Henry Kuadilu

How and Whom the questionnaires were administered to

The school visited during teaching practise period was the Rosary secondary school – Kondiu in the Simbu Province.
The school’s Librarian was briefed about the questionnaires who called for two grade 12 volunteers preferably a male and a female who were in the Library at the time to take the questionnaires. Two students volunteered to do them.

I interviewed them together at the table going through the questionnaire reading and explaining what was required to be done. I made it clear to them that:

i) They were not to discuss on what to write on, but fill it in individually from their own knowledge.
ii) If unable to think of anything to express then they had to leave it blank.
iii) The questionnaires were to be done at their own pace in their own free time and submit it to the collecting point.

As expected, filled in questionnaires were returned after 2 hours. Both interviewees (as I now decide to call them) were about the same age around 16 to 18 years of age. However, the male was from the Gumine District in the south of Simbu while the female was from the Kamtai District in the central part of Simbu. Both of their native languages are quite different with perhaps a very slight variation with some words or phrases in the usage. The culture – way of life is the same for both, that is, the typical traditional Simbu culture.

1.2 In writing up a summary of the findings from the two questionnaires that were administered to two student interviewees, the following leadings are used:
1. Background information
2. Counting system
3. Measurement
4. Patterns and Designs
5. Games and puzzles
6. Providing explanations
7. Traditional money

Again, as there were 2 interviewees I see it relevant in writing up the summary to make comparisons between the two responses given. As such, the summary is presented in a Tabular Form.

SUMMARY OF FINDINGS FROM QUESTIONNAIRE ADMINISTERED
HEADINGS & SUB-HEADINGS USED MALE INTERVIEWEE FEMALE INTERVIEWEE
1. Background Information
• First language (mother tongue)
• Name of language group
Sub-District & Province
• No. of languages spoken
Yui.
Yui
Kilau in Simbu
Could speak 3 languages
Gunangi
Sinasina
Sinasina in Simbu
Could speak 4 languages
2. Counting System Could count in mother tongue from 1 to 14. Then unable to count from 15 to 19. But could count 20. No more counting beyond 20. Was able to count in Mother tongue from 1 to 10. But could not count from 11 to 19. Then manage to count 20. No more counting beyond 20.
Is there equivalent words or phrases in native tongue for the following:
2.1 Fractions. Could express a word in native tongue ‘Dibama’. Has a word in native tongue called ‘Kore’.
2.2 Negative Numbers - -
2.3 Zero Has a word to express
Non-existence ‘Dikima’ Has a word to express non – existence called ‘Tadikima’.
2.4 Counting days & weeks. Has phrase or even a sentencve for counting using the appearance of the moon as the bases. E.g. the interval between 2 appearances would claim a lapse of a certain number of weeks. The same applies here where she also has similar or almost the same expression in her native tongue.
3. Measurement
Explaining how following measurement activities are measured in culture & describing instruments used.
3.1. Size of a garden.
(Eg. Area) Using sticks lining them to enclose the garden area.
3.2. Perimeter of a Garden Using rope to mark boundary around garden. Using sticks and lining them around garden.
3.3 Perimeter of a House Using rope to tie around the house. Using rope & typing around the house.
3.4 Length & Width. Using long sticks by placing them up and along forming length and width. -
3.5 Distance between two villages. Using paces of walking while counting Using a known distance as an approximation to measure required distance.
3.6 Keeping calendar. By observing the size and appearance of the moon. By observing and predicting the intervals between wet and dry seasons of the year in terms of months.
3.7 Time By observing the positions of the sun. By observing lengths of the sun’s shadows over oneself and objects.
4. Patterns & Designs
Traditional activities creating patterns and designs. Making bilums, weaving matt. He was able to illustrate patterns or designs of some bilums and matt activities.
He drew a pattern that resembles the diamond shape – geometrical. Making bilums, weaving blind.
She also did the same.

She drew a triangular pattern used in making bilum – also geometrical.
5. Games & Puzzles.
5.1 Counting He was able to describe a counting game but had no name for it. She described a named counting game called ‘cucumber’.
5.2 Measuring He described a jumping game for measuring distance. -
5.3 Time He expressed using the length of the sun’s shadow over oneself and objects. -
5.4 Chance - -
6. Providing explanation for events or phenomena. He used the boiling of kaukau under extreme heat as symbolic of explaining volcanic eruptions. She generally explained any natural calamity as a punishment from a divine living being.
7. Traditional money where it was used. He did not answer the question properly, gave examples of traditional money as: pigs teeth, shells. She answered the question well by stating where traditional money are used: In pig killing & peace keeping ceremonies.
How wealth is measured in traditional society. He stated that wealth was measured by the number of pigs, wives, garden plots one has. She stated that the more number of pigs a person had, the wealthier he became.

Conclusion

After comparing the findings between the two (male & female) interviewees on this questionnaire it reveals that:

1. Both had no expression for negative numbers.
2. In the area of Measurement the male interviewee dominated in expressing all that was required while the female did not indicate any expression for: Size of garden, length and width with measuring and time in the games and puzzles section.
3. However, both could not express anything on ‘chance’ also in the games and puzzles section.
4. Generally, both students satisfied the requirements of the questionnaire by expressing something in all areas.

The comparison of findings between the two interviewees has encouraged me to state that the male interviewee seems to dominate over the female in expressing knowledge of cultural mathematics in their respective cultures. That is, the male sufficiently displays more indigenous mathematical knowledge than the female.

Then, it poses a question here, Do males learn effectively and efficiently knowledge or practices in the same culture more than females? Or could there by any other reason for it? I see that this question needs research which I shall leave it for now. But it maybe useful for someone to pursue a research in it in the future and provide further knowledge.

1.3 This time the findings will be discussed using Bishop’s fundamental activities which are common to all cultures being: counting, measuring, classifying, designing, locating and playing.

1.3.1 Counting. Both the interviewee’s native counting systems produced almost the same pattern of counting with a base 10 and maybe it will go in multiples of 10 with units to be added if required.

1.3.2 Locating. In the course of doing the questionnaires they explored their spatial environment and tried to draw something like symbols, patterns and designs carrying geometrical meanings which represented the indigenous mathematical activities in their cultures that could well explain the roles of orientation, navigation, astronomy and geography.

1.3.3 Measuring. They expressed how measuring activities were carried out, named some instruments (objects) that were used. However, the female did not manage to complete all that were required, the male did. But both explained the usefulness (value) of traditional money as a unit for economic wealth well.

1.3.4 Designing. Each interviewee produced a geometrical shape. The male designed the diamond shape of the blind weaving activity while the female designed the triangular shape of the pattern used in bilum making. Both shapes are geometrical in meaning. They gave examples of traditional activities which created geometrical patterns and designs and illustrated the particular patterns or designs used in culture.
1.3.5 Playing. Both interviewees explained a counting game each where the female actually giving the name of the game as being “cucumber’ while the male explained about collecting flowers and counting them to see who collected the most but had no name for it. The different games devised and played had some kind of rules which the players had to abide by.
1.3.6 Explaining. Each managed to give an explanation of an event or phenomena where although the explanation did not explore the patterns of number, location, measure, etc which should depict mathematical relationship, gave only general explanations. The female used a phenomena (e.g. a natural calamity) as a punishment for disobedience to God. The male used the boiling of kaukau under extreme heat as symbolizing volcanic eruptions as mentioned in the first part of the summary.

Conclusion

Both interviewees in filling out the questionnaires have covered all of Bishop’s ‘Universal’ cultural activities of mathematics as described above. They could not express anything in any greater detail than what was required on the questionnaires, but they did sufficiently express something relevant to the activities as described by Bishop.

This Ethnomathematics project as I see it firmly confirms Bishop’s ideas of Universal Cultural activities of mathematics common to all cultures where PNG (Simbu) cultures are of no exception to practice those mathematical activities as described by Bishop.