This study examined the different types of
mathematical tasks used in the classroom to explore the nature of mathematics
instruction of three sixth grade teachers in an elementary school. Case
studies, instructional observations,
and classroom artifacts were used to collect data. The results showed that the
three teachers used different types of mathematical tasks and implementation
methods. One teacher focused on high cognitive demand tasks, most of which
involved substantial group discussion and students working cooperatively. Even
though the other two also used many high cognitive demand tasks, these were
mainly presented via teacher-student dialogue. By examining the types of
mathematical tasks and their implementation, it was found that the group discussion tasks were generally
all high cognitive demand tasks, in which the students fully explained the
solution process. As for the tasks administered through teacher-student dialogue, due to the usage of large
amounts of closed-ended dialogue, the students used low cognition to solve the mathematical tasks and
did not have the opportunity to completely explain their thinking about the solutions. Thus, in order to
fully understand the nature of mathematics instruction by teachers, there should be simultaneous
consideration of the types of mathematical tasks used as well as how the tasks
were implemented.
References
[1]
Anderson, C. W. (2003). How can schools support teaching for understanding in mathematics and science? In A. Gamoran et al. (Eds.), Transforming: How schools and districts can support change (pp. 3-21). New York: Teachers College.
[2]
Artzt, A. F., & Armour-Thomas, E. (2002). Becoming a reflective mathematics teacher: A guide for observations and self-assessment. Mahwah, NJ: Lawrence Erlbaum.
[3]
Becker, J. P., & Selter, C. (1996). Elementary school, practices. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 511-564). Dordrecht: Kluwer Academic. doi:10.1007/978-94-009-1465-0_17
[4]
Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside school. Teacher College Record, 110(3), 608-645.
[5]
Boaler, J. & Brodie, K. (2004). The importance, nature and impact of teacher questions. In D. E. McDougall, & J. A. Ross (Eds.), Proceedings of the 26th Conference of the Psychology of Mathematics Education (North America, pp. 773-781). Toronto: OISE/UT.
[6]
Chung, C. (2005). Analyzing mathematics curriculum evolving of Tai wan in tens years. Journal of Education Research, 133, 124-134.
[7]
Cohen, D. K., & Peterson, P. L., Wilson, S., Ball, D., Putnam, R., Prawat, R., Heaton, R., Remillard, J., & Weimers, N. (1990). Effects of state-level reform of elementary school mathematics curriculum on classroom practice.
http://ncrtl.msu.edu/http/rreports/html/pdf/rr9014.pdf
[8]
Cowan, P. (2006). Teaching mathematics: A handbook for primary and secondary school teachers. London: Routledge.
doi:10.4324/9780203416013
[9]
Feldman, A. (2003). Mathematics instruction: Cognitive, affective, and existential perspectives. In J. M. Royer (Ed.), Mathematics cognition. Greenwich, CT: Information Age.
[10]
Fuson, K. C., et al. (2000). Blending the best of the twentieth century to achieve a mathematics equity pedagogy in the twenty-first century. In M. J. Burke, & F. R. Curcio (Eds.), Learning mathematics for a new century (pp. 197-212). Reston, VA: NCTM.
[11]
Grouws, D. A., Smith, M. S., & Sztajn, P. (2004). The preparation and teaching practice of U.S. Mathematics teachers: Grades 4 and 8. In P. Kloosterman, & F. Lester (Eds.), The 1990 through 2000 mathematics assessments of the National Assessment of Educational Progress: Results and interpretations (pp. 221-269). Reston, VA: NCTM.
[12]
Gutstein, E. (2003). Teaching and learning mathematics for social justice in an urban, Latino school. Journal for Research in Mathematics Education, 34, 37-73. doi:10.2307/30034699
[13]
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhabit high level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28, 524-549. doi:10.2307/749690
[14]
Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371-404). Gweenwich, CT: Information Age.
[15]
Kilpatrick, J., & Silver, E. A. (2000). Unfinished business: Challenges for mathematics educator in the next decades. In M. J. Burke, & F. R. Curcio (Eds.), Learning mathematics for a new century (pp. 223-235). Reston, VA: NCTM.
[16]
Lott, J. W., & Souhrada, T. A. (2000). As the century unfolds: A perspective on secondary school mathematics content. In M. J. Burke, & F. R. Curcio (Eds.), Learning mathematics for a new century (pp. 96-111). Reston, VA: NCTM.
[17]
Ministry of Education in Taiwan (2003). The learning domain of ma thematics of grade 1-9 curriculum guidelines. Taipei: Ministry of Education.
[18]
Mullis, I. V. S., Martin, M. O., Gonzales, E. J., & Chrostowski, S. J. (2004). TIMSS 2003 international mathematics report: Findings from IEA’s trends in international mathematics and science study at the fourth and eighth grades. Chestnut Hill, MA: TIMSS & PIRLS International Study Center.
[19]
NCTM (1991). Professional standards for teaching mathematics. Re ston, VA: NCTM.
[20]
NCTM (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
[21]
Rodriguez, A. J. (2005). Teachers’ resistance to ideological and pedagogical change: Definitions, theoretical framework, and significance. In A. J. Rodriguez, & R. S. Kitchen (Eds), Preparing mathematics and science teachers for diverse classrooms: Promising strategies for transformative pedagogy (pp. 1-16). Mahwah, NJ: Laurence Erlbaum.
[22]
Silver, E. A., Mesa, V. M., Morris, K. A., Star, J. R., & Benken, B. M. (2009). Teaching mathematics for understanding: An analysis of lessons submitted by teachers seeking NBPTS certification. American Educational Research Journal, 46, 501-531.
doi:10.3102/0002831208326559
[23]
Stein, M., Smith, M., Henningsen, M., & Silver, E. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York: Teacher College.
[24]
Stein, M. K., Remillard, J., & Smith M. S. (2007). How curriculum influences student learning. In F. K. Lester Jr. (Ed.), Second hand book of research on mathematics teaching and learning (pp. 319-369). Gweenwich, CT: Information Age.
[25]
Verschaffel, L., & De Corte, E. (1996). Number and arithmetic. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 99-137). Dor drecht, Netherlands: Kluwer Academic.
doi:10.1007/978-94-009-1465-0_5
[26]
Weiss, I. R., Banilower, E. R., McMahon, K. C., & Smith, P. S. (2001). Report of the 2000 national survey of science and mathematics education. Chapel Hill, NC: Horizon Research.
[27]
Willoughby, S. S. (2000). Perspectives on mathematics education. In M. J. Burke, & F. R. Curcio (Eds.), Learning mathematics for a new century (pp. 1-15). Reston, VA: NCTM.
