APPENDICES.

Appendix 1 Trial Teacher Questionnaire - Section A format

No.	Questionnaire item	Scale	+ / -
1	Mathematics is learnt in schools only.	1	-
2	Humans discover the mathematical formulas, rules and facts that already exist.	2	-
3	Using the lecture type of method teach mathematics is just as effective as the problem solving method	3	-
4	Counting in your own mother tongue is not as important as counting in English.	4	-
5	Mathematics can also be found in traditional cultural activities	1	+
6	Mathematical knowledge is created by the human mind	2	+
7	School mathematics is useful in traditional societies.	3	+
8	Mathematics identified in traditional cultural activities should also be taught in schools.	4	+
9	The only mathematics students learn are those taught to them by teachers in schools.	1	-
10	School mathematics is made up of abstract concepts and ideas which are value free.	2	-
11	The most effective way to teach is to the method which follows this pattern : Explanation- example - exercise	3	-
12	Mathematics found in traditional cultural activities is not as important as the “real mathematics” that is learnt in schools.	4	-
13	Students can learn mathematics out of school when participating in ordinary every day activities.	1	+
14	Mathematics consists of a body of knowledge whose truths should be questioned.	2	+
15	Teachers should use problem solving methods which show how mathematics is used in variety of ways	3	+
16	Showing examples of mathematics in traditional culture will give me a sense of cultural identity.	4	+
17	Mathematical knowledge is found only in mathematics textbooks	1	-
18	Mathematics is about learning arithmetic, algebra and geometry.	2	-
19	In schools, teachers should teach only the mathematics that is found mathematics textbooks.	3	-
20	Mathematics identified in traditional culture is too simple.	4	-
21	Mathematical knowledge can be gained by taking part in traditional cultural activities such as fishing, building traditional houses etc.	1	+
22	Humans are constantly adding to the mathematical knowledge by inventing more mathematical theories and ideas	2	+
23	When teaching mathematics teachers should take into account students prior knowledge learnt out of school.	3	+
24	Mathematical concepts found in traditional culture will be lost if they are not taught in schools	4	+
25	Mathematical knowledge is transmitted from the textbooks to the learner by the teacher.	1	-
26	Rules are the basic building blocks of all mathematical knowledge.	2	-
27	In the problem solving method of teaching mathematics, the students don’t learn very much.	3	-
28	Students come to school to learn “school mathematics”, not cultural mathematics.	4	-
29	Some of the students prior knowledge is learnt out of school while participating in traditional cultural activities.	1	+
30	School mathematics should teach students about values in life.	2	+
31	Some mathematics found in cultural activities should be included in the secondary mathematics curriculum.	3	+
32	It is the teachers mathematical knowledge that gets transferred to the students	4	+
33	Humans are constantly adding to the mathematical knowledge by discovering more mathematical theories and ideas.	1	-
34	School mathematics has no real use in a traditional society.	2	-
35	To acquire mathematical knowledge the learner organises the concepts in his own mind	3	-
36	Mathematical practices such as counting, measuring, drawing are also found in traditional cultural activities.	1	+
37	When teaching mathematics teachers should show examples of mathematics from traditional culture	2	+
38	All of the students’ mathematical knowledge is learnt in schools only.	3	+
39	Mathematical knowledge consists of facts, theories and formulae which are unquestionably true.	1	-
40	Any mathematical concept can be understood by the student if properly explained by the teacher.	2	-
41	Students can learn mathematics out of school when participating in ordinary every day activities.	3	-
42	School mathematics contains ideas that can also be found in traditional cultural activities.	1	+
43	Mathematics is about learning how to count, measure or make patterns in your own culture.	2	+
44	It is the mathematical knowledge from the textbooks that gets transferred to the students	3	+
45	Mathematics is culture free	1	-
46	Traditional mathematics found in ones own culture should not be taught in schools.	2	-
47	Some mathematical knowledge can be taught to the learner by the village elders.	3	-
48	Mathematics should show the applications of maths in real life	1	+
49	School mathematics is useful in traditional societies.	2	+
50	Mathematics is learnt from teachers only.	3	+
51	Mathematics found in traditional culture is not real mathematics	1	-
52	Mathematics is about knowing when to use rules and formulas to find answers to problems.	2	-
53	Mathematics is not culture free	3	-
54	School mathematics teaches students about how to deal with problems they face in real life.	1	+
55	Mathematics consists of statements which are unquestionably true.	2	+

Appendix 2 Teacher Questionnaire

[CF1] Research project : The cultural dimension of the mathematics curriculum in Papua New Guinea : Teacher beliefs and teacher practices.

MONASH UNIVERSITY

Faculty of Education

TEACHER QUESTIONNAIRE.

Instructions.

There are three sections to this questionnaire. Section A contains statements which describe what your beliefs are about mathematics. Section B contains a list of activities and you are asked to state how much mathematics is required to perform the activity. Section C asks you for some personal information.

Section A.

Read the statements carefully and respond to each one of them. Your answers to the statements should be given by circling the appropriate symbol next to each statement. Draw a circle around :

SA if you Strongly Agree with the statement

A if you Agree with the statement.

D if you Disagree with the statement.

SD if you Strongly Disagree with the statement.

NS if you are Not Sure and cannot decide whether you agree or disagree with the statement.

If you change your mind about an answer, just cross it out and circle another one. Please respond to all the statements. There are no right or wrong answers. Your answers will not be shown to anyone.

1	Mathematics can also be found in traditional cultural activities	SA	A	D	SD	NS
2	Mathematics consists of a body of knowledge whose truths should be questioned	SA	A	D	SD	NS
3	School mathematics is useful in traditional societies	SA	A	D	SD	NS
4	Mathematics identified in traditional cultural activities should also be taught in schools	SA	A	D	SD	NS
5	The only mathematics students learn are those taught to them by teachers in schools	SA	A	D	SD	NS
6	School mathematics is made up of abstract concepts and ideas which are value free	SA	A	D	SD	NS
7	Traditional mathematics found in ones own culture should not be taught in schools	SA	A	D	SD	NS
8	Mathematics found in traditional cultural activities is not as important as the “real mathematics” that is learnt in schools	SA	A	D	SD	NS
9	Students can learn mathematics out of school while participating in ordinary everyday activities	SA	A	D	SD	NS
10	Traditional practices such as counting , measuring, drawing are also mathematical	SA	A	D	SD	NS
11	Teachers should show how mathematics is used in cultural contexts	SA	A	D	SD	NS
12	Showing examples of mathematics in traditional culture will give the students a sense of cultural identity	SA	A	D	SD	NS
13	Mathematical knowledge is found only in mathematics textbooks	SA	A	D	SD	NS
14	Mathematics is about learning arithmetic, algebra and geometry. etc	SA	A	D	SD	NS
15	In schools, teachers should teach only the mathematics that is prescribed in the syllabus and textbooks	SA	A	D	SD	NS
16	Mathematics identified in traditional culture is too simple (at the arithmetic level)	SA	A	D	SD	NS
17	Mathematical knowledge can be gained by taking part in traditional cultural activities such as fishing, building traditional houses etc.	SA	A	D	SD	NS
18	Mathematics is about showing the applications of maths in real life	SA	A	D	SD	NS
19	When teaching mathematics teachers should take into account students prior knowledge learnt out of school	SA	A	D	SD	NS
20	Mathematical concepts found in traditional culture will be lost if they are not taught in schools	SA	A	D	SD	NS
21	Mathematics is learnt in schools only	SA	A	D	SD	NS
22	Rules are the basic building blocks of all mathematical knowledge	SA	A	D	SD	NS
23	Mathematics is about knowing when to use rules and formulaes to find answers to problem	SA	A	D	SD	NS
24	Students come to school to learn “school mathematics”, not cultural mathematics	SA	A	D	SD	NS
25	Some of the students’ prior knowledge is learnt out of school while participating in traditional cultural activities	SA	A	D	SD	NS
26	School mathematics should teach students about values in life.	SA	A	D	SD	NS
27	Some mathematics identified in cultural activities should be included in the secondary mathematics curriculum.	SA	A	D	SD	NS
28	Counting in your own mother tongue is not as important as counting in English	SA	A	D	SD	NS
29	All of the students prior knowledge is learnt in schools only	SA	A	D	SD	NS
30	Mathematical knowledge consists of facts, theories and formulae which are unquestionably true	SA	A	D	SD	NS
31	Any mathematical concept can be understood if properly explained by the teacher	SA	A	D	SD	NS
32	Mathematics is culture free	SA	A	D	SD	NS
33	Students can learn out of school when participating in ordinary every day activities	SA	A	D	SD	NS
34	School mathematics contains concepts and ideas that can also be found in traditional cultural activities	SA	A	D	SD	NS
35	Mathematics is about learning how to count, measure or make patterns in your own culture	SA	A	D	SD	NS
36	Mathematics identified in traditional cultural activities is useful to a modern PNG society	SA	A	D	SD	NS

Section B.

Instructions for Questions 37 - 50.

The following is a list of activities. For each activity put a circle around :

If you change your mind about an answer cross it out and circle another number.

37 - pilot flying an aeroplane	1	2	3
38 - carpenter building a house	1	2	3
39 - estimating the height of a tree	1	2	3
40- measuring the height of a student	1	2	3
41 - making patterns on bamboo walls	1	2	3
42 - villagers building a traditional house	1	2	3
43 - children playing a traditional game	1	2	3
44 - woman weaving a mat	1	2	3
45 - building a canoe	1	2	3
46 - painting a haus tambaran	1	2	3
47 - selling (betelnut) buai	1	2	3
48 - the warrior counting his arrows using own counting system	1	2	3
49 - villager using the stars to navigate by canoe from one island to another	1	2	3
50 - the teacher counting the number of students in the classroom.	1	2	3

SECTION C - PERSONAL INFORMATION.

Please fill in the following details about yourself. All information you give will be kept strictly confidential.

Name_____________________________ Male ¨ Female ¨

School_____________________________ Province___________________

Number of years of teaching _____________ Education officer level _________________

Number of years of teaching mathematics ______________________

To what grades are you teaching mathematics this year ? ____________________

Specialist subject areas _______________________________

Qualifications (list all - tick):
¨Dip.of sec.teaching; Institution obtained____________Year______
¨PGDE Institution obtained_____________Year________
¨Degree _____________ Institution obtained__________Year________
(name of Degree )
Other ______________ Institution obtained___________Year________

Thank you for your help in filling in this questionnaire.

Note : Please return this questionnaire to the T.I.C - Mathematics who will return it by using the self addressed envelope.

Appendix 3 Student questionnaire

[CF2] Research project : The cultural dimension of the mathematics curriculum in Papua New Guinea : Teacher beliefs and teacher practices.

MONASH UNIVERSITY

Faculty of Education

STUDENT QUESTIONNAIRE.

Instructions.

Section A.

Read the statements carefully and respond to each one of them. Your answers to the statements should be given by circling the appropriate symbol next to each statement. Draw a circle around :

SA if you Strongly Agree with the statement

A if you Agree with the statement.

D if you Disagree with the statement.

SD if you Strongly Disagree with the statement.

NS if you are Not Sure and cannot decide whether you agree or disagree with the statement.

If you change your mind about an answer, just cross it out and circle another one. Please respond to all the statements. There are no right or wrong answers. Your answers will not be shown to anyone.

1	Mathematics can also be found in traditional cultural activities.	SA	A	D	SD	NS
2	Some mathematical knowledge can be taught to the learner by the village elders.	SA	A	D	SD	NS
3	School mathematics is useful in traditional societies.	SA	A	D	SD	NS
4	Mathematics identified in traditional cultural activities should also be taught in schools.	SA	A	D	SD	NS
5	The only mathematics students learn are those taught to them by teachers in schools.	SA	A	D	SD	NS
6	Mathematics identified in traditional cultural activities is useful to a modern PNG society.	SA	A	D	SD	NS
7	Traditional mathematics found in ones own culture should not be taught in schools.	SA	A	D	SD	NS
8	Mathematics found in traditional cultural activities is not as important as the “real mathematics” that is learnt in schools.	SA	A	D	SD	NS
9	Students can learn mathematics out of school while participating in ordinary everyday activities.	SA	A	D	SD	NS
10	Traditional practices such as counting , measuring, drawing are also mathematical.	SA	A	D	SD	NS
11	When teaching mathematics teachers should show examples of mathematics from traditional culture.	SA	A	D	SD	NS
12	Showing examples of mathematics in traditional culture will give the students a sense of cultural identity.	SA	A	D	SD	NS
13	Mathematical knowledge is found only in mathematics textbooks.	SA	A	D	SD	NS
14	School mathematics contains concepts and ideas that can also be found in traditional cultural activities.	SA	A	D	SD	NS
15	In schools, teachers should teach only the mathematics that is prescribed in the syllabus and textbooks.	SA	A	D	SD	NS
16	Mathematics identified in traditional culture is too simple.	SA	A	D	SD	NS
17	Mathematical knowledge can be gained by taking part in traditional cultural activities such as fishing, building traditional houses etc.	SA	A	D	SD	NS
18	Mathematics is about showing how maths is used in real life.	SA	A	D	SD	NS
19	When teaching mathematics teachers should take into account students prior knowledge learnt out of school.	SA	A	D	SD	NS
20	Mathematical concepts found in traditional culture will be lost if they are not taught in schools.	SA	A	D	SD	NS
21	Mathematics is learnt in schools only.	SA	A	D	SD	NS
22	Rules and formulas form the basis of all mathematical knowledge.	SA	A	D	SD	NS
23	Mathematics is about knowing when to use rules and formulaes to find answers to problem.	SA	A	D	SD	NS
24	Students come to school to learn “school mathematics”, not cultural mathematics.	SA	A	D	SD	NS
25	Mathematics is learnt from teachers only.	SA	A	D	SD	NS
26	School mathematics should teach students about values in life.	SA	A	D	SD	NS
27	Some mathematics identified in cultural activities should be included in the secondary mathematics curriculum.	SA	A	D	SD	NS
28	Counting in your own mother tongue is not as important as counting in English.	SA	A	D	SD	NS
29	All of the students mathematical knowledge is learnt in schools only.	SA	A	D	SD	NS
30	Mathematics consists of facts, rules and formulas which are unquestionably true.	SA	A	D	SD	NS

Section B.

Instructions for Questions 31 - 44.

The following is a list of activities. For each activity put a circle around :

1 if you decide the person performing the task requires no mathematics at all.

2 if you decide the person performing that task requires a small amount of mathematics.

3 if you decide the person performing the task requires a lot of mathematics

If you change your mind about an answer cross it out and circle another number.

31 - pilot flying an aeroplane	1	2	3
32 - carpenter building a house	1	2	3
33 - estimating the height of a tree	1	2	3
34- measuring the height of a student	1	2	3
35 - making patterns on bamboo walls	1	2	3
36 - villagers building a traditional house	1	2	3
37 - children playing a traditional game	1	2	3
38 - woman weaving a mat	1	2	3
39 - building a canoe	1	2	3
40 - painting a haus tambaran	1	2	3
41 - selling (betelnut) buai	1	2	3
42 - the warrior counting his arrows using own counting system	1	2	3
43 - villager using the stars to navigate by canoe from one island to another	1	2	3
44 - the teacher counting the number of students in the classroom.	1	2	3

SECTION C - PERSONAL INFORMATION.

Please fill in the following details about yourself. All information you give will be kept strictly confidential.

Name_____________________________ Male ¨ Female ¨

School__________________ Grade __________ Age ________

Province _____________

Home Province _________________

Name of your mathematics teacher this year ______________________

Thank you for your help in filling in this questionnaire.

Appendix 4 Interview Schedule.

[CF3] Research project : The cultural dimension of the mathematics curriculum in Papua New Guinea : Teacher beliefs and teacher practices.

TEACHER INTERVIEW SCHEDULE.

Name____________________________ School _________________________

Instructions.

I will ask you some questions; you answer as best as you can. There are no right or wrong answers . What you think is important. I will explain a question if you don’t know what it means. If you cannot answer a question just say I am not sure.

1 The philosophy of eduction and the educational policies emphasise a “community oriented and a culturally appropriate” education.

(1a) Do you think it is possible to have a culturally appropriate mathematics curriculum ? (maths curriculum with examples from maths in traditional curriculum ). Yes or No.

If yes; how can this be done ? ...............................

At what level (primary / secondary). ...........................

If no; why not ? ..................................

(1b) Do you think that the current secondary mathematics curriculum falls into the category of “culturally appropriate curriculum”? .................

2 Should teachers use examples of everyday applications of mathematics which are not included in the textbooks (syllabus or curriculum) ? Yes or No.

If no, why not ? ..............

3. The mathematics that you teach in schools, do you think one can find examples of mathematics in traditional activities or artefacts? Yes or No.

If yes, give examples..................

If no, why not ?......................

4 Should out-of -school mathematics (maths in traditional culture ) be incorporated into the school curriculum ? Yes or No.

If no, why not ? ..............

What are some factors which may hinder this ? .................

5 Even if a teacher believes there is maths in culture, what do you see as possible factors that may hinder a teacher from using examples (of maths found in culture) in the classroom. .............

6 When teaching, Do you think it is important or is it not too important for students to see that there is maths in culture? Why ? ..........

7 Have you heard or read about the term “ethnomathematics” ? Yes or No.

If yes , can you tell me what it means ? ............

8 Section B of questionnaire - for the activities, ask why the respondent indicated “no, some, a lot” of mathematics.

9 For the following statements answer “agree” or “disagree” (if you need to qualify an answer, do so).

(i) Mathematics can be identified in some cultural activities.

(ii) The mathematics identified in some cultural activities is too simple, it is only at the arithmetic level.

(iii) This mathematics cannot be taught at the secondary level.

Appendix 5 Observation Schedule

[CC4]

Observation Schedule.

Teacher Observed ____________________ School _______________________

Grade _____________________ Date ___________________

Topic ___________________________

Unstructured observation but the following areas will be looked at to determine if there are any similarities (or differences) in the practice of those with differing views.

Comments.

1. Use of text books ______________________________________________________________________________

2. Content - Use of examples. ______________________________________________________________________________

3. How mathematics is portrayed. ______________________________________________________________________________

4. Are answers or methods of solution negotiable? Does the teachers approach suggest they are ? Are other methods possible ? ______________________________________________________________________________

5. Methodologies employed, mode of teaching, styles of teaching, authoritative etc. ______________________________________________________________________________

6. Style of classroom management. ______________________________________________________________________________

7. Resource Use - What conceptions of maths do they portray ? ______________________________________________________________________________

8. Teacher response to mistakes

______________________________________________________________________________

9. Classroom organisation. ______________________________________________________________________________

10. Other comments. ______________________________________________________________________________

11. Overall impression of lesson. ______________________________________________________________________________

12. After thoughts. ______________________________________________________________________________

Appendix 6 Item reliability analysis

Appendix 7 Factor analysis

Appendix 8 Teacher responses to questionnaire items

Teacher responses to questionnaire items - section A.

		SA	A	NS	D	SD
	Statement	%	%	%	%	%
ITM1	Mathematics can also be found in traditional cultural activities	35	65	0	0	0
ITM2	Mathematics consists of a body of knowledge whose truths should be questioned	24	44	13	10	9
ITM3	School mathematics is useful in traditional societies	33	48	5	11	3
ITM4	Mathematics identified in traditional cultural activities should also be taught in schools	39	43	4	12	2
ITM5	The only mathematics students learn are those taught to them by teachers in schools	13	13	1	49	24
ITM6	School mathematics is made up of abstract concepts and ideas which are value free	8	37	13	31	11
ITM7	Traditional mathematics found in ones own culture should not be taught in schools	5	15	4	45	31
ITM8	Mathematics found in traditional cultural activities is not as important as the “real mathematics” that is learnt in schools	8	11	2	37	42
ITM9	Students can learn mathematics out of school while participating in ordinary everyday activities	51	40	1	4	4
ITM10	Traditional practices such as counting , measuring, drawing are also mathematical	67	33	0	0	0
ITM11	Teachers should show how mathematics is used in cultural contexts	48	47	1	4	0
ITM12	Showing examples of mathematics in traditional culture will give students a sense of cultural identity	45	46	6	2	1
ITM13	Mathematical knowledge is found only in mathematics textbooks	4	3	1	39	53
ITM14	Mathematics is about learning arithmetic, algebra and geometry.	8	35	4	36	17
ITM15	In schools, teachers should teach only the mathematics that is prescribed in the syllabus and textbooks	7	9	1	41	42
ITM16	Mathematics identified in traditional culture is too simple (at the arithmetic level)	14	44	10	31	1
ITM17	Mathematical knowledge can be gained by taking part in traditional cultural activities such as fishing, building traditional houses etc.	19	72	1	5	3
ITM18	Mathematics is about showing the applications of maths in real life	43	50	2	5	0
ITM19	When teaching mathematics teachers should take into account students prior knowledge learnt out of school	39	50	1	9	1
ITM20	Mathematical concepts found in traditional culture will be lost if they are not taught in schools	33	36	4	21	6
ITM21	Mathematics is learnt in schools only	0	4	2	44	50
ITM22	Rules are the basic building blocks of all mathematical knowledge	33	42	7	15	3
ITM23	Mathematics is about knowing when to use rules and formulas to find answers to problem	26	45	3	22	4
ITM24	Students come to school to learn “school mathematics”, not cultural mathematics	11	16	3	49	21
ITM25	Some of the students’ prior knowledge is learnt out of school while participating in traditional cultural activities	20	72	3	4	1
ITM26	School mathematics should teach students about values in life.	31	54	10	4	0
ITM27	Some mathematics identified in cultural activities should be included in the secondary mathematics curriculum.	36	46	7	9	2
ITM28	Learning how to count in your own mother tongue is as important as counting in English	54	37	3	4	2
ITM29	All of the students prior knowledge is learnt in schools only	1	9	1	52	37
ITM30	Mathematical knowledge consists of facts, theories and formulae which are unquestionably true	17	42	10	28	3
ITM31	Any mathematical concept can be understood if properly explained by the teacher	45	41	1	11	2
ITM32	Mathematics is culture free	15	24	25	29	7
ITM34	School mathematics contains concepts and ideas that can also be found in traditional cultural activities	22	65	5	8	0
ITM35	Mathematics is about learning how to count, measure or make patterns in your own culture	14	63	4	16	3
ITM36	Mathematics identified in traditional cultural activities is useful to a modern PNG society	13	54	11	17	5

Teacher responses to section B of the questionnaire.

For the following activities, the teachers were required to put a circle around :

1 if you decide the person performing the task requires no mathematics at all.

2 if you decide the person performing that task requires a small amount of mathematics.

3 if you decide the person performing the task requires a lot of mathematics

Teacher responses to section B of the questionnaire.

	1 ( %)	2 (%)	3 (%)
37 - pilot flying an aeroplane	1	2	97
38 - carpenter building a house	1	29	70
39 - estimating the height of a tree	3	70	27
40 - measuring the height of a student	4	81	15
41 - making patterns on bamboo walls	34	56	10
42 - villagers building a traditional house	17	64	19
43 - children playing a traditional game	42	58	0
44 - woman weaving a mat	27	64	9
45 - building a canoe	16	70	14
46 - painting a haus tambaran	25	60	15
47 - selling (betelnut) buai	8	82	10
48 - the warrior counting his arrows using own counting system	13	74	13
49 - villager using the stars to navigate by canoe from one island to another	17	55	28
50 - the teacher counting the number of students in the classroom.	10	78	12

See mean, mode and standard deviation for teacher responses over page.

Appendix 9 Student teacher responses to questionnaire

Student Teacher responses to section A of the questionnaire

		SA	A	NS	D	SD
	Statement	%	%	%	%	%
ITM1	Mathematics can also be found in traditional cultural activities	48	50	2	0	0
ITM2	Mathematics consists of a body of knowledge whose truths should be questioned	19	43	21	12	5
ITM3	School mathematics is useful in traditional societies	12	45	9	24	10
ITM4	Mathematics identified in traditional cultural activities should also be taught in schools	19	47	9	22	3
ITM5	The only mathematics students learn are those taught to them by teachers in schools	12	12	2	52	22
ITM6	School mathematics is made up of abstract concepts and ideas which are value free	17	31	28	19	5
ITM7	Traditional mathematics found in ones own culture should not be taught in schools	5	19	10	45	21
ITM8	Mathematics found in traditional cultural activities is not as important as the “real mathematics” that is learnt in schools	16	9	5	41	29
ITM9	Students can learn mathematics out of school while participating in ordinary everyday activities	39	57	0	2	2
ITM10	Traditional practices such as counting , measuring, drawing are also mathematical	62	36	2	0	0
ITM11	Teachers should show how mathematics is used in cultural contexts	40	50	7	0	3
ITM12	Showing examples of mathematics in traditional culture will give students a sense of cultural identity	26	52	15	7	0
ITM13	Mathematical knowledge is found only in mathematics textbooks	7	7	2	31	53
ITM14	Mathematics is about learning arithmetic, algebra and geometry.	14	45	15	14	12
ITM15	In schools, teachers should teach only the mathematics that is prescribed in the syllabus and textbooks	9	12	3	43	33
ITM16	Mathematics identified in traditional culture is too simple (at the arithmetic level)	26	33	19	22	0
ITM17	Mathematical knowledge can be gained by taking part in traditional cultural activities such as fishing, building traditional houses etc.	21	55	16	5	3
ITM18	Mathematics is about showing the applications of maths in real life	41	47	5	7	0
ITM19	When teaching mathematics teachers should take into account students prior knowledge learnt out of school	35	47	7	8	3
ITM20	Mathematical concepts found in traditional culture will be lost if they are not taught in schools	15	40	7	29	9
ITM21	Mathematics is learnt in schools only	3	2	2	40	53
ITM22	Rules are the basic building blocks of all mathematical knowledge	36	50	9	3	2
ITM23	Mathematics is about knowing when to use rules and formulas to find answers to problem	33	52	2	8	5
ITM24	Students come to school to learn “school mathematics”, not cultural mathematics	14	24	9	36	17
ITM25	Some of the students’ prior knowledge is learnt out of school while participating in traditional cultural activities	5	79	9	7	0
ITM26	School mathematics should teach students about values in life.	21	45	19	10	5
ITM27	Some mathematics identified in cultural activities should be included in the secondary mathematics curriculum.	16	45	17	14	8
ITM28	Learning how to count in your own mother tongue is as important as counting in English	52	34	9	2	3
ITM29	All of the students prior knowledge is learnt in schools only	10	4	2	43	41
ITM30	Mathematical knowledge consists of facts, theories and formulae which are unquestionably true	21	26	22	22	9
ITM31	Any mathematical concept can be understood if properly explained by the teacher	69	20	2	2	7
ITM32	Mathematics is culture free	16	29	24	24	7
ITM34	School mathematics contains concepts and ideas that can also be found in traditional cultural activities	17	62	14	3	3
ITM35	Mathematics is about learning how to count, measure or make patterns in your own culture	17	50	12	16	5
ITM36	Mathematics identified in traditional cultural activities is useful to a modern PNG society	14	43	27	16	0

Student Teacher responses to section B of the questionnaire

Activity	1 ( %)	2 (%)	3 (%)
37 - pilot flying an aeroplane	0	0	100
38 - carpenter building a house	0	37	63
39 - estimating the height of a tree	4	68	28
40 - measuring the height of a student	7	75	18
41 - making patterns on bamboo walls	51	42	7
42 - villagers building a traditional house	21	70	9
43 - children playing a traditional game	49	49	2
44 - woman weaving a mat	30	63	7
45 - building a canoe	30	63	7
46 - painting a haus tambaran	47	49	4
47 - selling (betelnut) buai	10	70	19
48 - the warrior counting his arrows using own counting system	18	61	21
49 - villager using the stars to navigate by canoe from one island to another	19	49	32
50 - the teacher counting the number of students in the classroom.	7	65	28

See Mean, mode and standard deviation for student teacher responses over page.

Appendix 10 Student responses to questionnaire items

		SA	A	NS	D	SD
ITM	Statement	%	%	%	%	%
1	Mathematics is learnt in schools only	3	12	5	47	33
2	Counting in your mother tongue is not as important as counting in English	13	21	11	32	23
3	Mathematics can also be found in traditional cultural activities.	34	47	10	6	3
4	School mathematics is useful in traditional societies.	14	32	18	23	13
5	Mathematics identified in traditional cultural activities should also be taught in schools.	25	42	15	13	5
6	The only mathematics students learn are those taught to them by teachers in schools.	12	22	5	41	20
7	Mathematics found in traditional cultural activities is not as important as the “real mathematics” that is learnt in schools.	20	22	13	27	18
8	Students can learn mathematics out of school when participating in ordinary every day activities.	37	45	4	11	3
9	Showing examples of mathematics in traditional culture will give me a sense of cultural identity.	19	36	27	14	4
10	Mathematics knowledge is found only in mathematics text books.	9	11	4	40	36
11	In schools, teachers should teach only the mathematics that is found in mathematics text books.	14	20	5	34	27
12	Mathematics identified in traditional culture is too simple.	26	40	17	12	5
13	Mathematical knowledge can be gained by taking part in traditional cultural activities. Such as fishing, building traditional house etc.	16	35	17	16	16
14	Mathematical ideas found in traditional culture will be lost if they are not taught in schools.	33	33	8	15	11
15	Mathematical knowledge is transmitted from the text books to the learner by the teacher.	52	34	3	7	4
16	Students come to school to learn “school mathematics”, not cultural mathematics	26	27	10	24	13
17	Students can learn mathematics out of school while participating in traditional cultural activities	18	52	12	10	8
18	Some mathematics identified in cultural activities should be included in the high school mathematics text books.	28	41	10	13	7
19	School mathematics has no real use in a traditional society.	11	13	13	39	24
20	Mathematical activities such as counting, measuring, drawing are also found in traditional culture	45	37	7	6	5
21	When teaching mathematics, teachers should show examples of mathematics from traditional culture.	11	21	12	36	20
22	All of the students mathematical knowledge is learnt in schools only	8	14	7	38	33
23	School mathematics contains concepts and ideas that can also be found in traditional cultural activities.	19	52	11	11	7
24	Mathematics is about knowing when to count, measure or make patterns in your own culture	28	37	12	16	7
25	It is the mathematical knowledge from the text books that that gets transferred to the students.	33	44	7	12	4
26	Traditional mathematics found in ones culture should not be taught in schools.	7	17	16	36	24
27	Some mathematical knowledge can be taught to the learner by the village elders.	15	52	12	13	8
28	School mathematics is useful in traditional societies	19	41	11	18	11
29	School mathematics is learnt from teachers only.	3	6	3	43	46
30	Mathematics is about knowing when to use rules and formulas to find answers to problems.	54	33	2	7	4

Student responses to section B of the student questionnaire

	1 ( %)	2 (%)	3 (%)
31 - pilot flying an aeroplane	1	12	87
32 - carpenter building a house	3	45	52
33 - estimating the height of a tree	9	55	36
34 - measuring the height of a student	10	63	27
35 - making patterns on bamboo walls	53	39	8
36 - villagers building a traditional house	42	45	13
37 - children playing a traditional game	75	24	1
38 - woman weaving a mat	48	47	5
39 - building a canoe	34	55	11
40 - painting a haus tambaran	49	40	11
41 - selling (betelnut) buai	18	63	19
42 - the warrior counting his arrows using own counting system	12	64	24
43 - villager using the stars to navigate by canoe from one island to another	18	44	38

Student sample mean, mode and standard deviation

Appendix 11 Comparison of teachers, student teachers and students responses

Items showing significant differences between Teachers and students - Section A

	Statement	significance level
ITM1	Mathematics can also be found in traditional cultural activities	.000
ITM3	School mathematics is useful in traditional societies	.000
ITM4	Mathematics identified in traditional cultural activities should also be taught in schools	.004
ITM7	Traditional mathematics found in ones own culture should not be taught in schools	.047
ITM8	Mathematics found in traditional cultural activities is not as important as the “real mathematics” that is learnt in schools	.000
ITM9	Students can learn mathematics out of school while participating in ordinary everyday activities	.006
ITM10	Traditional practices such as counting , measuring, drawing are also mathematical	.000
ITM11	Teachers should show how mathematics is used in cultural contexts	.000
ITM12	Showing examples of mathematics in traditional culture will give students a sense of cultural identity	.000
ITM13	Mathematical knowledge is found only in mathematics textbooks	.000
ITM15	In schools, teachers should teach only the mathematics that is prescribed in the syllabus and textbooks	.000
ITM16	Mathematics identified in traditional culture is too simple (at the arithmetic level)	.012
ITM17	Mathematical knowledge can be gained by taking part in traditional cultural activities such as fishing, building traditional houses etc.	.000
ITM19	When teaching mathematics teachers should take into account students prior knowledge learnt out of school	.000
ITM21	Mathematics is learnt in schools only	.000
ITM23	Mathematics is about knowing when to use rules and formulas to find answers to problem	.000
ITM24	Students come to school to learn “school mathematics”, not cultural mathematics	.000
ITM25	Some of the students’ prior knowledge is learnt out of school while participating in traditional cultural activities	.000
ITM27	Some mathematics identified in cultural activities should be included in the secondary mathematics curriculum.	.005
ITM29	All of the students prior knowledge is learnt in schools only	.000
ITM34	School mathematics contains concepts and ideas that can also be found in traditional cultural activities	.001

Section B	Significance Level (p<0.05)
37 - pilot flying an aeroplane	.008
38 - carpenter building a house	.001
41 - making patterns on bamboo walls	.003
42 - villagers building a traditional house	.000
43 - children playing a traditional game	.000
44 - woman weaving a mat	.000
45 - building a canoe	.001
46 - painting a haus tambaran	.000
48 - the warrior counting his arrows using own counting system	.039

Appendix 12 Student Sample ANOVA results : Across all schools

The items that showed significant differences at 5 % level of significance.

ITM	Statements Section A	Significance level (p £ 0.05)
1	Mathematics is learnt in schools only	.007 *
2	Counting in your mother tongue is not as important as counting in English	.406
3	Mathematics can also be found in traditional cultural activities.	.001 *
4	School mathematics is useful in traditional societies.	.028 *
6	The only mathematics students learn are those taught to them by teachers in schools.	.023 *
12	Mathematics identified in traditional culture is too simple.	.014 *
13	Mathematical knowledge can be gained by taking part in traditional cultural activities. Such as fishing, building traditional house etc.	.041 *
17	Students can learn mathematics out of school while participating in traditional cultural activities	.028 *
29	School mathematics is learnt from teachers only.	.018 *
30	Mathematics is about knowing when to use rules and formulas to find answers to problems.	.003*

Appendix 13 Student Sample ANOVA results : Across all Grades


ITM	Statements Section A	Significance level (p £ 0.05)
1	Mathematics is learnt in schools only	.000 *
9	Showing examples of mathematics in traditional culture will give me a sense of cultural identity.	.003 *
13	Mathematical knowledge can be gained by taking part in traditional cultural activities. Such as fishing, building traditional house etc.	.004*
22	All of the students mathematical knowledge is learnt in schools only	.000 *
26	Traditional mathematics found in ones culture should not be taught in schools.	.007 *
29	School mathematics is learnt from teachers only.	.001 *
30	Mathematics is about knowing when to use rules and formulas to find answers to problems.	.007 *

Appendix 14 Student Sample ANOVA results : Classes grouped according to teachers


ITM	Statements Section A	Significance level (p £ 0.05)
1	Mathematics is learnt in schools only	.003 *
3	Mathematics can also be found in traditional cultural activities.	.000 *
9	Showing examples of mathematics in traditional culture will give me a sense of cultural identity.	.007 *
12	Mathematics identified in traditional culture is too simple.	.020 *
14	Mathematical ideas found in traditional culture will be lost if they are not taught in schools.	.024 *
17	Students can learn mathematics out of school while participating in traditional cultural activities	.009 *
21	When teaching mathematics, teachers should show examples of mathematics from traditional culture.	.053 *
22	All of the students mathematical knowledge is learnt in schools only	.001 *
24	Mathematics is about knowing when to count, measure or make patterns in your own culture	.034 *
29	School mathematics is learnt from teachers only.	.002 *
30	Mathematics is about knowing when to use rules and formulas to find answers to problems.	.005 *

Appendix 15 Student Sample ANOVA results : School A - CMO (Grades 8A & 8B) V/s INT (Grade 8C)


ITM	Statements Section A	Significance level (p £ 0.05)
5	Mathematics identified in traditional cultural activities should also be taught in schools.	.052 *
7	Mathematics found in traditional cultural activities is not as important as the “real mathematics” that is learnt in schools.	.052 *
14	Mathematical ideas found in traditional culture will be lost if they are not taught in schools.	.001 *
16	Students come to school to learn “school mathematics”, not cultural mathematics	.024 *
19	School mathematics has no real use in a traditional society.	.037 *
24	Mathematics is about knowing when to count, measure or make patterns in your own culture	.018 *
30	Mathematics is about knowing when to use rules and formulas to find answers to problems.	.024 *

Appendix 16 Student Sample ANOVA results : School A - Grade 8 v/s Grade 9 (same teacher)


ITM	Statements Section A	Significance level (p £ 0.05)
4	School mathematics is useful in traditional societies.	.041*
8	Students can learn mathematics out of school when participating in ordinary every day activities.	.035*
13	Mathematical knowledge can be gained by taking part in traditional cultural activities. Such as fishing, building traditional house etc.	.005*
16	Students come to school to learn “school mathematics”, not cultural mathematics	.047*

Appendix 17 Student Sample ANOVA results : School B - SMO Grade 8A v/s SMO Grade 8B (Different teachers)

Table which shows that there were only two items showing significant difference between grade 8 classes taught by different SMO teachers.


ITM	Statements Section A	Significance level (p £ 0.05)
1	Mathematics is learnt in schools only	.416
2	Counting in your mother tongue is not as important as counting in English	.697
3	Mathematics can also be found in traditional cultural activities.	.675
4	School mathematics is useful in traditional societies.	.590
5	Mathematics identified in traditional cultural activities should also be taught in schools.	.118
6	The only mathematics students learn are those taught to them by teachers in schools.	.210
7	Mathematics found in traditional cultural activities is not as important as the “real mathematics” that is learnt in schools.	.476
8	Students can learn mathematics out of school when participating in ordinary every day activities.	.123
9	Showing examples of mathematics in traditional culture will give me a sense of cultural identity.	.045 *
10	Mathematics knowledge is found only in mathematics text books.	.968
11	In schools, teachers should teach only the mathematics that is found in mathematics text books.	.197
12	Mathematics identified in traditional culture is too simple.	.128
13	Mathematical knowledge can be gained by taking part in traditional cultural activities. Such as fishing, building traditional house etc.	.350
14	Mathematical ideas found in traditional culture will be lost if they are not taught in schools.	.827
15	Mathematical knowledge is transmitted from the text books to the learner by the teacher.	-
16	Students come to school to learn “school mathematics”, not cultural mathematics	.648
17	Students can learn mathematics out of school while participating in traditional cultural activities	.357
18	Some mathematics identified in cultural activities should be included in the high school mathematics text books.	.297
19	School mathematics has no real use in a traditional society.	.087
20	Mathematical activities such as counting, measuring, drawing are also found in traditional culture	.620
21	When teaching mathematics, teachers should show examples of mathematics from traditional culture.	.644
22	All of the students mathematical knowledge is learnt in schools only	.326
23	School mathematics contains concepts and ideas that can also be found in traditional cultural activities.	.038 *
24	Mathematics is about knowing when to count, measure or make patterns in your own culture	.177
26	Traditional mathematics found in ones culture should not be taught in schools.	.450
27	Some mathematical knowledge can be taught to the learner by the village elders.	.809
29	School mathematics is learnt from teachers only.	.648
30	Mathematics is about knowing when to use rules and formulas to find answers to problems.	.544

Appendix 18 Student Sample ANOVA results : School C - Grade 8 v/s Grade 10 (Different teachers)

Table with the items showing significant difference between grade 8 and grade 10


ITM	Statements Section A	Significance level (p £ 0.05)
1	Mathematics is learnt in schools only	.010 *
3	Mathematics can also be found in traditional cultural activities.	.036 *
9	Showing examples of mathematics in traditional culture will give me a sense of cultural identity.	.013 *
17	Students can learn mathematics out of school while participating in traditional cultural activities	.013 *
22	All of the students mathematical knowledge is learnt in schools only	.001 *
26	Traditional mathematics found in ones culture should not be taught in schools.	.041 *
29	School mathematics is learnt from teachers only.	.043 *

Appendix 19 Student Sample ANOVA results : School C - Grade 8A v/s grade 8B (same teacher)

The following table shows that there was significant difference on only one item.

ITM	Statements Section A	Significance level (p £ 0.05)
1	Mathematics is learnt in schools only	.723
2	Counting in your mother tongue is not as important as counting in English	.404
3	Mathematics can also be found in traditional cultural activities.	.093
4	School mathematics is useful in traditional societies.	.216
5	Mathematics identified in traditional cultural activities should also be taught in schools.	.068
6	The only mathematics students learn are those taught to them by teachers in schools.	.315
7	Mathematics found in traditional cultural activities is not as important as the “real mathematics” that is learnt in schools.	.656
8	Students can learn mathematics out of school when participating in ordinary every day activities.	.112
9	Showing examples of mathematics in traditional culture will give me a sense of cultural identity.	.122
10	Mathematics knowledge is found only in mathematics text books.	.602
11	In schools, teachers should teach only the mathematics that is found in mathematics text books.	.208
12	Mathematics identified in traditional culture is too simple.	.659
13	Mathematical knowledge can be gained by taking part in traditional cultural activities. Such as fishing, building traditional house etc.	.961
14	Mathematical ideas found in traditional culture will be lost if they are not taught in schools.	.375
15	Mathematical knowledge is transmitted from the text books to the learner by the teacher.	-
16	Students come to school to learn “school mathematics”, not cultural mathematics	.124
17	Students can learn mathematics out of school while participating in traditional cultural activities	.245
18	Some mathematics identified in cultural activities should be included in the high school mathematics text books.	.372
19	School mathematics has no real use in a traditional society.	.135
20	Mathematical activities such as counting, measuring, drawing are also found in traditional culture	.768
21	When teaching mathematics, teachers should show examples of mathematics from traditional culture.	.832
22	All of the students mathematical knowledge is learnt in schools only	.607
23	School mathematics contains concepts and ideas that can also be found in traditional cultural activities.	.687
24	Mathematics is about knowing when to count, measure or make patterns in your own culture	.763
26	Traditional mathematics found in ones culture should not be taught in schools.	.959
27	Some mathematical knowledge can be taught to the learner by the village elders.	.908
29	School mathematics is learnt from teachers only.	.095
30	Mathematics is about knowing when to use rules and formulas to find answers to problems.	.006 *

Appendix 20 Student Sample ANOVA results : Schools A & B - CMO v/s SMO students

ITM	Statements Section A	Significance level (p £ 0.05)
3	Mathematics can also be found in traditional cultural activities.	.001*
5	Mathematics identified in traditional cultural activities should also be taught in schools.	.037*
12	Mathematics identified in traditional culture is too simple.	.033*
14	Mathematical ideas found in traditional culture will be lost if they are not taught in schools.	.009*
18	Some mathematics identified in cultural activities should be included in the high school mathematics text books.	.017*
21	When teaching mathematics, teachers should show examples of mathematics from traditional culture.	.005*
24	Mathematics is about knowing when to count, measure or make patterns in your own culture	.009*

Appendix 21 Total Response Scale (Teachers)