Mathematics education in Singapore is a shared responsibility of the Ministry of Education (MOE) and the National Institute of Education (NIE). The MOE overseas the intended, implemented and attained curriculum in all schools while the NIE is involved in teacher preparation and development and also research in mathematics education. Therefore this report has two sections respectively, the first describes the education system and school mathematics curricula while the second briefly provides relevant information on teacher preparation and development and mathematics education research in Singapore.

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Mathematics Education in Singapore

Berinderjeet Kaur, Cheow Kian Soh, Khoon Yoong Wong,

Eng Guan Tay, Tin Lam Toh, Ngan Hoe Lee, Swee Fong Ng,

Jaguthsing Dindyal, Yeen Peng Yen, Mei Yoke Loh,

Hwee Chiat June Tan and Lay Chin Tan

Abstract Mathematics education in Singapore is a shared responsibility of the

Ministry of Education (MOE) and the National Institute of Education (NIE). The

MOE overseas the intended, implemented and attained curriculum in all schools

while the NIE is involved in teacher preparation and development and also research

in mathematics education. Therefore this report has two sections respectively, the

first describes the education system and school mathematics curricula while the

second briefl y provides relevant information on teacher preparation and develop-

ment and mathematics education research in Singapore.

Keywords Singapore Mathematics education Curriculum Teacher educa-

tion Research

Introduction

Mathematics education in Singapore is a shared responsibility of the Ministry of

Education (MOE) and the National Institute of Education (NIE). MOE develops the

national mathematics curriculum and oversees its implementation in all schools,

while the NIE is involved in teacher preparation and development and also research

in mathematics education. This report comprises two sections: the first describes the

education system and school mathematics curricula while the second provides

relevant information on teacher preparation and development and mathematics

education research in Singapore.

B. Kaur (& ) K.Y. Wong E.G. Tay T.L. Toh N.H. Lee S.F. Ng J. Dindyal

National Institute of Education, Nanyang Technological University, Singapore, Singapore

e-mail: berinderjeet.kaur@nie.edu.sg

C.K. Soh (& ) Y.P. Yen M.Y. Loh H.C.J. Tan L.C. Tan

Ministry of Education, Singapore, Singapore

e-mail: SOH_Cheow_Kian@moe.edu.sg

©The Author(s) 2015

S.J. Cho (ed.), The Proceedings of the 12th International Congress

on Mathematical Education, DOI 10.1007/978-3-319-12688-3_21

311

The Education System and School Mathematics Curricula

Education in Singapore has evolved through a continual process of change,

improvement and refi nement since the country gained independence in 1965.

Today, all children receive at least 10 years of general education in over 350

primary, secondary and post-secondary schools. There are diverse pathways and

opportunities for students to discover their talents, realize their potential, and

develop a passion for life-long learning. Singapore' s education system largely

follows a 6-4-2 structure, with 6 years of primary (Grade 1–6), 4 years of secondary

(Grade 7– 10) and 2 years of pre-university (Grade 11– 12) education (MOE 2012).

Mathematics is a compulsory subject from Primary 1 up to the end of secondary

education. In the early grades, about 20 % of the school curriculum time is devoted

to mathematics so that students build a strong foundation to support further learning

in later years. The mathematics curriculum is centrally planned by MOE. However,

flexibility is given to schools to implement the curriculum to best meet the abilities

and interests of students. The mathematics curriculum is reviewed every 6 years

with consultation of key stakeholders and partners to ensure that it meets the needs

of the nation.

The mathematics curriculum aims to enable students to acquire and apply

mathematical concepts and skills; develop cognitive and metacognitive skills

through a mathematical approach to problem solving; and develop positive attitudes

towards mathematics. A single mathematics curriculum framework (MOE 2007)

unifi es the focus of the mathematics curriculum for all levels from primary to pre-

university. The focus is on developing students' mathematical problem-solving

abilities through fi ve integral components namely, concepts, skills, processes,

attitudes, and metacognition.

A spiral approach is used in the design of the mathematics syllabuses from

primary to pre-university. At every level, the syllabuses comprise a few content

strands (e.g. number and algebra, geometry and measurement, statistics and prob-

ability), facilitating connections and inter-relationships across strands. The content

in each strand is revisited and taught with increasing depth across levels. There is

differentiation in the content, pace and focus among syllabuses within the same

levels to cater to different student profiles.

Primary 1– 4 students follow a common mathematics syllabus, covering the use of

numbers in measurements, understanding of shapes and simple data analysis. At

Primary 5– 6, there are two syllabuses: the Standard Mathematics syllabus builds on

the concepts and skills studied in Primary 1– 4, whereas the Foundation Mathematics

syllabus revisits some of the important concepts and skills taught earlier. At the

secondary level, there are 5 different syllabuses for students in the Express, Normal

(Academic) and Normal (Technical) courses. These syllabuses include concepts and

skills in number and algebra, measurement and geometry, and statistics and

probability. Calculus and trigonometry are covered in the additional mathematics

syllabuses for Secondary 3– 4 students who are more mathematically-inclined. At

the pre-university level, mathematics is an optional subject. Three syllabuses

312 B. Kaur et al.

(H1, H2 and H3) are available to prepare students for different university courses and

the use of graphing calculators is expected.

There are also programmes to support the slow progress students and stretch

those talented in mathematics. Primary 1 students (about 5 %) who lack age-

appropriate numeracy skills are given support through the Learning Support Pro-

gramme for Mathematics where they are taught in small groups by specially-trained

teachers. For gifted learners, there is an enriched mathematics curriculum that

emphasizes problem solving, investigations, making conjectures, proofs and con-

nections among concepts. The NUS High School of Mathematics and Science also

offers mathematically talented students a broad-based 6-year programme that

includes undergraduate level topics and a mathematics research component.

For the teaching of mathematics at the primary levels the Concrete-Pictorial-

Abstract (C-P-A) approach, introduced in 1980, is prevalent. Since 1990s, it has

been used together with activity-based learning to encourage active participation by

students in the learning process. In the early 1980s, MOE also developed the model

method for solving word problems at the primary level (MOE 2009 ). This method

provides a visual tool for students to process and analyse information and develop a

sequence of logical steps to solve word problems. The model method is also used

with algebra to help students formulate algebraic equations to solve problems in

lower secondary mathematics. This facilitates the transition from a dominantly

arithmetic approach at the primary level to an algebraic one at the secondary level.

At the secondary and pre-university levels, teacher-directed inquiry and direct

instruction are common. These approaches are used with other activities and group

work to engage students in learning mathematics.

Resources are critical to curriculum implementation and effective delivery of

mathematics lessons. Textbooks are essential materials to help teachers understand

the emphases and scope of the syllabuses, and for students to learn independently. In

the late 1990s, MOE devolved textbook writing to commercial publishers to allow

for a greater variety of textbooks. Quality is assured through a rigorous textbook

authorization and approval process by MOE. Besides textbooks, MOE also produces

additional materials to support teachers especially at the primary levels.

Teacher Preparation and Development, and Research

in Mathematics Education

The NIE and Teacher Education

The National Institute of Education (NIE) is an autonomous institute within the

Nanyang Technological University and sole teacher education institution in Sin-

gapore. It offers both pre-service and in-service education programmes ranging from

diploma to doctorate levels. Its present model of Teacher Education for the 21st

century (TE

21

) is unique and has six foci intended to enhance the key elements of

teacher education. The foci are the Values

3

, Skills and Knowledge (V

3

SK) model,

Mathematics Education in Singapore 313

the Graduand Teacher Competencies (GTC) framework, strengthening the theory-

practice nexus, an extended pedagogical repertoire, an assessment framework for

21st century teaching and learning, and enhanced pathways for teacher professional

development (NIE 2009 ). In particular the V

3

SK model explicates three dimensions

of values for the teacher, viz. learner-centredness, teacher identity and service to the

profession and community, without which the beginning teacher may easily lose her

focus in an increasingly technological and knowledge-driven world. The GTC

framework makes clear the competencies to which the student teacher should aspire

to attain or be aware of in his studies at NIE. This is a distinct attempt to state what

must be achieved in one' s pre-service teacher education and also what should be

reasonably accomplished only after some years of experience as a teacher.

Pre-service Education of Mathematics Teachers

Pre-service education provides the crucial initial training that can have long-term

impacts on the quality of future teachers in an education system. Besides education

courses and the practicum, trainee teachers take mathematics-related courses called

Curriculum Studies (methodology), Subject Knowledge (deeper understanding of

school mathematics), and Academic Studies (tertiary mathematics). These courses

are taught by mathematicians, mathematics educators, and " mathematician educa-

tors" (those with expertise in both areas) from the same Mathematics and Mathe-

matics Education Academic Group. These courses stress the rigour of mathematics

contents and relevance to local school contexts and school mathematics, in partic-

ular, the model method used in problem solving. Locally developed resources (Lee

and Lee 2009a ,b ) used in these courses combine local experience and research with

international " best practices" . Blended learning is used in teacher education courses

in response to the signifi cant roles of ICT in instruction as well as the changing

characteristics of the trainee teachers. Findings from IEA' s Teacher Education and

Development Study in Mathematics (TEDS-M) (Tatto et al. 2012 ) show that NIE

trainee teachers scored above international average in mathematics content and

pedagogical content knowledge, and most of them expressed strong commitment to

the teaching profession as their life-long career.

Professional Development of Mathematics Teachers

Since 1998 all teachers in Singapore are entitled to 100 h of training and core-

upgrading courses each year to keep abreast with current knowledge and skills. The

Professional Development (PD) is funded by the MOE. Teachers have different

pathways to upgrade their knowledge and skills through the Professional Devel-

opment Continuum Models (PCDM) of the MOE. The MOE works closely with

NIE to design courses for practicing teachers. Numerous academic courses offered

314 B. Kaur et al.

by NIE lead to postgraduate degrees. For example, in order to upgrade mathematics

teachers' content knowledge, a unique master degree programme MSc (Mathe-

matics for Educators) is offered by NIE. The mathematics chapter of the Academy

of Singapore Teachers (AST), the Association of Mathematics Educators (AME)

and the Singapore Mathematical Society (SMS) are also actively engaged in the PD

of teachers. They hold relevant annual meetings, seminars and conferences for

teachers. Teachers may also attend international conferences or study trips to widen

their perspectives on mathematics education. Lastly, teachers are also engaging in

professional learning and development by participating in research projects at the

school level. Examples of two such projects are the Enhancing the pedagogy of

mathematics teacher (EPMT) project (Kaur 2011) and the Think-Things-Through

(T3) project (Yeap and Ho 2009).

Mathematics Education Research in Singapore

Research is undertaken by graduate students and university scholars. Since 2002,

the MOE through the Offi ce of Education Research (OER) at NIE has funded

research to inform policy and practice so as to improve education in Singapore.

Some of the projects in mathematics education that have been funded and com-

pleted are as follows: An exploratory study of low attainers in primary mathematics

(Kaur and Ghani 2012 ); The Singapore mathematics assessment and pedagogy

project (Wong et al. 2012 ); Individual differences in mathematical performance:

social-cognitive and neuropsychological correlates (Lee and Ng 2011 ); Mathe-

matical problem solving for everyone (Toh et al. 2011 ), Student perspective on

effective mathematics pedagogy (Kaur 2009 ), and Teaching and learning mathe-

matical word problems: A comparison of the model and symbolic methods (Lee

et al. 2011 ). These projects were carried out by university scholars in collaboration

with students, teachers and research staff at NIE. Research studies undertaken by

graduate students almost always culminate in dissertations, thesis or academic

reports, all of which are available at the NIE library repository.

Open Access This chapter is distributed under the terms of the Creative Commons Attribution

Noncommercial License, which permits any noncommercial use, distribution, and reproduction in

any medium, provided the original author(s) and source are credited.

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... All stakeholders in society are therefore in agreement that effective mathematics problem solving skills are extremely desirable in students for many reasons and that they are currently often not prevalent in the majority of school leavers. It is such conclusions that have led to some countries trying to adapt their education system to ones in which the teaching and learning of problem solving skills can be employed more successfully than they currently are (OECD, 2009a(OECD, , 2009bQCA, 2008;Soh, 2008). However the challenge of improving teaching and learning in the area of problem solving skills has never been underestimated (Wallace et al., 2009). ...

In 2010 a mathematics curriculum was introduced in Irish second level schools entitled 'Project Maths' (PM). It aimed to refocus second level mathematics teaching and learning away from an over emphasis on procedural mathematics towards problem solving and real understanding [Department of Education and Skills (DES). (2010). Report of the Project Maths implementation support group. https://www.education.ie/en/Publications/Policy-Reports/Report-of-the-Project-Maths-Implementation-Group.pdf]. This paper aims to examine the performance of 1st year undergraduate students' procedural and problem solving skills after the introduction of PM. A diagnostic test was developed to determine students' skills in each area and findings demonstrated that students perform statistically significantly better in the procedural skills in mathematics when compared to problem solving skills. These findings raise concerns around the lack of anticipated improved problem solving skills of a cohort of students exposed to this style of teaching and learning. The paper raises discussion surrounding the intended and actual teaching and learning taking place in second level classrooms along with consideration for the potential role of learned helplessness and the literacy issues. Recommendations are made for follow up qualitative research with stakeholders in mathematics education to better understand the 'why' of the results presented here.

... Research also highlights issues around students' ability to transfer the mathematical skills they have mastered in their formal education to work place situations or for the study of further mathematics (Treilibs 1979). Many countries, such as Ireland, are therefore attempting to change their mathematics curricula at second level education in an attempt to overcome such issues and ensure that students are developing the necessary problem solving skills for success in further study and future work (OECD 2009;QCA 2008;Rocard 2007;Soh 2008). ...

... In addition, Fowler (2015) reported that Singaporean mathematics textbooks provided more questions requiring higher cognitive demand levels than US textbooks on linear functions topics. Singaporean textbook reflected simple features of text density and enriched use of visual elements, more number of mathematics topics, and an easier inner organization to follow (Erbas, Alacaci, & Bulut, 2012;Soh, 2008) On the other hand, Indonesian curriculum has been implementing realistic mathematics education approach to school mathematics which is widely recognized as providing one of the best and most detailed elaborations of the problem-based approach to mathematics education (Hadi, 2002). Wijaya et al. (2015) argued that the lacking opportunityto-learn in Indonesian mathematics textbooks may cause Indonesian students' difficulties in solving tasks. ...

  • Kai Kow Joseph Yeo
  • Lu Pien Cheng

Mathematics education in Singapore schools in the twenty-first century is still going through the period of change and innovation that began in the early 1990s: changes in emphasis from rote memorisation to meaningful understanding of concepts and problem-solving; from a dependence on paper and pencil and manipulative calculations and skills to mental computations and thinking strategies; and from teaching by telling to activity-based learning, group work, and communication in mathematics. This chapter makes an attempt to describe how the mathematics curriculum in Singapore has responded to such changes and innovations. At the same time, the chapter has chosen three out of many major innovations in Singapore mathematics education and discusses them in relation to school mathematics: problems in real-world contexts (PRWC), Learning Support for Mathematics (LSM), and Improving Confidence and Achievement in Numeracy (ICAN). These innovations are selected because the ways Singapore has approached them might be of theoretical and practical interest to international readers.

  • Tin-Lam Toh Tin-Lam Toh

This chapter discusses how Singapore strives for excellence in mathematics education in various ways. The chapter begins with the importance that Singapore has placed in identifying and developing its mathematically talented students for the prestigious mathematics competitions. Simultaneously, local mathematics community attempt to popularise mathematics competition among more interested student population and even attempt to align mathematics competition with the school curriculum, so as to benefit more student population in a variety of ways. The chapter continues to discuss the notion of mathematics competitive activities to include mathematics research and real-world problem-solving in order to identify and nurture a much wider group of mathematics talents among the Singapore students. At the systemic level, various attempts to develop and stretch our talents are emplaced, such as the Gifted Education Programme and the Integrated Programme. Within the curriculum structure, much has been done to provide differentiated instructions for students from primary to preuniversity education. This will culminate in the imminent subject-based banding, which will be implemented in full scale in the near future.

  • Tin-Lam Toh Tin-Lam Toh

In this paper, the Singapore school calculus curriculum at the upper secondary and the pre-university levels is examined in the light of the Singapore mathematics curriculum framework. Three key features of the calculus content are discerned: (1) an intuitive approach to calculus supported by the use of technology; (2) an emphasis on techniques; and (3) an emphasis on procedural over conceptual knowledge. Following that analysis, a review of the performance of a group of pre-university students on selected calculus tasks in a calculus survey prior to and after their learning of pre-university calculus is discussed. The students' performance in the survey shows that many students did not visually identify calculus concepts that were studied procedurally. They demonstrated a lack of conceptual understanding of the calculus procedures. This study suggests that the partial calculus knowledge acquired in the early upper secondary levels might not necessarily facilitate the acquisition of a more complete concept at the pre-university level. Furthermore, the students' procedural knowledge of calculus did not seem to develop their procedural fluency or flexibility.

Cognitive pattern recognition is known to be an important skill for academic subjects such as mathematics, science, languages, or even humanities. In this study, we investigate the relationships between creativity, critical thinking, and pattern recognition among 203 private school students in Singapore. The instruments used include a creativity test (modified Creativity Selected Elements Questionnaire), a Critical Thinking Test (modified Cornell Critical Thinking), and a pattern recognition test. The main data analysis is done using the SMART-PLS structural equation modeling software. The results of the study reveal that creativity is a weak predictor of pattern recognition (β = 0.131, p > 0.05, f² = 0.024) but critical thinking is a good predictor (β = 0.517, p < 0.05, f² = 0.374). An implication of the research outcome is that more training on critical thinking should be given to the students to improve their pattern recognition ability.

  • Berinderjeet Kaur Berinderjeet Kaur

The evolution of Singapore's school mathematics curriculum is in tandem with developments in the education system of Singapore. In the last six decades, economic policies of the government that are necessary for the survival of Singapore in a fast changing world have shaped the aims of the school mathematics curriculum. The present-day curriculum can best be described as one that caters for the needs of every child in school. It is based on a coherent framework that has mathematical problem solving as its primary focus. The curriculum may be claimed to be one of the four factors that contributes towards Singapore's performance in benchmark studies such as TIMSS and PISA.

  • Berinderjeet Kaur Berinderjeet Kaur

Enhancing the pedagogy of mathematics teachers (EPMT) project is a hybrid model of professional development (PD) that reflects a gradual shift in the centre of gravity away from the University-based, "supply-side", "off-line" forms of knowledge production conducted by university scholars for teachers towards an emergent school-based, demand-side, on-line, in situ forms of knowledge production conducted by teachers with support from university scholars. The aims of the EPMT project were threefold: to provide teachers with training, to facilitate teachers' work (practice and feedback) at the school level and to enthuse and support teachers to contribute towards the development of fellow teachers. This paper examines two project participants' infusion of their learning in classroom practice. From the lessons enacted by the two teachers it was apparent that both teachers were able to apply their learning in their lessons. The teachers also manifested changes in their perception of teaching mathematics.

The IEA Teacher Education and Development Study in Mathematics (TEDS-M) is a comparative study of primary and secondary mathematics teacher education. It examined how different countries have prepared their teachers to teach mathematics in primary and lower-secondary school. TEDS-M paid particular attention to links between teacher education policies, practices, and outcomes. By participating in the study, countries were provided with an opportunity to conduct research on their own teacher education system and to learn from the approaches used in other countries. TEDS-M asked several key research questions: What is the national policy context for mathematics teacher education? What are the main characteristics of mathematics teacher education programs, and how do they vary across countries? What is the level of mathematics and related teaching knowledge acquired by prospective primary and secondary mathematics teachers? An additional smaller study linked to TEDS-M compared the salaries of primary and secondary teachers with those of individuals in other mathematics-oriented professions, such as engineering, scientific research, and accounting, in 20 countries. It also investigated the relationship between what mathematics teachers were paid and how well students performed on international mathematics tests. Target population TEDS-M surveyed teacher education institutions, educators of future teachers, and future teachers (primary and secondary level). Participating education systems Botswana, Canada, Chile, Chinese Taipei, Georgia, Germany, Malaysia, Norway, Oman, Philippines, Poland, Russian Federation, Singapore, Spain, Switzerland (German speaking cantons), Thailand, and United States.

Although mathematical pattern tasks are often found in elementary school curricula and are deemed a building block for algebra, a recent report (National Mathematics Advisory Panel, 2008) suggests the resources devoted to its teaching and assessment need to be rebalanced. We examined whether children's developing proficiency in solving algebraic word problems is related to their proficiencies in patterns, computational, and working memory tasks. Children (N = 151 10-year-olds) were tested twice, 1 year apart, and were administered tests of updating capacities (2 complex span and 1 running span task), computation (from the Wechsler Individual Achievement Test), patterns (function machine, number patterns), and algebraic word problems. Proficiencies on the patterns and computational tasks predicted algebraic proficiency. Proficiencies on the computational and patterns tasks are, in turn, predicted by updating capacity. These findings suggest that algebraic reasoning may be difficult if the child has poor updating capacity and either poor facility with computation or difficulty in recognizing and generalizing rules about patterns. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

  • Kerry Lee Kerry Lee
  • Swee Fong Ng

Much of the neuroimaging research has focused on how mathematical operations are performed. Although this body of research has provided insight for the refinement of pedagogy, there are very few neuroimaging studies on how mathematical operations should be taught. In this article, we describe the teaching of algebra in Singapore schools and the imperatives that led us to develop two neuroimaging studies that examined questions of curricular concerns. One of the challenges was to condense issues from classrooms into tasks suitable for neuroimaging studies. Another challenge, not particular to the neuroimaging method, was to draw suitable inferences from the findings and translate them into pedagogical practices. We describe our efforts and outline some continuing challenges.

  • Berinderjeet Kaur Berinderjeet Kaur

This paper examines the instructional approaches of three competent grade 8 mathematics teachers. It also examines their students' perception of the lessons they taught as well as characteristics of good lessons. The findings of teachers' practice and students' perception are juxtaposed to elicit characteristics of good teaching in Singapore grade 8 classrooms. With limitation, the findings of the paper suggests that good mathematics teaching in Singapore schools centres around building understanding and is teacher-centred but student focused. Some characteristic features of good lessons are that their instructional cycles have specific instructional objectives such that subsequent cycles incrementally build on the knowledge. The examples used in such lessons are carefully selected and vary in complexity from low to high. Teachers actively monitor their student's understanding during seatwork, by moving from desk to desk guiding those with difficulties and selecting appropriate student work for subsequent whole-class review and discussion. Finally, during such lessons teachers reinforce their students' understanding of knowledge expounded during whole-class demonstration by detailed review of student work done in class or as homework.

This book is the first of its kind, as it includes both mathematics content and pedagogy. It is a professional instructional manual on how mathematical problem solving curriculum can be implemented in the classrooms. The book develops from the theoretical work of Polya and Schoenfeld, and explicates how these can be translated to the actual implementation in schools. It represents the work of a group of researchers from the Singapore National Institute of Education, after experimenting with it in the Singapore school classrooms. This book includes a set of scheme of work, lesson plans and a choice of mathematics problems that teachers can actually use in teaching problem solving. Certain pedagogical considerations are developed and suggested in this book. In addition, the book includes an assessment framework on how mathematical problem solving can be assessed. © 2011 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.

  • Berinderjeet Kaur Berinderjeet Kaur
  • Masura GHANI

Low Attainers in Primary Mathematics focuses on data from students in Singapore schools. It is widely acknowledged that students from Singapore do well in mathematics in international studies. This book provides readers with a glimpse of students from Singapore who are at the other end of the ability spectrum. The book is based on a study that explored the mathematics content knowledge of Primary 4 low attainers in mathematics, their behaviours, affects and home backgrounds, and learning experiences. Based on the findings of the study, the book has recommendations for teachers of low attainers in primary mathematics. This book serves as a must-have resource for teachers and graduate students in Singapore who are working with or studying low attainers in primary mathematics. It also makes a worthy contribution towards literature on low attainers in the field of mathematics education. © 2012 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.

  • K. Y. Wong
  • K.-S. Oh
  • Q. T. Y. Ng
  • J. S. K. Cheong

The purposes of an online system to auto-mark students' responses to mathematics test items are to expedite the marking process, to enhance consistency in marking and to alleviate teacher assessment workload. We propose that a semi-automatic marking and customizable feedback system better serves pedagogical objectives than a fully automatic one. The two pedagogical objectives to be addressed are that teachers should know about the range of students' solutions and that they should provide meaningful feedback to students through the utilization of 'customisable feedback'. Both objectives are aligned with using assessment data for learning. Our proposed IT-based system consists of a marking component and a feedback component, and it is designed to provide close linkage between IT-based marking and these pedagogical objectives. © The Author 2012. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications. All rights reserved.

  • Ban Har Yeap
  • Siew Yin Ho

This chapter describes a study on teacher change within a large research project which investigated the effects of using word problems that require students to engage in sense-making. Case studies of several teachers who participated in the study were used to develop a model of teacher change. This model, referred to as the 4-I Model, describes teacher change when a new initiative is introduced and is exemplified by four types of teachers who: ignore the initiative; imitate practices recommended for the implementation of the initiative; integrate the principles of the new initiative into their instructional practice; internalise the principles of the initiative.

Primary mathematics syllabus Singapore: Author Ministry of Education (MOE, 2012) The Singapore education landscape The Singapore model method for learning mathematics

Ministry of Education (MOE, 2007). Primary mathematics syllabus. Singapore: Author Ministry of Education (MOE, 2012). The Singapore education landscape. Retrieved December 3, 2012, from http://www.moe.gov.sg/education/landscape/ Ministry of Education (MOE, 2009). The Singapore model method for learning mathematics. Singapore: Marshall Cavendish Education NIE (National Institute of Education) (2009). TE21: A teacher education model for the 21 st century. Singapore: Author.