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Multilingual Elementary School Teaching in
|
Kay Owens Charles Sturt University, kowens@csu.edu.au |
Rex Matang University of Goroka, Matangr@uog.ac.pg |
Elementary
Schooling in
There are 800
different languages in
Recent reforms to education in
The village schools generally consist of three small classrooms with kunai grass thatch or sago palm roofs, split bamboo woven walls and floors (unless they are on the coast where sand may act as floor and place to write or draw). They are built by the villagers. There are generally no desks, a blackboard is at one end and each child has a blackboard slate, an exercise book and pencil. The main concrete aid for mathematics is a tin of small stones. In some schools they will also use sticks. The classrooms are crowded with up to 40 students in each grade. There is supposed to be a teacher for each grade. Students attend school from 8am to 12 noon.
The teachers study under another teacher at the school with short two to six week courses with distance education materials. Their pay is increased from nothing up to full salary over the first two years if things go to plan. There are moves to have the training at colleges in future. Despite the training difficulties, the teachers that I have met have good approaches to early childhood education. The curriculum is brief and community oriented. Teachers are busy with their own gardens and school gardens and marketing the produce. The teachers are local villagers as they need to speak the local language but this means the teacher still has to cope with all the village connections and responsibilities and interplays between groups.
Most lessons are oral. They may read a story that the teacher has written on the board, they may tell a story from a picture that the teacher has drawn. They talk about village life and culture. They are likely to count orally and do some simple additions and subtractions based on a picture. The pictures will frequently have garden pictures. They have counted stones.
Vernacular Counting Systems and Other Mathematics
Each language has its own counting system and mainly only the coastal Austronesian languages have cycles of 10 and 100. Among these coastal or island languages there is one group that have 6 as double 3 and 8 as double 4 with 7 and 9 as one more respectively. Another group has 7 as 3 before 10, 8 as 2 before 10 and 9 as 1 before 10.
Most other languages will have cycles of 2, with most of these also having cycles of 5 and 20. There are others that have cycles of 4, some with additional cycles of 8. Other systems are body-part tally systems in which the body parts from the small finger on the left hand tallies 1, and after the fingers tallies up the parts of the arm, across the head and down the other side. Depending on the language the complete cycle will be anywhere between 20 and 60 with many other variations. (For more details see Owens, 2001.)
By using the older people, teachers who did their own schooling in English and who generally speak Tok Pisin fluently as well as their Tok Ples, have revived their own language dialect’s counting system. These languages are very fluid and there are often changes in the counting system over the last 50 years.
Classroom Context
Gahuku-Asaro elementary schools around Goroka service villages where there are several families in which one parent’s first language is different to the other. While parents generally learn to understand the other parent’s language, it is often easier to communicate in Tok Pisin. Many students in the elementary schools understand Tok Pisin and for some it is their main language. They will have varying levels of the vernacular dialect. The teachers have been using a mixture of Tok Pisin and Tok Ples in the classrooms. In Elementary 3 they are beginning to use some English. We taught an Elementary 3 class before they were due to use English for literacy and numeracy. Some students had hearing problems and a couple had sight problems.
The following
table gives some of the counting words. The Gahuku-Asaro
language has 2 and 5 cycles. At Gavehumito, unlike
other villages, they have also developed higher numbers such as 10, 100 and
1000. In the past, it is likely that 15 was ligizani luga luga
ligizani luga. Originally, there
were words for 1, 2 and 5 with other numbers having related morphs or variant
words for these number frame words.
Table 1
Counting Words
|
English |
Tok Pisin |
Gahuku-Asaro Gavehumito |
|
one |
wanpela |
hamo |
|
two |
tupela |
losi |
|
three |
tripela |
losive makole |
|
four |
fopela |
losive losive |
|
five |
faivpela |
ligizani luga |
|
six |
sikispela |
ligizani luga hamo |
|
sevem |
sevenpela |
ligizani luga losi |
|
eight |
aitpela |
ligizani luga losive makole |
|
nine |
nainpela |
ligizani luga losive losive |
|
ten |
tenpela |
ligizani luga luga or asasi hamo |
|
eleven |
tenpela na wan |
asasigi hamoki |
|
twelve |
tenpela na tu |
asasigi losigi |
|
thirteen |
tenpela na tri |
asasigi losi hamo |
|
fourteen |
tenpela na fo |
asasigi losive losive |
|
fifteen |
tenpela na faiv |
asasigi ligizani luga |
|
sixteen |
tenpela na sikis |
asasigi ligizani luga hamo |
|
seventeen |
tenpela na seven |
asasigi ligizani luga losi |
|
eighteen |
tenpela na ait |
asasigi ligizani luga losive makole |
|
nineteen |
tenpela na nain |
asasigi ligizani luga losive losive |
|
twenty |
tupela ten |
asasi losi |
|
twenty one |
tupela ten na wan |
asasi losi hamo |
|
one hundred |
tenpela ten o hundred |
asasi ligizani luga luga (stick) |
|
two hundred |
tupela ten ten o tupela hundred |
go’ hamo (bilum) |
|
thousand |
tenpela tenpela ten o thousand |
mulisi (hip = heap) |
Note: The neighbouring school did not have a separate word for 10 based on a stick. Instead they continued to refer to two hands.
Lesson Trials
Arranging Counting Words in Order and Before and After Numbers
We wrote the vernacular words on paper in large print and asked a group of students (holding 1 to 5) to stand and order themselves. We then said the counting words, hid one or two and asked what they were, we then counted in Tok Pisin and English pointing to each Tok Ples word as we went. We continued with the next 5 numbers (6 to 10) and so on 11 to 15, 16 to 20, 21 to 15, 40, 43 in Tok Ples. By this time, the students were stand around three edges of the room. We gave out English words and numerals and students stood in front of the student with the corresponding Tok Ples word. We counted from different starting numbers in all three languages, hiding words and saying them.
I taught in Tok Pisin using the Tok Ples numbers. The teacher repeated what I said occasionally and taught in Tok Ples and Tok Pisin. Different students were more comfortable with one language or another.
In groups, the students took their sets of paper numbers and matched them. The sets had Tok Ples, Tok Pisin, English, dots in ten frame patterns and numerals. Again some students had greater fluency with the Tok Ples than others. For some, we gave them just the first 10 numbers. They were beginning readers so this task was a reading as well as numeracy lesson.
Hidden Stones
The students took ten stones and placed them in two rows of five. They took their exercise book and covered some and asked their partner how many were hidden. Some students counted the visible stones in Tok Ples and then counted up to two hands keeping track on their fingers but others counted on from the visible stones. Others just gave the number and some of these worked in Tok Pisin or English in preference to Tok Ples. Some just guessed or did not try. Overall the pairs enjoyed the game.
Skip Counting
The students did quite well in skip counting in twos and fives. However, only the teacher seemed to be able to easily skip count in threes.
Issues
Numbers of More Than One Syllable
Li and Anderson (2003) suggest that the length of time taken to count a series of numbers was considerably more in some languages like English than in most Asian languages. For this reason, they felt the longer time made the learning of the counting sequence harder. Each number especially above 2 has many syllables in many PNG languages. Is this making it hard for students to count in their language? Anecdotally, adults tell us that the students are counting in Tok Ples very quickly amazing them just as they amazed their grandparents when they came home from school and quickly counted in English.
Order of Quantity of Multiunit, Value Name of the Multiunit then Units
Miura (1993) pointed out the difference between Asian numerical language patterns and English. Chinese used quantity of multiunit, value name of multiunit followed by units. The tens structure is more explicit for numbers between 10 and 20 as well as for larger tens in Asian languages than in English. Asian students are more likely to use sticks or longs from the base 10 sets to represent numbers like 42 and to count in tens than to represent with ones and to count by ones as English-speaking students tend to do at the same age. This is similar in most PNG languages where the multiunit is given, followed by the number of these units followed by the units or unit combination. For this reason, multiunit structures should be more explicit in Tok Ples than in English. The concepts and sounds of the words are of course more familiar to students.
Number Combinations other than Building on Two and Five
The number patterns building on two and five were being used by the students to decide on numbers before and after a given number.
They intuitively used the number patterns for the counting words while counting and doing simple additions. Nevertheless, did this make it difficult to know combinations other than those that incorporated the numbers one, two and five. For example, students were able to give numbers that added to 8 using the number patterns giving us 5 and 2 and 1 but were less quick at giving us 4 and 4 in Tok Ples. Students familiar with English or Tok Pisin were more likely to reply and answer in these languages, translating back into Tok Ples. Macgregor and Moore (1991) acknowledge that students are likely to switch codes to assist them to solve problems in mathematics. However, this switch was not expected.
Students were quite good at counting in twos and fives. Twos were losi, losive losive, ligizani luga hamo, ligizani losive makole, asasi hamo, asasigi losive losive, asasigi ligizani luga hamo, and fives were ligizani luga, ligizani luga luga, asasigi ligizani luga, asasi losi. However, it seemed harder for students to skip count in threes as if the combinations of number patterns dominated their numeral usage. Losive makole, ligizani luga hamo, ligizani losive losive, asasigi losigi, asasigi ligizani luga. However, this might just have been a new experience for the class and a little practice would help. Even grouping stones in rows of threes and skip counting did little to help them catch on in the lesson.
Teacher Developed Curriculum
The Cultural Maths syllabus for Elementary
3 provides outcomes for learning. Teachers are encouraged to use vernacular
words, events, and representations to teach mathematics. In the second half
of the year, they begin the transition to English. By this stage students should
have used all four operations, basic fractions as well as space, attributes
of objects that are measured in informal measurement. All aspects should be
applicable in their culture. The details are left up to the teacher. Teachers
are shown how to select cultural themes and prepare related lessons using a
fairly standard lesson format. The day is generally divided up into literacy
and numeracy before the break with other curriculum areas after the break.
Roberts (2001) emphasises the importance of teacher background and cultural
change in
curriculum development for Maori students in Aotearoa,
Glides and Truncations
Thirteen is a variant on three and ten. Similarly we find in the Gahaku-Asaro dialect above that a number of variations are given on losi, agasi etc. These extensions help the lilt of the words so they flow more easily but also increase the syllables and make it more difficult for students to see the connection between losi and losive losive. Then there are the use of two words for the one number like hamo and makole. Other words come in as actions in the language. For example, ligizani luga means something like that completes one hand.
Further Research
We believe that the operative number patterns in the various languages should assist students to learn arithmetic strategies in English. For example, languages with only one and two for building up their number sequence may have various ways of saying seven such as two plus two plus two plus one (6 plus 1) or two plus two plus one plus two (5 plus 2). In areas in which cycles are 5 and 20, 90 is generally 4 twenties (man) plus ten (two hands). Access to multiunits is assisted by the close link to hands and man.
Acknowledgement: Sendy Hagi is Teacher in Charge at Gavehumito Elementary School and she teaches the 80 students in prep and 1. She lives in the village where the school is situated. She wrote out the counting system for us. It differed slightly but not in structure from the recorded language given by Lean (1991) up to 10. The next school up the valley used different words with less variation from Lean’s records up to 20. Schools closer to town were using more Tok Pisin. Lenke Alex generally teaches Elementary 3 at Gavehumito. We thank Sendy and Lenke for their involvement in this project.
References
Lean, G. (1991). Counting systems of
Li, Y. R., & Anderson, J. (2003). Language and learning in mathematics: A reflection on Chinese learners, Reflections, 28 (4), 28-32.
Macgregor, M., & Moore, R. (Eds) (1991). Teaching mathematics in the multicultural classroom. Melbourne: Institute of Education, University of Melbourne.
Miura, I.
(1993). Exploring Asian numerical cogition.
In G. Bell (Ed.), Asian perspectives on mathematics education
(pp. 36-41). Canberra:
Commonwealth of
Owens, K. (2001). The
work of Glendon Lean on the counting systems of
Robers, T. (2001). An Indigenous community doing mathematics curriculum development. Mathematics Education Research Journal, 13(1), 3-14.