1 |
Hunting, R. P., & Sharpley, C. F. (1988). Preschoolers' cognitions of fraction units. British Journal of Educational Psychology, 58, pp.172-183.
DOI
|
2 |
Konold, C., & Pollatsek, A. (2002). Data analysis as the search for signals in noisy processes. Journal for Research in Mathematics Education, 33, pp.259-289.
DOI
ScienceOn
|
3 |
Bakker, A., & Gravemeijer, K. P. E. (2006). An historical phenomenology of mean and median. Educational Studies in Mathematics, 62, pp.149-168.
DOI
ScienceOn
|
4 |
Mevarech, A. R. (1983). A deep structure model of students' statistical misconceptions. Educational Studies in Mathematics, 14, pp.415-429.
DOI
|
5 |
Plackett, R. L. (1970). The principle of the arithmetic mean, In E. Pearson & M. G. Kendall (Eds.), Studies in the history of statistics and probability, 1, Griffin, London.
|
6 |
Marnich, M. (2008). A knowledge structure for the arithmetic mean: relationships between statistical conceptualizations and mathematical concepts. Unpublished Doctoral dissertation, University of Pittsburgh.
|
7 |
McGatha, M., Cobb, P., & McClain, K. (2002). An analysis of students' initial statistical understandings: Developing a conjectured learning trajectory. Journal of Mathematical Behavior, 16, pp.339-355.
|
8 |
Murray, F. B., & Holm, J. (1982). The absence of lag in conservation of discontinuous and continuous materials, Journal of Genetic Psychology, 141, pp.213-217.
DOI
ScienceOn
|
9 |
Miller, K. (1984). Child as measurer of all things: Measurement procedures and the development of quantitative concepts. In C. Sophian (Ed.), Origins of cognitive skills Hillsdale, NJ : Lawrence Earlbaum Associates.
|
10 |
Mokros, J., & Russell, S. (1995). Children's concepts of average and representativeness. Journal for Research in Mathematics Education, 26(1), pp.20-39.
DOI
ScienceOn
|
11 |
Kieren, T. E. (1988). Personal knowledge of rational numbers. In M. Behr & J. Hiebert (Eds.), Number concepts and operations in the middle grades (pp.162-181). Reston, VA: Erlbaum.
|
12 |
Leavy, A. M., & O'Loughlin, N. (2006). Moving beyond the arithmetic average: Preservice teachers understanding of the mean. Journal of Mathematics Teacher Education, 9(1), pp.53-90.
DOI
ScienceOn
|
13 |
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp.1-27). Hillsdale, NJ: Lawrence Erlbaum Associates.
|
14 |
Leon, M., & Zawojewski, J. (1990). Use of the arithmetic mean: An investigation of four properties Issues and preliminary results. Paper presented at The Third International Conference on Teaching Statistics (ICOTS III) . Dunedin, New Zealand.
|
15 |
Lovell, K. (1961). A follow-up study of Inhelder and Piaget's 'The growth of logical thinking.'. British Journal of Psychology, 52, pp.143-153.
DOI
ScienceOn
|
16 |
MacCullough, D. (2007). A study of expert's understanding of the arithmetic mean. Unpublished Doctoral dissertation, Pennsylvania State University.
|
17 |
Jackson, S. (1965). The growth of logical thinking in normal and subnormal children. British Journal of Educational Psychology, 35, pp.255-258.
DOI
ScienceOn
|
18 |
Aufmann, R. N., Lockwood, J. S., Nation, R. D., & Clegg, D. K. (2007). Mathematical excursions. Boston, MA: Houghton Mifflin Company.
|
19 |
Bakker, A. (2004). Design research in statistics education : on symbolizing and computer tools. Unpublished Doctoral dissertation.
|
20 |
Hardiman, P., Pollatsek, A., & Well, A. (1986). Learning to understand the balance beam. Cognition and Instruction, 3, pp.63-86.
DOI
ScienceOn
|
21 |
Zawojewski, J. S. (1986) The Teaching and Learning Processes of Junior High Studeas Under Different Modes of Instruction in Measures of Central Tendency. Unpublished doctoral dissertation, Northwestern University. Evanston, Illinois.
|
22 |
Heath, T. H. (1981). A history of greek mathematics. Dover, NY.
|
23 |
Hardiman, P., Well, A., & Pollatsek, A. (1984). Usefulness of a balance model in understanding the mean. Journal of Educational Psychology, 76, pp.792-801.
DOI
|
24 |
Groth, R. E., & Bergner, J. A. (2006). Preservice elementary teachers' conceptual and procedural knowledge of mean, median, and mode. Mathematical Thinking and Learning, 8, pp. 7-63.
|
25 |
김우철 외. (1991). 현대통계학, 영지문화사.
|
26 |
이영하.남주현 (2005). 통계적 개념 발달에 관한 인식론적 고찰, 한국수학교육학회지 시리즈 A <수학교육>, 44(3), pp.457-475.
과학기술학회마을
|
27 |
Goodchild, S. (1988). School pupils' understanding of average. Teaching Statistics. 10, pp. 7-81.
|
28 |
Groth, R. E. (2005). An investigation of statistical thinking in two different contexts: Detecting a signal in a noisy process and determining a typical value. Journal of Mathematical Behavior, 24, pp.109-124.
DOI
ScienceOn
|
29 |
Cortina, J. L. (2002). Developing instructional conjectures about how to support student understanding of the arithmetic mean as a ratio. International Conference on Teaching Statistics 6. Retrieved September 10, 2009 from http://www.stat.auckland.ac.nz/~iase/publications/1/2a 2_cort.pdf
|
30 |
Fischbein, E., Deri, M., Nello, M., & Marino, M. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal of Research in Mathematics Education, 16, pp. -17.
|
31 |
Schwartzman, S. (1994). The words of mathematics: An etymological dictionary of math terms used in English. Washington, DC: Mathematical Association of America.
|
32 |
Tukey, J. W. (1977). Exploratory data analysis. Reading, MA: Addison-Wesley.
|
33 |
Van deWalle, J. A., & Lovin, L. H., (2006). Teaching student centered mathematics. Boston, MA: Pearson Education, Inc.
|
34 |
Cortina, J., Saldanha, L., & Thompson, P. W. (1999). Multiplicative conceptions of arithmetic mean. In F. Hitt (Ed.). Proceedings of the Twenty-first Annual Meeting of the International Group for the Psychology of Mathematics Education. Cuernavaca, Mexico:Centro de Investigaciὁn y de Estudios Avanzados.
|
35 |
Watson, J. M., & Moritz, J. B. (2000). The longitudinal development of understanding of average. Mathematical Thinking and Learning, 2, pp.11-50.
DOI
|
36 |
Siegler, R. S. (1976). Three aspects of cognitive development. Cognitive Psychology, 8, pp.481-520.
DOI
|
37 |
Stigler, S. M. (1986). The History of Statistics. The Measurement of Uncertainty Before 1900, Harvard University Press, Cambridge, MA.
|
38 |
Strauss, S., & Bichler, E. (1988). The development of children's concept of arithmetic average. Journal for Research in Mathematics Education, 19, pp.64-80.
DOI
ScienceOn
|
39 |
Russell, S., & Mokros, J. (1996). Research into practice: What do children understand about average? Teaching Children Mathematics, 2(6), pp.360-364.
|
40 |
Carpenter, T. P., Corbitt, M. K., Kepner, H. S., Lindquist, M. M., & Reys, R. E. (1981). Results from the second mathematics assessment of the national assessment of educational progress. National Council of Teachers of Mathematics, Reston. VA.
|
41 |
Pollatsek, A., Lima, S., & Well, A. D. (1981), Concept or Computation: Students' Misconceptions of the Mean, Educational Studies in Mathematics, 12, pp.191-204.
DOI
|
42 |
Boyer, C. B. (1991). A history of mathematics. NY: John Wiley and Sons, Inc.
|
43 |
Porter, T. M. (1986). The Rise of Statistical Thinking, 1820-1900. Princeton University Press, Princeton.
|
44 |
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
|
45 |
Cai, J. (1998). Exploring students' conceptual understanding of the averaging algorithm. School Science and Mathematics, 98(2), pp.93-98.
DOI
ScienceOn
|