Figure 1. An example of a structured number line
Figure 2. The number line for the natural numbers (Tapia et al. as cited in Herbst, 1997)
Figure 3. Example of incorrect identification of the unit
Figure 4. Example of unjustifiable identification of the unit and direction
Figure 5. A number line for sorting even and odd numbers
Figure 6. A curved number line showing that 24 rounded to the nearest ten is 20
Figure 7. Coin lines
Table 1. Examples of misconceptions
Activity 1. Place the given numbers on the number line.
Activity 2. Mark the direction and the beginning on the number line
Activity 3. Place the given numbers on the number line.
참고문헌
- Bartolini Bussi, M. G. (2015). The number line: A "western" teaching aid. In X. Sun, B. Kaur, & J. Novotna (Eds.), Conference proceedings of the ICMI Study 23: Primary mathematics study on whole numbers (pp. 298-306). Macau, Chaina: University of Macau.
- Bright, G., Behr, M., Post, T., & Wachsmuth, I. (1988). Identifying fractions on number lines. Journal for Research in Mathematics Education, 19(3), 215-232. https://doi.org/10.2307/749066
- Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 669-705). Charlotte, NC: Information Age.
- Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and algebra in early mathematics instruction. Journal for Research in Mathematics Education, 37(2), 87-115.
- Carraher, D. W., Schliemann, A. D., & Schwartz, J. L. (2008). Early algebra is not the same as algebra early. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 235-272). New York, NY: Lawrence Erlbaum.
- Cramer, K., Ahrendt, S., Monson, D., Wyberg, T., & Miller, C. (2016). Making sense of thirdgrade students' misunderstandings of number line. Investigations in Mathematics Learning, 9(1), 19-37.
- Davydov, V. V., Gorbov, S. F., Mikulina, G. G., & Saveleva, O. V. (1999). Mathematics: Class 1, Binghamton: State University of New York.
- Frykholm, J. (2010). Learning to think mathematically with the number line: A resource for teachers, a tool for young children. Salem, OR: Math Learning Center.
- Gullberg, J. (1997). Mathematics from the birth of numbers. New York: Norton and Company.
- Herbst, P. (1997). The number line metaphor in the discourse of a textbook series. For the Learning of Mathematics, 17(3), 36-45.
- Kanopka, K. (2016). Beyond the number line: Coordinate systems and vector arithmetic. Yale National Initiative. Retrieved from http://teachers.yale.edu/curriculum/viewer/initiative16.05.04_u.
- Lee, J. (2002). An analysis of difficulties encountered in teaching Davydov's mathematics curriculum to students in a US setting and measures found to be effective in addressing them. Doctoral Dissertation, State University of New York at Binghamton.
- Lee, J. (2006). Teaching algebraic expressions to young students: The three-day journey of 'a+2'. School Science and Mathematics, 106 (2), 98-104. https://doi.org/10.1111/j.1949-8594.2006.tb18139.x
- National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: NGA & CCSSO.
- Schmittau, J. (2003). Cultural historical theory and mathematics education. In A. Kozulin, B. Gindis, V. Ageryev, & S. Miller (Eds.), Vygotsky's educational theory in cultural context (pp. 225-245). Cambridge, UK: Cambridge University Press.
- Schmittau, J. (2010). The relevance of Russian elementary mathematics education. In A. Karp, & B. R. Vogeli (Eds.), Russian mathematics education: History and world significance (pp. 253-278). Hackensack, NJ: World Scientific.
- Suh, B., Shin, H., & Na, J. (2005). An analytic study on the figure of number line. Journal of Educational Research in Mathematics, 23(2), 135-152.
- van de Walle, J., Karp, K., & Bay-Williams, J. M. (2013). Elementary and middle School mathematics: Teaching developmentally (8th ed.). NJ: Pearson.