Galtha

––– (1997mer) “Beliefs about Teaching Stochastics Held by Primary Pre-service Teaching Students” Pp. 538–545 in Biddulph & Carr People in Mathematics Education

––– (1998) “Is it Luck, is it Random, or Does the Dice [sic] Know?” Pp. 757–763 in Pereira-Mendoza et al. Statistical Education

––– (in press) “Children’s Perceptions of Their Control over the Behaviour of Random Generators” In Proceedings of the Mathematics, Science and Environment Education Symposium Deakin U Vic, 5–6 Dec 94 [I was assured in July 1998 that this document was still “in press”!!]

––– (in preparation) Young Children’s Understanding of Random Generators MEd Thesis being prepared for submission to the U of Adelaide

Truran, Kathleen M.; Ritson, Rene (1997) “Perceptions of Unfamiliar Random Generators—links between research and teaching” Vol. 4, pp. 238–245 in Pehkonen Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education

Truran, Kathleen M.; Truran, John M. (1994mavpri) “Chance & Data and the Profiles in Primary Schools” Pp. 126–131 in Beesey & Rasmussen Mathematics without Limits

Tukey, John W. (1977) Exploratory Data Analysis Reading MA: Addison-Wesley

Turner, Ian; Factor, June; Lowenstein, Wendy (1969/1978) Cinderella Dressed in Yella Richmond Vic: Heinemann Educational Australia

Turner, Irené F. (1979) “Event Probabilities and Information as Determinants of Children’s Sequential Behaviour Irish Journal of Psychology iv (2): 95–100

Tversky, A.; Kahneman, D. (1974) “Judgement under Uncertainty: heuristics and biases” Science 185: 1124–1131. [Page references are given to the reprint of this article found in Kahneman, Slovic & Tversky (1982).]

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CITATION INDEX

Wherefore seeing we also are compassed about with so great a cloud of witnesses.1

Only direct citations are listed here. So to find all references to an author’s ideas, it is necessary to refer to his or her name in the General Index as well.

“A ‘New’ Syllabus” (1965) 272 AAMT/DEET Project 451 Ableman (1989) 205 Abraham (1975) 297, 299 Abrahamson (1967) 307 Acredolo et al. (1989) 162, 435, 535,

557 Adelaide Teachers’ College Handbook

308 Adler, I. (1973) 326 Adler, J. (1998) 20, 129 Advertiser (1996) 81 Against all Odds, see Moore &

McCabe (1989tv) Agenda for Action, An, see National

Council of Teachers of Mathematics (1980)

Agnoli & Krantz (1989) 721 Ahlgren & Garfield (1991) 98, 712,

764 Ahlgren, see also Garfield Akhmanova (1987) 20 Alarcon (1982) 156, 633, 665 Ali (1975) 107 Allee et al. (1949) 189, 202 Allendoerfer (1965) 103, 221, 222, 224 Almeida & Ernest (1996) 36 American Mathematical Monthly

(1962) 247 American Psychological Association.

Publication Manual 27, 28

1 Hebrews 12: 1 (King James Version)

Amir & Williams (1994) 86, 571 Amir et al. (1999) 535, 643, 662 Anderson & Pegg (1988) 711 Anderson et al. (1985) 711 Andrew (1993) 405 Andrewartha & Birch (1984) 191-193 Andrews (1998) 105, 383 Andrich (1988) 474 Annual Reports of Western Teachers’

College 308, 309 Apple

(1988) 41, 203 (1992) 45, 685 (1993) 278, 281

Archer et al. (1993) 353 Armstrong (1972) 716 Arnold & Truran (1999) 750 Arnold, Matthew (1885) 785 Arnold, Michael, pers. comm. 735 Arthurs (1965) 334 Askerøi & Høie (1996) 693 Askew et al. (1997) 667, 670, 776, 777 Association des Professeurs de Math-

ématiques de l’Enseignement Publique (various dates) 325

Astill (1998) 4 Attainment Levels—Fact, Fear or

Fantasy 411 Aune (1987) 85 Australian Association of

Mathematics Teachers (1981) 365

Index

Australian Broadcasting Commission

(1963) 357 Education Program Notes (1978) 357 (1981) 357 Australian Council for Educational

Research (1964) 252 (1964a) 211, 231, 242, 243, 253, 254,

255, 295 (1965) 254 (1966) 251, 255, 294, 312 (1972) 255, 350, 363 Archives Radford 357 212, 244, 251 vol. 224 251, 252, 253, 254, 255 vol. 321 330, 331 Australian Education Council (1989) 418 (1991) 23, 44, 419-421, 432, 433, 458,

461, 488 (1994a) 23, 116, 164, 419, 433, 458, 462,

812 Number 443 Outcome 1.23 423, 436 Outcome 3.23 437 Outcome 4.23 437 Outcome 5.23 437 Outcome 6.23 439 Working Mathematically 438, 443 (1994b) 419, 433, 440, 441, 559 Chance and Data 1 424, 434, 884 Chance and Data 8 437, 885 Chance and Data 13 444, 886-887 Chance and Data 17 440, 888-889 Chance and Data 20 443, 890-891 Number 444 Working Mathematically 438 (1994c) 445 (1994d) 444, 445, 446, 894-897 Australian Education Council

Review Committee (1991) 354, 414

Australian Encyclopaedia (1988) 296 Australian Item Bank Project (1978)

483

Australian Mathematics Education Project, see Curricul-um Development Centre (ndp, ?1982)

Australian Mathematics Teacher 36, 128 (1962) 247, 248 (1983) 339

Australian Way 341 Australian-American Educational

Foundation (1990) 234, 238 Ayres & Way

(1998ico) 150 (1998mer) 150

Azcárate Goded (1996) 451, 699

Background in Mathematics 255-256

Backhouse (1967) 334 Backhouse et al. (1992) 57 Baker (1938) 193 Balacheff

(1997) 724 pers. comm. 63

Ball, D. (1993) 51 Bar-Hillel & Falk (1982) 157 Barcan

(1980) 314, 821 (1996) 340, 349, 350, 379

Barnard (1927) xx Barnes & Horne (1996) 200 Barnes, E. (1967) 307 Barnes, M.

(1994) 719 (1998) 719

Barter (1961) 234 (1967) 314

Bartlett, J. (1855/1980) 119, 696 Bartlett, L. (1993) 353, 382, 417 Barton (1983) 339, 358 Batanero

Fischbein bibliography 154 public comments 176 see also Godino, Cañizares

Index

Batanero et al. (1994) 164 (1996) 662 (1997) 470 (1998) 163

Baxter, B. (1977) 367 Baxter, J.

(1972) 8, 233, 234, 240, 248, 264, 268, 273, 274, 275, 288, 296, 320, 327, 409, 476

Bea & Scholz (1994) 166 Beare (1989) 791 Beaton et al. (1996) 477, 614, 619 Bechervaise (1992) 60 Becker, C. (ndp, ?1994) 739 Becker, J. (1977) 347 Beeby (1966) 114 Beerbohm (1911) 119 Begle (1979) 222, 696, 821 Bell et al.

(1983) 343, 660 (1985) 348

Bell, A. (1976) 474 (1993) 50, 690 (1993b) 704

Bell, E. & R. (1985) 750 Bell, J. (1987) 10 Benn & Burton (1996) 37, 44 Bentz & Borovcnik (1985) 542, 543,

545, 571 Bentz (1982) 19 Berndt

(1960) 239 pers. comm. 239, 240

Bernet & Jaquet (1998) 680 Bertie, e-mail comment 709 Bessant (1989) 381 Best (1945) 208 Betjeman/Guest (1978) 800 Bibby (1986) 219 Bible

Genesis 38, 127, 497 Psalms xxvi Proverbs 85 Ecclesiastes 818 Isaiah 208 Ecclesiasticus 1001 →→→→

Bible →→→→ Matthew 485, 1007 Luke xxvii, 247, 450, 739 John 770, 1023 Acts 56 Corinthians I 738 Hebrews 977

Biehler et al. (1994) 681 Biggs & Collis (1982) 140 Biggs, see also Collis Bishop & Nickson (1983) 343 Bishop et al. (1996) 129 Blackmore (1999) 203 Blainey (1966) 182 Blakers

(1970) 231, 261, 326 (1975) 331 (1976) 223, 235, 254, 258, 270, 295, 368 (1978) 320, 336

Blane (1992) 665, 666 Bloom et al. (1956) 116, 752 Bobis et al. (1999) 668, 669 Boden (1979) 138 Boero et al. (1996) 700, 765 Bognár & Nemetz (1977) 709, 719 Bohm (1957) 76, 78 Boileau-Despreaux (1674) 17 Bolle (1987) 84 Bolon (1994) 122 Boomer (1986) 383 Booth (1984) 62 Borasi & Rose (1989) 750 Borg (1998) 720 Borovcnik

(1993) 760 pers. comm. 18, 19 see also Kapadia, Bentz

Borovcnik & Bentz (1991) 473, 533, 542, 543, 628

Borovcnik & Peard (1996) 129-130, 454, 740

Bostock & Riley (1855) 513 Boswell/Cotterill (1775/1902) 73 Bourke & Lewis (1976) 330, 482 Bourke et al. (1981) 482, 483 Bowen (1973) 791 Brady (1983) 110, 111, 771

Index

Brazil (1925) 687 Brecht (1956) 22 Brereton (1977) 707, 712, 722 Bright & Harvey (1986) 709 Bright & Hoeffner (1993) 709 Bright (1985) 713 Bright et al. (1981) 713 Brinkworth (1970) 8, 211, 241, 242,

243, 244, 245, 252, 256, 292, 293, 311, 320

Bronfenbrenner (1979) 765 (1993) 92, 190

Brousseau (1970–1990/1997) 325, 680, 682

Brousseau et al. (?1972) 325 Brown et al. (1988) 479, 600, 601 Brown, G. (1996) 177 Brown, T. (1996) 60 Browne (1932) 206 Bruce et al. (1992) 453 Bruner

(1963) 44, 220 (1966) 691

Buck (1976) 11, 15, 56 Bullen (1960) 220 Bullock et al. (1990) 396, 409 Bungartz (1989) 709 Bunge et al. (1971) 138, 657 Burns (1990) 10 Burton (1986) 32 Bush, G., comment 634 Buttrose (ndp., ?1973) 209 Butts (1957) 205, 206, 210, 214, 215 Buxton

(1969) 96 (1970) 96

Byrt (1973) 300

C&EN 36 Callingham et al. (1995) 699, 768 Cambridge Conference on School

Mathematics (1963) 249, 250, 255, 344

Cameron (1932) 41 Campbell & Lack (1985) 189, 190,

193, 196 Campbell & Stanley (1963) 720 Campbell (1985) 205

Cañizares & Batanero (1998) 161

Cañizares et al. (1997) 161 Carlson

(1969) 139 (1970) 139

Carmina Burana 78 Carpenter et al.

(1978) 480, 594, 598-599 (1981a) 479, 480, 602-603 (1981b) 479, 509, 602

Carroll, L., see Carroll/Gardner (1960)

Carroll/Gardner (1960) 57-59, 73, 107, 125, 128, 154, 284, 495

Carss (1979) 354 (1982) 354 (1986) 347, 348

Casse (1977) 366 Caucasian Chalk Circle, see Brecht Chalmers (1976) 465, 803 Chapman, R. (1975) 161 Chapman, R.W. (1953) 179 Chaucer, Canterbury Tales 30, 822 Cherry (1962) 247 Chi et al. (1981) 500 Chick (1998) 724 Chinnappan & Lawson (1994) 63 Chong (1962) 246, 247, 322 Cizek, attributed comment 762 Clapp (1967) 277 Clapp et al.

(1966) 276, 310 (1967) 276, 310

Clarke & Hollingsworth (1994) 689 Clarke, David

(1985) 711, 712 (1988a) 360 (1988b) 360 (1988c) 360

Clarke, Doug (1996) 359 Clarke, S. (1997) 777 Clay, C. 107 Clements

(1978) 181 (1999) 665 correspondence 185, 237 →→→→

Index

Clements →→→→ generic term 181 pers. comm. 301 see also Ellerton

Clements & Ellerton (1994) 661 (1996) 185 (1996apr) 183, 661

Clements & Thomas (1996) 185 Clements et al. (1989) 181-182, 269,

341, 348, 378, 409 Cleveland, D. & A. (1990) 29, 30 Close (1962) 246 Cobb (1989) 46 Cobb et al. (1991) 665 Cockburn (1991) 209 Cockcroft (1982) 44, 342, 343, 350 Cohen & Chechile (1997) 470 Cohen & Hansel (1955) 503 Cohen, D. (1985) 120 Cohen, J. (1964) 86, 174 Cohen, L.J. (1979) 149 Cohen, M. (1995) 59 Cole (1932) 206 Coleridge (1797–1798) 820 Colgan

(1977) 367 (1978) 374

Collected (1976cd) 44 (1976luck) 718

College Entrance Examination Board (1957) 223, 298 (1959a) 14, 223, 224, 303 (1959b) 223, 261, 312, 831-832

Collins (1993) 417 (1994) 417

Collis (1974) 642 (1978) 642 (1988) 141, 143 public comments 144 see also Biggs, Callingham, Watson, J.

Collis & Biggs (1991) 140

Collis & Romberg (1992) 488, 608-609, 635, 660

Colmez (1979) 337 Commission Française pour l’En-

seignement des Mathématiques (1996) 230

Commonwealth Department of Education (1985) 318

Condon (ndp, c. 1991) 378, 379 Confrey (1991) 47 Connell

(1957) 789 (1980) 210, 232 (1993) 114, 261, 263, 277, 294, 299, 319,

320, 321, 336, 340, 365, 789 Contemporary School Mathematics 265 Conzelmann (1987) 85 Cooney (1994) 698, 700 Cooney et al. (1993) 667 Cooper

(1985) 8, 226, 227, 260, 275 (1985rd) 272, 275 (1993) 323

Core Curriculum for Australian Schools, see Curriculum Development Centre (1980)

Costello (2000) 665 Costello et al. (1985) 358 Courant & Robbins (1941) 60 Cowban (1964) 257, 259, 270, 272 Copyright Amendment Act 17 Craig & Myers (1963) 139, 552 Craig (1994) 687 Crawford (1997) 711 Cribb

(1984) 359 (1986) 300, 302

Cribb et al. (1988) 384 Crittenden (1986) 42, 317 Crocker (1983) 209 Crombie (1994) 183, 187-188, 790 Croucher (1981) 347 Cullotta (1957) 676 Cunningham & Radford (1938) 208 Current Affairs Bulletin (1961) 245

Index

Curriculum Development Centre

(1980) 353, 354 (1988) 427 (ndp, ?1982) 354, 362, 384

Curriculum Development Centre & Australian Association of Math-ematics Teachers (ndp, c. 1988) 340

Curriculum Development Corporation

(1988) 358 curriculum@work (2001) 359

da Ponte, J.P., see also Ponte Dale (1977) 691, 728 Darroch & Pedler (1971) 333 David (1962) 77, 91 Davidson & Swift (1986) 370, 371 Davidson (1972) 327 Dawe (1995) 65 Dawkins (1976) 202 Dawson, C.J.

(1992) 86 pers. comm. 505, 661, 817

Dawson, Carolyn (1972) 311 De Corte & Verschaffel (1991) 70 de Lange

(1992) 665, 666 (1994) 116, 718 (1995) 718

de Moivre (1718/1738) 74 de Selincourt/Moorman (1968) 805 Declaration of Goals for Australia’s

Schools 413 Dekkers et al. (1986) 365 delMas et al. (1998) 492 Delpit (1988) 45 Dennett (1995) 201, 202 Department of Employment,

Education and Training (1991) 318

Desforges & Cockburn (1987) 13, 687, 766, 769, 776

Dewey (1916) 43 (1929) 92, 204, 408, 678

Dickens (1837) 670 (1854/1954) 40, 706, 763

Dickson et al. (1984) 57 Dienes (1964) 230, 292 Disraeli 7 Dodgson, C.L., see Carroll, L. Dodson (1962) 251 Dolly 81 Dossey & Swafford (1993) 493 Dossey (1992) 91 Douglas (1970) 267, 297, 312, 346 Downs, correspondence 254 Doyle (1977) 685, 686 Drake (1993) 709 Dubinsky, e-mail comment 53 Dudley & Vidovich (1995) 382 Duncan

(1967) 307 (1967lj) 301 (1968) 290

Dunn, correspondence 252, 253 Dupuis et al. (1992) 436 Dupuis, pers. comm. 156 Durkin & Shire

(1991a) 64 (1991b) 65

Durran (1970) 332 Education Department of South

Australia (1944) 211 (1947) 211 (1952) 211 (1953) 211 (1956) 211 (1958) 211 (1973c) 327, 328 (1974a) 306, 320, 324, 328, 350 (1974b) 324 (1974cm) 327, 328, 329 (1974d) 309, 317, 322, 323, 324, 350 (1974jsms) 335 (1975) 330 (1977r) 350, 351 (1980mcg) 351, 362, 416 (1981ostp) 349, 351, 352 (1983ln) 352 (1984mcg) 351→→→→

Index

Education Department of South Australia

→→→→ (1985) 364, 365, 456 (1992) 425 (ndp, c. 1978) 369 (ndp, c. 1984) 365 (various dates, c.1980) 371, 372 Archives

GRG 18/142 241, 293 GRG 18/160 294 GRG 18/98 248, 265, 266, 267, 275 GRS 1049/1 215 GRS 1049/2 244, 253, 292, 293 GRS 1049/3 121, 329

High Schools Advisory Curriculum Board, citation 268

Mathematics Curriculum Committee (ndp, c. 1987) 392, 393, 395

Mathematics Syllabus Committee, citation 264

Research and Planning Division (1975) 320 (?1971) 324

Education Department of Western Australia (1979) 329

Education Gazette. New South Wales (1956) 297

Education Gazette. South Australia (1959) 215, 233, 234, 236 (1960) 237, 238 (1962) 212 (1963) 310, 311 (1964) 210, 234, 253, 254, 273, 311 (1965) 245, 264, 292 (1966) 243 (1967) 212, 264, 265 (1979) 366

Edwards (ndp) 768 Efron (1978) 92 Eisner (1985) 11, 109, 111, 123, 310,

685, 765

Ellerton & Clements (1991) 57, 61, 64, 65, 70, 71, 77, 661 (1992) 49, 51 (1994) 417, 419, 465 (1994mav) 417 (1997) 665

Ellerton, see also Clements Ellis, K. (1983) 339 Elton (1927/1966) 190 Engel

(1966) 708 (1970) 326, 708 (1970a) 346, 409 (1973) 326 (1975) 326 (1987) 326

Engel et al. (1974) 326 English

(1991) 134 (1993) 134, 663 (1998) 53

Erickson (1996) 108, 497 Ernest

(1991) 37, 38, 40, 43 (1994) 46

Esselbach (1967) 308 Estepa Castro & Sánchez Cobo (1998)

702 Estes (1972) 139 Evans, K. (1985) 348 Evans, R. (1973) 134 Even, pers. comm. 166 Everybody Counts, see Mathematical

Sciences Education Board of the National Research Council (1989)

Eyssautier-Laborderie (1973) 326, 525

Falk (1979) 157 (1982) 157, 161 (1983) 157 (1989) 157 see also Bar-Hillel

Falk & Konold (1992) 157 (1994) 157

Falk et al. (1980) 157, 440, 658

Index

Félix (1966) 230 Fenner (1940) 7, 206, 207 Fey (1969) 533 Fiddler on the Roof, see Stein Fifth International Congress on

Mathematical Education (1984op) 348 (1984pp) 348

Finch (1970) 302 Findlay (1983) 342 Finlay & Lowe (1993) 104, 128, 384,

694, 711, 749 Finn Report 414 Finucan (1975) 331 Fischbein

(1975) 134, 150, 153, 160, 266, 502, 504 (1987) 153 see also Lecoutre

Fischbein & Gazit (1984) 163, 524-525, 526-527, 528-529, 530-531, 532, 534-535, 536-537, 538-539, 635, 639, 646, 647, 715

Fischbein & Schnarch (1997) 153 Fischbein et al. (1991) 68, 511 Fischer et al. (1993) 473 Fisher

(1935/1966) 68, 85 apocryphal 754

Fitzgerald, A. (1976) 349 (1993a) 349 (1993b) 349

Fitzgerald, R. (1973) 209, 212, 213 (1975) 208

FitzSimons & Money (1990) 371 Flavell (1970) 97 Fletcher (1964) 230 Fong et al. (1986) 721 Forbes (1994) 493 Ford (1916) 216, 678 Foxman (1993) 472

Foxman et al. (1980a) 481 (1980b) 481, 482, 503, 520, 521, 522-

523 (1981) 635

Foyster (1988) 349 Freudenthal

(1957) 326 (1965) 137 (1973) 99, 384, 409, 410 (1974) 19, 94, 760

Freudenthal (1978) 682 (1983) 682 (1991) 63

Frid (2000) 811

Gaerntner-Jones (1993) 403 Gaffney

(1969) 273, 356 (1986) 356, 358, 359, 362, 372, 373

Gage (1991) 820 Gal & Garfield (1997) 165, 470, 661 Galbraith & Carr (1987) 358 Galbraith et al. (1992) 385 Garfield

see also Ahlgren, delMas, Gal Garfield & Ahlgren

(1988) 19, 166 Garfield & Green (1988) 346 Garfunkel & Steen (1988) 388 Garlikov, e-mail message 54 Gates (1989) 387 Gattegno

(1971) 230 (1974) 230

Gerth & Mills (1957) 706 Geyman (2000) 779 Gibbon (1776–1788) 807 Gigerenzer et al. (1989) 93 Gilbert

(1875) 3, 802 (1879) 146, 170 (1881) 21 (1885) viii, 27 (1889) 901

Gilbert & Low (1994) 108, 109 Gilding (1988) 396, 452 Giles, G. (1977) 710

5

Index

Giles, J. (1970) 39, 77, 319 Gipson (1971) 715 Glaeser

(1978) 125, 283 (1983) 156

Glass et al. (1981) 126 Glastonbury

(1963a) 244 (1963b) 244 (1966) 245, 268 correspondence 254

Glaymann & Varga (1973) 326 Glazer (1974) 680, 819 Glencross & Laridon (1994) 148, 662 Glencross (1998) 20 glima too, see Cribb (1984) Gödel (1931) 64 Godino

(1993) 202 see also Batanero, Estepa

Godino & Batanero (1996) 51 (1996b) 202

Godino et al. (1994) 148, 652, 655, 656 Golding (1975) 242 Golding et al.

(1969–1972) 292, 294 (1969–72) 328, 372 (1972) 294

Gómez da Silva (1985) 74 Goodman, E. (2001) 634 Goodman, T. (1997) 339, 381, 386 Goodnow (1958) 152, 658 Goodwood High School, Course

R586 392 Gorseth Prayer 3, 821 Gough, J. (1980) 359 Gough, N.

(1989) 120, 685 (1994) 109

Gould (1989) 123, 124, 196, 472 Grafton (1997) 29, 170, 807 Graham

(1987) 388 (1993) 543

Grand Old Duke of York, The 410

Gras & Totohasina (1995esm) 166 (1995rdm) 166

Gray (1962) 246 (1967) 312

Great Britain. Department of Education and Science (1989) 460, 462

Great Britain. Parliament (1989) 460

Green (1979) 146, 338, 378 (1981) 75, 78, 146 (1982a) 146, 147, 172, 508, 540-542,

543, 546-547, 548-549, 550-551, 552-553, 554-557, 558-559, 560-561, 562-563, 564-565, 566-567, 568-569, 635, 641, 650, 651

(1982b) 146, 540, 631 (1982c) 134, 146, 541, 542, 545, 546,

547, 548, 552, 555, 557, 558, 560, 562, 565, 566, 568, 569-571, 635, 641, 644, 646, 658, 660

(1982d) 146 (1983a) 69, 71, 146, 161, 566, 567, 631 (1983b) 146, 150, 552, 555, 556 (1983c) 567 (1983six) 146, 164, 173, 627 (1986) 662 (1987) 714 (1989) 163 (1991a) 147, 161 (1991b) 147, 161 (1991long) 168, 631 (1993) 709 (1995) 710 pers. comm. 146 see also Batanero, Estepa

Greene (1971) 80-81 Greig-Smith (1964) 191 Grey et al. (1982) 346 Grice (1975) 57-59, 110 Griffith & Mullins (1972) 126 Griffiths & Howson (1974) 117, 279,

306

Index

Grimison, see Clements Gronlund (1968) 640 Grossmith, G. & W. (1894) 361 Grouws & Meier (1992) 380 Grouws (1992) 129, 454, 700 Gruber & Vonèche (1977) 134 Gruen & Weir (1964) 713 Grünewald (1991) 708 Guardian Weekly 634 Gubbins et al. (1982) 358 Guderian 52 Guildford & Fruchter (1973) 402 Guttman

(1944) 147, 474 (1947a) 147, 474 (1947b) 147, 474 (1950) 147, 474

Hacking (1975) 74, 75, 96, 790 (1990) 75, 76, 194, 316, 790

Haese et al. (1980) 377 (1982m1) 377 (1982m1s) 377 (1983) 66 (1993) 453

Haggarty (1992) 456 Haimes & Malone (1993) 455, 698 Half, R. 386 Hall (ndp, c. 1994) 406, 456 Halliday (1978) 59, 63, 66 Hamann 330

(1975a) 332 (1975b) 314, 315, 319, 320, 321, 330 1965 Conference minutes 264 archival record 267 correspondence 296

Hamilton (1975) 121 Hamley (1938) 208 Hammersley (1968) 220, 322 Handy (1988) 490 Hannaford (1986) 723, 789 Hannan (1989) 418 Hardy (1940) 11, 92 Hargreaves

(1992) 699 (1994) 114, 685

Hargreaves & Fullan (1992) 47

Harradine, public comment 756 Harris (1991) 85 Hart

(1980) 146, 474, 570, 587, 667 (1981) 146 (1981fr) 473

Havelock (1969) 683 Hawkins & Kapadia (1984) 128 Hawkins, A. & P. (1997) 83 Haydn (1796) 8, 75 Hazlitt (1839) 186 Hedegaard (1990) 473 Heitele (1975) 19, 152 Helme & Stacey (2000) 809 Henderson et al.

(1968–1970) 292, 328 (1968–70) 372 (1971) 294

Herrington et al. (1992) 687 Higgins & Davies (1996) 740 High School Papers (c. 1975) 370 Hillage et al. (1998) 684 Hilliard (1991) 285, 308, 320 Hinde & St John Parker (1997) 180 Hirst (1974) 88, 89, 196, 386 Hitchcock (1980) 347 Hoemann & Ross

(1971) 128 (1982) 128

Hoffer (1978) 719 Hoffman

(1975) 332 (1980) 329

Hofstadter (1979) 64 Hogben, D. (1980) 684, 702 Hogben, L. (1951) 312 Holmes, pers. comm. 505, 533, 545 Horwood

(1992) 249, 274, 296, 320 (1994) 184, 285, 300 (1997) 184 (1998) 184 (c. 1993) 184 (ndp) 184

Howden & How (1996) 113, 226, 286, 385

Howson & Wilson (1986) 89, 93, 384

Index

Howson et al. (1981) 13, 111, 118-119

Howson, A.G. (1979) 221 (1983) 343 (1987) 270

Howson, C. (1995) 137 Hudson (1995) 76 Hughes & Wilson (1966–1968) 295 Hughes, M. (1986) 62 Hughes, P.

(1960) 219, 231, 313, 314 (1966) 35, 789 pers. comm. 255, 295

Hume (1966) 302 (1969) 313, 325, 326 (1970) 303, 346

Hunt (1969) 139 Hunting & Davis (1991) 691 Hunting & Doig (1992) 469, 634 Hunting et al. (1993) 469, 669 Hunwick (1970) 8, 222, 279, 280, 320 Hyde, pers. comm. 28, 334

Immelmann (1972) 193 Industry Education Forum, The 413 Inglis (1985) 220 Inhelder & Piaget (1955/1958) 137 Inhelder, see also Piaget Initial Thoughts on Level 7 & 8 &

Chance & Data 423 Institut de Recherche sur L’Enseigne-

ment des Mathématiques de Montpellier (1971) 325

Irving (1824) 381 Isaacs (1980) 85 Izard

(1977) 640 (1992) 148, 519 (1993) 494 pers. comm. 295

Izard et al. (1965, 1970) 294

Jacobs (1977) 393 James, A.T., pers. comm. 754 Jardine (1994) 192 Jaworski (1994) 47, 52

Jefferson, T. 339 Jeffery

(1975) 330 (1985) 455

Johnson & Glenn (1961) 273 Johnson & Kotz (1977) 94 Johnson, D. (1989) 692, 720 Johnson, L. (1981) 347 Johnson, S. 73, 179 Joliffe & Sharples (1993) 503 Jones et al.

(1997) 157, 158, 662, 663 (1999) 158

Jones, A.W. (1958) 234 (1959) 215, 236 (1970) 213, 236, 243, 311, 315 (1971) 311 (1978) 285, 323, 333, 366 (1985) 212, 213, 234 correspondence 215

Jones, G.A. (1974) 150, 157, 505, 719 (1977) 129, 150, 157, 719 (1979) 378

Jones, G.V., pers. comm. 735 Jones, Keith

(1991) 83 (1995) 418, 436 e-mail message, 1997 452 e-mail message, 1998 684

Jowett, B. 177

Kahneman & Tversky (1971) 149 (1972) 571, 589

Kahneman et al. (1982) 151, 668 Kahneman, see also Tversky Kapadia

(1984) 160 (1984mt) 97 see also Hawkins

Kapadia & Borovcnik (1991) 129 Karmel (1971) 209, 210, 212, 213, 306,

321 Karplus et al. (1983) 631 Kee (1975) 254, 255, 256, 268, 329

Index

Keeves (1959) 231 (1965) 222, 266, 270, 276, 315 (1981sa) 352 (1982) 119, 682, 683, 697, 806 (1982sa) 352, 355, 361 pers. comm. 232, 235, 239, 240, 242,

251, 252, 253, 254, 255, 256, 257, 258, 293

Keeves & Stacey (1999) 340 Keitel, pers. comm. 63 Kekulé, A. 111 Kelly, B. (1998) 93 Kelly, G. (1962) 247 Kelly, R.A. (notes) 57-59, 110 Kempster (1982) 164, 172, 226, 257,

303, 326, 375, 486, 487, 503, 509, 572-573, 574-575, 576-577, 578-579, 580-581, 582-583, 584-585, 635, 658, 711, 719, 720

Kendall (ndp) 469 Kennedy et al. (1995) 419 Kerslake

(1974) 69, 172, 586-587, 612, 627 (1986) 587

Key Competencies and How They Can Help Your Business 415

Kilpatrick (1981) 681 (1992) 679, 680, 681

King & McLeod (1999) 8 King, A. (1945) 208 King, E. (1975) 310, 330 Kleijne & Schuring (1993) 470 Kliebard (1986) 821 Kline (1973) 220 Kluge (1989) 73 Knight, interview 38-39 Knott (1994) 710 Koestler (1959) 791, 1023 Konold

(1989) 151, 435 (1989pme) 151 (1991) 104 (1995) 476 see also Falk, Pollatsek

Konold et al. (1993) 70, 151, 497, 533, 563, 588, 589, 663

Krajcsik (1996) 131 Kramer (1954) 223 Kreckel (1981) 59 Krisjansen (1997) 109 Krygowska (1979) 355 Küchemann (1981) 60, 757

Laborde (1989) 682, 769 Lack

(1956/1973) 199 (1966) 191

Lafleur et al. (1973) 320 Lagemann (2000) 809 Lajoie (1998) 165 Lambdin (1993) 667 Lamon (1993) 161 Lange (ndp, c. 1988) 755, 818 Laplace, P.S. de 107 Larkin (1978) 40, 689, 698 Larousse, see Libraire Larousse Lawton

(1980) 108 (1981) 475

Leake (1962) 658 Lecoutre & Fischbein (1998) 153, 157 Lecoutre (1992) 161, 171, 563, 710 Leff (1968) 284 Leffin (1968) 162, 485, 658 Lehman et al. (1988) 89 Leo et al. (1974) 402 Lerman

(1998) 53 e-mail comment 20

Lesh (2000) 811 Lester & William (2000) 821, 822 Lewin (1997) 187 Lewis & Short (1962) 107 Libraire Larousse (1973) 74 Lightner (1991) 107 Lingard (1993) 382 Lingard et al. (1993) 110 Linkletter (1965) 131 Lipson (1994) 701 Livy 85 Lodge (1975) 125

Index

Lokan (1997) 766, 768 pers. comm. 241, 243

Lokan & Frigo (1995) 430 Lokan et al.

(1996) 476, 477, 614-615, 616-617, 618-619, 620-621

(1997) 477, 614-615 Long

(1989) 692 (ndp) 49

Longfellow (1886) 15, 469 Loosli-Usteri (1931) 133, 656 Lortie (1975) 699 Loveday (1958) 267, 273, 298 Lovell (1971) 681, 716 Lovitt & Clarke

(1988a) 360 (1988b) 360

Lovitt & Lowe (1983a) 384 (1983b) 384 (1993a) 104, 128, 139, 435, 436, 441,

442, 464, 694, 711, 749 (1993b) 104, 128, 427, 464, 694, 711,

749 Lovitt (1980) 359 Lowe

(1988) 358 (1991) 358 see also Finlay, Lovitt

Lowe & Lovitt (1984a) 359 (1984b) 359

Lucas & James (1968am, 1968pm) 301 unspecified textbook 301

Lupton (1892) 219 Lushey (1932) 206 Lynch et al. (1977) 377 Lynn & Jay

(1981) 380, 402 (1986) 72, 84, 515, 664 (1987) 64, 723

MacDonald & Walker (1976) 119

MacDonald (1975) 331

MacGregor (1988) 60 Papers 428

MacGregor & Stacey (1995) 70, 757 Machin & Tilsley (1985) 373 Mack (c. 1986) 391 Macquarie Dictionary (1987) 19 Maddern, pers. comm. 85 Magnusson (1994) 72, 83 Maguire et al. (1986) 777 Malone & Taylor (1993) 46 Mander-Jones, correspondence 251,

252 Mangan (1994) 710 Mann (1984) 342 Mansfield & Thompson (various

dates) 265 Mansfield (1966) 269 March (1970) 229, 281 Marks, J. & G. (1948) 17 Marsh & Stafford (1988) 111, 112 Masters

(1993) 429, 474 (1993nief) 413, 429

Mathematical Association of South Australia Workshops (1994/95) 428, 454

Mathematical Association of Tas-mania-Education Department (1972) 402

Mathematical Association [UK] (1959) 230 (1975) 327 archives 271

Mathematical Sciences Education Board of the National Research Council (1989) 345, 350

Mathematics at Work 355-357, 358 Mathematics for the Majority (1971)

327 Mathematics in Australia 245 Mathematics Profiles Draft

Level 1 441 Level 5 441 Levels 1–8 425

Mathematics Teacher Education and Development 648

Index

Mathematics Today Series 452 Mathematics, Measurement and Me 359 Matthews, G., public comment 225 Matthews, R. (1997) 504 Mattingley & Hampton (1988) 85 Maugham (1951) 45 Maxwell & Calver (1998) 200 Mayer Committee

(1992) 414, 415, 811 (ndp) 354, 414

Maynard (1966) 264, 265, 266, 274, 292

McAloon (1975) 221 McBride (1989) 109 McCall (1994) 96 McConnan, N.

correspondence 729 pers. comm. 266

McGaw (1994) 474 (1995) 120, 423, 447 (1997) 420, 430

McGaw et al. (1989) 483, 484, 485, 518-519 (1992) 121, 122, 767

McKinlay (1993) 697 McMullen

(1958) 222, 232 (1959) 232 (1960) 232

McMullen & Williams (1965) 299 (c. 1963) 232, 259 (various dates) 265, 298

McNally (1967) 286 McQualter

(1980a) 39, 246 (1980mea) 316 (1980ocs) 92, 274 (1982) 263, 317

McTaggart et al. (1996) 350, 382 Meinig (1962/1988) 446 Messick & Solley (1957) 504 Metz (1997) 470 Michell & Stephens (1995) 380 Milbourne (1983) 277

Millard (1988) 699 Miller, L.D. (1991) 750 Miller, P. (1986) 205 Miller, W. (1959) 640 Minnick (1987) 634 Mocciola (1975) 329 Mode (1966) 334 Module 27 371, 372 Montmort (1713) 75, 90 Moon (1986) 8 Moore & McCabe

(1989) 388 (1989tv) 388

Moore, D. (1991) 458 (1993) 223, 224, 247, 255

Moore, J. (1996) 201 Moore, P. (1958) 267, 268, 273 Moore, W. (1970) 819 Moorhead (1992) 777 Morgan et al. (1966) 279 Morin (1992) 202 Moritz

(1998) 169 see also Callingham, Watson, J.

Moritz et al. (1996) 159 Morley (1975) 718 Moroney (1956) 312 Mort (1946) 77 Mosteller et al.

(1961) 224, 312 (1973a–d) 327

Mountford (1965) 85 Mousley, e-mail comment 52 Mullet & Rivet (1991) 68 Munro (1990) 80 Murray-Smith (1986) 723 Musgrave

(1985) 684, 701 (1988) 821

Nation at Risk, A, see National Commission on Excellence in Education (1982)

National Assessment of Educational Progress

(1972) 479 (1976) 480 (1979b) 480 →→→→

Index

National Assessment of Educational Progress

→→→→ (1979y) 590-591 (1981) 479

National Council of Teachers of Mathematics

(1961) 222, 223, 283 (1980) 44, 343, 344, 398 (1989) 345, 460, 462, 470 (1995) 665, 666 (2001) 633

National Industry Education Forum (ndp, c. 1993) 775

Neill (1962/1968) 785 Neumann (1966) 299 New Scientist 633 New Shorter Oxford English Dictionary

(1993) 18, 154 New South Wales

Board of Senior School Studies (1965) 298

Department of Education (1960) 297, 298 (1967) 256

Department of Education for the Board of Senior School Studies (1965a–c) 298

Department of Education for the Secondary Schools Board (1962) 232, 298 (1963a–b) 298 (1963b) 244

New Zealand. Ministry of Education (1992) 461, 462

Newman & Wall (1974) 300 Newman (1983) 57, 660 Newton, B. (1988) 383 Newton, I. 152 Neyland (1996) 761 Nicholas (1969) 209 Nicholls (1980) 359 Nicholson (1823) 219 Nisbet (1978) 256 Nisbett et al. (1983) 721, 755 Niss (1993cas) 470 Noddings (1992) 775

Noelting (1980a) 161, 631 (1980b) 631

Nolan (1980) 366 Nolder & Johnson (1995) 115, 379 Noss (1990) 463, 465 NUD•IST, see Qualitative Solutions

and Research (1992) Nuffield Mathematics Project

(1967a–c) 269 (1969) 269, 328

O’Connell (1971) 49 O’Daffer (1993) 51 O’Reilly (1940) 87 Odum (1971) 189, 190 Official Yearbook of the Commonwealth

of Australia 342 Oguntebe & Lappan (1983) 716 Ojeda Salazar (1994) 166 Ojemann et al. (1965) 715 Olssen

(1987) 711 (1988) 354

Olssen et al. (1994) 427 Openshaw

(1991) 38-39 (1992) 272, 304 (ndp., c. 1988) 790

Openshaw et al. (1993) 186, 304, 316 Opie, I. & P. (1959) 500 Oppenheimer (1993) 22 Organisation for European Economic

Cooperation (1961) 14, 224, 225, 235, 312

Ortiz de Haro (1996) 702 see also Cañizares

Orton (1988) 710 Orwell (1945) 685 Osborn

(1993) 41 pers. comm. 211

Osler, W. 457 Osmond, correspondence 252, 255

Index

Our Schools and Their Purposes, see Education Department of South Australia (1981ostp)

Owen et al. (1988) 360 Oxford and Cambridge Schools

Examination Board (1967) 649 Oxford English Dictionary (1989) 18,

19, 20, 24, 73, 74, 107, 350

Paauw (2000) 780 Page (1959) 313 Papy (1964) 230 Partington (1996) xx, xxi, 7, 131, 152,

167, 186, 192, 216, 341, 361, 381, 457, 460, 637, 656, 670, 678, 785

Pascal, B. 91, 464 Patching (1967) 270 Pattinson, B.

correspondence 213 public statement, 1959 233

Peard (1992) 65, 150, 159 (1993) 434, 508, 604, 605, 606-607, 647 (1994) 95, 159, 738 (1995) 95, 159 (1995mer) 97 see also Borovcnik

Pedler (1977a) 329, 579 (1977b) 329, 579 (1980) 329 see also Darroch

Pegg, see Anderson, Grimison (bibliography), Reading

Peter-Koop, pers. comm. 165, 659 Peters (1995) 24, 27, 478 Petersen (1971) 302 Petocz (1990) 371 Pfannkuch & Brown (1994) 701 Pfannkuch & Wild (1998) 166 Pfannkuch (1993) 76, 89

see also Wild Phillips, R. (1975) 353 Phillips, S. (1972) 54, 222

Piaget (1941/1952) 513 (1950) 133 (1971/1984) 138, 657 (1981/1987) 138, 657 (1983/1987) 138, 657 see also Inhelder

Piaget & Inhelder (1951/1975) 132-139, 147, 161, 507, 508, 525, 571, 658, 833

Pimm (1987) 59, 62, 64 Pinar (1975) 107 Piper (1997) 416, 419 Pirie (1991) 62, 66 Pitman

(1990) 452 pers. comm. 248, 289

Plato 240, 653, 1023 Pliny 513 Pollatsek et al. (1984) 149, 152, 660 Pollatsek, see also Konold Ponte et al. (1994) 37, 117 Ponte, J.P., see also da Ponte Pope

(1711a) 167 (1711b) 460

Popkewitz (1988) 187, 806 Porter (1996) 44 Potts (1974) 220, 322 Pouw-Bray (1979) 795 Power, J.O’C. 7 Powers (1972) 302 Pratt & Noss

(1998ico) 160 (1998pme) 160

Pratt (1998) 159, 713 Preston & Watterson (1972) 301 Preston (1975) 331 Price (1961) 221 Prideaux (1988) 319, 352 Primary Mathematics Notes 1992 448,

704 Print (1993) 112, 114, 411 Probability Theory 369 Project CAM, see Costello et al. (1985)

Index

Public Examinations Board (1956) 216 (1961) 216, 273 (1966) 265, 273, 288 (1966a) 288 (1967) 265, 266 (1968) 267, 273, 287, 289 (1969a) 284, 285, 289, 333, 649 (1969b) 287 (1970) 287, 288, 289, 290 (1971s) 332 (1972) 334 (1972s) 333 (1973s) 334, 365 (1974s) 334, 365 (1976) 376 (1977) 374 (1978) 333, 375, 376, 486 (1980) 376, 377 (1982) 367 (1982ex) 376 (1982exm1) 375 (1983) 367 (1983exm1) 376

Publication Manual of the American Psychological Association 27, 28

Quadling (1983) 196 (1996) 272, 457

Qualitative Solutions and Research (1992) 142

Rackham (1960) 513 Råde

(1970) 313 (1975) 327

Radford Background in Mathematics 251 correspondence 251, 252, 254, 255

Ransley (1994) 694, 699 Rasch (1960/1980) 474 Read et al. (1996) 12 Reading & Pegg (1995) 65 Reading & Shaughnessy (2000) 164,

662 Reed, E.S. (1993) 191 Reed, R.A. (1975) 212

Reichle et al. (1975) 190 Reid, A. (1995) 430 Renner (1978) 474 Republic 240, 653, 1023 Resnick (1983) 47, 500, 700 Reys (1978) 480, 592-593, 594-595,

596-597 Richardson, submission 309 Ridgway & Passey (1993) 489 Ritson

(1998) 168-169 see also K. Truran

Roach (1971) 472 Roberts (1994) 380 Robertson, A. (1977) 337 Robertson, B. (1994) 28 Robitaille & Donn (1993) 478 Robitaille & Travers (1992) 615, 619,

665 Rodda (1987) 72 Rogerson

(1982) 709 (1987) 92 (1990) 371

Romberg (1983) 155 see also Collis

Romberg & Shepler (1973) 716 Room & Mack (1966) 298 Room (1960) 220 Rosier (1980) 276, 317, 350 Ross (1966) 658 Rouan & Pallascio (1994) 175 Rouncefield & Holmes (1989) 388 Rousseau (1762) 758, 759 Rowell, pers. comm. 242 Royal Statistical Society and the In-

stitute of Statisticians (1979) 342 Royaumont Seminar, see

Organisation for European Economic Cooperation (1961)

Runcie (1985) 48, 439 Ruthven

(1980) 260, 280, 281 (1999) 693

Ruttkay (1997) 83

Index

Sáenz Castro (1998) 717 Santhanan (1996) 693 SATAC Guide

(1993) 393 (1996) 405, 406 (1997) 406

Sawley (1967) 290 Sawley et al. (1974) 333, 334 Scarne (1973) 520 Schoenfeld

(1988) 63 (1994) 54

Scholes (1970) 459 Scholz

(1991) 129 see also Bea

Scholz & Waller (1983) 128, 584 Schön (1983) 50, 404, 819 School Mathematics Journal 237, 312 School Mathematics Project

(1965a) 276 (1965c) 264 (1967a) 276, 367

School Mathematics Project (1968d) 270, 278 (1969) 6, 726, 727 (1970tg5m) 6, 726, 727 (1974) 279 (various dates) 228-229, 265

School Mathematics Study Group (various dates) 257

Schools Council Research Studies (1973) 111, 271

Schroeder (1989) 20 Schuck (1999) 768 Schupp (1986) 19, 708 Schweiger (1994) 62 Scotland Yard 79 Scott, M.B. (1968) 97, 326, 525 Scott, M.M. (1995) 208 Scott, P.

(1975) 331 (1996) 780 pers. comm. 281

Searle & Jones (various dates) 234, 282

Secada (1992) 57, 64, 71

Secondary Science Curriculum Committee (1977) 337

Seddon (1989) 119, 820 (1999) 634, 649

Seeger & Steinbring 97 Seidel (1976) 359 Sellar & Yeatman (1930) 35, 219, 645 Senior Secondary Assessment Board

of South Australia (1983) 377 (1983exm1) 375 (1984ar) 366 (1985ar) 366 (1985ex1s) 377 (1985–1990) 50, 395, 398, 402, 403, 404 (1986) 376, 391 (1986ar) 392 (1987) 486 (1987ar) 393 (1989pesm) 398, 399 (1991cma) 400, 402 (1991mem42) 396

Senior Secondary Assessment Board of South Australia

(1991mem86) 396 (1991mss) 399 (1992) 452, 453 (1992am) 394 (1992ar) 400 (1992qm) 400, 401 (1994ar) 405 (ndp) 394 (ndp, ?1987) 398 (ndp, c. 1986) 392 (ndp, c. 1987) 397 (ndpa) 397

Shakespeare Hamlet xxiv, xxxi, 9 King Lear 22 Macbeth 810 Tempest 1023

Sharma & Begg (1995) 156 Sharma (1997) 167, 527, 551, 662

Index

Shaughnessy (1977) 717, 720 (1992) 19, 57, 97, 127, 129, 130, 458,

470, 659, 713, 717, 720, 740 (1993) 719 (1997) 164

Shaughnessy & Bergman (1993) 19, 709, 717

Shaughnessy et al. (1996) 659 Shaw

(1903) 4, 777 (1923/1953) 808 date unknown 3

Shepler (1969) 716 see also Romberg

Sherlock (1964) 265 Sherman, pers. comm. 300 Sherrington et al. (1987) 380, 821 Shulman (1987) 703 Shulte & Smart (1981) 454 Siegel & Andrews (1962) 658 Siegel (1956) 401 Siegler (1976) 161 Sierpinska & Kilpatrick (1998) 7 Sierpinska et al. (1993) 176 Siet (1993) 708 Singer & Resnick (1992) 631 Skemp

(1971/1986) 61, 65, 131, 374, 402, 752 (1976) 416, 767

Smith & Lovat (1991) 107 Smith, A.G.R. (1972) 781 Smith, E. (1959) 214 Smith, R. (1994) 709 Smith, T. (2000) 811 Soliman (1977) 695 Soucek (1993) 417 South Australia. Department of

Education, Training and Em-ployment (2001) 810, 811, 812, 814

South Australia. Department of Transport (1997) 416

South Australia. Parliamentary Papers No 44 (1959) 213

South Australian Institute of Technology (1989) 387

South Australian Mathematics Teacher (1967) 237, 290, 300, 313 (1968) 291

South Australian Science Teachers’ Journal (1966) 276

South Australian Teachers’ Journal (1959) 4, 234 (1961) 213

South Australian Year Book 318, 382 Southwell et al. (1984) 348 Sowey

(1995) 105 (1998) 702

Spiegel (1961) 334 Spinolla (1997) 176, 663 Spode Group

(1986) 393 Stacey

(1994) 417 see also Helme, Keeves, MacGregor

Standards Association of Australia (1993) 415

Starr (1987) 368, 369, 372, 373, 382 Steedman (1991) 37, 41, 46, 50, 132 Steen (1999) 7, 8 Steffe & Wiegel (1992) 46, 52 Stehn (1997) 424, 425, 426, 427 Stein (1964) 22 Steiner, G. (1989) 3, 179, 1023 Steiner, H.-G. (1987) 681 Stephens & Money (1993) 470 Sterling & Scott (1985) 1023 Stevens (1979) 318 Stevenson & Zigler (1958) 658 Stevenson (1885) xxi Stewart (1996) 79 Stoppard

(1967) 725 (1993) 74, 205, 381, 803

Stoyanov (1986) 19, 710 Strachey (1923) 103 Strauss & Corbin (1990) 10, 15

Index

Style Manual for Authors, Editors and Printers 27

Sullivan et al. (1996) 19, 181 Sumner & Lafleur (1972) 320 Sumner (1969) 8, 213, 231, 238, 239,

258, 261, 265, 268, 275, 320 Sweeney (1990) 711 Swinson

(1977) 707 (1978) 257 (1993) 455, 456

Szendrei (1990) 19 Tamlin (1968) 290 Tanur et al. (1978) 82, 327 Tarr & Jones (1997) 663 Tasmanian Education Department.

Curriculum Centre (1966) 295 Tate (1932) 206 Taylor & Biddulph (1994) 709 Taylor (1995) 709 Taylor et al. (1993) 48 Teaching Statistics 128, 346 Teigen (1983) 173-174, 500, 506, 610-

611, 612-613 Teilhard de Chardin (1959/1969)

1023 Teloh (1986) 64 Temple (1930) 42 Tesch (1990) 10 Thiele (1975) 205, 206, 207, 208, 209,

211, 314, 318, 319 Thomas (2001) 669 Thompson, M.D. (1986) 60 Thompson, W. (1963) 222, 234, 235 Thoreau (1850) 656 Thwaites

(1961) 226, 227, 228 (1972) 264, 266

Tims (1994) 493 Tinbergen (1953) 198, 199 Tirosh & Dreyfus (1998) 152 Tobin & Capie (1981) 487 Tobin & Fraser (1988) 13, 688, 769,

776 Tobin (1982) 487, 488, 622-623, 624-

625, 647

Todhunter (1865) 69 (1875) 219, 679

Tolkein (1954) 59 Toohey (1995) 95, 162, 571, 662 Toon & Ellis (1973) 111 Tosh (1991) 179, 180 Torok & Watson (2000) 164 Treffers (1987) 116 Treilibs & Gaffney (1980) 357 Treilibs (1979) 356 Trésor de la langue française 19

Truran, J. (1964) 235 (1973a) 6, 282, 369, 729, 730, 731, 733,

752 (1973b) 6, 282, 369, 729 (1973fsg) 7 (1983) 782, 783 (1985) 79, 86, 348, 529 (1986) 348 (1989) 486, 736, 737-738 (1990) 70 (1991) 367 (1992) 6, 7, 19, 30, 56, 65, 69, 71, 79, 80,

93, 98, 99-103, 127, 131, 133, 135, 139, 150, 156, 160, 161, 301, 434, 440, 455, 473, 479, 486, 502, 504, 505, 506, 507, 509, 510, 511, 521, 533, 535, 542, 545, 557, 577, 610, 713, 715, 716, 737, 738, 757, 760, 767, 802 Appendix VII 736 errors 738

(1992a) 150 (1993anzhes) 93-103, 185, 237 (1993mav) 498 (1994amtprob) 82, 98, 454, 727 (1994icohis) 179, 183 (1994icovar) 70, 164, 581 (1994mavinf) 98 (1994merga) 129, 498 (1994merhis) 179, 183, 456 (1994mob2) 18, 73 (1994pme) 160, 440, 507, 535 (1994solo) 489 (1994voi) 42 →→→→

Index

Truran, J. →→→→ (1995aamtinf) 98 (1995aare) 179, 183 (1995mef) 88 (1996) 446 (1996pme) 150 (1997anzhes) 179, 460 (1997merhis) 179, 183 (1998iconh) 402, 702 (1998pmehab) 171, 174, 740 (1999ausico) 450 (2000aamtjou) 775 (2000phd) 449 (2000pmehab) 740 (2000saoa) 675 (2001phd) 802 (2001pmefra) 649 (in press) 94, 453 (ndp, c. 1980) 733 correspondence 185 diary 725, 726, 728 personal memories 343, 347, 365, 388,

389, 399, 403, 405, 406, 407-408, 648, 667

personal notes 228 see also Arnold, Truran, K. unpublished (Lahti, 1997) 130

Truran, J. & Arnold (in preparation) 777

Truran, J. & K. (1995) 129, 154 (1996) 19, 69, 127, 129, 175, 200, 738 (1997ind) 99, 440, 738 (1998) 604 (1998pmehab) 535 (1999mer) 661 (1999pmehab) 557, 740 (2000merfai) 648, 664

Truran, K. (1992) 491 (1992pma) 449 (1993) 272 (1994) 163 (1995) 79, 163 (1997mer) 451, 699 (1998) 165, 529, 533 →→→→

Truran, K. →→→→(in preparation) 65, 70, 163-164,

497, 500, 503, 511, 551, 570, 644, 662

(in press) 163, 500 pers. comm. 146, 373, 505, 577, 757,

767, 812 see also Truran, J.

Truran, K. & J. (1994mavpri) 18, 19 Truran, K. & Ritson (1997) 502 Tukey (1977) 388 Turner (1979) 504 Turner et al. (1969/1978) 500 Tversky & Kahneman (1974) 149,

151, 721 Twain

(1869) 341 (1897) 263

Tyler (1949) 112 Tynan, pers. comm. 456

Unattributed comments 301, 492, 816

United Nations Educational Cultural and Scientific Organisation (1965) 256, 257, 258, 259

University of Adelaide (1949cal) 236 (1960cal) 236 (1966cal) 307 (1967cal) 307

University of Adelaide (1969) 307 (1969cal) 307 (1970) 307 (1971) 307 (1971cal) 307 (1972cal) 307 Barr Smith Library records 235 Statutes 285

University of Illinois Committee on School Mathematics

(1960) 222 Bielefeld collection 223, 232

Valero et al. (1997) 693 Vallance (1983) 110 van der Veer & Valsiner (1991) 21

Index

Van Tyne & Berger (1959/1971) 460

Varga (1982) 164, 626 see also Engel, Glaymann

Varga & Dumont (1973) 326 Vaughan & Scotford-Archer (1971)

706 Vaughton & Gaffney (1980) 356, 357,

389 Vere-Jones (1990) 371, 379 Victoria. Ministry of Education

(Schools Division) (1988) 483, 484

Village (1990) 199, 201 Vinculum 359

(1965) 300 (1967) 278 (1973) 357 (1976) 359 (1980) 359 (1987) 247

Vinner (1994) 13, 41, 77 von Glaserfeld

(1989) 46 (1991ste) 58 (1995) 35, 51, 104, 186

Vonèche pers. comm. 133, 135, 136, 657 see also Gruber

Wadsworth (1971) 132 Wallent (1964) 244, 298 Ward (1990) 82 Waring (1979) 8, 38, 222, 694 Warmuth (1991) 708

Watson & Collis (1993) 141, 143, 175, 660 (1994) 19, 129

Watson & Moritz (1998) 169, 170, 632, 654

Watson & Reeves (1993) 711 Watson et al.

(1994) 69, 129, 141, 143, 173, 527, 529, 544, 626, 654, 662

(1995) 129

Watson et al. (1997) 141, 142, 143, 145, 175, 491, 533,

544, 626-627, 628-629, 630-632 Watson, Campbell & Collis (1993)

143 Watson, Collis & Moritz (1993) 163 Watson, F.R. (1995) 466 Watson, J.

(1992) 141, 175, 449, 458 (1993) 72, 454 (1993cm) 72 (1994) 129, 141 (1994aamt) 141, 428, 435, 441, 711 (1995) 65, 719 (1997amt) 450 (1998) 141, 544, 654 1994aamt) 428 see also Callingham, Moritz, Torok

Watson, M. (1968) 268, 309 Watterson

(1971) 302 pers. comm. 300, 302

Waugh, A. (1917/1955) 687 Waugh, E. (1928/1953) 5, 6 Way

(1994) 644 (1996) 165 (1997) 161, 631 (1998ico) 165 (1998mer) 164 see also Ayres

Weaver (1963) 312 Webb (1992) 666 Websters Dictionary (1981) 19 Weiner (1994) 12, 796 Wells (1931) 696 Westbury (1980) 452 Wheal

(1990) 394 (1991) 395 (1991mob) 389 (1993) 395 (1994) 395 (1994text) 389, 390 (ndp, c. 1986) 389 pers. comm. 389

Index

Wheeler, D. (1996) 32, 40 Wheeler, M. (1984) 20, 21 White, D. (1989) 705 White, R. (1992) 310, 765, 772 White, S. correspondence 252, 253 Whitford (1988) 347, 358, 388 Whitteridge (1971) 781 Whitworth (1878) 137 Who’s Who in Australia (1965) 236, 240 Why Change School Mathematics

Syllabuses? 238 Whyte (1956/1969) 53, 221 Wilberforce, S. 123 Wild & Pfannkuch

(1998) 166 (1999) 386, 415

Wilde (1994) 397, 909 Wilkinson & Nelson (1966) 579, 708,

720 William, D.

e-mail comment 762 see also Lester

Williams, J. pers. comm. 543 see also Amir

Williams, R. (1985) 87 Wilmot (1952) 52, 87, 148 Windschuttle (1994) 804 Wollring

(1994) 165, 529 (1994th) 165

Wolpert (1992) 82, 97, 176 Wordsworth

(1814) 192 correspondence 805

Wright & Masters (1982) 474 Wright, B. (1994) 698 Wubbels (1992) 53 Wyndham, correspondence 251, 252,

255

Yackel et al. (1992) 665 Yates, G. & S. (1990) 45 Year Book Australia 382 Yes, Prime Minister, see Lynn & Jay Yost et al. (1962) 658 Yusa (1987) 78, 84

Zahn (1982) 415 Zaleska (1974) 502, 504, 511 Zeisel & Kalven (1978) 83 Zimmer (1983) 83

INDIVIDUALS AND INSTITUTIONS INDEX

And some there be, which have no memorial. Their glory shall not be blotted out.2

1962 Conference 246-249, 322 1964 Conference 251-256, 292, 294-

295, 309, 330, 420 1965 Conference 256-260, 286, 735 1975 Conference 330-332, 405 Adelaide Consortium for

Mathematics Education 388, 407, 684

Adelaide Mathematics Project 240 Ahlgren, A. 742 Allen, Dave 93 Amir, G. 155 Anders, D. 266 Applied Probability Trust 346, 347 Arnold, A. 750-754 Assessment of Performance Unit 472,

481-482, 523 Association of Teachers of

Mathematics 227, 260, 694-695 Australian and New Zealand History

of Education Society 661 Australian Association of Math-

ematics Teachers 248, 347 critique of National Statement 421 withdrawal from Australian Mathe-

matical Sciences Council 816

Australian Education Council 418 Australian Mathematics Teacher 213,

358, 453 Australian Senior Mathematics Journal

454

Barnach, B. 220 Barnes, E.S. 4, 236-237, 257, 356

1 Ecclesiasticus 44: 9

Batanero, C. 672, 673 Baxter, J. 347, 354, 362, 363, 386, 392 Becker, C. 740 Begle, E.G. 222, 225, 257, 702 Benger, G. 392 Bentz, H.-J. 553 Berkeley, G. 255 Berndt, K.L. 238-240, 244, 257, 309 Blakers, A.L. 247, 303, 374 Boomer, G. 382-383, 408, 425-427 Borovcnik, M. 346, 553 Bourbaki, N. 230-231 Brinkworth, P.C. 107 Brown, G.McK. 253 Bruner, J.S. 43, 222, 240, 327 Butts, R.F. 210, 214-215, 216

Calculator-Aware Number Project 693, 696

Callaghan, J. 323 Cambridge Conference on School

Mathematics 384, 708 Carnegie Corporation 221, 232 Carroll, L. 59 Carss, M. 354 Cawte, F.G.N. 293 Cerf, V. 28 Children’s Mathematics Frameworks

Project, see Johnson, D. (1989) Clarke, Doug 379 Clements, M.A.

and curriculum reform 302 and Muddling Through Model 185 generic term 181 on Barnes 237 stochastics textbook 301

Close, F. 264, 363

Subject Index

Close, R.W. 237, 238, 246, 264, 271, 309, 363

Cochrane Library 779 Cockcroft Committee 523 Cockcroft Report 342-343, 367 Colgan, L. 375 College Entrance Examination Board

223-224, 225, 231, 245, 247 Collis, K.F. 488, 661 Commission Internationale pour l’Et-

ude et l’Amélioration de l’En-seignement des Mathématiques 680

Concepts in Secondary Mathematics and Science Project, see Hart (1980, 1981)

Cornish, E.A. 236 Crombie, A. 804 Crowther Report 350 Curriculum Development Centre

321, 353-355

d’Alembert, J. le R. 69 Davies, M. 359 Dawkins, J. 382 Dawson, C.J. 186 Delpit, L.D. 51 Dewey, J. 43, 415 Dienes, Z.P. 5, 240-242, 292 Doig, B. 661 Duckworth, E. 54

Educational Studies in Mathematics 46, 718

Eisner, E.W. 4, 179, 805 Engel, A. 313 Ernest, P. 38

Falk, R. 346, 659, 660, 661 Feklistova, O. 21 Fenner, C.A.E. 207 Fischbein, E. 152-154, 346, 539, 544,

657, 658, 659, 660, 662, 713 Fitzpatrick, B. 301 Freudenthal Institute, see Institute for

the Development of Mathemat-ical Education

Freudenthal, H. 152, 408, 680 Fulbright Awards 238

Gaffney, J. 356, 362, 363, 392, 408 Galileo, G. 123 Gammage, P. 817 Gattegno, C. 230, 231, 237, 680 Giles, J.P. 282 Glastonbury, J.O.G. 239, 242, 243,

244-245, 252, 267, 293, 335 Glaymann, M. 325 Glickman, L.V. 94 Gödel, K. 220 Golding, F.W. 241, 242, 243, 294 Goldsworthy, R. 237 Goodnow, J.J. 175 Graduate Certificate In Mathematics

Education 388 Gras, R. 166 Gray, M.C. 237 Green, D.R. 126, 148, 157, 163, 346,

462, 474, 493, 659, 662, 663, 669, 710, 738

Grimison, L. 297 Gunton, J.D. 901

Hall, R. 388, 402 Hamann, K. 239, 257, 265-266, 363 Harvey, W. 780-781 Hawkins, A. & P. 155 Hearly, M.G. 258 Heisenberg, W.K. 247 Hennequin, P. 325, 346 Hannaford, B.D. 793, 796 Hitler, A. 52 Hoffman, N. 302 Holding, C. 382 Holmes, P. 126, 346 Holtham, R. 687 Horwood, J. 184, 820 Howson, A.G. 117 Hudson, H.R. 318 Hughes, P. 254, 255 Hunt, J.H. 585 Hunting, R.P. 471

Illich, I. 490 Industry Education Forum 413, 429 Institute for the Development of

Mathematical Education 718 Institute of Statisticians 346

Subject Index

International Association for the Evaluation of Educational Achievement 248

International Conference on the Teaching of Statistics 346-347, 370-371

International Congress on Mathe-matics Education 347-348, 356, 407

International Statistical Institute 346 International Study Group for Math-

ematics Learning 242 IOWO, see Institute for the Develop-

ment of Mathematical Educat-ion

Izard, J. 652

Jeromson, B.J. 73 Johnson, S. 74, 204 Jones, A.W. 213-215, 233-234, 282,

318-319 Jones, G.A. 157-158, 166, 486, 659, 663 Journal for Research in Mathematics

Education 46 Journal for Structural Learning 242 Journal of Statistics Education 750 Jowett, G.H. 302

Kahneman & Tversky 657 Keeves, J.P. 237, 255, 350 Kempster, G.T. 486-487, 659, 669 Ketley, M.A. 1023 Ketteridge, S.J. 775, 780 King, E. 253 Kline, M. 247 Konold, C. 175, 660, 661, 662, 663

Lakatos, I. 465, 803 Lang, I.P. 237, 309 Lavoisier, A.L. 179 Learning the Unlikely at Distance

Delivered as an Information Technology Enterprise (LUDDITE) 450

Lecoutre, M.-P. 585, 661 Leffin, W. 485-486 Lewin, K. 92

Linnaeus, C. 156, 177 Lovitt, C. 359, 379

Mack, J. 347 Magnusson, E. 155 Mander-Jones, E. 212, 318 Marjoribanks, K. 198 Mathematical Association of South

Australia 320, 386, 454 and Public Examinations Board 285 and South Australian Science

Teachers’ Association 312 foundation 236-237 sponsor of syllabus changes 265

Mathematical Association of Victoria 734

Mathematical Association [UK] 237, 271

Mathematical Reviews 220 Mathematics Curriculum and Teach-

ing Program 358-361, 400 Mathematics Education Research

Group of Australasia 661 Matthews, G. 265, 270 Mesa, V. 619, 641 Messent, P. 81 Möbius 454 Moore, D. 388 Mosteller, F. 223, 247, 255 Muller, Br 237 Murray Committee 236

Nagy, R. 432 National Assessment of Educational

Progress 478-481 National Council of Teachers of

Mathematics 400 Neal, L.F. 4-5 New Education Fellowship 43, 207-

208, 816 Newton, I. 381, 791, 796, 818 Nuffield Mathematics Project 181,

265, 269-270 Nuffield Science Project 38, 694 Nunn, T.P. 215

Openshaw, R. 706

Subject Index

Opie, J. 202 Osborn, T.G.B. 211

Papy, G. 680 Parkinson, M. 752 Peano, G. 63 Peard, R. 370 Pedler, P. 330 Pegg, J. 711 Pereira-Mendoza, L. 154 Petersen, B. 219 Phillips, B. 371 Piaget, J. 116, 134, 656, 657, 680 Playford, T. 209 Popper, K. 202 Potts, R.B. 4, 236, 347, 356 Pratt, D. 662 Primary Mathematics Teachers’

Association 320 Probability and Statistics Study

Group 346 Psychology of Mathematics

Education 661

Qualifications Curriculum Authority (UK) 451

Råde, L. 326 Radford, W.C. 251-256 Rasch, G. 474 Rawlinson, R. 256 Reality in Mathematics Education

359 Richards, C.A. 212 Richardson, J. 308 Rigby Ltd 293-294 Ritson, I. 158 Rogerson, A. 717 Romberg, T. 488, 661 Rourke, R.E.K. 225 Rousseau, J.-J. 415 Royal Statistical Society 346 Royaumont seminar 14, 225-226, 300 Ruthven, K. 229

Sanderson, R. 805 Saunders, H.W. 236 Schoenfeld, A. 680

School Mathematics Project 6, 181, 226, 255, 257, 270-272, 278-279, 725-726, 729, 735

School Mathematics Research Foundation (Victoria) 300-301

School Mathematics Study Group (USA) 118, 222, 223, 231, 239, 247, 249

Schools Abingdon 6 Edmonton Grammar 5-6, 270 Enfield High 213, 238 Goodwood High 392 Melbourne Grammar 6-7, 282, 301,

306, 729-736, 768 St Peter’s College 4, 282, 1023 Unley High 5, 214 Westbourne Park Primary 4

Schools Commission 114, 321 Scott, P.R. 55 Senior Secondary Assessment Board

of South Australia 366-367, 391-396

Senior Secondary Certificate (SA) 323, 333, 366

Shaughnessy, J.M. 346, 471, 659 Shell Centre for Mathematics

Education 400 Sherman, B.F. 91, 186 Smith, E.R. 214 Smith, R. 282 Socrates 64 South Australian Certificate of

Education 396 South Australian Curriculum, Stand-

ards and Accountability Frame-work

see South Australia. Department of Education, Training and Employ-ment (2001)

Southampton Conference 226-228 St Dunstan’s College Booklets 265 Statistical Society of Australia 402 Statistics Education Research Group

346 Steinbring, H. 712 Swinson, K. 659

Subject Index

Teaching Statistics 346, 347, 750 Teigen, K.H. 504, 505, 613, 644 Teilhard de Chardin, P. 202 Tertiary institutions

Adelaide Teachers’ College 4-5 Ball State Teachers’ College 223 Bedford Park Teachers’ College 308 Boston College 223 Chelsea College 146, 692

see also Hart (1980, 1981), Johnson, D. (1989)

Colleges of Advanced Education 320 Flinders University of South

Australia 285, 347 Institute of Technology (SA) 206, 364 Open University (UK) 400 School of Mines (SA) 206 South Australian amalgamations,

1991 396 University of Adelaide xxviii, 4-5, 750 University of Bielefeld xxviii University of South Australia 285,

816-817 Western Teachers’ College 308

Third International Mathematics and Science Study 476-478, 615

Thwaites, B. 226, 257, 408 Tinbergen, N. 198-199 Toilet Test 790-791 Treilibs, V. 356, 363, 392 Trethewey, L. 179 Truran, J.M.

autobiography 3-8, 41-42, 81, 85, 109, 126, 156, 211, 238, 241, 270, 271, 274, 282, 284, 293, 296, 303, 306, 308, 342, 386, 396, 453, 724-754, 769, 777, 781, 807, 1023

research involvement 814 textbooks 6, 729-733

Truran, J.M. & K.M. 19

Truran, K.M. 29, 158, 161, 174, 501, 814, 817

Truran, T.D. 396 Tucker, A.W. 223, 225 Tukey, J. 388 Turing, A.M. 220

University of Illinois Com-mittee on School Mathematics 221-223, 232, 235, 238, 239, 245, 247, 249, 300

University of Maryland Mathematics Project 222

Valero, P. 619 Varga, T. 242, 346 von Glaserfeld, E. 104 von Linné, C., see Linnaeus, C. Vygotsky, L.S. 21, 473, 636

Walcott, C.D. 124 Walker, J.S. 318 Watson, J.M. 140, 147, 635, 647, 663,

669 Way, J. 497, 669 Weber, M. 706 Wells, H.G. 702 Westgarth, W. 252 Westpac Mathematics Competition

641 Wheal, M. 381, 386, 389, 392, 403, 405 Whitlam, E.G. 321 Wilberforce, S. 123 Williams, J. 553 Wollring, B. 659 Woods Hole Conference 43, 222, 241 Wyndham, H.S. 232

Yates, G.C.R. 89 Yates, S. 814 Yelland, N. 200

Ziman, J.M. 220

GENERAL INDEX

Seek, and you shall find.3

Architectural analogies 800, 819

Assessment and context 527 and creativity 50-51 and culture 643-644 and national curricula 429-430 and pedagogy 356, 477, 615, 691 and philosophy 686, 691 Basic Skills Tests 492 competency-based 414-418, 423 criterion-based 395 dynamic assessment movement 634 examiners’ comments 288, 289-290,

374-378, 405-406 facility, technical meaning 483 influence of penalties 713 influence of reward 86, 504, 506 objectives 634-635 of complexity 691 of probabilistic situations 473-474 of teaching 782-783 of young children 436 outcomes-based 422-423, 439, 812 political use 621, 633-634 regression of expertise 168, 416, 439,

448 see also Questions situation specific 118 skills of teachers 665-668 test construction 649-650

Australasia, definition 154 Australia. Education

1959–1994 789 background 209, 210-212, 317-318,

339-340, 350, 381-382, 413, 810 →→→→

1 Matthew 7: 7

Australia. Education →→→→ curriculum officers 212 isolation of States 296 New South Wales

influence in South Australia 244, 245 New Mathematics 39 probability 815 University of Illinois Committee on School Mathematics 232 Wyndham reforms 244, 298-299

Queensland 209, 370, 378 see also South Australia. Education Victoria 211-212, 380, 384, 729, 818 Western Australia 209, 231

Back to Basics movement, see Educational philosophies, back to basics

Biological examples alpine ecology 87-88 asynchronous hatching 197 behavioural studies 11 Burgess Shale 124 Common Swift 199 European Kestrel 199 grasshoppers 199 Herring Gull 198-199 Kittiwake 191 ornithology 5 superphosphate 85, 746 Willy Wagtail 199-200

Broad-Spectrum Ecological Model “hard core” of research programme

465, 805-807 and Colonial Echo Model 188, 196,

459, 462, 820 and equilibrium 338 →→→→

Index

Broad-Spectrum Ecological Model →→→→ and Muddling Through Model 188 and obuchennyi 759-761 and quantum changes 195 antecedents 55-56, 181-188, 804 application to mathematics education

771-774 application to medicine 783-785 definition 186-192, 195, 196, 758-763,

769-771 diversity within an Environment 364 Environment, Charismatic 305, 316,

705-706 definition 769-770

Environment, Intellectual definition 180, 188, 195 dissemination of ideas 94 limitations of current knowledge 728 value for effective change 248, 753-754

Environment, Pedagogical 316, 704-705 definition 305, 363

Environment, Physical definition 188, 195

Environment, Social definition 180, 188, 195

evaluation 771-785 factor-force distinction 190-191 force-environment interplay 806 graphical form 770 in depauperate environment 412 individuals and groups 203 similar models 683, 685 use for interpretation 305, 363-364,

771-774, 783-785 1910–1959 207 1959–1994 789-801 1965 Conference 259 1965–1970 281-284, 291-292 1970–1975 321-322 1975–1985 344, 352-353, 363, 379-380 1985–1990 386 1985–1994 406-410 →→→→

Broad-Spectrum Ecological Model →→→→ adoption of School Mathematics Project 274-275 assessment 517, 656-664 Back to Basics movement 324 Berndt’s experiment 240 Convergence 305, 306, 462-465 curriculum change 243, 319, 349 interstate comparisons 305-306 mass surveys 483 Mathematics Education 671-676 Melbourne Grammar School 736 national curricula 416-418, 429, 430, 436, 457-459, 463-465 New Mathematics 221, 224, 227-228, 260-261, 314-316 Optimisation 282 reports of classroom practice 710 school-based assessment 367 Scottish changes 280-281 support materials 442 Ultimate forces 348, 755-756 upper secondary syllabuses 335 Variation 369

use for prediction 810-818 zoom model 670-676, 808

Calculators 340 Chance

& Data 18 and causality 76 and contraceptives 81 and decision-making 87-88 and random breath testing 81 and rare events 81-82 animistic interpretations 85, 746 dual models 86 meaning 18, 74-82, 163, 479 religious interpretations 84-85 see also Probability

Clinical interviews 134-136, 469, 471, 604, 607, 666

Colonial Echo Model and Clements 302 and Convergence 185, 196 and homology 196-197 and Social ecology 188 criticisms 183, 270, 305, 462-463 definition 181-186

Index

Colonial Echo Model →→→→ see also Broad-Spectrum Ecological

Model support from Connell 263 support from McQualter 316 use for interpretation 260

adoption of School Mathematics Project 269-274 New Mathematics 237-238 South Australia 246

Combinatorics and algebra 92, 137-138, 287 and probability 134-139, 153, 287, 297,

833 in secondary syllabuses 334 part of stochastics 18-20, 93, 833

Complexity 110, 201, 418, 430, 465, 513, 685-686, 696, 766, 769, 778-779

Concept development 402 Connoisseurship 4, 11, 109-111, 123,

128, 385, 474, 695-696, 805 Constructivism 811

and assessment 423, 471, 491, 665 and linguistics 61 and misconceptions 47, 159 and national statements 419 and nature of mathematics 813-817 and pedagogy 160, 383, 432, 442, 739-

740 and probability 739-740 and social change 815 and society 90 and syllabuses 46-47, 438, 463 decline 811 general description 45-55 transmission 61

Curriculum affective 420, 422 and industry 226 change 766

Balkanisation 114, 350, 362 Biological Science Curriculum Study 279-280 buzz words 121 challenge to society 723, 746, 754 Imperative Present 458

Curriculum →→→→ Melbourne Grammar School 735-736 Moralistic Should 458 need for time 768-769 Scotland 280-281 unconformity 412

debased 240 etymology 107 general education 353, 475 holistic 419 nineteenth century 219, 679 perspectives 108, 111-119, 689

for mathematics 117-119 integration of 113 Research-Development-Dissemination model 319, 455 Technological 705

school based development 114 teachers’ perceptions 120-122 use for control 184

Darwinism 123, 156, 177, 180, 805

Data, meaning 18 Decimalisation of currency 251, 271 Developmental Theories, see stage-

related theories DIME Probability Kit, see Giles (1977) Dynamic Assessment Movement 634

Ecological principles 189-201 and business systems 187, 201-202 concepts 192-198 Convergence 196-197, 807 Energy 190, 194-195 Entropy 190 methodology 11, 13, 180, 198-201 Optimisation 186, 194-196, 806 Parsimony 185, 807 Proximate forces 193, 194, 807 Satisfaction 186 Ultimate forces 193-194, 807 Variation 197, 806

Educational philosophies 37-38, 385 and mathematics 44 back to basics 49, 122, 247, 322-325,

342, 349 →→→→

Index

Educational philosophies buzz words 121, 684 Constructivist, see Constructivism debased 38-40, 44, 49, 53, 108, 113,

114, 118-119 disempowering 44-45, 490-491 diversity 56 Humanising 44-45, 116, 382 integration 55-56, 724 Liberal-Humanist 8, 42, 205, 350, 383-

384, 475 Marxist 45, 180 neo-behaviourist 222 Post-modernist 47, 60, 109, 111, 1023 Technological 43, 382, 413-418, 472 Traditional 40-42, 43, 55 Utilitarian 42-43, 350, 383, 471, 475

Evolution 796 Exploratory Data Analysis 388-389,

402

Fuzzy logic 83

Gambler’s fallacy see Questions, Heuristics, negative

recency Gambling 159

and aboriginals 85 and history of probability 75 and probability 65, 82, 606 and probability teaching 361 and subjective probability 97

Gender differences 71, 147, 148, 306, 479, 480, 482, 484, 485, 487, 493, 519, 606, 716

Guilford's φ 474 Handbook Model 513, 740-742 Heuristics

animism 165 availability 149, 171-173, 175, 746 Baconian (inductive) reasoning 149,

552 based on outcomes 150 based on predictions 150, 645 definition 20 →→→→

Heuristics →→→→ difference from strategies 20, 565 equiprobability bias 161, 563 inconsistent use 149-151 maximisation of reward 511 negative recency 150, 505, 510, 532-

533, 540-541, 552-553, 601, 647 outcome approach 151-152, 174, 372,

505, 535, 741, 742, 748 Pascalian (deductive) reasoning 149 positive recency 150, 510, 552, 627 representativeness 149, 173-174, 644

Historical writing 179-180, 790, 804, 806, 820

Conspiracy theory, see Ecological principles: Parsimony

critical discourse 109 Foucauldianism 109 Triangulation 10

Independence 99, 167, 352, 354-355, 357, 727, 728, 731-734, 745, 747

and linked dice 737 classical 99-100, 736-737 coin has no memory 730, 737 distinguishable events 731 of events 99-100 of random generators 100, 730, 737 of three dice 68 pedagogy 99, 736-738 see also Probability, conditional sequential events 731-733 simultaneous events 731-733 two meanings 737-738 unrecognised 100

Inference 98, 438, 439, 727, 728, 730, 734, 745

Baconian reasoning 510 Bayesian 201, 329, 334, 404, 504, 569 hypothesis testing 751 see also heuristics statistical 833, 834

Index

International air fares 341-342 International findings

Brazil 148 Canada 148 Colombia 619 England

textbooks 298 France 282 Germanic 708 Hungary 105, 383 Iran 619 Japan 614

early stochastics teaching 219 Kuwait 619 Lithuania 619 Netherlands 614

curriculum development 44 New Zealand

New Mathematics 38-39, 272, 304-305

Scotland 260, 280-281 New Mathematics 229

South Africa 147, 148, 619 Spain 148, 451, 655 United States of America 283, 614

textbooks 298 Intuition 152-153, 157, 266, 504, 539,

544 Key Competencies 414-416 Language 57-72

and assessment 644, 647 classroom 59 domestication of technical terms 66,

433 mathematical 60-64 technical 18, 446, 479, 643 vernacular 18, 59, 446, 479

Learning Area, definition 442 Lines of Best Fit 401 Linguistics, see Language Loevinger’s Hij 474 Mathematics

and arithmetic 253 and Constructivism 46, 48, 50-52, 813-

817 and educational philosophies 44 and gender 109 and industry 226 →→→→

Mathematics →→→→ and intuition 152-153 and statistics 20, 92-93 applied 63, 91-92, 247, 340, 342, 357,

403, 411-412 nature of 37, 44-45, 51, 60, 91-93, 109,

152, 202, 249 problem solving 63-64 pure 91-92, 247

and New Mathematics 222, 224 and probability 267, 291, 299, 315, 328

pure and applied 92, 248 and probability 229, 249

secondary and tertiary 248, 728 status in schools 246, 304, 321

Mathematics education 7-8, 180, 340, 464, 679-682, 703, 821

and mathematicians 734 and pedagogy 752 and textbooks 729 beginnings 125 forces for change 36-37 need for theory 92, 204, 678, 681-682 need for vision 104-105 not seen as research 673, 754 numericisation 438, 675-676 precision of research 517 relevance to classroom 682

Medical analogies 32, 43, 93, 118, 450, 635, 636, 669, 682, 683-684, 702, 705, 721, 722, 764, 775-785, 819

Memes 201-203, 204, 237, 260, 805 Minitab© 347, 348, 402 Modules 362, 364-365, 371-373, 382 Muddling Through Model 181-186,

188 Musical analogies 42, 119, 696, 703

National Curriculum documents, definition 425

National testing programmes 483 New Mathematics 6, 8-9, 24, 118, 208,

209, 220-231 and applied mathematics 220 and Euclidean geometry 225, 236, 271

→→→→

Index

New Mathematics →→→→ and pedagogy 227, 277 and probability 221, 222-224 and psychology 220-222 and sets 225, 265 and stochastics 227 and structure 220 and transformation geometry 265-

266, 272 articulation with earlier forms 288 Australian investigations 222, 229,

233-236, 253, 260, 270-271 Clements’ views 181-182 Europe 230-231 justification 832-833 South Australia 238-246

introduction 313-316, 806 Sputnik 221-222, 224 United Kingdom 226-230 United States of America 221-224 weaknesses 52, 247, 322-324

NUD•IST, see Qualitative Solutions and Research (1992)

Numeracy 89, 349-350, 352, 354-355, 483

Obuchennyi 20-21, 759-761 Outcome approach, see Heuristics

Pedagogy and professional associations 701 and teachers 456, 692-693 Boomer’s views 382-383 change 385, 688-703 comparison with consulting 778-779 Cuisenaire materials 231, 237 didactical contract 680 discovery methods 52, 329 evaluation 687-688, 691, 703-705 four major perspectives 55-56 industrial model 736 instrumental and relational

approaches 752-753 journal keeping 750-753 musical 42 →→→→

Pedagogy →→→→ nature of knowledge 48, 416, 439 personal influence 686-687, 695 problem solving 354, 403 regression of expertise 283 rote learning 41-42 support facilities 781-782 transmission 61 Zone of Proximal Development 473

Piagetian Theory 132 accommodation 133, 502 and Artificial Intelligence 138 and combinatorics 134-139 and curriculum 681 and Cybernetics 138 and Fischbein’s intuition approach

139 and pedagogy 139, 283 and probability 132-139, 177 equilibration 133 Fischbein’s criticisms 502 Neo-Piagetian forms 140 role for today 139-140

Prevocational Mathematics 351

Probability 747 & Statistics 18 Adam’s task 350 and combinatorics 134-139, 219, 225,

334, 336, 470, 833 and complexity 157 and computers 470 and mathematics 89, 442-444, 487, 832 and numeracy 89 and proportion 143, 147, 440, 488,

507, 715 and statistics 166, 274, 287, 323-324,

350, 351, 352, 362, 727, 728, 730, 734, 812

and Studies of Society and Environment 444-447

applications 71-72, 83, 85, 89, 155, 349, 352, 726, 727-728, 831

applied 355-357 →→→→

Index

Probability →→→→ assessment, see Assessment,

Questions conditional 67, 166-167, 731

Falk phenomenon 157 see also Independence simultaneous events 732

culture 84-86, 155, 501 academic construct 90 conflicts with society 723, 746 differences between countries 619 language 64 male construct 90 playing cards 520, 644 western construct 90

different forms 67, 96-97, 357, 372, 436, 444, 462, 475, 509, 726, 727, 730, 745-746, 747

fuzzy logic 83 intuition 712-713 justification 345-346, 397, 801 meaning 18, 73-90, 94-98, 126, 643,

1023 tensions between approaches 97

measurement 65, 133, 502 non-concrete 65 non-deterministic 9 outcomes 506 paradoxes 709 questions, see Questions rare events 82 see also Chance subjective 80-82, 96, 464, 644, 710, 747 transfer of training 721 transmission 76-77 value for historical studies 8-9, 14

Probability. Curriculum and inference 222, 401-402 and pedagogy 353 and statistics 267-268 and technology 400 applied approach 392-393, 394, 400,

406 Australia 296-297 →→→→

Probability. Curriculum →→→→ Australian Capital Territory 299,

300 debased 336, 559 introduction into schools 477 junior secondary 250, 266-267 justification 249, 354-355, 363, 384-

385, 386, 831-832, 833, 834 Markov processes 367 national curricula 431-432, 447-449 New South Wales 297-299 primary 249, 254, 292-295 primary/secondary interface 412 Queensland 391 South Australia 397-400 tertiary 306-308 upper secondary 287-292 Victoria 300-302 Western Australia 302-303, 391

Probability. Language 64-72, 163, 420-421, 422-423, 436, 444, 486, 533

and assessment 290 certain 524-525, 747 chance 65, 477, 509 degrees of conviction 326, 525 fair 65, 94, 96, 159, 508, 536, 558-559,

713 for fractions 444, 521 impossible 747 mathematical register 61-67 odds 65, 68, 159, 523 possible 747 research 68-72 spelling 444 symbolic 98 technical terms 509 uncertain 747 vernacular 433

Index

Probability. Learning and age 147 and culture 148, 470 and epistemology 470 and intelligence 147 and locality 479 and socio-economic level 479 animistic 165 conjunction fallacy 721 development 133 effect of teaching 168, 172, 502, 524-

525, 526-527, 532, 534, 538, 546 intuitive 152-153 pre-requisites 392 predictor of overall success 289, 291 probability matching behaviour 153,

504, 712-713 social influences 159 success by weak students 375, 486,

577

Probability. Mathematics 98-103

“Law” of Small Numbers 149 and set theory 832, 833 axiomatic system 832 binomial theorem 708 deterministic approaches 99, 138, 714 elementary events 95-96, 503 events 95-96, 503 Law of Large Numbers 94, 133, 436 measure 96 outcomes 509 six basic ideas 745

Probability. Pedagogy 98-104, 309-310, 325-327, 332, 344, 384, 387-391, 721, 722, 729-734, 740, 756

1970s 707 absence of algorithms 291 →→→→

Probability. Pedagogy →→→→ and applied approaches 394-396 and Dienes 241 and mathematics 734 and misconceptions 709 and music 709 anecdotal reports 707-712 Bayesian approach 709 calculators 367 cartographic summary 742 complexity 157, 741, 744 computers 749 conditional probabilities 731 Constructivist 720-721, 739-740 debasement 409-410 dissemination 278, 306, 311-313, 453-

457, 465, 756-757 equiprobability bias 710, 747 examiners’ comments 376-378 four major aspects 744 Handbook Model 740-749 independence 731 inference 303 influence of examinations 452-453 Keeves’ proposals 255 lattices 726 mapping diagrams 730 modelling 389-390 need for background 441 nineteenth century 219-220 number line 161-162, 435, 747 practical 709, 714 primary schools 709 see also Pedagogy sources of support 711, 712, 713-718,

734 South Australia 276-279, 368-374 teachers’ knowledge 225, 303, 450,

452, 699 television 357-358 tertiary 699-701, 750-753 textbooks 66-67, 368-369, 373, 701-702 transfer of training 89, 721 →→→→

Index

Probability. Pedagogy →→→→ trees 166, 306, 334, 726, 731-733 use of counter-examples 76, 138, 160,

565, 710 use of intuition 266-267 use of journals 752 use of Profiles 747 Venn diagrams 377, 726, 731-733 Western Australia 329

Probability. Research and national curricula 449 and statistics research 130, 165-166 classroom experience 127 complexity 157 cross-cultural studies 167 dice 171-175, 741-742 dissemination 126, 127-128, 130-131,

174-176, 346, 453-457, 486, 668-669, 738-739, 765-766

eclectic 129, 551, 579 equiprobability bias 161, 503, 559,

563, 585 future directions 165-167 historical stages 656-664 influence on assessment 469-471, 656-

664 influence on curriculum 153 integration of findings 126, 165-167,

174-176, 490, 570-571, 579, 662-663, 738

isolation of researchers 663, 669 language development 157 linguistic divisions 130, 134, 156-157,

166, 175, 346, 436, 648, 657, 680 literature reviews 170-176 longitudinal studies 167-170 methods 10-11, 150, 551 pedagogical stream 657-660 place of experts 490-492, 519, 537 proportional reasoning 160-162 psychological tradition 129, 139, 174-

175, 610, 657-660 random generators 163-164 randomness 157, 162-163 →→→→

Probability. Research →→→→ refereeing procedures 648, 738 regression of expertise 491-492 relevance 764-765 replication 539 see also Research teaching experiments 486-487 variation 164, 166

Process Mathematics 49, 53, 139, 448 Professionalism 259, 277, 636-637,

667-669, 775-783 iatrogenesis 490-491 interactive definition 818-819

Proportional reasoning 160-162, 554-557

Questions 747-749 “Don’t Know” responses 482, 503,

535, 541, 593, 594, 641 “Insufficient information” responses

542, 641 about “the” probability 602-603, 643,

727, 749 about complements 480 about opposites 173 analysis

ACER 1 483-485, 518-519, 641, 643 APU 1 520, 643, 644 APU 2 521, 643, 644, 646 APU 3 522-523, 638, 641, 643 Fischbein 1 524-525, 563, 638, 645 Fischbein 2 526-527, 644 Fischbein 3 528-529 Fischbein 4 530-531, 637, 639 Fischbein 5 532-533 Fischbein 6 534-535, 538, 541 Fischbein 7 536-537 Fischbein 8 534, 538-539 Fischbein all 655-656 Green 1 161, 540-542, 547, 626, 627, 635, 644 Green 2 546-547, 629 Green 3 548-549, 560, 565, 627, 643 Green 4 172-173, 550-551, 579 Green 5 552-553, 570, 601 Green 6 554-557, 571, 627, 632, 643 Green 9 558-559 →→→→

Index

Questions →→→→ Green 17 560-561, 565, 627, 643 Green 18 525, 562-563, 638, 642 Green 19 560, 564-565, 627, 643 Green 23 566-567 Green 25 568-569, 638, 639 Green all 655-656 Kempster 2 572-573 Kempster 3 573, 574-575 Kempster 11 576-577, 643 Kempster 12 172, 578-579, 581 Kempster 18 580-581, 637, 639 Kempster 22 582-583, 643 Kempster 31 503, 584-585, 638, 645 Kerslake 1 172-173, 550, 586-587, 627, 638, 639, 643, 646 Konold 1 151, 553, 570, 588 Konold 2 151, 589, 631 NAEP 1 583, 590-591, 637, 638, 639, 641 NAEP 2 592-593, 600, 625, 641 NAEP 3 480, 594-595, 643 NAEP 6 596-597, 638 NAEP 21 598-599 NAEP 23 593, 600, 638 NAEP 26 601 NAEP 98 602-603, 638 NAEP all 646, 647 Peard 1 604 Peard 2 605 Peard 3 606-607 SOLO 1 488-489, 608-609, 635, 639, 641, 643 Teigen 1 173-174, 610-611 Teigen 2 612-613 Teigen all 646 TIMSS 1 477, 614-615, 616, 641, 643 TIMSS 2 477, 616-617, 618, 646 TIMSS 3 477, 618-619, 647 TIMSS 4 477, 620, 621, 638, 644 Tobin 1 583, 622-623, 625 Tobin 2 583, 624-625 Watson 1 141, 175, 551, 570, 626-627, 628 Watson 2 628-629, 641 Watson 3 141-146, 161, 571, 630-632, 647

and culture 481-482 and intelligence 487 →→→→

Questions →→→→ Bayesian inference 568-569, 639 channels 656 coins and dice 481 committee probabilities 290 comparison of random generators

161-162 comparison of spinners 564-565, 590-

591 comparison of urns 135, 142, 147, 534-

535, 536-537, 538-539, 554-557, 630-632, 713

consistency of responses 70, 546 criteria for construction 640-645 debasement of quality 648-649, 757 different forms 70-71, 151, 505-509,

748-749 distractors 477, 615, 617 fairness 604, 605, 606-607 final draw 612-613 firing at targets 287 forced responses 503 gambler’s fallacy 532-533, 588 How Old is the Captain? 63 human guessing 608-609 human randomisers 620-621 in national curriculum 434-442 independence of events 307 independence of random generators

526-527, 601 influence of age 536-537 interpretation 636 involving no random generator 584-

585 knowledge of random generator 504,

713 language 433-434, 486, 589, 649 linking probability and statistics 490 Logger problem 36 long term pay-offs 598-599 mathematical expectation 558-559 meaning of probability 582-583 multiple-choice 473, 480, 487, 523,

641-642 →→→→

Index

Questions →→→→ negative recency 552-553, 601 nineteenth century 679 no response 537 number required for test reliability

484 open-ended 480, 523 playing cards 520 Potato problem 35-36, 39, 44 prediction of outcome 505, 748-749 prediction of set of outcomes 505,

596-597, 645 probability scale 435, 584-585, 645 raindrop distribution 571 random generators

compound 289, 439-440 simple 424-425, 434-435, 477

randomness 714 reasons for answers 549, 622-623, 624-

625 regression of expertise 490 relation with number skills 483, 642 reliability and validity 482, 488 reporting 645-649 runs 530-531, 552-553, 714 see also Assessment, Random

generators selection of outcome 506, 747 sequences 589 spinners 486, 521, 548-549

asymmetric 564-565, 576-577 non-contiguous 560-561, 564-565

super-items 608 superstitions 526-527 tossing a coin 552-553, 582-583 tossing a die 141, 171-173, 437-438,

448, 462, 491, 518-519, 550-551, 578-579, 580-581, 586-587, 612, 626-627, 636, 747-748

tossing a disc 540-542 tossing a drawing pin 437-438, 566-

567 tossing three dice 448 tossing two dice 708, 715 trialing 542, 547 →→→→

Questions →→→→ urns 290, 307, 522-523, 524-525,

528-529, 530-531, 532-533, 534-535, 536-537, 538-539, 572-573, 574-575, 592-593, 594-595, 600, 602-603, 610-611, 612-613, 614-615, 622-623, 624-625, 628-629 slightly asymmetric 546-547

urns and dice 619 urns without replacement 562-563 using probabilities for calculations

616-617, 618-619 variation 70, 643, 645 with complex structure 488

Random generators 94-95, 163-164, 741-742

and operator 502, 513 asymmetric 168, 439, 645

slightly 500, 503 very 504

baseball bats 501 coins 79 colour, see surface features infra comparison 506, 508 computer micro-worlds 159-160 concurrent operation 68, 510-511 counting-out rhymes 500-501 deceptive 504 dice 94, 102, 708, 741-742

non-standard 645, 709 two dice 441

drawing pins 95, 255 electronic 645, 711, 714 for decision-making 84, 85-86 gender of children 96 human 506, 644

heptophilia 500 independence 68, 100, 440-441 infinite outcomes 498 multiple embodiments 742 paper clips 710 playing cards 501, 520 polystyrene cups 95, 501 raffles 506 real-life situations 500 Russian roulette 80-81 →→→→

Index

Random Generators →→→→ see also Questions sequences of outcomes 508 share market 506 size, see surface features infra spinners 96, 500, 644 static 513 successive trials 68 surface features 500, 708 symmetric 439, 742 tennis rackets 501 two-up board 501 urns 500, 645 weather 506

Randomness 95, 157, 162-163, 167, 448, 708, 714, 730, 751

Rasch analysis 429, 484, 632, 635

Research accessing knowledge 63 action 114 Adam’s Task 108-111, 177, 497, 769 and practice 809 auxiliary hypotheses 808 Behavioural studies 11-13 cross-disciplinary 32-33 current difficulties xxvii-xxviii dissemination 648, 658, 659, 684, 700,

738, 756-757, 779-782 Eve’s Task 108-111, 156, 769 findings provisional 48, 439 funding 661 future needs 763-764 Grounded theory 15 Hawthorne effect 720 influence of Internet 359 influence on classrooms 69, 682-686,

763-774 slogans 684-685

influence on textbooks 69 Lakatos’ criteria 803-804 lesson from Burgess Shale 124 linkage models 683-684, 685-686, 688,

698, 701-703, 806 meta-analysis 126 nature of evidence 109 neglect of theses 738 →→→→

Research →→→→ Normal Science 155-156, 764 Occam’s Razor, see Ecological

principles: Parsimony Omega Point 1023 personal stories 4, 491, 724-725 precision 517 publication of conference

proceedings 661 qualitative 4, 108, 662, 686, 724-725,

805 refereeing procedures 663-664 situated cognition 53, 471 teaching experiments 690-691, 742-

745, 749-750 Triangulation 10

Scalogram analysis 147 Scientific thinking 82-83 Significance, see Inference Social justice and academic rigour

44-45, 431 Social Mathematics 350-351 SOLO Taxonomy 140-146, 159, 169-

170, 623, 626, 629, 630-632 reliability and validity 144-145

South Australia. Education 1870–1970 183 1910–1945 205-207 1945-1959 208-216 1959–1964 4-5 1960s changes 284-286 1965–1970 314 1975–1985 365 1994–2001 810-818 administrators 212 background 208-209, 212-213, 215-

216, 381 curriculum

applied courses 356 citizenship 208 consultants 266, 319 curriculum officers 212 Euclidean geometry 367, 391, 399 hexagonal course 206 Mathematics 3 400, 406 primary 206, 211, 324, 327, 330, 362-364 →→→→

Index

South Australia. Education →→→→ removal of probability 397-400 secondary 206, 207, 211, 332-336, 364-368 statistics introduction 273-274 time reduction 365 university entrance 405-406 vegie maths 396

Freedom and Authority Memorandum 242, 318-319, 324

in-service training 310-311 non-government schools 215-216 public examinations 206, 215-216,

284-285 1970–1975 332-334 1975–1985 365-367 1985–1994 392-406 Mathematics 1S 289 Qualifying Certificate 208, 210 school-based assessment 366-367, 393 teachers’ influence 285-286 university entrance 393

School Mathematics Project 264-275, 277, 279

School Mathematics Study Group (USA) 239

science teaching 8, 206-207 Scottish influence 211 Snowball model 311 teachers 207, 212, 213-215, 275, 306,

308-309, 368-374, 382 technical high schools 211 uniformity 214-215 university influence 206, 211, 215,

284-286, 289, 290, 291 University of Illinois Committee on

School Mathematics 238, 239, 245 Woods Hole Conference 241

Stage-related Theories 131, 167-170 and curriculum developers 132 and developmental theories 143 and Profiles 747 Piagetian 133 qualitative 132-146 SOLO Taxonomy 143 transitional conceptions 168

Statistics 92-93 and Exploratory Data Analysis 403 and mathematics 20, 92, 93, 403, 404,

831 applications 5-7, 83, 211 confidence in 82 Eve’s task 350 for citizenship 208 inference 82-83, 403-404, 831 null hypothesis 402 pedagogy 403-404 see also stochastics service courses 750 tetrachoric coefficient 402 two-sided sign test 401-402

Stochastics and combinatorics 92, 93 justification for teaching 223, 343-344 links in curricula 489-490 meaning 18-20, 93 pre-eminence in school mathematics

812-813 teacher preparation 834

Strategies, definition 20

Textbooks author’s writing experiences 6-7, 726,

728, 729-734, 736, 738 construction 94, 728-729 influence on curriculum 743, 780 influence on pedagogy 281 local production 275-278, 281-282,

293-294, 300 power 278 tendency to clone 737, 816

Variation 164, 505, 533, 580-581, 662, 747

Vietnam War 320

Whalan report 323-325, 327-330, 344, 350, 351

Zone of Proximal Development 636

POSTLUDE

Afterword

Whereof what’s past is prologue; what to come, In yours and my discharge1

The opening Gorseth prayer asked for “God and all Goodness”. For Plato Good-ness was the seeking after reality.2 Teilhard saw Point Omega as a “logical con-clusion of the theory of complexity”.3 For Post-modernists, who allow no absol-ute reality and no universal purpose, there can be no conclusion. Yet

[w]hat I affirm is the intuition that where God's presence is no longer a tenable supposition and where his absence is no longer a felt, indeed overwhelming weight, certain dimensions of thought and creativity are no longer attainable.4

Koestler has written

[An] example of the hubris of modern science is the rigorous banishment of the word ‘purpose’ from its vocabulary. … From Galileo onward, ‘final causes’ (or ‘finality’ for short) were relegated into the realm of superstition, and mechanical causality reigned supreme.5

In this thesis I have tried to understand an idea I believe to be real enough, to un-ravel the complexity of probability, and to set this Knowledge into a world whose complexity I cannot even conceptualise. I have had only partial success. But any seeking after truth will never be complete. Point Omega will never be attained in this life. But I have travelled a path, seen much Goodness in this Existence along the way, and gained some creative insights into the countries where I have tra-velled. Perhaps too I may have glimpsed God.

I have come near to the end of my earthly journeyings, but this one has been completed, and of it I can contentedly say, “It is accomplished.” May it serve as a prologue for the journeys of others.

Τετ′ελεσται.6

1 Shakespeare Tempest II (1) ll. 261–262 2 Plato The Republic Book VIII, para 517 3 Teilhard de Chardin (1959/1969) p. 127 4 G. Steiner (1989, p. 229) 5 Koestler (1959, pp. 546 - 547) 6 It is accomplished. John 19:30. I am grateful to Mr Martin Ketley for explaining to me at St

Peter’s College the teleological meaning which is lost in the usual translation.

AN END AND A BEGINNING