Content and Pedagogical Characteristics of US and Chinese Elementary Mathematics Lessons in Contexts of Teaching Reform

• In Event: Highlighted Session: Exploring teacher agency, beliefs, identity, practices and quality

Proposal

Purpose

The mathematics curriculum reform is pressing teachers to change their popular procedural based teaching towards a conceptual based instruction in US and China (China’s Ministry of Education, 2001; Common Core State Standards Initiative, 2010). Thus, it is important to explore if teachers can move towards conceptual oriented teaching in both countries successfully as the reform expects. This study examines the extent to which the mathematics content and pedagogical characteristics of US and Chinese lessons reflect the conceptual and procedural oriented teaching practices in the reform contexts.

Conceptual Frameworks

The conception of mathematics knowledge for teaching (Ball, Thames, & Phelps, 2008) guides the analysis of the mathematics content and pedagogical characteristics of mathematics teaching in the two place. The first component of such knowledge is mathematics content knowledge covering common mathematics knowledge about mathematics concepts used in our daily life, specialized mathematics knowledge necessary for teachers to represent and explain mathematics ideas, and horizon mathematics knowledge about how mathematics ideas are related with each other. The second component is pedagogical content knowledge consisting of understanding about student conceptions and misconceptions, knowledge of how to sequence content, identify, and use teaching methods and tools, and understanding how mathematics topics in the curriculum are related to each other.

The conception of mathematics teaching as culturally scripted by the curriculum, assessment, and organization contexts in which it is situated and any teaching transformation is gradual by blending with both traditional and reform components in infiltrating manner (Stigler & Hiebert, 2009). It guides the examination about the extent to which are the mathematics and pedagogical characteristics of mathematics lessons in the two countries reflect the expectation of reform or that of teaching culture and organization.

Methods

Participants and Contexts
Participants were three US and three Chinese fifth-six grade teachers teaching in different urban school contexts schools using the same reformed curriculum materials in each place. Who received trainings on how to teach the reformed curriculum and ongoing support during teaching in each place. US participants had been teaching mathematics individually on their own (Little, 1990) while Chinese teacher had been teaching under the centralized curriculum standards (Eckstein, 1993) and in the teaching research group where they plan, observe, and discuss teaching collaboratively (Wang & Paine, 2003).

Data and Analysis
Two kinds of data were sued for this study. A lesson on multi-steps of multiplication and division that each participant taught, which were observed, videotaped, and transcribed with Chinese lesson transcripts translated into English and offered the chances for me to identify the content and pedagogical characteristics of mathematics teaching in each country. The relevant curriculum standards and textbooks that each participant used for their lessons were also used to capture the relationship between participants’ mathematics lessons and their reform curriculum materials.

Each lesson transcript was coded to identify the themes based on the conception of mathematics knowledge for teaching as emerged (Strauss & Corbin, 1990), which were compared with those from the participants in the same countries first and then across two countries. The curriculum that each participant used were coded for the specific requirements and suggestions for teaching qualitatively (Merriam, 1998). The results were compared with the results of the lesson analysis to identify the influences of reform curriculum in each place.

Results

Mathematics Characteristics
US and Chinese participants used mathematics problems from their textbook and used verbal and written representations and a series questions to engage their students in solving these problems. However, while US teachers often asked students to use no more than two concepts that they had already learned in solving problems, Chinese teachers used multiple mathematics concepts including those they had learned and they were going to learn. Chinese teachers were more often than US teachers in helping students clarify the reasoning in solving problems.

Pedagogical Characteristics
Both US and Chinese lessons demonstrated similar lesson phases and sequence resembling direct instruction (Rosenshine,1985). However, US teachers devoted more time to the practice phases of their lessons in which students worked individually while Chinese teacher spent almost equal amount of time on new content and practice phases of their lessons in which teachers and students worked in the whole class or group forms. Chinese participants developed more teacher-initiated interactions with students than their US counterparts while US teachers devoted more interactions than their Chinese counterparts to direct and manage students’ behaviors.

Discussions and Conclusions

By showing that both US and Chinese teachers used the mathematics problems from reform curriculum in their lessons to engage students in solving them, the study confirms the finding that US teachers often use the problems in the curriculum in teaching (Moyer, Cai, Wang, & Nie, 2011) while it is the tradition of Chinese teachers who teach following centralized mathematics curriculum (Ni, Zhou, Li, & Li, 2014). It also reveals that Chines participants were more likely than their U.S. counterparts by engaging students in using multiple mathematics concepts in solving a problem and justifying their solutions, which echoes the finding that Chinese teachers were more likely to use and analyze various mathematics concepts during instruction (Huang & Leung, 2005). It further shows that although still resembling the direct instruction (Rosenshine, 1985), the U.S. lessons were no longer filled with activities and various visual and concrete tools (Huang & Cai, 2011). The Chinese lessons also changed in that teachers reduced lecture while giving students more chances to develop their own ideas before new content instruction (Perry, 2000). Finally, it demonstrates that US participants spent more time having students practice individually while interacting with them in one-on-one form, which echoes the western individualist culture value, in which knowledge is seen individually constructed (von Glasersfeld, 1995). Chinese participants spent more time on teaching new content and interacting with their students in whole class and group form as consistent with the traditional Chinese cultural value in which teachers are highly respected as an authority (Watkins & Biggs, 2001) and individual ideas need to be adapted to the centralized ideology (Wong & Tjosvold, 2006).

References:

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of teacher education, 59(5), 389-407.

China’s Ministry of Education. (2001). Mathematics curriculum standards: Grades 1 to 9. Beijing, China: Beijing Normal University Press.

Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Washington, DC:: National Governors Association Center for Best Practices and the Council of Chief State School Officers.

Eckstein, M. A. (1993). Secondary school examinations: International perspectives on policies and practice. New Haven, CT: Yale University Press.

Huang, R., & Cai, J. (2011). Pedagogical representations to teach linear relations in Chinese and U.S. classrooms: Parallel or hierarchical? The Journal of Mathematical Behavior, 30(2), 149-165.

Huang, R., & Leung, F. K. S. (2005). Deconstructing teacher-centeredness and student-centeredness dichotomy: A case study of a shanghai mathematics lesson. Mathematics Educator, 15(2), 35-41.

Little, J. W. (1990). The persistence of privacy: autonomy and initiative in teachers' professional relationship. Teachers College Record, 91(4), 509-536.

Merriam, S. B. (1998). Qualitative Research and Case Study Applications in Education. San Francisco, CA: Jossey-Bass Publishers.

Moyer, J. C., Cai, J., Wang, N., & Nie, B. (2011). Impact of curriculum reform: Evidence of change in classroom practice in the United States. International Journal of Educational Research, 50(2), 87-99. doi:http://dx.doi.org/10.1016/j.ijer.2011.06.004

Ni, Y., Zhou, D., Li, X., & Li, Q. (2014). Relations of instructional tasks to teacher–student discourse in mathematics classrooms of Chinese primary schools. Cognition & Instruction, 32(1), 2-43. doi:10.1080/07370008.2013.857319

Perry, M. (2000). Explanations of mathematical concepts in Japanese, Chinese, and U. S. first- and fifth-grade classrooms. Cognition & Instruction, 18(2), 181-207. doi:10.1207/S1532690XCI1802_02

Rosenshine, B. (1985). Direct instruction. In T. Husen & T. N. Postlethwaite (Eds.), International Encyclopedia of Education (Vol. 3, pp. 1395-1400). Oxford: Pergamon Press.

Stigler, J. W., & Hiebert, J. (2009). Closing the teaching gap. Part of a special issue: Bridging Gaps in Education, 91(3), 32-37.

Strauss, A., & Corbin, J. (1990). Basics of qualitative research: Grounded theory procedures and techniques. New York: Sage.

von Glasersfeld, E. (1995). Radical constructivism : A way of knowing and learning. Washington, D.C.: Falmer Press.

Wang, J., & Paine, L. W. (2003). Learning to teach with mandated curriculum and public examination of teaching as contexts. Teaching and teacher education, 19(1), 75 - 94.

Watkins, D., & Biggs, J. B. (Eds.). (2001). Teaching Chinese learner: Psychological anf pedagogical Perspective. Hong Kong/Melburne: Compartaive Eduducation Research Center, University of Hong Komg and Australia counucil of Educational Reserch.

Wong, A., & Tjosvold, D. (2006). Collectivist values for learning in organizational relationships in China: the role of trust and vertical coordination. Asia Pacific Journal of Management, 23(3), 299-317. doi:10.1007/s10490-006-9000-9

Author

• Jian Wang, Texas Tech University