Developmental stages and important periods of probability cognition in 6 to 14 year-old students

Referencias

Amir, G. S., & Williams, J. S. (1999). Cultural influences on children’s probabilistic thinking. Journal of Mathematical Behavior, 18 (1), 85-107. Australian Education Council. (1991). A national statement on mathematics for Australian schools. Carlton, VIC: Curriculum Corporation, Department of Education and Science and the Welsh Office. Ausubel, D. I., Novak, J. D., & Hanesian, H. (1983). Psicología educativa. Un punto de vista cognoscitivo, Mexico: Trillas. Batanero, C., & Serrano, L. (1999). The meaning of randomness for secondary students. Journal for Research in Mathematics Education, 30, 558-567. Biggs J. B., & Collis K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy (pp. 17-35). New York: Academic Press. Carpenter T P. (1981). What are the chances of your students knowing probability? The Mathematics Teacher, 74, 342-343. Che, L. (2014). Research on learning process and characteristic representations about permutation and combination in the second grade primary school. Master’s thesis of Hangzhou Normal University, Hangzhou.[In Chinese]. Chernoff, E. J. (2008). The state of probability measurement in mathematics education: a first approximation. Philosophy of Mathematics Education Journal, 23, 1-23. Chernoff, E. J. (2009). Sample space partitions: an investigative lens. Journal of Mathematical Behavior, 28(1), 19-29. Chernoff, E. J., & Zazkis, R. (2011). From personal to conventional probabilities: from sample set to sample space. Educational Studies in Mathematics, 77, 15-33. China Ministry of Education. (2001). Mathematics Curriculum Standards for Compulsory Education (Experimental Edition). Beijing Normal University Press. [In Chinese]. China Ministry of Education. (2011). Mathematics Curriculum Standards for Compulsory Education (2011 Edition). Beijing Normal University Press. [In Chinese]. Copeland, R. W. Li, Q., & Kang, Q. (1985). How do children learn mathematics?. Shanghai: Shanghai Educational Publishing House. Department of Education and Science and the Welsh Office. (1991). National curriculum: Mathematics for ages 5 to 16. York, UK: Central Office of Information. Engel, J., & Sedlmeier, P. (2005). On middle-school students’ comprehension of randomness and chance variability in data. Zentralblatt für Didaktik der Mathematik (ZDM), 37(3), 168-177. Fan, L. (2006). Mathematics (7th (semester 2)).. Zhejiang: Zhejiang Education Publishing House.[In Chinese]. Fan, L. (2010). Mathematics (9th (semester 2)). Zhejiang: Zhejiang Education Publishing House.[In Chinese]. Fischbein, E., & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? Educational Studies in Mathematics, 7, 15-19. Gal, I. (2005). Towards probability literacy for all citizens: Building blocks and instructional dilemmas. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 39-63). New York: Springer. Gao, H. (2011). The understanding of probability concepts in 6-12 year old pupils. Master’s thesis.f Hangzhou Normal University, Hangzhou.[In Chinese]. Gong, Z. & Song, N. (2006). Teaching and learning of statistics and probability: reflections and suggestions. People’s Education, 10, 1-6. [In Chinese]. Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1999). Students’ probabilistic thinking in instruction. Journal for Research in Mathematics Education, 30, 487-519. Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1997). A framework for assessing and nurturing young children’s thinking in probability. Educational Studies in Mathematics, 32, 101-125. Jones, G. A., Langrall, C. W., & Mooney, E. S. (2007). Research in probability: Responding to classroom realities. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 909-955). Reston: The National Council of Teachers of Mathematics. Lagnado D. A. & Shanks D. R. (2003). The influence of hierarchy on probability judgment. Cognition, 89,157-178. Li, J. (2002). Developmental structure in understanding of probability, Journal of Mathematics Education, 4, 1-5.[In Chinese]. Li, J. (2003). Learning and teaching of probability in primary and secondary schools. Shanghai: East China Normal University Press.[In Chinese]. Li, W., Zhang, H., & Shoo, H. (2014). Quantitative research methods and statistic analysis in education and psychology. Beijing, Beijing Normal University Press. [In Chinese]. Lu, J., & Yang, G. (2009). Mathematics (3th (semester 1)).. Beijing, People’s Education Press. [In Chinese]. Lu, J., & Yang, G. (2010a). Mathematics (5th (semester 1)). Beijing, People’s Education Press. [In Chinese]. Lu, J., & Yang, G. (2010b). Mathematics (6th (semester 2)). Beijing, People’s Education Press. [In Chinese]. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM. Nikiforidou, Z. & Pange, J. (2010). The notions of chance and probabilities in preschoolers. Early Childhood Education Journal, 38, 305-311. Nilsson, P., & Li, J. (2015). Teaching and learning of probability. In. S. J. Cho (Ed.). The Proceedings of the 12th International Congress on Mathematical Education: Intellectual and Attitudinal Challenges (pp. 437-442). New York: Springer. Piaget, J. & Inhelder, B. (1975). The origin of the idea of chance in children. New York: Norton. Sharma, S. (2012). Cultural influences in probabilistic thinking. Journal of Mathematics Research, 4 (5), 63-77. Shen, J., & Liu, F. (1984). Study on the cognition of volume for students aged 5-17. Acta Psychologica Sinica, 155-164. [In Chinese]. Wang, H. (2012). Study on elementary teachers’ probability knowledge. Master’s thesis Hangzhou Normal University, Hangzhou.[In Chinese]. Watson, J. D. & Moritz, J. B. (2003a). Fairness of dice: A longitudinal study of students’ beliefs and strategies for making judgments. Journal for Research in Mathematics Education, 34, 270-304. Watson, J. D. & Moritz, J. B. (2003b). The development of comprehension of chance language: evaluation and interpretation. School Science and Mathematics, 103, 65-80. Watson, J. M., Collis, K. F., & Moritz, J. B. (1997). The development of chance measurement. Mathematics Education Research Journal, 9, 60-82. Yan, B. (2007). A study of questions of statistics and probability in teaching in elementary mathematics. Master’s Thesis.Southwest University, Chongqing. [In Chinese]. Zhang, Z., Liu, F., Zhao, S., Sun, C., & Zuo, M. (1985). A study of the development of 5 to 15- year-old’ concept of probability. Acta Psychologica Sinica, 1-6. [In Chinese]. Zhang, Z., Liu, Z., & Qiu, M. (1983). On the budding and developing of the cognitive structure for the notion of probability in children of 5-11. Journal of the southwest teachers college, 2, 29-42. [In Chinese].