current issues in mathematical education

Current Issues in Current Issues in Mathematical Mathematical

EducationEducationBy:By:

Ak Alif Wira Putra Bin Pg Awang (06B0410)Ak Alif Wira Putra Bin Pg Awang (06B0410)

Mufidah Binti Haji Kasim (06B0413)Mufidah Binti Haji Kasim (06B0413)

IntroductionIntroduction Mathematics has been one of the most Mathematics has been one of the most

important subject in the school curriculum.important subject in the school curriculum.

Nearly one quarter of the periods each week Nearly one quarter of the periods each week in schools are for mathematics.in schools are for mathematics.

It is widely accepted by educators, teachers It is widely accepted by educators, teachers and pupils in schools that mathematics is and pupils in schools that mathematics is difficult to teach and learn.difficult to teach and learn.

IntroductionIntroduction Despite the use of modern teaching Despite the use of modern teaching

methods, the availability of modern teaching methods, the availability of modern teaching materials and the provision of specialized materials and the provision of specialized training for all teachers, teachers still find in training for all teachers, teachers still find in teaching mathematics because their pupils teaching mathematics because their pupils have problems in learning it.have problems in learning it.

However, there are issues that lead to the However, there are issues that lead to the mathematical educationmathematical education

Current issues that lead to the mathematical Current issues that lead to the mathematical education are:education are:

Curricular Change in Mathematics in BruneiCurricular Change in Mathematics in Brunei SPN 21 (Sistem Pendidikan Negara Abad ke-SPN 21 (Sistem Pendidikan Negara Abad ke-

21)21) The use of ICT in MathematicsThe use of ICT in Mathematics

Language problemLanguage problem

Learning environmentLearning environment

Curricular Change Curricular Change in Mathematics in in Mathematics in Brunei Brunei

In January 2006, a new primary mathematics In January 2006, a new primary mathematics curriculum was introduced at the Primary 1 and curriculum was introduced at the Primary 1 and Primary 4 in all primary schools in Brunei. Primary 4 in all primary schools in Brunei.

Mathematics instructions in Brunei has focused too Mathematics instructions in Brunei has focused too much on efficient computation and not enough on much on efficient computation and not enough on mathematical understanding and problem solving.mathematical understanding and problem solving.

Students’ work consisted almost entirely of learning Students’ work consisted almost entirely of learning

formulas, algorithms, or procedures without much formulas, algorithms, or procedures without much attention to why or when it make sense to do so.attention to why or when it make sense to do so.

The new curriculum besides having reduced content The new curriculum besides having reduced content load has refocused teachers’ attention to the load has refocused teachers’ attention to the teaching of basic skills, problem solving, mental teaching of basic skills, problem solving, mental computation, mathematical thinking and on the computation, mathematical thinking and on the development of attitudes and values. development of attitudes and values.

There are six features of the new primary There are six features of the new primary mathematics curriculum: mathematics curriculum:

1.1. Content reductionContent reduction

2.2. Mathematical thinking and problem solvingMathematical thinking and problem solving

3.3. Mental computation and estimation Mental computation and estimation

4.4. ICTICT

5.5. Values in MathematicsValues in Mathematics

6.6. Development of concepts and skills through Development of concepts and skills through meaningful activitiesmeaningful activities

1. Content reduction 1. Content reduction

The content has been reduced compared to the The content has been reduced compared to the previous one so that the teachers would have more previous one so that the teachers would have more time to carry out meaningful activities to develop the time to carry out meaningful activities to develop the children understanding of the concept and ideas. children understanding of the concept and ideas.

This also were taken to ensure that the curriculum This also were taken to ensure that the curriculum was balanced and well coordinated.was balanced and well coordinated.

The one that can provide a solid information for the The one that can provide a solid information for the competencies and in other discipline to develop competencies and in other discipline to develop within a reasonably short time. within a reasonably short time.

2. Mathematical Thinking and Problem 2. Mathematical Thinking and Problem Solving Solving

The main objective of the new curriculum is to enable The main objective of the new curriculum is to enable learners to develop their ability to solve problems both learners to develop their ability to solve problems both within mathematics itself and the real life situation. within mathematics itself and the real life situation.

Learners must be able to analyze and bring varied Learners must be able to analyze and bring varied reasoning and problem solving skills in an integrated reasoning and problem solving skills in an integrated manner when solving problems.manner when solving problems.

Also the new curriculum has been designed to Also the new curriculum has been designed to provide learners the opportunity to become engaged provide learners the opportunity to become engaged with problems that are rich and varied enough to with problems that are rich and varied enough to encourage the developments of these skills.encourage the developments of these skills.

3. Mental Computation and 3. Mental Computation and Estimation Estimation

Mental mathematics is the combination of cognitive Mental mathematics is the combination of cognitive strategies that enhances flexible thinking and number strategies that enhances flexible thinking and number senses. senses.

It also provide a foundation for all estimation It also provide a foundation for all estimation processes and offers a variety of alternative processes and offers a variety of alternative algorithms and non standard techniques for finding algorithms and non standard techniques for finding answers to computations.answers to computations.

The new curriculum also specifies children should The new curriculum also specifies children should taught a range of mental strategies for quick recall of taught a range of mental strategies for quick recall of the basic number facts.the basic number facts.

4. ICT4. ICT

Recent advances in technology and the availability of Recent advances in technology and the availability of calculators, graphing calculators, computers and other calculators, graphing calculators, computers and other technological devices in the classroom have had profound technological devices in the classroom have had profound impact on the mathematics curriculum in terms of content impact on the mathematics curriculum in terms of content that can be covered and strategies for teaching and that can be covered and strategies for teaching and learning mathematics. learning mathematics.

The new curriculum supports these development by The new curriculum supports these development by placing clear emphasis upon the sensible use of ICT in placing clear emphasis upon the sensible use of ICT in concept development.concept development.

Suggested opportunities for teachers and learners to use Suggested opportunities for teachers and learners to use ICT as they learn particular topic have been included in ICT as they learn particular topic have been included in the syllabus. the syllabus.

5. Values in Mathematics5. Values in Mathematics It is important that learners values mathematics and It is important that learners values mathematics and

appreciate its beauty. appreciate its beauty.

It can stimulate moments of pleasure and wonder when It can stimulate moments of pleasure and wonder when the learner solves the problem for the first time and the learner solves the problem for the first time and discovers a more elegant solution to that problem.discovers a more elegant solution to that problem.

Opportunities have been made available in the new Opportunities have been made available in the new mathematics for learners to explore patterns and mathematics for learners to explore patterns and appreciate the nature of mathematics. appreciate the nature of mathematics.

Teachers are expected to teach mathematics in a Teachers are expected to teach mathematics in a manner that will make the study of mathematics manner that will make the study of mathematics interesting and promote positive attitudes towards the interesting and promote positive attitudes towards the subject.subject.

6. Development of concepts and skills 6. Development of concepts and skills through meaningful activitiesthrough meaningful activities

Pupils should be actively involved in the learning of Pupils should be actively involved in the learning of mathematics through the use of variety of mathematics through the use of variety of representations. representations.

The new curriculum recommends that the manipulation The new curriculum recommends that the manipulation of concrete materials and models should be the starting of concrete materials and models should be the starting point upon which the children can actively build point upon which the children can actively build mathematical ideas.mathematical ideas.

Mathematical understanding occurs when the learner is Mathematical understanding occurs when the learner is able to move smoothly from one mode of representation able to move smoothly from one mode of representation to another.to another.

SPN 21 SPN 21 (Sistem Pendidikan (Sistem Pendidikan Negara abad ke-21Negara abad ke-21

What is SPN 21What is SPN 21 SPN 21 is the acronym for Sistem SPN 21 is the acronym for Sistem

Pendidikan Negara Abad Ke-21Pendidikan Negara Abad Ke-21

The National Education System for the 21st The National Education System for the 21st Century which has been approved by the Century which has been approved by the Ministry of Education. Ministry of Education.

This system makes provision for several This system makes provision for several major educational changes. major educational changes.

When it is ImplementedWhen it is Implemented

In stages: In stages:

• • Interim (transitional) stage in 2008 for Year 7 Interim (transitional) stage in 2008 for Year 7 [PSR 2007 cohort] [PSR 2007 cohort]

• • At the primary level, it will be implemented in At the primary level, it will be implemented in 2009 for Year 1 and Year 4 2009 for Year 1 and Year 4

• • Full implementation at primary level in 2011 Full implementation at primary level in 2011

Why the education system needs to be Why the education system needs to be changed?changed?

SPN 21 aims to: SPN 21 aims to: • • meet the social and economic challenges of the meet the social and economic challenges of the

21st Century 21st Century

• • realise the Ministry of Education's vision and realise the Ministry of Education's vision and mission mission

• • equip students with 21st Century skills equip students with 21st Century skills

• • fulfill the Strategic Themes as outlined in the fulfill the Strategic Themes as outlined in the Ministry of Education's Strategic Plan (2007-Ministry of Education's Strategic Plan (2007-2011) 2011)

Rationale for the change Rationale for the change Brunei Vision 2035 By 2035, Brunei Darussalam is Brunei Vision 2035 By 2035, Brunei Darussalam is

recognised everywhere for: recognised everywhere for:

o The accomplishment of its well-educated and highly o The accomplishment of its well-educated and highly skilled people skilled people

o The quality of life o The quality of life

o The dynamic and sustainable economy o The dynamic and sustainable economy

• • 8 policy directions in the Education Strategy, Brunei 8 policy directions in the Education Strategy, Brunei Vision 2035 Vision 2035

• • Fulfillment of the Ministry of Education's mission Fulfillment of the Ministry of Education's mission 'Provide Holistic Education To Achieve Fullest Potential 'Provide Holistic Education To Achieve Fullest Potential For All' For All'

Comparison with Education Systems and Curricula of various Comparison with Education Systems and Curricula of various countries countries

• • Raising students' achievement in the 3 core subjects: English Raising students' achievement in the 3 core subjects: English Language, Mathematics and Science Language, Mathematics and Science

• • Increasing the percentage of students' enrollment into higher Increasing the percentage of students' enrollment into higher education from 14% to 30% by 2011 education from 14% to 30% by 2011

• • Strengthen proficiency in Bahasa Melayu Strengthen proficiency in Bahasa Melayu

• • Local researchers and consultants from overseas have Local researchers and consultants from overseas have identified certain aspects of the National Education System identified certain aspects of the National Education System that need to be improved that need to be improved

Local researchers and consultants from overseas have Local researchers and consultants from overseas have identified certain aspects of the National Education System identified certain aspects of the National Education System that need to be improved that need to be improved

What are the benefits of SPN 21What are the benefits of SPN 21

Greater emphasis on 'character building' Greater emphasis on 'character building'

No retention from Year 1 to Year 10/11 (except No retention from Year 1 to Year 10/11 (except for those with less than 85% attendance for those with less than 85% attendance

Multiple pathways to higher education Multiple pathways to higher education

Multiple choices of educational programmes Multiple choices of educational programmes based on students' interests, needs and abilities based on students' interests, needs and abilities

Opportunities to pursue 4-year or 5-year Opportunities to pursue 4-year or 5-year programmes before sitting for the Brunei- programmes before sitting for the Brunei- Cambridge General Certificate of Education 'O' Cambridge General Certificate of Education 'O' Level examination Level examination

Continuous and seamless curriculum from Continuous and seamless curriculum from Years 7-10/11Years 7-10/11

Acquisition of basic technical, vocational and Acquisition of basic technical, vocational and business skills that is useful for self-business skills that is useful for self-employment and other career opportunities employment and other career opportunities

Opportunities for technical and vocational Opportunities for technical and vocational education in higher institutions education in higher institutions

Special Educational Needs Programme for Special Educational Needs Programme for students with special needs students with special needs

Specialised Education Programme for the Specialised Education Programme for the gifted and talented gifted and talented

Opportunities for acquisition of valuable and Opportunities for acquisition of valuable and marketable skills marketable skills

Improvement in students' achievement Improvement in students' achievement

Improvement in national standards with Improvement in national standards with benchmarking against international benchmarking against international standards standards

Improvement in teaching and learning Improvement in teaching and learning standards standards

How is the School Curriculum OrganisedHow is the School Curriculum Organiseda. Key Features: a. Key Features:

• • Based on Learning Areas and Learning Outcomes Based on Learning Areas and Learning Outcomes

• • Specified 8 Learning Areas: Specified 8 Learning Areas:

o Languages o Languages o Mathematics o Mathematics o Science o Science o Humanities and Social Sciences o Humanities and Social Sciences o Arts and Culture o Arts and Culture o Technology o Technology o Islamic Religious Knowledge & Malay Islamic o Islamic Religious Knowledge & Malay Islamic

Monarchy Monarchy o Health and Physical Education o Health and Physical Education

Common curriculum at primary level (Year 1 to Year Common curriculum at primary level (Year 1 to Year 6) and secondary level (Year 7 to Year 8) 6) and secondary level (Year 7 to Year 8)

Emphasis on essential skills: Emphasis on essential skills:

o Communication Skills (reading, writing, listening o Communication Skills (reading, writing, listening and speaking) and speaking)

o Numeracy Skills o Numeracy Skills

o Scientific and ICT Skills o Scientific and ICT Skills

o Problem-Solving Skills (thinking and creativity)o Problem-Solving Skills (thinking and creativity)

o Work and Study Skills o Work and Study Skills

o Self-Management and Competitive Skills o Self-Management and Competitive Skills (entrepreneurship) (entrepreneurship)

o Interpersonal Skills o Interpersonal Skills

o Physical Skills o Physical Skills

o Aesthetic Skills o Aesthetic Skills

o Other 21st Century skills in Digital Age Literacy o Other 21st Century skills in Digital Age Literacy

Integration of Core Values and Integration of Core Values and Attitudes: Attitudes:

o Self-confidence and self-o Self-confidence and self-esteem esteem

o Empathy and o Empathy and appreciativeness appreciativeness

o Self-reliance and o Self-reliance and independence independence

o Tolerance and mutual respect o Tolerance and mutual respect

o Caring, concern and o Caring, concern and sensitivity sensitivity

o Integrity o Integrity

o Patriotism o Patriotism

o Piousness o Piousness

o Competitiveness o Competitiveness

o Proactive and vigilance o Proactive and vigilance

What are the subjects offered in SPN 21?What are the subjects offered in SPN 21?

Subjects being offered from Year 1 to Year 10/11 Subjects being offered from Year 1 to Year 10/11 Year 1 to Year 3 All students are required to learn all Year 1 to Year 3 All students are required to learn all

compulsory core subjects and compulsory complementary compulsory core subjects and compulsory complementary subjects as listed below:subjects as listed below:

A. COMPULSORY CORE A. COMPULSORY CORE

SUBJECTSSUBJECTS B. COMPULSORY B. COMPULSORY

COMPLEMENTARY SUBJECTSCOMPLEMENTARY SUBJECTS Bahasa MelayuBahasa Melayu Islamic Religious KnowledgeIslamic Religious Knowledge

English Language English Language Physical EducationPhysical Education

ScienceScience Co-curriculumCo-curriculum

MathematicsMathematics Fine Arts and Technology Fine Arts and Technology

o Module 1: ICT o Module 1: ICT

o Module 2: Art and Design o Module 2: Art and Design

o Module 3: Music and Drama o Module 3: Music and Drama

Year 4 to Year 6 All students are required to learn all Year 4 to Year 6 All students are required to learn all compulsory core subjects and compulsory complementary compulsory core subjects and compulsory complementary subjects as listed below: subjects as listed below:

A. COMPULSORY CORE A. COMPULSORY CORE

SUBJECTSSUBJECTS B. COMPULSORY B. COMPULSORY

COMPLEMENTARY SUBJECTSCOMPLEMENTARY SUBJECTS Bahasa MelayuBahasa Melayu Islamic Religious KnowledgeIslamic Religious Knowledge

English Language English Language Physical EducationPhysical Education

ScienceScience Co-curriculumCo-curriculum

MathematicsMathematics Social StudiesSocial Studies

Fine Arts and Technology Fine Arts and Technology

o Module 1: ICT o Module 1: ICT

o Module 2: Art and Design o Module 2: Art and Design

o Module 3: Music and Drama o Module 3: Music and Drama

In addition, according to Hjh Aishah (2008) during In addition, according to Hjh Aishah (2008) during the second dialogue session about the SPN 21 the second dialogue session about the SPN 21 that took place between the Minister of Education that took place between the Minister of Education and school leaders that and school leaders that

..”the ability, competency and effectiveness of ..”the ability, competency and effectiveness of school leaders in leading their schools will be school leaders in leading their schools will be important during the implementation of the important during the implementation of the system, as it would significantly alter the whole system, as it would significantly alter the whole planning, development, and performance at all planning, development, and performance at all

levels as well as the educational level.”levels as well as the educational level.”

She strongly believed that school leaders are the leading She strongly believed that school leaders are the leading agents responsible for bringing about success and agents responsible for bringing about success and continuous excellence, equipped with leadership skills continuous excellence, equipped with leadership skills and able to look forward and and able to look forward and "ready to think outside "ready to think outside the box"the box" or or "dare to think differently""dare to think differently" that every school that every school leader could shape their school with their own character leader could shape their school with their own character and uniqueness. and uniqueness.

The Department of Schools, she added, is aware of the The Department of Schools, she added, is aware of the many issues that still require attention such as efforts of many issues that still require attention such as efforts of strengthening the leadership towards the desired strengthening the leadership towards the desired excellence of SPN 21 and that the department needs the excellence of SPN 21 and that the department needs the continuous cooperation from all parties involved with the continuous cooperation from all parties involved with the system. system.

The Use of ICT in The Use of ICT in MathematicsMathematics

The global development of technology in education are The global development of technology in education are costly and include the introduction of Information and costly and include the introduction of Information and communications technology (ICT) into the school communications technology (ICT) into the school curricula and teacher education. curricula and teacher education.

Many people do not seem to realize that teachers ask Many people do not seem to realize that teachers ask questions, give examples, lecture, guide discussion, drill, questions, give examples, lecture, guide discussion, drill, use small groups, individualize instruction, organize use small groups, individualize instruction, organize project-based learning, and craft blends of these project-based learning, and craft blends of these teaching practices teaching practices

Any improvement in education takes dedication on the Any improvement in education takes dedication on the part of teachers, school leadership and parents to part of teachers, school leadership and parents to learner-centered education, and for that paradigm shift, learner-centered education, and for that paradigm shift, there is much good research to point the way. there is much good research to point the way.

Technology has great potential for raising student Technology has great potential for raising student achievement. achievement.

However, a laptop alone will not do it. There are many more However, a laptop alone will not do it. There are many more factors that have to be in place.factors that have to be in place.

If the teacher knows how to use the software and can If the teacher knows how to use the software and can model it effectively, then the technology can make an model it effectively, then the technology can make an impact on student understanding and achievement. impact on student understanding and achievement.

Schools must rise to such challenges of educating all Schools must rise to such challenges of educating all students to utilize technology effectively and efficiently. students to utilize technology effectively and efficiently.

The fact that some teachers and lecturers in Brunei are The fact that some teachers and lecturers in Brunei are already buying their own laptops and LCD projectors to use already buying their own laptops and LCD projectors to use in class shows the usefulness of this technology.in class shows the usefulness of this technology.

There are many constraints of high-stakes testing and There are many constraints of high-stakes testing and examination-oriented curricula, inadequate budgets and examination-oriented curricula, inadequate budgets and ICT facilities that teachers and students face in schools. ICT facilities that teachers and students face in schools.

These and other constraints drive teachers to use ICT in These and other constraints drive teachers to use ICT in very instrumental ways, such as presenting lessons very instrumental ways, such as presenting lessons passively and also delivering drill and practice of passively and also delivering drill and practice of examination questions using technology. examination questions using technology.

All school teachers in Brunei Darussalam are encouraged All school teachers in Brunei Darussalam are encouraged to integrate ICT into the teaching and learning of subjects to integrate ICT into the teaching and learning of subjects across the curriculum in pedagogically sound ways. across the curriculum in pedagogically sound ways.

Technology should be used to support learning activities Technology should be used to support learning activities such as exploration, manipulation and articulation of what such as exploration, manipulation and articulation of what they are learning (speculation, conjecturing, hypothesis they are learning (speculation, conjecturing, hypothesis testing, and reflection on what they do). testing, and reflection on what they do).

ICT teachers help subject teachers with the necessary ICT teachers help subject teachers with the necessary technology preparations and resources for lessons with ICT technology preparations and resources for lessons with ICT resources. Subject teachers are learning ICT skills to be resources. Subject teachers are learning ICT skills to be more independent.more independent.

These two groups of teachers share expertise and These two groups of teachers share expertise and experience, and learn from each otherexperience, and learn from each other

These two groups of teachers share expertise and These two groups of teachers share expertise and experience, and learn from each other.experience, and learn from each other.

With the availability of technology, there is a danger of With the availability of technology, there is a danger of teachers switching from “chalk-and-talk” with “drill-and-teachers switching from “chalk-and-talk” with “drill-and-practice” to “show-and-tell” with “interactive drill-and-practice” to “show-and-tell” with “interactive drill-and-practice”.practice”.

Teachers were seen to be doing and explaining. Pupils are Teachers were seen to be doing and explaining. Pupils are the ones who need the practice and should be the ones the ones who need the practice and should be the ones doing, exploring, explaining and communicating creatively.doing, exploring, explaining and communicating creatively.

Very cleverly, some teachers have been able to combine Very cleverly, some teachers have been able to combine various effective strategies in teaching mathematics with various effective strategies in teaching mathematics with their own resources. Pupils worked (individually, in pairs, or their own resources. Pupils worked (individually, in pairs, or in threes) on the PCs doing the activities while it was also in threes) on the PCs doing the activities while it was also being demonstrated on the LCD projection screen being demonstrated on the LCD projection screen

There could be more open-ended cognitive and There could be more open-ended cognitive and metacognitive tasks and mini-projects/practical investigative metacognitive tasks and mini-projects/practical investigative activities that promote meaningful learning and activities that promote meaningful learning and investigations of the content and processes of mathematics investigations of the content and processes of mathematics

Demonstration of concepts with the use of a variety of Demonstration of concepts with the use of a variety of verbal, visual and aesthetic stimuli helps children to verbal, visual and aesthetic stimuli helps children to comprehend better and challenges them to think (Miller, comprehend better and challenges them to think (Miller, Averis, Door & Glover, 2005). Averis, Door & Glover, 2005).

Computers and technology should take their place as a Computers and technology should take their place as a natural and powerful part of the teaching and learning natural and powerful part of the teaching and learning process, affecting both aspects of teaching and learning process, affecting both aspects of teaching and learning in three ways. in three ways.

This new technology influences how information is This new technology influences how information is presented; how students interact both with the medium presented; how students interact both with the medium and through the medium with the teacher and other and through the medium with the teacher and other learners; and how knowledge is structured. learners; and how knowledge is structured.

Brumfit (1998) discussed issues of bilingual texts Brumfit (1998) discussed issues of bilingual texts generating questions about awareness, the relationship generating questions about awareness, the relationship between control and freedom in language learning, the between control and freedom in language learning, the positive effects of ICT on motivation, and also the close positive effects of ICT on motivation, and also the close interaction between the data that we can derive from our interaction between the data that we can derive from our teaching materials and research data that previously had teaching materials and research data that previously had not been available. not been available.

Multimedia technology offers opportunities for creative Multimedia technology offers opportunities for creative expression and exploration in instructional activities that expression and exploration in instructional activities that integrate mathematics, science and technology integrate mathematics, science and technology

There is an urgency to monitor the progress and future There is an urgency to monitor the progress and future development of teachers so that they could share and development of teachers so that they could share and enhance their skills and achieve higher levels of enhance their skills and achieve higher levels of interactivity in their teaching. interactivity in their teaching.

Language and Language and Mathematics Mathematics

Learning in BruneiLearning in Brunei

LANGUAGE AND MATHEMATICS LANGUAGE AND MATHEMATICS LEARNING IN BRUNEILEARNING IN BRUNEI

The policies within Brunei which encourage The policies within Brunei which encourage bi-lingualism within education are bi-lingualism within education are applaudable, although the outcome is applaudable, although the outcome is perhaps less than would be desired.perhaps less than would be desired.

Language issues within maths education in Language issues within maths education in Brunei Darussalam are probably the most Brunei Darussalam are probably the most important factor affecting achievement.important factor affecting achievement.


Significantly, Bruneian pupils do no better Significantly, Bruneian pupils do no better on maths problems posed in Bahasa on maths problems posed in Bahasa Melayu than problems posed in English.Melayu than problems posed in English.

The language development issues within The language development issues within mathematics education are true for mathematics education are true for achievement of literacy in both English and achievement of literacy in both English and Bahasa Melayu.Bahasa Melayu.


With limited English language proficiency, With limited English language proficiency, pupils in Brunei will undoubtedly have pupils in Brunei will undoubtedly have difficulty in trying to understand their difficulty in trying to understand their teacher’s explanation in Mathematics. teacher’s explanation in Mathematics.

Pupils have to learn a number of new Pupils have to learn a number of new technical terms, for examples; product, technical terms, for examples; product, quotient, coordinates, Venn diagram, reflex quotient, coordinates, Venn diagram, reflex angle, cube/cuboid.angle, cube/cuboid.


Some of these terms have meanings in Some of these terms have meanings in mathematics which are different from mathematics which are different from those in daily life. For examples; those in daily life. For examples; table, table, set.set.

Several different terms can be used for Several different terms can be used for the same operations: e.g. the same operations: e.g. Multiply, times, Multiply, times, find the product of.find the product of.


Pupils need to know the meanings of Pupils need to know the meanings of general vocabulary items in order to general vocabulary items in order to understand a problem. E.g from the PSR: understand a problem. E.g from the PSR: share equally, pond, flowerbed, to pour, share equally, pond, flowerbed, to pour, identical, to lower, respectively, identical, to lower, respectively, consequently.consequently.

The syntax of a problem may be too The syntax of a problem may be too complex for students to operationa.lise itcomplex for students to operationa.lise it

LANGUAGE AND MATHEMATICS LANGUAGE AND MATHEMATICS LEARNING IN BRUNEILEARNING IN BRUNEI Some key mathematics terms may Some key mathematics terms may

indicate different operations. E.g. indicate different operations. E.g. Altogether can indicate subtraction as Altogether can indicate subtraction as well as addition.well as addition.

Some structures may be used randomly, Some structures may be used randomly, e.g:e.g:

- How many fewer buckets than Dollah - How many fewer buckets than Dollah does Faridah have?does Faridah have?

- Kartika has 2 dolls less than Hamizah.- Kartika has 2 dolls less than Hamizah.


The problem as stated in the text may The problem as stated in the text may have to be changed around in order to do have to be changed around in order to do the operation. E.gthe operation. E.gKartika has some dolls. Hamizah has 4 Kartika has some dolls. Hamizah has 4 dolls. They have 12 dolls altogether. dolls. They have 12 dolls altogether. How many dolls does Kartika have?How many dolls does Kartika have?

If pupils have been told that the key word If pupils have been told that the key word altogetheraltogether indicates addition, they will indicates addition, they will probably get the question wrong.probably get the question wrong.


A child who lacks the concrete A child who lacks the concrete experiences connected with experiences connected with mathematical concepts will be unable to mathematical concepts will be unable to relate using words to experiences he relate using words to experiences he hasn’t had, and will thus have great hasn’t had, and will thus have great difficulty being involved in any dialogue difficulty being involved in any dialogue with others about the ideas. This will with others about the ideas. This will inhibit concept developmentinhibit concept development


A child who relies on code-switching to Malay A child who relies on code-switching to Malay to understand a mathematical idea in English, to understand a mathematical idea in English, may well imperfectly ‘translate’ the idea may well imperfectly ‘translate’ the idea involved in their mind, and vice-versa.involved in their mind, and vice-versa.

The child may lack the vocabulary needed to The child may lack the vocabulary needed to translate a statement into Malay and back into translate a statement into Malay and back into English again, or lack comprehension of the English again, or lack comprehension of the meaning intended in either English or Malay.meaning intended in either English or Malay.


Whilst translating from English into Malay, the Whilst translating from English into Malay, the child may well mis-translate the key logical child may well mis-translate the key logical words or sentences that in English help unlock words or sentences that in English help unlock the structure of the question.the structure of the question.

Teachers often use informal, everyday Teachers often use informal, everyday language in mathematics lessons before or language in mathematics lessons before or alongside technical mathematical vocabulary.alongside technical mathematical vocabulary.


Although this can help children to grasp Although this can help children to grasp the meaning of different words and the meaning of different words and phrases, there would be a structured phrases, there would be a structured approach to the teaching and learning of approach to the teaching and learning of vocabulary is essential if children are to vocabulary is essential if children are to move on and begin using the correct move on and begin using the correct mathematical terminology as soon as mathematical terminology as soon as possible.possible.

Helping children to use Helping children to use mathematical language correctlymathematical language correctly

Encourage children to talk about what they Encourage children to talk about what they are doing/ have done and to listen to each are doing/ have done and to listen to each other.other.

Model language by describing what children Model language by describing what children are doing a you work alongside them. E.g are doing a you work alongside them. E.g ‘You made the car go straight ahead and ‘You made the car go straight ahead and then turn left’then turn left’

Value children’s own spontaneous language, Value children’s own spontaneous language, e.g. e.g. ‘My shape has three point bits’‘My shape has three point bits’

Helping children to use Helping children to use mathematical language correctlymathematical language correctly

Extend what children have said in different Extend what children have said in different words. e.g. words. e.g. ‘Yes, it’s got three corners’‘Yes, it’s got three corners’

Set up activities which encourage children Set up activities which encourage children to describe and explain, e.g. to describe and explain, e.g. ‘Say what ‘Say what you can feel in the feely bag’you can feel in the feely bag’

Encourage children to compare, e.g. Encourage children to compare, e.g. ‘How ‘How are these two shapes different?’are these two shapes different?’

Learning Learning EnvironmentEnvironment

LEARNING ENVIRONMENTLEARNING ENVIRONMENT

The classroom learning environment can The classroom learning environment can take a physical form such as the color of take a physical form such as the color of the walls, the number of posters, or the the walls, the number of posters, or the quality of the desks and resources. quality of the desks and resources.

However, the environment also takes a However, the environment also takes a more important psychological and social more important psychological and social form. form.


The psychosocial classroom environment The psychosocial classroom environment is the psychological and social is the psychological and social relationships which exist between relationships which exist between students, and between students and their students, and between students and their teacher. teacher.

It is frequently different from one class to It is frequently different from one class to another. another.


Students developed more positive Students developed more positive attitudes towards their mathematics in attitudes towards their mathematics in classes where the teacher was perceived classes where the teacher was perceived to be highly supportive, equitable, place a to be highly supportive, equitable, place a strong emphasis on understanding the strong emphasis on understanding the work, were involved in investigations, work, were involved in investigations, showed leadership, helping-friendly showed leadership, helping-friendly behaviour and minimal admonishment of behaviour and minimal admonishment of students. students.

LEARNING ENVIRONMENTLEARNING ENVIRONMENT Pupils showed the greatest cognitive Pupils showed the greatest cognitive

gains in classes where students gains in classes where students perceived that the teacher emphasized perceived that the teacher emphasized understanding the work.understanding the work.

The least cognitive gains occurred in The least cognitive gains occurred in classes where pupils perceived that the classes where pupils perceived that the teacher was dissatisfied, gave them too teacher was dissatisfied, gave them too much freedom and responsibility, and much freedom and responsibility, and where they were involved in where they were involved in investigations.investigations.


Teachers are aware that there is more to Teachers are aware that there is more to teaching than delivering a syllabus. teaching than delivering a syllabus.

Teachers constantly make judgments Teachers constantly make judgments about what questions to ask in class, about about what questions to ask in class, about who should answer them, about when to who should answer them, about when to intervene in discussions, when to move on intervene in discussions, when to move on or when to slow down, about when to or when to slow down, about when to reprimand, and when to encourage.reprimand, and when to encourage.


The list could go on and on. The list could go on and on. Teachers are also aware that all classes Teachers are also aware that all classes

are different. are different. Even when teachers teach two classes in Even when teachers teach two classes in

the same year level with the same the same year level with the same course, the classes frequently are course, the classes frequently are different. Each class develops its own different. Each class develops its own unique learning environment. unique learning environment.

LEARNING ENVIROMENTLEARNING ENVIROMENT

This environment develops out of the This environment develops out of the relationships between the teacher and relationships between the teacher and his or her students. his or her students.

Over time, norms of behaviour are Over time, norms of behaviour are established, both on the part of the established, both on the part of the teacher as well as by the students, as teacher as well as by the students, as values and expectations on both sides values and expectations on both sides become clear. become clear.


A pattern of behaviour results, based on A pattern of behaviour results, based on the knowledge that students have of their the knowledge that students have of their teacher and visa versa. teacher and visa versa.

This learning environment may be a very This learning environment may be a very encouraging one in which students enjoy encouraging one in which students enjoy their work and feel valued. their work and feel valued.

On the other hand it may be discouraging On the other hand it may be discouraging if the work ethos and satisfactory if the work ethos and satisfactory relationships are absent.relationships are absent.

LEARNING ENVIROMENTLEARNING ENVIROMENT Research into classroom learning Research into classroom learning

environments (Fraser, 1986, 1994; Wubbels environments (Fraser, 1986, 1994; Wubbels & Levy, 1993) is based upon students' & Levy, 1993) is based upon students' perceptions of their learning environment.perceptions of their learning environment.

The premise here is that students' learning The premise here is that students' learning behaviour in class will be largely determined behaviour in class will be largely determined by the way in which they perceive their by the way in which they perceive their learning environmentlearning environment


Classes where pupils perceive that Classes where pupils perceive that - they have a high level of cohesion, - they have a high level of cohesion, - they frequently use investigative methods,- they frequently use investigative methods,- they are on task, - they are on task, - that the class operates equitably - that the class operates equitably

These pupils show a more positive These pupils show a more positive attitude attitude towards their mathematics.towards their mathematics.

LEARNING ENVIRONMENTLEARNING ENVIRONMENT In classes where pupils view their teacher In classes where pupils view their teacher

as mostly showing high levels of as mostly showing high levels of Leadership, Helping/Friendly, and Leadership, Helping/Friendly, and Understanding behaviour, and give high Understanding behaviour, and give high levels of Student Responsibility and levels of Student Responsibility and FreedomFreedom

The pupils have much healthier The pupils have much healthier attitudes towards their class and enjoy their attitudes towards their class and enjoy their lessons more than in classes when the lessons more than in classes when the other side of teacher behaviour is common. other side of teacher behaviour is common.

LEARNING ENVIRONMENTLEARNING ENVIRONMENT Where teachers show high levels of Strict, Where teachers show high levels of Strict,

Admonishing, Dissatisfied and Uncertain Admonishing, Dissatisfied and Uncertain behaviour, students do not enjoy their behaviour, students do not enjoy their classes as much and develop more classes as much and develop more negative attitudes towards the subject.negative attitudes towards the subject.

It is also interesting to note that girls see It is also interesting to note that girls see their teacher's behaviour much more their teacher's behaviour much more positively than do boys.positively than do boys.

LEARNING ENVIRONMENTLEARNING ENVIRONMENT Girls from coeducational classes perceived Girls from coeducational classes perceived

statistically significantly more Helping/Friendly statistically significantly more Helping/Friendly and Understanding behaviour whilst boys and Understanding behaviour whilst boys perceived more Uncertain, Dissatisfied, perceived more Uncertain, Dissatisfied, Admonishing and Strict behaviours. Admonishing and Strict behaviours.

Boys see more of the behaviours in their Boys see more of the behaviours in their teachers which are associated with negative teachers which are associated with negative attitudes towards the subject and poorer results. attitudes towards the subject and poorer results. Girls perceive more of the behaviours which are Girls perceive more of the behaviours which are associated with more positive outcomes.associated with more positive outcomes.

ConclusionConclusion The use of Information Communication The use of Information Communication

Technology (ICT) as a teaching and Technology (ICT) as a teaching and learning tool will begin to take a central role learning tool will begin to take a central role in enhancing the learning process in line in enhancing the learning process in line with the new, 21st century national with the new, 21st century national educational system. educational system.

In keeping abreast with the advances of In keeping abreast with the advances of ICT, changes will be made to more school ICT, changes will be made to more school subjects to incorporate the use of ICT subjects to incorporate the use of ICT

ConclusionConclusion

The school leaders (principals and headmasters) The school leaders (principals and headmasters) and education leaders (deputy academic and education leaders (deputy academic principals, senior academic teachers, heads of principals, senior academic teachers, heads of subject departments and subjects teachers) also subject departments and subjects teachers) also need to understand their tasks, strengthen their need to understand their tasks, strengthen their commitment and work as a team in implementing commitment and work as a team in implementing their tasks and responsibilities in contributing their tasks and responsibilities in contributing towards the effectiveness of SPN 21. towards the effectiveness of SPN 21.

ConclusionConclusion

Also the teacher readiness to implement change Also the teacher readiness to implement change where their need in depth training and close on-where their need in depth training and close on-site help.site help.

For this to happen a phased implementation of For this to happen a phased implementation of new curricular programme should be seriously new curricular programme should be seriously considered. considered.

The definitive test of the effectiveness of change in The definitive test of the effectiveness of change in mathematics education lies in pupil attainment and mathematics education lies in pupil attainment and understanding. understanding.

CONCLUSIONCONCLUSION In order to improve the quality of teaching In order to improve the quality of teaching

Mathematics in Primary school, we need to Mathematics in Primary school, we need to have high quality and skilled teachers that have high quality and skilled teachers that havehaveAbility to explain clearlyAbility to explain clearlyTo ask intelligent and thought-provoking To ask intelligent and thought-provoking

questionsquestionsTo assess pupils’ progressTo assess pupils’ progressTo manage class effectivelyTo manage class effectively

Pupils developed more positive attitudes Pupils developed more positive attitudes towards their mathematics in classes towards their mathematics in classes when the teacher when the teacher perceived to be highly supportive,perceived to be highly supportive,equitable, equitable, emphasis on understanding the work, emphasis on understanding the work, involved in investigations, involved in investigations, showed leadership, showed leadership, helping-friendly behavior and helping-friendly behavior and minimal admonishment of students. minimal admonishment of students.

In teaching mathematics to the children, the In teaching mathematics to the children, the teacher have to be aware that not only they teacher have to be aware that not only they are teaching one subject but they also teach are teaching one subject but they also teach another subject to them, English.another subject to them, English.

Teacher should use simple English words Teacher should use simple English words and explain clearly when teaching in class.and explain clearly when teaching in class.

When pupils having difficulty in When pupils having difficulty in understanding the mathematical concepts, understanding the mathematical concepts, teacher may use the mother tongue teacher may use the mother tongue language to explain the terms.language to explain the terms.

current issues in mathematical education

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