Mathematics Education in Singapore pp 269-285 | Cite as

# Students’ Perspectives of Good Mathematics Lessons, Homework and How Their Teachers Facilitate Learning of Mathematics

## Abstract

This chapter presents data and findings from the Learner’s Perspective Study (LPS) carried out in Singapore, about students’ perspectives of good mathematics lessons and the role of homework in their learning of mathematics. It also presents data and findings from the Study of school mathematics curriculum enacted by competent teachers in Singapore secondary schools that examines students’ perspectives of how two competent teachers facilitate the learning of mathematics in their classrooms. Both the studies are motivated by a strong belief that the characterization of the practices of mathematics classrooms must attend to learners’ practice with at least the same priority as that accorded to teacher practice. Post-lesson student interview and survey data from LPS and post-lesson interview data from the Study of school mathematics curriculum enacted by competent teachers are used to examine student practice. In the LPS, students deemed mathematics lessons as good when teachers performed specific actions as part of the teachers instruction pattern which is the **D** (Whole class demonstration)—**S** (Seatwork/Out of class assignments)—**R** (Review and feedback) cycle. Students’ perspective of homework illuminated six roles it performed which included improving or enhancing understanding of mathematics concepts, preparing for test or examination and extending mathematical knowledge. In the Study of the enacted school mathematics curriculum, students in both the classes of the teachers affirmed that their teachers’ carefully prepared instructional materials engaged them in learning mathematical concepts and developing the necessary procedural fluency. Though both teachers, A and B, adopted classroom discourse approaches skewed more towards student-centredness, they facilitated their students’ learning differently. Teacher A had a more structured seating for her students, while Teacher B let her students to form their own clusters (friendship oriented) and sit together during the lessons. The activities for the group-based work were also dissimilar for the students in the two classes.

## Keywords

Students’ perspectives Good mathematics lessons Homework How teachers facilitate learning of mathematics Learner’s perspective study (LPS) Enacted school mathematics curriculum Singapore## References

- Anthony, G., Kaur, B., Ohtani, M., & Clarke, D. (2013). The learner’s perspective study: Attending to student voice. In B. Kaur, G. Anthony, M. Ohtani, & D. Clarke (Eds.),
*Student voice in Mathematics classrooms around the world*(pp. 1–11). Rotterdam: Sense Publishers.Google Scholar - Anthony, G., & Walshaw, M. (2007).
*Effective pedagogy in Mathematics: Best evidence synthesis iteration [BES]*. Wellington: Ministry of Education.Google Scholar - Bossert, S. T. (1988–1989). Cooperative activities in the classroom.
*Review of Research in Education*,*15*, 225–252.Google Scholar - Clarke, D. J (1998). Studying the classroom negotiation of meaning: Complementary accounts methodology (Chapter 7). In A. Teppo (Ed.),
*Qualitative research methods in Mathematics education*, monograph*number 9 of the Journal for Research in Mathematics Education*(pp. 98–111). Reston, VA: NCTM.Google Scholar - Clarke, D. J. (Ed.). (2001).
*Perspectives on practice and meaning in mathematics and science classrooms*. Dordrecht, Netherlands: Kluwer Academic Press.Google Scholar - Clarke, D., Keitel, C., & Shimizu, Y. (2006). The learner’s perspective study. In D. Clarke, C. Keitel, & Y. Shimizu (Eds.),
*Mathematics classrooms in twelve countries: The insider’s perspective*(pp. 1–14). Sense Publishers.Google Scholar - City, E. A., Elmore, R. F., Fiarman, S. E., & Teitel, L. (2009).
*Instructional rounds in education: A network approach to improving teaching and learning*. Cambridge, MA: Harvard Education Press.Google Scholar - Cohen, E. G. (1994).
*Designing groupwork*(2nd ed.). New York, NY: Teachers College Press.Google Scholar - Glesne, C. (1999).
*Becoming qualitative researchers: An introduction*(2nd ed.). New York: Longman.Google Scholar - Gomez, L. F. (2016). Intention and pedagogical competence: Use of collaborative learning in the subject of mathematics in secondary school.
*Propósitos y Representaciones, 4*(2). 135–183. http://dx.doi.org/10.20511/pyr2016.v4n2.121. - Johnson, D. W., & Johnson, R. T. (1974). Instructional goal structure: Cooperative competitive or individualistic.
*Review of Education Research,**44,*213–240.CrossRefGoogle Scholar - Johnson, D., & Johnson, R. (2000). Cooperative learning, values, and culturally plural classrooms. In. M. Leicester, C. Modgil, & S. Modgil (Eds.),
*Classroom issues: Practice, pedagogy and curriculum*(pp. 15–28). Palmer Press: London.Google Scholar - 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.CrossRefGoogle Scholar - Kaur, B. (2009). Characteristics of good mathematics teaching in Singapore grade eight classrooms—A juxtaposition of teachers’ practice and students’ perspective.
*ZDM—The international Journal on Mathematics Education,**41*(3), 333–347.CrossRefGoogle Scholar - 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.CrossRefGoogle Scholar - Kaur, B., Anthony, G., Ohtani, M., & Clarke, D. (Eds.). (2013).
*Student voice in Mathematics classrooms around the world*. Rotterdam: Sense Publishers.Google Scholar - Kaur, B., Tay, E. G., Toh, T. L., Leong, Y. H., & Lee, N. H. (2018). A study of school mathematics curriculum enacted by competent teachers in Singapore secondary schools.
*Mathematics Education Research Journal,**30*(1), 103–116.CrossRefGoogle Scholar - MacBeath, J., & Turner, M. (1990).
*Learning out of school: Homework, policy and practice*. Glasgow: Jordanhill College of Education.Google Scholar - National Research Council. (2001).
*Adding it up: Helping children learn mathematics*. Report prepared by the Mathematics Learning Study Committee. Washington, DC: National Academy Press.Google Scholar - O’Donnell, A. M. (2006). The role of peers and group learning. In P. Alexander & P. Winne (Eds.),
*Handbook of educational psychology*(2nd ed.). Mahwah, NJ: Lawrence Erlbaum.Google Scholar - Slavin, R. E. (1977). Classroom reward structure: An analytical and practical review.
*Review of Educational Research,**47,*633–650.CrossRefGoogle Scholar - Slavin, R. E. (1995).
*Cooperative learning*(2nd ed.). Boston, MA: Allyn and Bacon.Google Scholar - Slavin, R., & Cooper, R. (1999). Improving intergroup relations: Lessons learned from cooperative learning programs.
*Journal of Social Issues,**55,*647–663. https://doi.org/10.1111/0022-4537.00140.CrossRefGoogle Scholar - Sullivan, P., & Mousley, J. (2007). Quality mathematics teaching: Describing some key components. In G. Leder & H. Forgasz (Eds.),
*Stepping stones for the 21st century—Australian Mathematics education research*(pp. 41–62). Rotterdam/Taipei: Sense Publishers.Google Scholar - Swan, M. (2006).
*Collaborative learning in mathematics: A challenge to our beliefs and practices*. London, England: National Research and Development Centre for Adult Literacy and Numeracy, and Leicester, England: National Institute of Adult Continuing Education.Google Scholar - Tam, V. C. W. (2009). Homework involvement among Hong Kong primary school students.
*Asia Pacific Journal of Education,**29*(2), 213–227.CrossRefGoogle Scholar - Webb, N. M., & Palincsar, A. S. (1996). Group processes in the classroom. In D. Berliner & R. Calfee (Eds.),
*Handbook of educational psychology*(pp. 841–873). New York, NY: Macmillan.Google Scholar