Mathematics

Description of Task Force

This is a research area that focuses on the teaching and learning of mathematics in Singapore schools. In tandem with the framework for school mathematics in Singapore, it advances research in pedagogy and pedagogical interventions in the following main areas:

  1. Mathematical problem-solving
  2. Mathematical processes (Reasoning, Communication & Connections/Thinking skills & Heuristics/Applications and Modelling)
  3. Metacognition
  4. Low achievers in mathematics
  5. Classroom practices
  6. Teacher learning and development
  7. Teaching and learning of algebra
  8. International comparative studies

In the sections that follow, we list research projects and publications of colleagues in the Mathematics and Mathematics Education (MME) Academic Group that are related to most of the above areas that are categorised as sub-themes.

List of team members:

  1. Prof Berinderjeet Kaur (Co-Convenor)
  2. A/P Toh Tin Lam (Co-Convenor)
  3. A/P Wong Khoon Yoong

Sub-theme 1: Mathematical Problem-solving

The Ministry of Education (MOE) syllabus document states explicitly the importance of problem solving: “Mathematical problem solving is central to mathematics learning. It involves the acquisition and application of mathematics concepts and skills in a wide range of situations, including non-routine, open-ended and real-world problems” (2007, p. 3). As to the direction of problem solving research, Alan Schoenfeld (2007) stressed that the current focus should lie in translating decades of theory building about problem solving into workable practices in the classroom. Appended below is a list of research projects whose objective is to translate the theory of problem solving to viable classroom practices.

To ensure the success of any innovative practice in the school classrooms, teachers must be equipped with the essential knowledge and skills to carry out the practice. Teachers need to “buy-in” to the idea of the innovation proposed by the researchers. A list of publications on introducing problem solving at the prospective teacher education is also listed below.

References:

  • Ministry of Education (2007). Mathematics syllabus – Secondary. Singapore: Author.
  • Schoenfeld, A. (2007). Assessing mathematical proficiency. Mathematical sciences research institute publications (Vol. 53). Cambridge, UK: Cambridge University Press.

List of research projects relating to Mathematical Problem-solving:

List of publications relating to Mathematical Problem-solving:

  • Dindyal, J., Tay, E. G., Toh, T. L., Leong, Y. H., & Quek, K. S. (2012). Mathematical problem solving for everyone: A new beginning. The Mathematics Educator, 13(1), 51–70.
  • Fang, Y. P., Ho, K. F., Lioe, L. T., Wong, K. Y., & Tiong, Y. S. (2009). Mathematical Problem Solving, Project 1: Developing the Repertoire of Heuristics for Mathematical Problem solving.
  • Leong, Y. H., Tay, E. G., Quek, K. S., Toh, T. L., Toh, P. C., Dindyal, J., & Yap, R. A. S. (2014). Making mathematics more practical: Implementation in the schools. Singapore: World Scientific.
  • Toh, T. L. (2009). Arousing students’ curiosity and mathematical problem solving. In B. Kaur, Y. B. Har & M. Kapur (Eds.), Mathematical problem solving: Yearbook 2009 (pp. 241262). Singapore: World Scientific.
  • Toh, T. L., Quek, K. S., Leong, Y. H., Dindyal, J., & Tay, E. G. (2009). Assessment in a problem solving curriculum. In R. Hunter, B. Bicknell & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australia (Vol. 1, pp. 686–689). Palmerston North, NZ: MERGA.
  • Toh, T. L., Quek, K. S., Leong, Y. H., Dindyal, J., & Tay, E. G. (2011). Assessing problem solving in the mathematics curriculum: A new approach. In B. Kaur & K. Y. Wong (Eds.), AME Yearbook 2011 (pp. 1–35). Singapore: World Scientific.
  • Toh, T. L., Quek, K. S., Leong, Y. H., Dindyal, J., & Tay, E. G. (2011). Making mathematics practical: An approach to problem solving. Singapore: World Scientific.
  • Toh, T. L., Quek, K. S., Tay, E. G., Leong, Y. H., & Dindyal, J. (2011). Enacting a problem solving curriculum in a Singapore school. In L. A. Bragg (Ed.), Maths is multi-dimensional (pp. 77–86). Melbourne, Australia: Mathematical Association of Victoria.
  • Wong, K. Y. (2008). Success and consistency in the use of heuristics to solve mathematics problems. In M. Goos, R. Brown & K. Makar (Eds.), Navigating currents and charting directions (Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia, Vol. 2, pp. 589–595). Adelaide: MERGA.
  • Wong, K. Y., & Tiong, J. (2006). Developing the repertoire of heuristics for mathematical problem solving: Student problem solving exercises and attitude.

Sub-theme 2: Mathematical processes (Applications and Modelling)

In mathematical modelling, students solve real-world problems mathematically. Mathematical modelling is a cyclic process (English, 2007) of translating a real-world problem into a mathematical problem by formulating and solving a mathematical model, interpreting and evaluating the solution in the real world context, and refining or improving he model if the solution is not acceptable (Balakrishnan, Yen & Goh, 2010). At the school level, when students engage in mathematical modelling the emphasis is on the process rather than the product.

References:

  • English, L. (2007). Interdisciplinary modelling in the primary mathematics curriculum. In J. Watson & K. Beswick (Eds.), Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia (pp. 275–284). Australia: MERGA.
  • Balakrishnan, G., Yen, Y. P., & Goh, L. E. E. (2010). Mathematical modelling in the Singapore secondary school mathematics curriculum. In B. Kaur, & J. Dindyal (Eds.), Mathematical applications and modelling (pp. 247–257). Singapore: World Scientific Press.

List of projects relating to Mathematical Processes:

  • Fan, L., Zhao, D., Cheang, W. K., Teo, K. M., & Ling, P. Y. (2010). Developing disciplinary tasks to improve mathematics assessment and pedagogy: An exploratory study in Singapore schools. Procedia Social and Behavioural Sciences, 2(2), 2000–2005.
  • Wong, K. Y., Oh, K. S., Ng, Q. T., & Cheong, S. K. (2012). Linking IT-based semi-automatic marking of student mathematics responses and meaningful feedback to pedagogical objectives. Teaching Mathematics and its Applications, 31(1), 57–63. doi: 10.1093/teamat/hrr023
  • Wong, K. Y., Zhao, D. S., Cheang, W. K., Teo, K. M., Lee, P. Y., Yen, Y. P., Fan, L. H., Teo, B. C., Quek, K. S., & So, H. J. (2012). Real-life mathematics tasks: A Singapore experience. Singapore: Centre for Research in Pedagogy and Practice, National Institute of Education, NTU.
  • Wong, K. Y., & Chen, Q. (2012). Nature of an attitudes toward learning mathematics questionnaire. In J. Dindyal, L. P. Cheng & S. F. Ng (Eds.), Mathematics education: Expanding horizons: Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia (pp. 793-800). Adelaide, Australia: MERGA.
  • Zhao, D. S., Cheang, W. K., Teo, K. M., & Lee, P. Y. (2011). Some principles and guidelines for designing mathematical disciplinary tasks for Singapore schools. In J. Clark, B. Kissane, J. Mousley, T. Spencer & S. Thorton (Eds.), Mathematics: Traditions and (new) practices: Proceedings of the AAMT-MERGA conference (pp. 1107–1115). Adelaide, Australia: Australian Association of Mathematics Teachers.
  • Stillman, G., & Ng, K. E. D. (2013). Embedding authentic real world tasks into secondary mathematics curricula. In A. Damlamian, J. F. Rodrigues & R. Sträßer (Eds.), Educational interfaces between mathematics and industry (pp. 299–307). Dordrecht, The Netherlands: Springer.
  • Ng, K. E. D. (2013). Teacher readiness in mathematical modelling: Are there differences between pre-service and experienced teachers? In G. Stillman, G. Kaiser, W. Blum & J. Brown (Eds.), Connecting to practice: Teaching practice and the practice of applied mathematicians (pp. 339–348). Dordrecht, The Netherlands: Springer.
  • Lee, N.H. (2013). Initial perspective of teacher professional development on mathematical modelling in Singapore: Problem posing and task design. In F. A. Stillman, G. Kaiser, W. Blum, & J.P. Brown (Eds.), Teaching mathematical modelling: connecting to research and practice (pp. 415–425). London, UK: Springer.

Sub-theme 3: Metacognition

Metacognition or thinking about thinking, refers to the awareness of and the ability to control one’s thinking processes, in particular the selection and use of problem-solving strategies. It includes monitoring of one’s own thinking and self-regulation of learning (Ministry of Education, 2012).

References:

  • Ministry of Education. (2012). Primary, O, N(A), N(T)-level Mathematics teaching and learning syllabuses. Singapore: Author.

List of research projects relating to Metacognition:

  • CRP 38/03 TSK: MPS: Developing the repertoire of heuristics for mathematical problem solving
  • CRP 47/03 WKY: Enhancing Mathematics Performance (EMP)

List of publications relating to Metacognition:

  • Lee, N. H., Lee, Y. Y. G., & Koo C. C. (2013). Teachers’ promoting of students’ metacognition in mathematical modeling lessons. In M. Inprasitha (Ed.), Innovations and exemplary practices in mathematics education: Proceedings of the 6th East Asia Regional Conference on Mathematics Education (EARCOME 6) (Vol. 2, pp. 74–83). Phuket, Thailand: Center for Research in Mathematics Education (CRME), Khon Kaen University, Thailand.
  • Wong, K. Y. (2012, 15 July). Use of student mathematics questioning to promote active learning and metacognition. Regular Lecture presented at the Electronic compilation of the 12th International Congress on Mathematical Education (ICME-12), Seoul.

Sub-theme 4: Low Achievers in Mathematics

The term “low attainers” refers to pupils who attain very much less in mathematics when compared to their contemporaries in the mainstream primary school (Haylock ,1991). Low attainment in mathematics has been found to be a result of not a single factor but the interplay of subject related difficulties, specific intellectual/behavioural characteristics of the pupils and pedagogical shortcomings (1991). According to Reusser (2000), there is sufficient evidence in research on mathematics learning and teaching that most observed failures and substandard performances are due to deficiencies in the teaching and learning environments rather than genetic factors.

References:

  • Haylock, D. (1991). Teaching mathematics to low attainers, 812. Paul Chapman Publishing Ltd.
  • Reusser, K. (2000). Success and failure in school mathematics: Effects of instruction and school environment. European Child & Adolescent Psychiatry, 9, II/17–II/26.

List of research projects relating to Low Achievers in Mathematics:

List of publications relating to Low Achievers in Mathematics:

  • Foong, P. Y., Ghani, M., & Chang, S. H. (2012). Characteristics of low attainers: Behaviours, affect and home backgrounds. In, B. Kaur & M. Ghani (Eds.), Low attainers in primary mathematics (pp. 87–132). Singapore: World Scientific Press.
  • Kaur, B. & Ghani, M. (2012). Learning experiences of low attainers. In, B. Kaur & M. Ghani (Eds.), Low attainers in primary mathematics (pp. 133–158). Singapore: World Scientific Press.
  • Kaur, B. & Ghani, M. (2012). Low attainers in primary mathematics. Singapore: World Scientific Press.
  • Koay, P. L., Chang, S. H., & Ghani, M. (2012). Mathematics content knowledge of low attainers. In, B. Kaur & M. Ghani (Eds.), Low attainers in primary mathematics (pp. 19–86). Singapore: World Scientific Press.
  • Leong, Y. H., Yap, S. F., & Tay, E. G. (2013). Four factors to consider in helping low achievers in mathematics. In V. Steinle, L. Ball & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow, Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 727–730). Adelaide, Australia: MERGA.
  • Tong, C. L., Quek, K. S., & Leong, Y. H. (2013). Positive feelings towards the learning of mathematics for low achievers. In V. Steinle, L. Ball & C. Bardini (Eds.), In V. Steinle, L. Ball & C. Bardini (Eds.), Mathematics Education: Yesterday, Today and Tomorrow, Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 735–738). Adelaide, Australia: MERGA.
  • Wong, K.Y., Quek, K. S., Hedberg, J., & Chua, P. H. (2005). Understanding in-class experiences of mathematically weak students. Paper presented at the Redesigning Pedagogy Conference: Research, Policy, Practice, Singapore.
  • Wong, K. Y., & Quek, K. S. (2009). Enhancing mathematics performance (EMP) of mathematically weak pupils: An exploratory study (Unpublished Technical Report).

Sub-theme 5: Classroom Practices

Teaching is a cultural activity (Stigler & Hiebert, 1999). Detailed studies of the practices of competent mathematics teachers can shed light on many aspects of the teaching learning nexus in our classrooms.

References:

  • Stigler, J.W., & Hiebert, J. (1999). The teaching gap. New York, NY: Free Press.

List of research projects relating to Classroom Practices:

  • CRP 03/04 BK: Student Perspective on Effective Mathematics Pedagogy: Stimulated Recall Approach Study

List of publications relating to Classroom Practices:

  • Kaur, B. (2006). School System and Mathematics Education in Singapore. In D. Clarke, C. Keitel & Y. Shimizu (Eds.), Mathematics classrooms in 12 countries: The insider's perspective (pp. 361–364). Rotterdam/Taipei: Sense Publishers.
  • Kaur, B. (2008). Teaching and learning of mathematics – What really matters to teachers and students? ZDM The International Journal on Mathematics Education, 40(6), 951–962.
  • Kaur, B. (2009). Characteristics of good mathematics teaching in Singapore grade eight classrooms – A juxtaposition of teachers’ practice and students’ perception. ZDM The international Journal on Mathematics Education, 41(3), 333–347.
  • Kaur, B. (2011). Mathematics homework: A study of three grade eight classrooms in Singapore. International Journal of Science and Mathematics Education, 9(1), 187–206.
  • Kaur, B., Low, H. K., & Seah, L. H. (2006). Mathematics teaching in two Singapore classrooms: The role of textbook and homework. In D. Clarke, C. Keitel & Y. Shimizu (Eds.), Mathematics classrooms in 12 countries: The insider's perspective (pp. 99–115). Rotterdam/Taipei: Sense Publisher.
  • Seah, L. H., Kaur, B., & Low, H. K. (2006). Case studies of Singapore secondary mathematics classrooms: The instructional approaches of two teachers. In D. Clarke, C. Keitel & Y. Shimizu (Eds.), Mathematics classrooms in 12 countries: The insider’s perspective (pp. 151–165). Rotterdam/Taipei: Sense Publisher.

Sub-theme 6: Teacher Learning and Development

In Singapore, a number of initiatives have been launched by the Ministry of Education since 1997 to enhance the practices of teachers to advance excellence in classroom instruction. The first of the initiatives was the Thinking Schools, Learning Nation (TSLN) vision launched (Goh, 1997). This vision places emphasis on the need for teachers to be lifelong learners so that schools keep abreast of advances in knowledge and learning both at the national and international fronts. In support of TSLN vision, as of 1998 all teachers in Singapore are entitled to 100 hours of training and core-upgrading courses each year to keep abreast with current knowledge and skills. The Professional Development (PD) is funded by the Ministry of Education.

References:

  • Goh, C. T. (1997). Shaping our future: “Thinking Schools” and a “Learning Nation”. Speeches, 21(3), 12–20. Singapore: Ministry of Information and the Arts.

List of research projects relating to Teacher Learning and Development:

List of publications relating to Teacher Learning and Development:

  • Cheng, L. P. (2013). The design of a mathematics problem using real-life context for young children. Journal of Science and Mathematics Education in Southeast Asia, 36(1), 23–43.
  • Cheng, L. P., & Lee, P. Y. (2011). A Singapore case of lesson study. The Mathematics Educator, 21(2), 34–57.
  • Cheng, L. P., & Zhao, D. S. (2011). Making connections. Mathematics Teaching, 223, 23–25.
  • Cheng, L. P. (2014). Teaching for mathematical abstraction. In, P.C. Toh, T. L.Toh, & B. Kaur (Eds.), Learning experiences to promote mathematics learning. Singapore: World Scientific.
  • Kaur, B. (2009). Enhancing the pedagogy of mathematics teachers (EPMT): An Innovative professional development project for engaged learning. The Mathematics Educator, 12(1), 33–48.
  • Kaur, B. (2011). Enhancing the pedagogy of mathematics teachers (EPMT) project: A hybrid model of professional development. ZDM The International Journal on Mathematics Education, 43(7), 791–803.
  • Kaur, B., & Yeap, B. H. (2009). Pathways to reasoning and communication in the primary school mathematics classroom. Singapore: National Institute of Education, NTU.
  • Kaur, B., & Yeap, B. H. (2009). Pathways to reasoning and communication in the secondary school mathematics classroom. Singapore: National Institute of Education, NTU.
  • Kaur, B., & Toh, T. L. (2011). Mathematical problem solving – Linking theory and practice. In O. Zaslavsky & P. Sullivan (Eds.), Constructing knowledge for teaching secondary mathematics: tasks to enhance prospective and practicing teacher learning (pp. 177–188). New York, NY: Springer.
  • Leong, Y. H., Dindyal, J., Toh, T. L., Quek, K. S., Tay, E. G., & Lou, S. T. (2011). Teacher preparation for a problem-solving curriculum in Singapore. ZDM – The International Journal on Mathematics Education, 43(6–7), 819–831.
  • Leong, Y. H., Tay, E. G., Toh, T. L., Quek, K. S., & Dindyal, J. (2011). Reviving Polya's “look back” in a Singapore school. Journal of Mathematical Behavior, 30(3), 181–193.
  • Toh, T. L., Quek, K. S., Tay, E. G., Toh, P. C., Ho, F. H., Leong, Y. H., & Dindyal, J. (2012). A problem solving approach to differential equations – Mathematics practical. Singapore: Pearson Publishing.
  • Toh, T. L., Quek, K. S., Tay, E. G., Leong, Y. H., Toh, P. C., Ho, F. H., & Dindyal, J. (2013). Infusing problem solving into mathematics content course for pre-service secondary school mathematics teachers. The Mathematics Educator, 15(1), 98–120.
  • Toh, P. C., Leong, Y. H., Toh, T. L., Dindyal, J., Quek, K. S., Tay, E. G., & Ho, F. H. (2014). The problem-solving approach in the teaching of number theory. International Journal of Mathematical Education in Science and Technology, 45(2), 241–255.
  • Yeap, B. H., & Kaur, B. (2010). Pedagogy for engaged mathematics learning. Singapore: National Institute of Education, NTU.

Sub-theme 7: Teaching and Learning of Algebra

Algebra is an integral part of the school mathematics curriculum in Singapore schools. Pupils are introduced to algebraic thinking in the early grades of elementary school through a representational method known as “The Model Approach” (Ferrucci, Kaur, Carter & Yeap, 2008, pp. 195–210). They are first introduced to the formal idea of using algebra as generalised arithmetic in Grade 6. In the following Grades from 7 to 10, the study of algebra revolves around all of the four conceptions of school algebra, as outlined by Usiskin (1988), i.e.,

  • algebra as generalised arithmetic;
  • algebra as a way to solve certain types of problems;
  • algebra as a study of relationships among quantities; and
  • algebra as a study of structures.

References:

  • Ferrucci, J. B., Kaur, B. Carter, J. A., & Yeap, B. H. (2008). Using a model approach to enhance algebraic thinking in the elementary school mathematics classroom. In C. E. Greenes & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics (pp. 195–210). VA: National Council of Teachers of Mathematics.
  • Usiskin, Z. (1988). Conceptions of school algebra. In A. F. Coxford & A.P. Shuttle (Eds.), The ideas of algebra, K12 (pp. 8–19). VA: National Council of Teachers of Mathematics.

List of research projects relating to Teaching and Learning of Algebra:

List of publications relating to Teaching and Learning of Algebra:

  • Lee, K., Khng, F., Ng S. F., & Ng, J. L. K. (2013). Longer bars for bigger numbers? Children’s usage and understanding of graphic representations of algebraic problems. Frontline Learning Research, 1, 81–96.
  • Ng, S. F. (2003). How Secondary Two Express Stream Students Used Algebra and the Model Method. The Mathematics Educator, 7, 1–17.
  • Ng, S. F. (2004). Developing algebraic thinking in early grades: Case study of the Singapore primary mathematics curriculum. Developing algebraic thinking in the earlier grades from an international perspective. The Mathematics Educator, 8, 39–59.
  • Ng, S. F. & Lee, K. (2005). How primary five pupils use the model method to solve word problems. The Mathematics Educator, 9(1), 60–83.
  • Ng, S. F., & Lee, K. (2008). As long as the drawing is logical, size does not matter. Korea Journal of Thinking and Problem Solving.
  • Ng, S. F., & Lee, K. (2009). The model method: Singapore children’s tool for representing ad solving algebraic word problems. Journal for Research in Mathematics Education, 40(3), 282–313.

Sub-theme 8: International Comparative Studies


Comparative studies are critical for benchmarking purposes as well as for the contribution of knowledge in the global world. Singapore participates in such studies for four main reasons. They are as follows:

  • to benchmark the outcomes of schooling, viz-a-viz the education system against international standards;
  • to learn from educational systems that are excelling;
  • to update school curriculum and keep abreast of global advances; and
  • to contribute towards the development of excellence in education internationally (Kaur, 2013).

References:

  • Kaur, B. (2013). What can we learn from international assessments such as TIMSS and PISA? Keynote address at the 5th International Conference on Science and Mathematics Education, Penang, Malaysia.

List of research projects relating to International Comparative Studies:

List of publications relating to International Comparative Studies:

  • Areepattamannil, S. (2012). First- and second-generation immigrant adolescents' multidimensional mathematics and science self-concepts and their achievement in mathematics and science. International Journal of Science and Mathematics Education, 10(3), 695–716.
  • Areepattamannil, S., & Kaur, B. (2013). Factors predicting science achievement of immigrant and non-immigrant students: A multilevel analysis. International Journal of Science and Mathematics Education, 11(5), 1183–1207.
  • Areepattamannil, S., & Caleon, I. S. (2013). Relationships of cognitive and metacognitive learning strategies to mathematics achievement in four high-performing East Asian education systems. The Journal of Genetic Psychology, 174(6), 696–702. doi:10.1080/00221325.2013.799057
  • Cai, J., Lew, H. C., Morris, A., Moyer, J. C., Ng, S. F., & Schmittau, J. (2005). The development of students’ algebraic thinking in earlier grades: A cross-cultural comparative perspective. Zentralblatt für Didaktik der Mathematik, 37(1), 5–15.
  • Hsieh, Feng-Jui, Wong, K. Y., & Wang, T.-Y. (2013). Are Taiwanese and Singaporean future teachers similar in their mathematics-related teaching competencies? International Journal of Science and Mathematics Education, 11(4), 819–846.
  • Kaur, B., Anthony, G., Ohtani, M., & Clarke, D. (Eds.). (2013). Student Voice in Mathematics Classrooms around the World. Rotterdam: Sense Publishers.
  • Kaur, B., Areepattamannil, S., & Boey, K. L. (2013). Singapore’s Perspective: Highlights of TIMSS 2011. Singapore: National Institute of Education, Singapore.
  • Kaur, B., Boey, K. L., Areepattamannil, S., & Chen, Q. (2012). Singapore’s Perspective: Highlights of TIMSS 2007. Singapore: National Institute of Education, NTU.
  • Mok, I. A. C., Kaur, B., Zhu, Y. & Yau, K. W. (2013). What really matters to students? A comparison between Hong Kong and Singapore mathematics lessons. In B. Kaur, G. Anthony, M. Ohtani & D. Clarke (Eds.), Student voice in mathematics classrooms around the world (pp. 189–208). Rotterdam: Sense Publishers.
  • Ng, K. T., Lay, Y. F., Areepattamannil, S., Treagust, D. F., & Chandrasegaran, A. L. (2012). Relationship between affect and achievement in science and mathematics in Malaysia and Singapore. Research in Science & Technological Education, 30(3), 225–237.
  • Shimizu, Y., & Kaur, B. (2013). Learning from similarities and differences: A reflection on the potentials and constraints of cross-national studies in mathematics. ZDM The International Journal of Mathematics Education, 45(1), 1–5.
  • Shimizu, Y., Kaur, B., Huang, R. & Clarke, D. (Eds.). (2010). Mathematical tasks in classrooms around the world. Rotterdam: Sense Publishers.
  • Thompson, D. R., & Kaur, B. (2011). Using a multi-dimensional approach to assess students' mathematical knowledge. In Kaur, B., Wong, K.Y. (Ed.), Assessment in the mathematics classroom (pp. 17–32). Singapore: World Scientific.
  • Thompson, D. R., Kaur, B., Koyama, M., & Bleiler, S. K. (2013). A longitudinal view of mathematics achievement of primary students: Case studies from Japan, Singapore, and the United States. ZDM The International Journal of Mathematics Education, 45(1), 73–89.
  • Toh, T.L., Kaur, B., Koay, P.L. (2013). Singapore pre-service secondary mathematics teachers’ content knowledge: Findings from an international comparative study. International Journal of Mathematics Teaching and Learning, Sep(2), 1–22.
  • Toh, T.L., Koay, P.L., Kaur, B. (2011). International comparative study in mathematics teacher training: Enhancing the training of teachers of mathematics. United Kingdom [Technical Report of ICSMTT (University of Plymouth)].
  • Wong, K. Y., Boey, K. L., Lim-Teo, S. K., & Dindyal, J. (2012). The preparation of primary mathematics teachers in Singapore: Programs and outcomes from the TEDS-M study. ZDM The International Journal on Mathematics Education, 44(3), 293–306.
  • Wong, K. Y., Lim-Teo, S. K., Lee, N. H., Boey, K. L., Koh, C., Dindyal, J., Teo, K. M., & Cheng, L. P. (2013). Preparing teachers of mathematics in Singapore. In J. Schwille, L. Ingvarson, & R. Holdgreve-Resendez (Eds.), TEDS-M encyclopedia: A Guide to Teacher Education Context, Structure, and Quality Assurance in 17 Countries: Findings from the IEA teacher education and development study in mathematics (TEDS-M) (pp. 195–207). Amsterdam, The Netherlands: International Association for the Evaluation of Educational Achievement.