[2]    Abrahamson, D., Bridging theory: Activities designed to support the grounding of outcome-based combinatorial analysis in event-based intuitive judgment-A case study, in Proc. Topic Study Group 13 at the 11th Int. Conf. Math. Educ. (ICME), M. Borovcnik, D. Pratt, eds., Monterrey, Mexico, 2008.
[3]    Abrahamson, D., Orchestrating semiotic leaps from tacit to cultural quantitative reasoning: the case of anticipating experimental outcomes of a quasi-binomial random generator, Cogn. Instr., 27 (2009), no. 3, 175–224.
[4]    Australian Curriculum, Assessment and Reporting Authority (ACARA), The Australian Curriculum: Mathematics, Author, Sydney, NSW, 2010.
[5]    Azcárate, P., Cardeñoso, J. M., Serradó, S., Randomness in textbooks: the influence of deterministic thinking, in Proc. Fourth Conf. Eur. Soc. Res. Math. Educ., M. Bosch, ed., ERME, Sant Feliu de Guixols, Spain, 2006.
[6]    Ball, D. L., Thames, M. H., Phelps, G., Content knowledge for teaching, J. Teach. Educ., 59 (2008), no. 5, 389–407.
[7]    Batanero, C., Understanding randomness: Challenges for research and teaching, plenary lecture in Ninth Eur. Conf. Math. Educ., Prague, Czech Republic, 2015.
[8]    Batanero, C., Arteaga, P., Serrano, L., Ruiz, B., Prospective primary school teachers’ perception of randomness, in Probabilistic Thinking: Presenting Plural Perspectives, E. Chernoff, B. Sriraman, eds., Springer, New York, 2014, 345–366.
[9]    Batanero, C., Biehler, R., Maxara, C., Engel, J., Vogel, M., Using simulation to bridge teachers’ content and pedagogical knowledge in probability, paper presented at the fifteenth ICMI Study Conf.: The Professional Education and Development of Teachers of Mathematics, Aguas de Lin-doia, Brazil, 2005.
[10]    Batanero, C., Henry, M., Parzysz, B., The nature of chance and probability, in Exploring Probability in School: Challenges for Teaching and Learning, G. A. Jones, ed., Springer, New York, 2005, 15– 37.
[11]    Batanero, C., Serrano, L., The meaning of randomness for secondary school students, J. Res. Math. Educ., 30 (1999), no. 5, 558–567.
[12]    Bernoulli, J., Ars Conjectandi, IREM, Rouen, 1987; original work published in 1713.
[13]    Biehler, R., Computers in probability education, in Chance Encounters: Probability in Education, R. Kapadia, M. Borovcnik, eds., Kluwer, Dordrecht, The Netherlands, 1991, 169–211.
[14]    Canizares, M. J., Ortiz, J. J., Batanero, C., Serrano, L., Probabilistic language in Spanish textbooks, in ICOTS-6 Papers for School Teachers, B. Phillips, ed., Int. Assoc. Stat. Educ., Cape Town, 2002, 207–211.
[15]    Chaput, B., Girard, J. C., Henry, M., Frequentist approach: Modelling and simulation in statistics and probability teaching, in Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education, C. Batanero, G. Burrill, C. Reading, eds., Springer, New York, 2011, 85–95.
[16]    Chernoff, E. J., Sample space partitions: An investigative lens, J. Math. Behav., 28 (2009), no. 1, 19–29.
[17]    Chernoff, E. J., Logically fallacious relative likelihood comparisons: the fallacy of composition, Exp. Educ., 40 (2012), no. 4, 77–84.
[18]    Chernoff, E. J., Recognizing revisitation of the representativeness heuristic: an analysis of answer key attributes, ZDM - Int. J. Math. Educ., 44 (2012), no. 7, 941–952.
[19]    Chernoff, E. J., Russell, G. L., The fallacy of composition: Prospective mathematics teachers’ use of logical fallacies, Can. J. Sci. Math. Technol. Educ., 12 (2012), no. 3, 259–271.
[20]    Chernoff, E. J., Sriraman, B., Introduction, in Probabilistic Thinking: Presenting Plural Perspectives, E. J. Chernoff, B. Sriraman, eds., Springer, New York, 2014, xv–xviii.
[21]    Chernoff, E. J., Sriraman, B., Commentary on probabilistic thinking: presenting plural perspectives, in Probabilistic Thinking: Presenting Plural Perspectives, E. J. Chernoff, B. Sriraman, eds., Springer, New York, 2014, 721–728.
[22]    Chernoff, E. J., Zazkis, R., From personal to conventional probabilities: from sample set to sample space, Educ. Stud. Math., 77 (2011), no. 1, 15–33.
[23]    Common Core State Standards Initiative (CCSSI), Common Core State Standards for Mathematics, National Governors Association for Best Practices and the Council of Chief State School Officers, Washington, DC, 2010, available at http://www.corestandards.org/Math/.
[24]    Drier, H. S., Children’s meaning-making activity with dynamic multiple representations in a probability microworld, in Proc. Twenty-second Annu. Meet. North Amer. Chapter Int. Group Psychol. Math. Educ., Vol. 2, M. Fernandez, ed., Tucson, AZ, 2000, 691–696.
[25]    Dugdale, S., Pre-service teachers’ use of computer simulation to explore probability, Comput. Sch., 17 (2001), no. 1–2, 173–182.
[26]    Eichler, A., Vogel, M., Three approaches for modelling situations with randomness, in Probabilistic Thinking: Presenting Plural Perspectives, E. J. Chernoff, B. Sriraman, eds., Springer, New York, 2014, 75–99.

[27]    Falk, R., The perception of randomness, in Proc. Fifth Conf. Int. Group Psychol. Math. Educ., University of Grenoble, Grenoble, France, 1981, 222–229.
[28]    Falk, R., Konold, C., Making sense of randomness: Implicit encoding as a basis for judgement, Psychol. Rev., 104 (1997), no. 2, 310–318.
[29]    Fischbein, E., The Intuitive Source of Probability Thinking in Children, Reidel, Dordrecht, The Netherlands, 1975.
[30]    Fischbein, E., Gazit, A., Does the teaching of probability improve probabilistic intuitions?, Educ. Stud. Math., 15 (1984), 1–24.
[31]    Fischbein, E., Nello, M. S., Marino, M. S., Factors affecting probabilistic judgments in children and adolescents, Educ. Stud. Math., 22 (1991), 523–549.
[32]    Fischbein, E., Pampu, I., Minzat, I., Comparison of ratios and the chance concept in children, Child Dev., 41 (1970), 377–389.
[33]    Fischbein, E., Schnarch, D., The evolution with age of probabilistic, intuitively based misconceptions, J. Res. Math. Educ., 28 (1997), 96–105.
[34]    Franklin, C., Mewborn, D., The statistical education of PreK-12 teachers: A shared responsibility, in NCTM 2006 Yearbook: Thinking and Reasoning with Data and Chance, G. Burrill, ed., National Council of Teachers of Mathematics, Reston, VA, 2006, 335–344.
[35]    Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., et al., Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework, American Statistical Association, Alexandria, VA, 2007.
[36]    Gigerenzer, G., Hertwig, R., Pachur, T., Heuristics: The Foundations of Adaptive Behavior, Oxford University Press, Oxford, MA, 2011.
[37]    Gilovich, T., Griffin, D., Kahneman, D., Heuristics and Biases: The Psychology of Intuitive Judgment, Cambridge University Press, New York, 2002.
[38]    Godino, J. D., Ortiz, J. J., Roa, R., Wilhelmi, M. R., Models for statistical pedagogical knowledge, in Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education, C. Batanero, G. Burrill, C. Reading, eds., Springer, New York, 2011, 271–282.
[39]    Green, D., The chance and probability concepts project, Teach. Stat., 1 (1979), no. 3, 66–71.
[40]    Green, D., School pupils’ probability concepts, Teach. Stat., 5 (1983), no. 2, 34–42.
[41]    Green, D. R., Schools students’ understanding of randomness, in Studies in Mathematics Education: The Teaching of Statistics, Vol. 7, R. Morris, ed., UNESCO, Paris, 1989, 27–39.
[42]    Groth, R. E., Bergner, J. S., Mapping the structure of knowledge for teaching nominal categorical data analysis, Educ. Stud. Math., 83 (2013), 247–265.
[43]    Groth, R. E., Xu, S., Preparing teachers through case analyses, in Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education, C. Batanero, G. Burrill, C. Reading, eds., Springer, New York, 2011, 371–382.
[44]    Heitele, D., An epistemological view on fundamental stochastic ideas, Educ. Stud. Math., 6 (1975), 187–205.
[45]    Henry, M., Evolution de l’enseignement secondaire français en statistique et probabilities [Evolution of French secondary teaching in statistics and probability], Stat. Enseign., 1 (2010), no. 1, 35–45.
[46]    Jones, J. L., Tarr, J. E., An examination of the levels of cognitive demand required by probability tasks in middle grade mathematics textbooks, Stat. Educ. Res. J., 6 (2007), no. 2, 4–27.
[47]    Jones, G. A., Thornton, C. A., An overview of research into the learning and teaching of probability, in Exploring Probability in School: Challenges for Teaching and Learning, G. A. Jones, ed., Springer, New York, 2005, pp. 65–92.
[48]    Jones, G. A., Langrall, C. W., Thornton, C. A., Mogill, A. T., A framework for assessing and nurturing young children’s thinking in instruction, Educ. Stud. Math., 32 (1997), 101–125.

[69]    Ministerio de Educación y Ciencia, MEC, Real Decreto 1467/2007, de 2 de noviembre, por el que se establece la estructura del bachillerato y se fijan sus enseñanzas mínimas [Royal Decree establishing the structure and minimum content for High School], Author, Madrid, 2007b.
[70]    Ministerio de Educación, Cultura y Deporte, MECD, Real Decreto 126/2014, de 28 de febrero, por el que se establece el currículo básico de la Educación Primaria [Royal Decree establishing the minimum content for Primary Education], Author, Madrid, 2014.
[71]    Ministerio de Educación, Cultura y Deporte, MECD, Real Decreto 1105/2014, de 26 de diciembre, por el que se establece el currículo básico de la Educación Secundaria Obligatoria y del Bachiller-ato [Royal Decree establishing the minimum content for Compulsory Secondary Education and High School], Author, Madrid, 2015.
[72]    Ministerio de Educación Pública, MEP, Programas de Estudio de Matemáticas [Study programs for mathematics], Author, San José, Costa Rica, 2012.
[73]    Ministry of Education, ME, The New Zealand Curriculum, Learning Media, Wellington, New Zealand, 2007.
[74]    National Council of Teachers of Mathematics, NCTM, Principles and Standards for School Mathematics, Author, Reston, VA, 2000.
[75]    Nilsson, P., Different ways in which students handle chance encounters in the explorative setting of a dice game, Educ. Stud. Math., 66 (2007), 293–315.
[76]    Nilsson, P., Conceptual variation and coordination in probability reasoning, J. Math. Behav., 28 (2009), no. 4, 247–261.
[77]    Nilsson, P., Experimentation in probability teaching and learning, in Probabilistic Thinking: Presenting Multiple Perspectives, E. Chernoff, B. Sriraman, eds., Springer, New York, 2014, 509–532.
[78]    Nunes, T., Bryant, P., Evans, D., Gottardis, L., Terlektsi, M. E., The cognitive demands of understanding the sample space, ZDM - Int. J. Math. Educ., 46 (2014), no. 3, 437–448.
[79]    Piaget, J., Inhelder, B., The Origin of the Idea of Chance in Children, Norton, New York, 1975.
[80]    Pratt, D., Making sense of the total of two dice, J. Res. Math. Educ., 31 (2000), no. 5, 602–625.
[81]    Pratt, D., Re-connecting probability and reasoning about data in secondary school teaching, paper presented at 58th ISI World Statistics Congress, Dublin, Ireland, 2011.
[82]    Pratt, D., Ainley, J., Chance re-encounters: Computers in probability education revisited, in Mit Werkzeugen mathematik und stochastik lernen–using tools for learning mathematics and statistics, T. Wassong, ed., Springer Fachmedien, Wiesbaden, 2014, pp. 165–177.
[83]    Pratt, D., Ainley, J., Kent, P., Levinson, R., Yogui, C., Kapadia, R., Role of context in risk-based reasoning, Math. Think. Learn., 13 (2011a), no. 4, 322–345.
[84]    Pratt, D., Davies, N., Connor, D., The role of technology in teaching and learning statistics, in Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education, C. Batanero, G. Burrill, C. Reading, eds., Springer, New York, 2011, pp. 97–107.
[85]    Prodromou, T., Connecting experimental probability and theoretical probability, ZDM - Int. J. Math. Educ., 44 (2012), no. 7, 855–868.
[86]    Prodromou, T., Developing a modelling approach to probability Using computer-based simulations, in Probabilistic Thinking: Presenting Multiple Perspectives, E. Chernoff, B. Sriraman, eds., Springer, New York, 2014, 417–439.
[87]    Raoult, J. P., La statistique dans l’enseignement secondaire en France [Statistics in secondary teaching in France], Stat. Enseign., 4 (2013), no. 1, 55–69.
[88]    Senior Secondary Board of South Australia (SSBSA), Mathematical Studies Curriculum Statement, SSBSA, Adelaide, Australia, 2002.
[89]    SEP, Plan de Estudios, Educación Básica, Secretaría de Educación Pública, México, 2011.

[90]    Shaughnessy, J. M., Misconceptions of probability: An experiment with a small-group, activitybased, model building approach to introductory probability at the college level, Educ. Stud. Math., 8 (1977), 285–316.
[91]    Shaughnessy, J. M., Misconceptions of probability: From systematic errors to systematic experiments and decisions, in Teaching Statistics and Probability: Yearbook of the National Council of Teachers of Mathematics, A. Schulte, ed., National Council of Teachers of Mathematics, Reston, VA, 1981, 90–100.
[92]    Shaughnessy, J. M., Research in probability and statistics: Reflections and directions, in Handbook of Research on Mathematics Teaching and Learning, D. A. Grouws, ed., Macmillan, New York, 1992, 465–494.
[93]    Stohl, H., Probability in teacher education and development, in Exploring Probability in Schools: Challenges for Teaching and Learning, G. Jones, ed., Springer, New York, 2005, 345–366.
[94]    Stohl, H., Tarr, J. E., Developing notions of inference with probability simulation tools, J. Math. Behav., 21 (2002), no. 3, 319–337.