[ii]

[iii]

[iv]

[v]

[vi]

Introduction ......................................................................................................... 1Mathematics Language and Its Use ................................................................... 2Context of the Study ............................................................................................ 3Summary of Study Context ................................................................................. 7Research Focus ................................................................................................... 8Aim and Research Questions .............................................................................. 9Researcher reflexivity .......................................................................................... 9Assumptions of the study ................................................................................... 10Limitations of the Study .................................................................................... 11Preliminary Definitions ..................................................................................... 12Overview of the thesis ........................................................................................ 12

Introduction ....................................................................................................... 13Mathematics and Languages ............................................................................ 13Pacific Education Issues ................................................................................... 21A Tentative Framework for Learning and Teaching ...................................... 30Conclusion ......................................................................................................... 37

Introduction ....................................................................................................... 39Research Paradigm ........................................................................................... 39Interpretivist Paradigm ..................................................................................... 40Phenomenology as a Research Methodology ................................................... 40Research Participants ....................................................................................... 42Research Methods ............................................................................................. 44Ethical Considerations ...................................................................................... 48Transcription of Data ........................................................................................ 49Thematic Analysis ............................................................................................. 50Conclusion ......................................................................................................... 54

Introduction ....................................................................................................... 55Teacher Quality ................................................................................................. 55Student Learning ............................................................................................... 63Algebraic Language .......................................................................................... 67

[vii]

Teaching and Learning Resources ................................................................... 75Class Sizes .......................................................................................................... 81Mathematics Assessment ................................................................................... 84Mathematics Syllabus Issues ............................................................................ 88Conclusion ......................................................................................................... 91

Introduction ....................................................................................................... 92Summary of Seven Dimensions ........................................................................ 92Learning Algebraic language ........................................................................... 97Teaching Algebraic Language .......................................................................... 98Recommendations ............................................................................................. 99Areas for further research .............................................................................. 100

Appendix A: Teacher Interview schedule ...................................................... 110Appendix B: Student Interview Questions ..................................................... 111Appendix C: Interview Questions for Assessment Officer ............................ 112Appendix D: Observation Form ..................................................................... 113

[viii]

[1]

“Students continue to struggle with problem solving tasks. These involve problems described (in English) using words ... It is very likely that the poor English skills of the students impede their ability to understand the actual tasks as the actual mathematical operations were straight forward.”

(Ministry of Education, 2016, p. 23)

[2]

.

[3]

Mathematics Curriculum

Secretariat of the Pacific Board for Educational Assessment

Education Quality and Assessment Program

Secretariat of the Pacific Community

[4]

National Education

Summit

cognitive benefits

2

[5]

Mathematics Teachers and Training

Kiribati Teachers College Kiribati Education

Improvement Program

Teaching English to Speakers of Other Language

Kiribati English Learning Program

[6]

The Australian Department of Foreign Affairs and Trade

Mathematics in Kiribati Social Context

[7]

Mathematics in the Classroom

[8]

[9]

Research Questions:

[10]

[11]

Curriculum Development and Resource Center

[12]

Algebraic language

simplify, rational, real numbers, integers, expression,

factorizing, inequalities, functions, indices, index and log form .

factorizing ( ), integration ( ), inequalities ( )

[13]

[14]

Fractal fuzzy

logic

Mathematical English

“borrowed” face, power, product, rational)

quadrilateral, parallelogram, hypotenuse)

Isosceles iso- skelos

tangent tangere-

[15]

division operation

pure

[16]

Mathematics Written Communication

unknown or variable”

unknown variables3

3 unknown variable

unknown variable

[17]

[18]

[19]

Talking Mathematics

exposition explaining

telling.

Kiribati Education Summit 2008

[20]

Writing Mathematically

[21]

[22]

Education Curriculum Issues and Development

I-

matang

Pakeha

[23]

Pakeha

Pakeha

Teaching and Learning Resources

[24]

Teacher Quality

[25]

[26]

Pacific Cultural Silence

[27]

kainabwaabu

kainabwaabu Boto Boto

Boto

Boto

kabitaia

wanawana

Palangi

[28]

kabitaia

Pacific Teaching and Learning Quality Issues

teacher-centred approach

student-centred approach

[29]

student-centred approach

National Curriculum and Assessment Framework

teacher-centred approach

learning-centred approach

student-centred

approach

[30]

[31]

English Skills in Mathematics

Pacific Region Integrated Mathematics and English

[32]

Bilingualism

[33]

everyday

[34]

[35]

Mathematics Literacy

[36]

[37]

[38]

[39]

[40]

[41]

pure

hermeneutic

How does Phenomenology Work?

[42]

Constructing Paradigm

Research participant

Data collection methods

Analysing

data

[43]

.

[44]

One-on-one Interview

[45]

Taona-tabon-inaaim

Taona-tabon-inaaim

inaai

amwarake

mweaka

Taona-tabon-inaaim

[46]

Taona-tabon-inaaim

[47]

Classroom Observation

[48]

taona-tabon-inaim

[49]

[50]

[51]

How does Thematic Analysis Works?

[52]

[53]

semantic approach

latent approach

semantic approach

latent approach

[54]

Teacher Quality, Student learning Algebraic language Teaching and

Learning resources Class size, Mathematics Assessment Mathematics syllabus

issues

[55]

Teacher Quality, Student

learning Algebraic language Teaching and Learning resources Class size,

Mathematics Assessment Mathematics syllabus issues

[56]

Teaching Qualifications

4

[57]

”

5

[58]

Professional Development

[59]

Sheltered Instruction Observation Protocol

[60]

[61]

[62]

[63]

Learning basic skills

6 unknown variable

unknown variable

[64]

[65]

[66]

Students’ Low Level of Commitment

teachers believe

[67]

[68]

Application Questions

[69]

[70]

[71]

[72]

Algebraic Key Words

simplifying solve quadratic and cubic

factors expansion factors reciprocal rational expression evaluate

[73]

rational expression equation

reciprocals numerator denominator

lowest

common factor collecting like terms addition subtraction

multiplication division

solve

factorizing expansion

solve

simplify solving

solve expanding

[74]

expansion solving power equation quadratic equation

simplifying unknown variable

logarithm power

equation

expansion,

Determinant

logarithm properties elimination of

multiplicative terms addition subtraction

[75]

simplify the expression

like terms

like terms

[76]

[77]

teaching by telling

[78]

student-centred approach

[79]

Theta 7

Theta

7

[80]

[81]

[82]

[83]

[84]

[85]

Exam Assessment

[86]

[87]

Common Assessment Task

[88]

Educational Quality and Assessment

Program

A Sense of Overloading in the Year 12 Syllabus

[89]

[90]

Gap between Year 11 and Year 12 Syllabi

Calculus Sequence and

Series

Kiribati National Certificate

Senior Secondary Certificate

differentiation, integration

differentiation,

integration, arithmetic geometric sequence, series, terms

summation notation

[91]

teacher quality issue; student

learning; problems with algebraic language; teaching and learning materials; large

class-size; Mathematics assessment; Mathematics syllabus issues

[92]

quality teaching, student learning, language complexity,

teaching and learning resources, class size, assessment Mathematics syllabus

issues

Teacher Quality

[93]

Student Learning

[94]

Algebraic Language

Teaching and Learning Resources

[95]

Class Sizes

Mathematics Assessment

[96]

Mathematics Syllabus Issues

[97]

[98]

[99]

[100]

[101]

Sky Journal of Educational Research, 2

A Samoan Perspective on Pacific Mathematics Education.

Journal of Educational Studies, 21

Re-thinking Education Curricula in the Pacific: Challenges and Prospects

Research Methods in Child Welfare

Foundations of Bilingual Education and Bilingualism

Early Childhood Research Quarterly, 22

Mathematics Education: A Handbook for Teachers

Theta Mathematics: NCEA Level 2

Language and Second/Additional Language Issues for School Education: A Reader for Teachers

Mathematics Teaching-Derby-

The Basics of Learning: Literacy and Numeracy in the Pacific

[102]

Social Science Research: Principles, Methods, and Practices

International Online Journal of Educational Sciences 5

Higher education, 32

Race and Class, 32

Learning and Instruction, 21

Journal of Teaching and Learning, 5

Qualitative research in psychology, 3

Journal of Educational Studies, 24

Asia Pacific Journal of Education, 33

Journal for Activist Science & Technology Education, 1

The Journal of General Education, 59

Vocabulary Strategies for the Mathematics Classroom

An International Journal, 4

[103]

Educational Research, Planning, Conducting, and Evaluating Quantitative and Qualitative Research

Algebra, symbols, and translation of meaning.

Australian Senior Mathematics Journal, 27

Introduction to mathematical thinking

A quarterly publication reporting on teaching, learning and assessment

Assessment

Re-thinking Education Curricula in the Pacific: Challenges and Prospects

Mathematical language and Advanced Mathematics Learning.

Bilingual Education in the 21st Century. A Global Perspective

Technology-Enriched Teaching of Secondary Mathematics: Factors Influencing Innovative Practice.

Kiribati Development Plan 2016-19

International Journal of Qualitative Methods, 3

[104]

Issues & Answers Report, REL 2007

Journal of Client Care, 1

Learning to Teach Mathematics in the Secondary School

The Basics of Learning: Literacy and Numeracy in the Pacific

NCEA Level 2 Mathematics. Questions & Answers

School Improvement Plan Standards

Media and the politics of climate change in Kiribati: A case study on jornalism in a "disapperaring nation".

International Journal of Qualitative Studies in Education, 19

The Basics of Learning Literacy and Numeracy in the Pacific

Interdisciplinary Undergraduate Research Journal, 2

Education Research and Reviews, 8

[105]

Educational studies in mathematics, 71

Mathematical Understanding and Tongan bilingual students' language switching- Is there a relationship?

An analysis of the effects of class size on student achievement in selected middle schools in the Sandhills region of North Carolina.

Mathematics Education: A Handbook for Teachers

American International Journal of Contemporary Research, 2

Submission on the Public Inquiry into Pacific Languages in ECE

Educational Ideas from Oceania

Introduction to Educational Research

English for Kiribati

Kiribati National Education Summit Outcomes

Kiribati National Curriculum and Assessment Framework (NCAF)

KSSC Exam results report 2013

[106]

Education for All 2015 National Review Report

KSSC Results for 2013 to 2015

Learning to Teach Mathematics in the Secondary School

Commissioned Papers on Language and Literacy Issues in the Common Core State Standards and Next Generation Science Standards, 94

Vugalei : voices and silences of what and how we know : indigenous Fijian epistemology and implications for education.

Kiribati National Curriculum and Assessment Framework

Teaching and Learning Research Initiative final report. Retrieved August

Learning to Teach Mathematics in the Secondary School

[107]

Rethinking Educational Reform: A Pacific Perspective

National center for analysis of longitudinal data in education research

Learning to Teach Mathematics in the Secondary School

International Journal of Educational Development, 31

Educational Research in an age of accountability

Current and Critical Issues in Curriculum and Learning

Journal of Science and Mathematics Education in Southeast Asia, 33

Cross-Cultural Approaches to Literacy

Re-thinking Education Curricula in the Pacific: Challenges and Prospects

Educational Ideas from Oceania

The Basics of Learning Leiteracy and Numeracy in

[108]

the Pacific

Re-thinking Education Curricula in the Pacific: Challenges and Prospects

Educational Ideas from Oceania

Educational Ideas from Oceania

Re-thinking Education Curricula in the Pacific: Challenges and Prospects

Canadian Journal of Education, 27

ZDM Mathematics Education, 46

Mai Review

Readings on the Development of Children

Learning to

[109]

Teach Mathematics in the Secondary School

Research Methods in Education: An Introduction

The Reading Teacher, 64

Foundations of Qualitative Research: Interpretive and Critical Approaches

Articles on Best Practice, 40

[110]

Teaching Methods

Using language

simplify, expansion, factorise, evaluate, as twice as, triple, times

Cultural silence

[111]

Tera mamaten nanon n am bwai n reirei ae ko reireiaki iai? Taiaoka angaa bukina bwa ibukin tera bwa ko tatangira te bwai n reirei anne.

Ko tatangira karaoan te Numera n te karaki ke koaki? Taiaoka angaa bukina bwa ibukin tera ngkai ko tatangiria ao ibukin tera ngkai ko aki.

E kanga aron am tia reirei n te Numera n reiakini ngkami inanon tain te reirei? Taiaoka kabwarabwara bwa e teimatoa n kabwarabwarai te naan taeka ni Imatang are a kabonganaaki ke eaki, tera te taetae ae e kabonganaa ibukin kain te reirei, e kanga arona n buokiia ataei ake iai aia titiraki, tera bwaai ae e anga reirei mai iai, ao e kanga arona ni kaina ami reirei.

Ko kakoaua ae rabakaum n te taetae ni Imatang (ko kona ongo ke koroboki) e irekereke ke e kona n roota am kekeiaki n te Numera ?

Anga tabeua te taetae ni Imatang aika a rang kabonganaaki n te Numera ae ko teimatoa n tuai atai nanoia, ke ngkana a kabonganaai ao koaki naba oota iai.

[112]

[113]

i. Communication

ii. Classroom arrangement