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Nomenclature Abbreviations Abbreviations * As a prefix, indicates a proto language word /?/ glottal stop 2′ compound for 3 = 2 + 1 or rarely 1 + 1 + 1 but numeral for 4 2″ distinct numeral for 3 but 4 is a compound, usually 2 + 2, rarely 5 - 1 or 2 + 1 + 1 AN Austronesian languages BC or BCE Before Christ, that is before the Current Era taken as before the period of Christ BP Before the present CE or AD In the current era, that is after the year of the Lord (Domino/Dominum) Christ CSQ, MQ Counting System Questionnaire; Measurement Questionnaire d. dialect IMP Indigenous Mathematics Project Manus type Lean used this to refer to counting systems that used subtraction from 10 such as 7=10-3, 8=10-2, 9=10-1, often with the meaning e.g. for 7 as 3 needed to com- plete the group MC Micronesian Motu type Lean used this to refer to counting systems that used pairs such as 6=2x3, 7=2x3+1, 8=2x4, 9=2x4+1 NAN Non-Austronesian (also called Papuan) languages NCQ, CQN Noun, classifier, quantifier; classifier, quantifier, noun NQC, QCN Noun, quantifier, classifier; quantifier, classifier, noun NTM New Tribes Mission, PNG PAN Proto Austronesian PN Polynesian PNG Papua New Guinea POC Proto Oceanic QC, CQ Order of quantifier-classifier; classifier-quantifier respectively SHWNG South Halmahera West New Guinea (AN Non-Oceanic language of the Central- Eastern Malayo-Polynesian, a subgroup of Proto-Malayo-Polynesian) after Tryon (2006) SIL Summer Institute of Linguistics SOV Order of words in a sentence: Subject Object Verb SVO Order of words in a sentence: Subject Verb Object TNG Trans New Guinea Phylum Nomenclature The Australian system of numbering is used. There is a space to mark the thousands so two thou- sand is written as 2 000; one million as 1 000 000. The exception is in reference to dates so the Census in 2000 is denoted without a space and likewise dates when books or articles were published. In general, italics is used for a non-English language word with the exception of proper nouns such as the name of a language which is denoted with a capital in plain font although many of them have a non-English origin and are usually the language word for a place or the language. The English translation of a morpheme or word is put in inverted commas so there is no confusion in reading the sentence. © Springer International Publishing Switzerland 2018 291 K. Owens et al., History of Number, History of Mathematics Education, DOI 10.1007/978-3-319-45483-2 292 Abbreviations The translation “man” may be translated “person” in many cases. Algebraic symbols are also put in italics e.g. 5+n. + usually denotes addition but in linguistic contexts may represent an added morpheme e.g., group + n may represent group × n or group with a classifier suffix. A prefix plus the number morpheme may be written as n+x. Appendix A Counting System Questionnaire Used By Lean Glen Lean Purpose of the Questionnaire The original aims of this study were, firstly, to elucidate the number and nature of the counting systems used in the traditional societies of Papua New Guinea (PNG) and, secondly, to investigate whether the accumulated data had any implications for understanding the history of number and for mathematics education. PAPUA NEW GUINEA UNIVERSITY OF TECHNOLOGY COUNTING SYSTEM RESEARCH PROJECT QUESTIONNAIRE SECTION 1 : LANGUAGE AND LOCATION 1. NAME OF YOUR VILLAGE : 2. CENSUS DIVISION : 3. SUB - PROVINCE : 4. PROVINCE : 5 a) NAME OF YOUR LANGUAGE : 5 b) ALTERNATIVE NAME (S) OF LANGUAGE : (IF ANY) SECTION 2 : TRANSLATION ENGLISH TRANSLATION (YOUR LANGUAGE) FIRST SECOND THIRD MAN HIS HAND MY HAND A HALF A THIRD AND SOME A FEW MANY © Springer International Publishing Switzerland 2018 293 K. Owens et al., History of Number, History of Mathematics Education, DOI 10.1007/978-3-319-45483-2 294 Appendix A SECTION 3 : TRANSLATION OF NUMBERS Please provide translations into your own language for each of the numerals given. If the trans- lated words have any further meaning (such as a part of the body) please provide that also. No TRANSLATION FURTHER MEANING 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 25 30 40 50 100 200 1000 2000 Appendix A 295 SECTION 4 : PHRASE TRANSLATION 1. ONE BIG PIG : 2. TWO BIG PIGS : 3. FIVE BIG PIGS : 4. THOSE TWO HOUSES : 5. THOSE THREE HOUSES : 6. THESE TWO MEN : 7. THESE FIVE MEN : 8. THESE TWO WOMEN : 9. THESE FIVE WOMEN : 10. THREE BANANAS : 11. FOUR BANANAS : 12. FIVE BANANAS : 13. TEN BANANAS : SECTION 5 : USE OF BODY PARTS FOR COUNTING In many parts of PNG, when people count they keep tally by marking the numbers on parts of the body, i.e. on fingers, toes, and so on. 1. If this type of tallying is not practised in this language, please tick : 2. If this is practised in this language, on the diagram below, please indicate how the tally system works, i.e. indicate the number which corresponds to each body part used in the tally. 296 Appendix A SECTION 6 : ALTERNATIVE WAYS OF COUNTING In some PNG languages there is more than one set of words used for counting, i.e. there is one set of counting words used to count stones, for example, and a different set of words used to count coconuts, or pigs, or yams, etc. Sometimes a different set of words is used to count collections of things such as bundles of taro or coconuts. 1. In your language is there only one way of counting? (please tick): YES NO If YES, ignore part 2. 2. If there is more than one way of counting, please give examples below. NAMES OF OBJECTS COUNTED 1. 2. 3. No. TRANSLATION TRANSLATION TRANSLATION 1 2 3 4 5 6 7 8 9 10 Number words used for counting You may use the space below for any further explanation of this : THANK YOU FOR COMPLETING THE QUESTIONNAIRE Appendix B Details of Counting Systems Discussed in Chapter 8 Glen Lean and Kay Owens Abstract Glen Lean collected over 1 200 counting systems from Papua New Guinea (PNG) and Oceania. His data were obtained from first contact records, later linguist data, and records such as gov- ernment reports as well as from thousands of Counting System Questionnaires (CSQ) given to PNG University of Technology students and lecturers, school teachers, linguists and others. These he col- lated and described in terms of their frame words (basic words from which other counting words are made), operative patterns (being the way in which the words are connected), and cycles (such as 2, 5, 20) or other kinds of systems such as body-tally systems. Selected languages referred to in the chapters, especially for Chapters 8, have been included in Appendix B while Appendix C refers to languages mainly referenced in Chapter 10. Reference maps are found in Appendix E. The languages are included in the order in which they are mentioned in Chapters 8. Similar types of systems are mentioned together. Keywords Details of counting system • Papua New Guinea and Oceania counting systems • Papuan, Austronesian, and Polynesian languages • non-base10 counting systems • cycles, frames and opera- tive patterns of counting systems Contents Introduction ������������������������������������������������������������������������������������������������������������������������������������� 298 Adzera ��������������������������������������������������������������������������������������������������������������������������������������������� 298 Grand Valley Dani ��������������������������������������������������������������������������������������������������������������������������� 300 Dobu ����������������������������������������������������������������������������������������������������������������������������������������������� 301 Hagen, Medlpa ������������������������������������������������������������������������������������������������������������������������������� 304 Mountain Arapesh ��������������������������������������������������������������������������������������������������������������������������� 308 Ponam ��������������������������������������������������������������������������������������������������������������������������������������������� 312 Mengen ������������������������������������������������������������������������������������������������������������������������������������������� 314 Arosi ����������������������������������������������������������������������������������������������������������������������������������������������� 316 Rennellese ��������������������������������������������������������������������������������������������������������������������������������������� 318 Pukapuka ����������������������������������������������������������������������������������������������������������������������������������������� 318 Tongareva ��������������������������������������������������������������������������������������������������������������������������������������� 319 Mota ����������������������������������������������������������������������������������������������������������������������������������������������� 320 Ere-Lele-Gele',-Kuruti ��������������������������������������������������������������������������������������������������������������������� 321 Kilivila ������������������������������������������������������������������������������������������������������������������������������������������� 327 Muyuw ������������������������������������������������������������������������������������������������������������������������������������������� 335 Budibud ������������������������������������������������������������������������������������������������������������������������������������������� 336 K. Owens (*) Charles Sturt
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