Research on children’s reasoning in comparing probabilities

  1. Luis Armando Hernández-Solís
  2. Carmen Batanero
  3. María M. Gea
  4. Rocío Álvarez-Arroyo
Revista:
BEIO, Boletín de Estadística e Investigación Operativa

ISSN: 1889-3805

Año de publicación: 2023

Volumen: 39

Número: 1

Tipo: Artículo

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Otras publicaciones en: BEIO, Boletín de Estadística e Investigación Operativa

Resumen

An important change in the recent curricular guidelines for Primary Education is the inclusion of probability content that help model many random phenomena. The success in learning of this topic requires taking into account the children’s capabilities in different stages of their development to work with probability. With the aim of guiding teachers, in this work we summarize the main research on strategies and reasoning levels of children in different ages in comparison of probabilities problems. We first analyse the pioneer work by Piaget and Inhelder and Fischbein, and follow with the analysis of studies performed after these authors. Different models of probabilistic reasoning levels, as well as associated strategies, and the main variables that affect the difficulty of comparing probabilities are described and the possible implications on teaching.

Referencias bibliográficas

  • ACARA. 2013. The Australian Curriculum: Mathematics. Sidney, NSW: Author.
  • Batanero, C. 2013. “La Comprensión de La Probabilidad En Los Niños:?‘ Qué Podemos Aprender de La Investigación.” Atas Do III Encontro de Probabilidades e Estatistica Na Escola, 9–21.
  • Batanero, C. 2020. “Making Sense of Probability in Professional and Everyday Life.” Quaderni Di Ricerca in Didattica, Numero Special, 7–16.
  • Batanero, C, E Chernoff, J Engel, H Lee, and E Sánchez. 2016. Research on Teaching and Learning Probability. Springer Nature.
  • Borovcnik, M. 2011. “Strengthening the Role of Probability Within Statistics Curricula.” In Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education, 71–83. Springer.
  • Borovcnik, M, and H Bentz. 1991. “Empirical Research in Understanding Probability.” In Chance Encounters: Probability in Education, 73–105. Springer.
  • Cañizares, M. 1997. “Influencia Del Razonamiento Proporcional y Combinatorio y de Creencias Subjetivas En Las Intuiciones Probabilísticas Primarias.” Unpublished Ph. D. University of Granada, Spain.
  • Cañizares, M, and C Batanero. 1997. “Influencia Del Razonamiento Proporcional y de Las Creencias Subjetivas En La Comparación de Probabilidades.” UNO: Revista de Didáctica de Las Matemáticas, España 14: 99–114.
  • CCSSI. 2010. “Common Core State Standards Initiatives.” Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
  • CME. 2001. Mathematics Curriculum Standards for Compulsory Education (Experimental Edition). Beijing Normal University Press.
  • Davies, C. 1965. “Development of the Probability Concept in Children.” Child Development, 779–88.
  • Falk, R, R Falk, and I Levin. 1980. “A Potential for Learning Probability in Young Children.” Educational Studies in Mathematics 11 (2): 181–204.
  • Fischbein, E. 1975. The Intuitive Sources of Probabilistic Thinking in Children. Dordrecht: Reidel.
  • Fischbein, E. 1987. “Intuition in Science and Mathematics. Dordrecht: d.” Holland: Reidel Publishing Company.
  • Fischbein, E, and A Gazit. 1984. “Does the Teaching of Probability Improve Probabilistic Intuitions?” Educational Studies in Mathematics 15 (1): 1–24.
  • Fischbein, E, E Pampu, and I Minzat. 1967. “The Child’s Intuition of Probability.” Enfance 2: 193–280.
  • Goldberg, S. 1966. “Probability Judgments by Preschool Children: Task Conditions and Performance.” Child Development, 157–67.
  • Gong, Z, and S He. 2017. “Developmental Stages and Important Periods of Probability Cognition in 6 to 14 Year-Old Students.” Avances de Investigación En Educación Matemática, no. 11: 47–68.
  • Green, D. 1982. “Probability Concepts in School Pupils Aged 11–16 Years.” PhD thesis, Loughborough University.
  • Hoemann, H, and B Ross. 1982. “Children’s Concepts of Chance and Probability.” In Children’s Logical and Mathematical Cognition, 93–121. Springer.
  • Jones, G, C Langrall, and E Mooney. 2007. “Research in Probability: Responding to Classroom Realities.” Second Handbook of Research on Mathematics Teaching and Learning 2: 909–55.
  • Jones, G, and C Thornton. 2005. “An Overview of Research into the Teaching and Learning of Probability.” Exploring Probability in School, 65–92.
  • Kahneman, D, S Slovic, P Slovic, and A Tversky. 1982. Judgment Under Uncertainty: Heuristics and Biases. Cambridge University Press.
  • Karplus, R, S Pulos, and E Stages. 1983a. “Early Adolescents’ Proportional Reasoning on ‘Rate’problems.” Educational Studies in Mathematics 14 (3): 219–33.
  • Karplus, R, S Pulos, and E Stages. 1983b. “Proportional Reasoning of Early Adolescents, t. Esh, r. A. Ve Landau, m. ACQuisition of Matmematics Concepts and Processes.” Academic Press.
  • Konold, C. 1989. “Informal Conceptions of Probability.” Cognition and Instruction 6 (1): 59–98.
  • Lecoutre, M. 1992. “Cognitive Models and Problem Spaces in ‘Purely Random’ Situations.” Educational Studies in Mathematics 23 (6): 557–68.
  • Maury, S. 1984. “La Quantification Des Probabilités: Analyse Des Arguments Utilisés Par Les éèves de Classe de Seconde.” Recherches En Didactique Des Mathématiques (Revue) 5 (2): 187–214.
  • MECD. 2014. Real Decreto 1105/2014, de 26 de Diciembre, Por El Que Se Establece El Currículo básico de La Educación Secundaria Obligatoria y Del Bachillerato. Madrid: Author.
  • MEP. 2012. Programas de Estudio de Matemáticas. I y II Ciclos de Educacón Primaria. III Ciclos de Educación General básica y Educaión Diversificada. San José: Author.
  • Metz, K. 1998. “Emergent Ideas of Chance and Probability in Primary-Grade Children.” Reflections on Statistics: Learning, Teaching, and Assessment in Grades K-12, 149–74.
  • NCTM. 2000. Principles and Standards for School Mathematics. Reston, VA: The Council.
  • Noelting, G. 1980a. “The Development of Proportional Reasoning and the Ratio Concept Part i-Differentiation of Stages.” Educational Studies in Mathematics, 217–53.
  • Noelting, G. 1980b. “The Development of Proportional Reasoning and the Ratio Concept Part II—Problem-Structure at Successive Stages; Problem-Solving Strategies and the Mechanism of Adaptive Restructuring.” Educational Studies in Mathematics 11 (3): 331–63.
  • Pérez-Echeverría, M, M Carretero, and J Pozo. 1986. “Los Adolescentes Ante Las Matemáticas: Proporción y Probabilidad.” Cuadernos de Pedagogía, no. 133: 9–13.
  • Piaget, J. 1975. “Psicología de La Inteligencia [Psychology of Intelligence].” Psique, Buenos Aires, Argentina.
  • Piaget, J, and B Inhelder. 1951. “La Genèse de l’idée de Hasard Chez l’enfant.”
  • Shaughnessy, M. 1992. “Research in Probability and Statistics: Reflections and Directions.”
  • Yost, P, A Siegel, and J Andrews. 1962. “Nonverbal Probability Judgments by Young Children.” Child Development, 769–80.
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