Abstract
According to the Singapore primary mathematics curriculum (2006), it is important that students tackle a variety of mathematical problems, including real-world problems, as they apply their mathematical problem-solving skills. This paper examines the challenges and affordances of using real-world problems with young children in a primary school in Singapore. Using the laboratory class cycle, the teachers in the study planned, observed and critiqued a mathematics lesson using real-world problems for primary two children. Data in this study includes the teachers’ conversations during the laboratory cycle and the students’ responses during the observed mathematics lessons using real-world problems. Our findings show that the real-world problem used in this study generated rich mathematical classroom discussion. The teachers’ learning from using real-world problems through the laboratory cycle and the challenges they faced were discussed in this study.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
A sample of the Bookshop and Restaurant problem appeared in Cheng (2013).
References
Albert, L., & Antos, J. (2000). Daily journals. Mathematics Teaching in the Middle School, 5(8), 526–531.
Ang, K. C. (2009). Mathematical modeling and real life problem solving. In B. Kaur, B. H. Yeap, & M. Kapur (Eds.), Mathematical problem solving: AME yearbook 2009 (pp. 159–182). Singapore: World Scientific Publishing.
Bennett, N., & Desforges, C. (1989). Matching classroom tasks to students’ attainments. The Elementary School Journal, 88, 221–234.
Beswick, K. (2011). Putting context in context: An examination of the evidence for the benefits of ‘contextualized’ tasks. International Journal of Science and Mathematics Education, 9, 367–390.
Boaler, J. (1993). Encouraging transfer of ‘school’ mathematics to the ‘real world’ through the integration of processes and content; context and culture. Educational Studies in Mathematics, 25, 341–373.
Chan, C. M. (2005, August). Engaging students in open-ended mathematics problem tasks: A sharing on teachers’ production and classroom experience (Primary). Paper presented at the third ICMI-East Asia regional conference on mathematics education conference, East China Normal University, Shanghai, China.
Charalambous, C. Y. (2008). Mathematical knowledge for teaching and the unfolding of tasks in mathematics lessons: Integrating two lines of research. In O. Figuras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepulveda (Eds.), Proceedings of the 32nd annual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 281–288). Morelia: PME.
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.
Cooper, B., & Harries, T. (2002). Children’s responses to contrasting ‘realistic’ mathematics problems: Just how realistic are children ready to be? Educational Studies in Mathematics, 49, 1–23.
Foo, K. F., & Fan, L. (2007). The use of performance tasks in a neighbourhood school. Paper presented at CRPP/NIE international conference on education: Redesigning pedagogy: Culture, knowledge and understanding (CD-ROM, 12 p.), Singapore.
Foong, P. Y. (2005). Developing creativity in the Singapore mathematics classroom. Thinking Classroom, 6(4), 14–20.
Foong, P. Y. (2009). Problem solving in mathematics. In P. Y. Lee & N. H. Lee (Eds.), Teaching primary school mathematics: A resource book (p. 56). Singapore: McGraw Hill.
Foong, P. Y., Yap, S. F., & Koay, P. L. (1996). Teachers’ concerns about the revised mathematics curriculum. The Mathematics Educator, 1(1), 99–110.
Fuchs, L. S., & Fuchs, D. (1996). Connecting performance assessment and curriculum-based measurement. Learning Disabilities Research and Practice, 11, 182–192.
Fuchs, L. S., Fuchs, D., & Courey, S. J. (2005). Curriculum-based measurement of mathematics competence: From computation to concepts and applications to real-life problem solving. Assessment for Effective Intervention Winter, 30(2), 33–46.
Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11, 199–219.
Goodman, J. (1995). Change without difference: School restricting in historical perspective. Harvard Educational Review, 65, 1–28.
Greer, B. (1997). Modeling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4), 293–307.
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., et al. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(4), 12–21.
Inoue, K. (2008). Minimalism as a guiding principle: Linking mathematical learning to everyday knowledge. Mathematical Thinking and Learning, 10(1), 36–67.
Kaur, B., & Dindyal, J. (2010). A prelude to mathematical applications and modeling in Singapore schools. In B. Kaur & J. Dindyal (Eds.), Mathematical applications and modeling: AME yearbook 2010 (pp. 3–18). Singapore: World Scientific Publishing.
Kim, M. C., & Hannafin, M. (2011). Scaffolding problem solving in technology-enhanced learning environments (TELEs): Bridging research and theory with practice. Computers & Education, 56(2), 403–417.
Kwon, O. N., Park, J. S., & Park, J. H. (2006). Cultivating divergent thinking in mathematics through an open-ended approach. Asia Pacific Education Review, 7(1), 51–61.
Merriam, S. B. (1988). Case study research in education. San Francisco: Jossey-Bass.
Ministry of Education. (2000). Mathematics syllabus—primary (2001). Singapore: Author.
Ministry of Education. (2006). Mathematics syllabus—primary (2007). Singapore: Author
Ministry of Education. (2012). Primary mathematics teaching and learning syllabus (2013). Singapore: Author
Polya, G. (1957). How to solve it: A new aspect of mathematical method (2nd ed.). Garden City: Doubleday.
Reusser, K., & Stebler, R. (1997). Every word problem has a solution – The social rationality of mathematical modellings in schools. Learning and Instruction, 7(4), 309–327.
Riedesel, C. A., Schwartz, J. E., & Clements, D. H. (1996). Teaching elementary school mathematics (6th ed.). Boston: Allyn and Bacon.
Rogoff, B., & Lave, J. (Eds.). (1984). Everyday cognition: Its development in social context. Cambridge, MA: Harvard University Press.
Rule, A. C., & Hallagan, J. E. (2007). Algebra rules object boxes as an authentic assessment task of preservice elementary teacher learning in a mathematics methods course. ERIC Online submission.
Schiefele, U., & Csikszentmihalyi, M. (1995). Motivation and ability as factors in mathematics experience and achievement. Journal for Research in Mathematics Education, 26, 163–181.
Schwartz, J. E. (2008). Elementary mathematics pedagogical content knowledge: Powerful ideas for teachers. Boston: Pearson/Allyn and Bacon.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Stillman, G. (2000). Impact of prior knowledge of task context on approaches to applications tasks. Journal of Mathematical Behavior, 19, 333–361.
Stylianides, A. J., & Stylianides, G. J. (2008). Studying the classroom implementation of tasks: High-level mathematical tasks embedded in ‘real-life’ contexts. Teaching and Teacher Education, 24, 859–875.
Sullivan, P., Griffioen, M., Gray, H., & Powers, C. (2009). Exploring open-ended tasks as teacher learning. Australian Primary Mathematics Classroom, 14(2), 4–9.
Trafton, P. R., Reys, B. J., & Wasman, D. G. (2001). Standards-based mathematics curriculum materials: A phrase in search of a definition. The Phi Delta Kappan, 83(3), 259–264.
Turner, E. E., Gutiérrez, M. V., Simic-Muller, K., & Díez-Palomar, J. (2009). “Everything is math in the whole world”: Integrating critical and community knowledge in authentic mathematical investigations with elementary Latina/o students. Mathematical Thinking and Learning, 11(3), 136–157.
Acknowledgement
The authors would like to express gratitude to associate professor Lee Peng Yee for his special insight into mathematics education.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media Singapore
About this chapter
Cite this chapter
Cheng, L.P., Toh, T.L. (2015). Mathematical Problem-Solving Using Real-World Problems. In: Cho, Y., Caleon, I., Kapur, M. (eds) Authentic Problem Solving and Learning in the 21st Century. Education Innovation Series. Springer, Singapore. https://doi.org/10.1007/978-981-287-521-1_4
Download citation
DOI: https://doi.org/10.1007/978-981-287-521-1_4
Publisher Name: Springer, Singapore
Print ISBN: 978-981-287-520-4
Online ISBN: 978-981-287-521-1
eBook Packages: Humanities, Social Sciences and LawEducation (R0)