Skip to main content

Changes in Instructional Tasks and Their Influence on Classroom Discourse in Reformed Mathematics Classrooms of Chinese Primary Schools

  • Chapter
  • First Online:
Transforming Mathematics Instruction

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

This chapter describes two studies that show the impact of China’s new mathematics curriculum on classroom instruction. The first study examined the cognitive features of instructional tasks implemented in primary-level mathematics classrooms adopting the new curriculum in comparison to those using the conventional curriculum. The results indicated that the reform-oriented classrooms used more tasks with high cognitive demand, multiple representations, and multiple solution methods than the non-reform classrooms did. The second study looked into how cognitive demands, multiple representations, and multiple solution methods were related to the nature of student-teacher discourse in the reformed classrooms. It was found that tasks of high cognitive demand were associated with teachers’ high-order questioning which, in turn, was related to students’ highly participatory responses. It was also found that tasks of high cognitive demand as well as teachers’ high-order questions were associated with the teacher’s authority in evaluating students’ answers. In contrast, tasks of multiple solution methods were showed to be related to teachers’ simple questions, and teachers’ simple questions led to more teacher-student joint authority in evaluating students’ responses. Some implications of the findings from the studies are discussed in order to further our understanding of the current instructional practice in Chinese mathematics classrooms and to help formulate strategies to sustain and affect the desirable changes in the classrooms.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Public lessons refer to the lessons that are conducted by the teachers whom are considered by respective school districts to be exemplary on teaching and are open to teachers in and outside of the schools. Public lessons are a regular part of teacher professional development activity in China. It also helps to efficiently disseminate socially and culturally favored teaching methods. Han and Paine (2010) documented the processes of preparing public lessons by a group of Chinese mathematics teachers.

References

  • Anderson, J. R. (2000). Cognitive psychology and its implications. New York: Worth.

    Google Scholar 

  • Ball, D. L. (1993). Halves, pieces, and twoths: Constructing and using representational contexts in teaching fractions. In T. P. Carpenter, E. Rennena, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 157–195). Hillsdale: Erlbaum.

    Google Scholar 

  • Ball, D. L. (2001). Teaching, with respect to mathematics and students. In T. Wood, B. S. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy: Teaching elementary school mathematics (pp. 11–22). Mahwah: Erlbaum.

    Google Scholar 

  • Baxter, J. A., & Williams, S. R. (2010). Social and analytic scaffolding in middle school mathematics: Managing the dilemma of telling. Journal of Mathematics Teacher Education, 13(1), 7–26.

    Article  Google Scholar 

  • Cai, J. (1995). A cognitive analysis of U. S. and Chinese students’ mathematical performance on tasks involving computation, simple problem solving, and complex problem solving. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An international analysis. American Educational Research Journal, 29, 573–604.

    Article  Google Scholar 

  • Engle, R. A., & Conant, F. C. (2002). Guiding principles for fostering productive disciplinary engagement: Explaining an emergent argument in a community of learners classroom. Cognition and Instruction, 20, 399–483.

    Article  Google Scholar 

  • Doyle, W. (1983). Academic work. Review of Educational Researcher, 53, 159–199.

    Article  Google Scholar 

  • Doyle, W. (1988). Work in mathematics classes: The context of students’ thinking during instruction. Educational Psychologists, 23, 167–180.

    Article  Google Scholar 

  • Guan, Q., & Meng, W. J. (2007). China’s new national curriculum reform: Innovation, challenges and strategies. Frontiers of Education in China, 2, 579–604.

    Article  Google Scholar 

  • Hamm, J., & Perry, M. (2002). Learning mathematics in first grade classrooms: On whose authority? Journal of Educational Psychology, 94, 126–137.

    Article  Google Scholar 

  • Han, X., & Paine, L. (2010). Teaching mathematics as deliberate practice through public lessons. The Elementary School Journal, 110(4), 519–541.

    Article  Google Scholar 

  • Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28, 524–549.

    Article  Google Scholar 

  • Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393–425.

    Article  Google Scholar 

  • Li, Q. (2004). Elementary school mathematics teachers’ subject matter knowledge and pedagogical content knowledge: Their relationship to classroom instruction. Unpublished doctoral dissertation, The Chinese University of Hong Kong, Hong Kong.

    Google Scholar 

  • Li, Q., & Ni, Y. J. (2011). Impact of curriculum reform: Evidence of change in classroom practice in the Mainland China. International Journal of Educational Research, 50, 71–86.

    Article  Google Scholar 

  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah: Erlbaum.

    Google Scholar 

  • Marx, R. W., & Walsh, J. (1988). Learning from academic tasks. Elementary School Journal, 88(3), 207–219.

    Article  Google Scholar 

  • Ministry of Education. (2001a). <基础教育课程改革纲要(试行)>. 北京:北京师范大学出版社 [The curriculum reform guidelines for the nine-year compulsory education (trial version)]. Beijing: Beijing Normal University Press (in Chinese).

    Google Scholar 

  • Ministry of Education. (2001b). <全日制义务教育数学课程标准(实验稿)>. 北京: 北京师范大学出版社 [Curriculum standards for school mathematics of nine-year compulsory education (trial version)]. Beijing: Beijing Normal University Press (in Chinese).

    Google Scholar 

  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston: Author.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1997). Improving student learning in mathematics and science: The role of national standards in state policy. Reston: Author.

    Google Scholar 

  • Ni, Y. J., & Zhou, Y. D. (2005). Teaching and learning fraction and rational numbers: The origin and implications of whole number bias. Educational Psychologist, 40, 27–52.

    Article  Google Scholar 

  • Ni, Y. J., Li, Q., Cai, J., & Hau, K. T. (2009). Has curriculum reform made a difference? Looking for change in classroom practice. Hong Kong: The Chinese University of Hong Kong.

    Google Scholar 

  • Ni, Y. J., Chiu, C. C., & Chan, Z. J. (2010). Chinese children learning mathematics: From home to school. In M. H. Bond (Ed.), The handbook of Chinese psychology (pp. 143–154). Oxford: Oxford University Press.

    Google Scholar 

  • Ni, Y., Li, Q., Li, X., & Zhang, Z.-H. (2011). Influence of curriculum reform: An analysis of student mathematics achievement in mainland China. International Journal of Educational Research, 50, 100–116.

    Article  Google Scholar 

  • Ni, Y. J., Zhou, D. H., Li, X., & Li, Q. (2012, April). Influence of instructional tasks on student/teacher discourse in mathematics classrooms of Chinese primary schools. Paper presented at the annual conference of American Educational Research Association, Vancouver, Canada.

    Google Scholar 

  • Nystrand, M., Wu, L. L., Gamoran, A., Zeiser, S., & Long, D. A. (2003). Questions in time: Investigating the structure and dynamics of unfolding classroom discourse. Discourse Processes, 35(2), 135–198.

    Article  Google Scholar 

  • Paine, L., & Ma, L. (1993). Teachers working together: A dialogue on organizational and cultural perspectives of Chinese teachers. International Journal of Educational Research, 19, 675–697.

    Article  Google Scholar 

  • Perry, M., VanderStoep, S. W., & Yu, S. L. (1993). Asking questions in first-grade Mathematics classes: Potential influences on mathematical thought. Journal of Educational Psychology, 85, 31–40.

    Article  Google Scholar 

  • Renkl, A., & Helmke, A. (1992). Discriminate effects of performance-oriented and structure-oriented mathematical tasks on achievement growth. Contemporary Educational Psychology, 17, 47–55.

    Article  Google Scholar 

  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–371). New York: Macmillan.

    Google Scholar 

  • Stein, M., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2, 50–80.

    Article  Google Scholar 

  • Stein, M. K., Grover, B. W., & Henningson, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reformed classrooms. American Educational Research Journal, 33(2), 455–488.

    Article  Google Scholar 

  • Stein, M., Smith, M., Henningsen, M., & Silver, E. (2000). Implementing standard-based mathematics instruction: A case book for professional development. New York: Teacher College Press.

    Google Scholar 

  • Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319–369). Greenwich: Information Age Publishing.

    Google Scholar 

  • Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Helping teachers learn to better incorporate student thinking. Mathematical Thinking and Learning, 10, 313–340.

    Article  Google Scholar 

  • Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world's teachers for improving education in the classroom. New York: Free Press.

    Google Scholar 

  • Stigler, J. W., & Hiebert, J. (2004). Improving mathematics teaching. Educational Leadership, 61, 12–16.

    Google Scholar 

  • Stigler, J. W., Fernandez, C., & Yoshida, M. (1996). Traditions of school mathematics in Japanese and American elementary classrooms. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin, & B. Greer (Eds.), Theories of mathematical learning (pp. 149–175). Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • Stylianides, G. J. (2009). Reasoning-and-proving in school mathematics textbooks. Mathematical Thinking and Learning, 11, 258–288.

    Article  Google Scholar 

  • Tarr, J. E., Chávez, Ó., Reys, R. E., & Reys, B. J. (2006). From the written to the enacted curricula: The intermediary role of middle school mathematics teachers in shaping students’ opportunity to learn. School Science and Mathematics, 106(4), 191–201.

    Article  Google Scholar 

  • Wang, J., & Paine, L. (2003). Learning to teach with mandated curriculum and public examination of teaching as contexts. Teaching and Teacher Education, 19, 75–94.

    Article  Google Scholar 

  • Williams, S. R., & Baxter, J. A. (1996). Dilemmas of discourse-oriented teaching in one middle school mathematics classroom. The Elementary School Journal, 97, 21–38.

    Article  Google Scholar 

Download references

Acknowledgement

The authors wish to thank the two anonymous reviewers for their constructive comments on an earlier version of the paper. The two studies described in the article were supported by the Research Grant Council of Hong Kong Special Administration Region, China (CERG-4624/05H; CERG-449807; CUHK Direct Grant-4450199), Hong Kong Institute of Educational Research at the Chinese University of Hong Kong (#6900840), and also the National Center for School Curriculum and Textbook Development, Ministry of Education of the People’s Republic of China. However, the findings and opinions expressed in the article do not necessarily reflect the positions of the funding agencies.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yu-Jing Ni .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Ni, YJ., Li, X., Zhou, D., Li, Q. (2014). Changes in Instructional Tasks and Their Influence on Classroom Discourse in Reformed Mathematics Classrooms of Chinese Primary Schools. In: Li, Y., Silver, E., Li, S. (eds) Transforming Mathematics Instruction. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-04993-9_13

Download citation

Publish with us

Policies and ethics