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Buin, Uisai – base 10 system in a Non-Austronesian Language with Manus pattern and classifiers

In this language,

1 to 5 have distinct numeral words

7 is 3 before 10 with 10 being implied

8 is 2 before 10 with 10 being implied

9 indicates completion of the counting before 10 kamporo

70, 80 and 90 have a similar pattern before 100.

Background

The counting words for Buin, Uisai are:

1

nonumoi (noikei)

 

2

keitako

 

3

paigami

 

4

korigami

 

5

upugami

 

6

tugigami

 

7

paigami tuo

3 before

8

keitako tuo

2 before

9

kampuro

complete

10

kiburo(kipuro)

10 cycle

11

noikei lugo

1 on top of

15

upugami lugo

5 on top of

20

kikoko

2 tens

30

paimaku

3 tens

40

korimaku

4 tens

50

upumaku

5 tens

60

tugimaku

 

70

paimaku tuo

30 before

80

kikoko tuo

20 before

90

kampuro (lopore)

Complete before 100

100

pore

100

200

kiporigo

 

300

paiporegi

 

400

koriporegi

 

500

upuporegi

 

600

tugiporegi

 

700

paiporegi tuo

 

800

kiporigo tuo

 

900

kampuro

 

1000

kukurei noikei

 

 

The idea of completion is also seen with the decades, 90 and hundreds 900 both containing kamporo. 70 and 80 as well as 700 and 800 follow the pattern of before 10 like 7 to 8. This pattern is found in languages from Manus Island too.

 

The construction of the numerals 11 to 19 follow a consistent pattern. The numeral 11 is noikei lugo (or noikei rugo) where lugo means on top of, i.e 11 is one on top of, the ten being understood. The numeral 15 is five on top of. A similar pattern occurs for all the decades so 26 is 20 and 6 on top of.

 

There are distinct words for the numerals 1000 and 10,000, the former being 'kukurei' and the latter 'tarina' or 'taarina'. The word for 'thousand', 'kukurei', has the meaning 'domestic fowl' as it does as well in Siwai and Nasioi.

 

Grisward's (1910) Buin numerals, collected almost 100 years ago, are in most respects identical to those given. The construction of the numerals 11 to 19 is different to that shown in System A. The numeral 11 is 'kiburo nonumoi lugobumoi', i.e 'ten one-on top of' so that the 'ten' is   explicit rather than understood. Parkinson's data were collected before the turn of the century and, except for irregularities in the numerals 1 and 2, are identical to the recently collected data. Sources of data can be found on the GLEC website for Buin or in Lean (1992).

 

The language also has noun classifiers for men, months, trees and animals. The general structure of a counting-set for counting the units of a particular noun class (although there are exceptions to this) appears to be:

1   no-M1

2   ke-M2

3   bai-M3

4   kori-(or ko-)M3

5   ubu-M3

6   tugi-M3

7   bai-M3 tuo

8   ke-M2 tuo

9   kamburo

where M1,M2,M3 are (usually) three different classifier morphs which are used only with a particular noun class and which, presumably, give an indication of the class in question. In counting tens for a given class a different counting-set is used, i.e the same structure is used but a different set of classifier morphs apply.

 

Grisward (1910, pp.89-90) also gives information on the number-sets used in counting various noun classes.

 

Counting Men            

Counting Months

Counting Animals

Counting Trees

1           nonumoru

nonorobira

noikei

naukeo

2           keorakino

kebirako

keitako   

keutako

3           baireia   

baibira

baiem 

bairui

4           korineia  

korebira

koiem                

keirui

5           ubureia  

ububira

ubum 

uburui

6           tugineia 

tugibira

tuginoi

tugirui

7           baireia tuo          

baibira tuo

baiem tuo roi

bairui tuo

8           keorakino tuo            

kebirako tuo

deitako tuo roi

kentako tuo

9           kamburo  

kamburo

kamburo roi

kamburo

10         kiburo   

kimburo

lagaturoi

kimburo

                                     

Current words are expected to vary slightly from these historical records.

Lesson Plan One

This plan illustrates how the classifiers in the language can be used to teach major mathematical concepts.

Subject: Cultural Mathematics

Grade: Elementary Prep

Unit: Our Community

Theme: What people do

Lesson Topic:  How people name and count different groups

Objective: By the end of the lesson each student will be able to count in vernacular the number of people, trees and animals in their family and around their home. For extension, students will be able to say how many in their extended family.

Preparation: Students will have drawn their family in front of their house with the plants and trees in the background. Arrange to take children to a nearby family group and house.

Introduction and motivation

Use the counting words without classifiers to the number that the students are comfortable with, e.g. kiburo10 or  kikoko 20.

Begin by taking the students to a nearby house and count the people there, the trees and the animals using the counting words with classifier suffix.

Explanation and demonstration

Use a picture of a family in front of their house with animals and trees to show the children how to count and talk about different aspects of their picture.

Count the number of people in the picture in vernacular

Count the number of trees in the picture in vernacular

Count the number of animals in the picture in vernacular. If there are two kinds of animals count each group, decide on the total number.

Discuss the morphemes that are common to counting each group and the approximate morpheme used to classify each type of object – man, trees, animals.

Student practice and activities

Students tell their small group about their picture. Encourage them to count the different groups of objects. If they have several types of animals or people in their group, ask them to say how many in each group and how many all together.

Listen to how well the students can count in each classifier.

Evaluation

Before the students are given their activities to do in groups, they need to be able to

Count in the vernacular in order

Use the different classifiers and explain what are the suffixes being used for the different groups.

Point and count one to one for each group.

 

Demonstration

Write the vernacular and symbols for the number of people, trees and animals next to each in the demonstration picture.

 

Student practice and activity

Each student records what is in their picture

The small group checks what they have written.

 

Evaluation

A member from each group shares what is in their picture with the whole class.

The teacher asks the class what morpheme indicates what the group is by pointing to the picture.

 

Follow Up

In a lesson on the calendar, discuss the words used to describe months. This theme lesson would list environmental changes, agricultural activities, cultural, school and community activities, and English month names used for the same period.

 

 

Lesson Plan Two

The plan illustrates how the pattern of 7 being 3 before 10 etc can be used for English addition and subtraction strategies (friends of 10). It also discusses the value of having 10 beginning a new set with the links to place value in the Hindu-Arabic system and 10 as a composite unit.

 

Subject: Cultural Mathematics

Grade: Elementary 2

Unit: Our Community

Theme: Complete groups

Lesson Topic:  Make 10 and making groups of 10

Objective: By the end of the lesson each student will be able to count in vernacular the general number words for 1 to 1000.

Preparation: Use stones for counting.

Introduction and motivation

Drop stones into a tin as the students count in unison in vernacular and in English

Drop stones into the tin as students count around the group giving help as needed.

Drop 7 stones into the tin. Ask how many more stones to make 10.

Drop 8 stones into the tin. Ask how many more stones to make 10

Repeat with 9, 6, and 5 stones.

Take the tins of 10 stones. Ask students to count the stones in groups of 10.

Explanation and Demonstration

The teacher demonstrates the game by making 10 dots on the board in two rows of five and covers some up with a book. Various students are asked to say how many are hidden and how they did it. Several examples are demonstrated and discussed.

The class do some examples in English. For numbers between 7 and 10, the teacher discusses the vernacular language structure and the matching English words and friends of 10, e.g. 7 and 3 are 10.

Student practice and activity

Students work in pairs. One puts 10 stones in two rows and covers some with their exercise book and asks the other student how many are hidden. The partner gives the answer in vernacular and explains how he/she did it. The students check. The partner then gives the answer in English and gives the whole statement e.g. 8 and 2 is 10.

Evaluation

The teacher listens to the answers and explanations to see if students are counting on from the number they can see, using the combinations of 7 being 3 to make ten in vernacular and English etc.

Demonstration and Explanation

The line of 12 students stand out the front each with a tin of 10 stones. The class counts the number of stones in 10s.

The class discuss the links such as 40 being 4 tens and 70 being 3 tens before a hundred.

Students count in hundreds.

Student practice and activity

In pairs, each student draws a number of tins and passes the picture to their partner to write the symbols, vernacular and English for the total number of stones if 10 is in each tin. The students repeat several times.

Evaluation

The teacher asks students to explain the meaning of the word 10 in vernacular and in English. Students explain the place value in the symbols and the groups of 10 stones or tins of 10 stones compared to single stones from 1 to 10.

The teacher asks students to model numbers said in vernacular and English or shown in symbols like 14, 17, 35, 58, 79

Follow up lessons

  1. Groups of 4 students have sets of cards with diagrams of tins and stones, symbols for numbers, vernacular and English words. They have to sort into similar groups.
  2. Play the game, number targets (from Richard Skemp). Students play in groups of 4 to 6 students. The group needs 6 tins (with 10 stones each or pretend they have 10 stones each) and at least 10 single stones. Each student writes down a number between 40 and 70 but keeps it hidden. Each student takes a turn to put either one tin or one stone in the centre and says the number in vernacular and English. Students can also take a tin or stone away to try to make their personal number.