Research on Teaching and Learning Probability

Research in probability education is now well established and tries to improve the challenges posed in the education of students and teachers. In this survey on the state of the art, we summarise existing research in probability education before pointing to some ideas and questions that may help in framing a future research agenda.

[1]  J. Keynes A Treatise on Probability. , 1923 .

[2]  A. Wald,et al.  Probability, statistics and truth , 1939 .

[3]  S. S. Wilks,et al.  Probability, statistics and truth , 1939 .

[4]  Kai Lai Chung,et al.  A Course in Probability Theory , 1949 .

[5]  David Lindley,et al.  Logical foundations of probability , 1951 .

[6]  K. Popper The Propensity Interpretation of Probability , 1959 .

[7]  The book on games of chance : "liber de ludo aleae" , 1961 .

[8]  A. Rényi,et al.  Calcul des probabilités , 1966 .

[9]  E. Fischbein Comparison of Ratios and the Chance Concept in Children. , 1970 .

[10]  Games, Gods and Gambling , 1970 .

[11]  T. Fine Theories of Probability: An Examination of Foundations , 1973 .

[12]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[13]  Dietger Heitele,et al.  An epistemological view on fundamental stochastic ideas , 1975 .

[14]  E. Fischbein,et al.  The intuitive sources of probabilistic thinking in children , 1975 .

[15]  J. Piaget,et al.  The Origin of the Idea of Chance in Children , 1975 .

[16]  J. Michael Shaughnessy,et al.  Misconceptions of probability: An experiment with a small-group, activity-based, model building approach to introductory probability at the college level , 1977 .

[17]  Notes on the Doctrine of Chances , 1978 .

[18]  D. R. Green The Chance and Probability Concepts Project , 1979 .

[19]  J. Hartigan Theories of Probability , 1983 .

[20]  D. Green School Pupils' Probability Concepts , 1983 .

[21]  E. Fischbein,et al.  Does the teaching of probability improve probabilistic intuitions? , 1984 .

[22]  C. Konold,et al.  Informal Conceptions of Probability , 1989 .

[23]  Manfred Borovcnik,et al.  Empirical Research in Understanding Probability , 1991 .

[24]  W. Wagenaar,et al.  The perception of randomness , 1991 .

[25]  E. Fischbein,et al.  Factors affecting probabilistic judgements in children and adolescents , 1991 .

[26]  Rolf Biehler,et al.  Computers in Probability Education , 1991 .

[27]  Clifford Konold,et al.  Understanding Students’ Beliefs About Probability , 1991 .

[28]  J. Shaughnessy Research in probability and statistics: Reflections and directions. , 1992 .

[29]  M. Lecoutre Cognitive models and problem spaces in “purely random” situations , 1992 .

[30]  Alexander Pollatsek,et al.  Inconsistencies in Students' Reasoning about Probability. , 1993 .

[31]  Richard P. Savage The Paradox of Nontransitive Dice , 1994 .

[32]  David S. Moore,et al.  The Basic Practice of Statistics [With CDROM] , 1999 .

[33]  Cynthia W. Langrall,et al.  A framework for assessing and nurturing young children‘s thinking in probability , 1997 .

[34]  Clifford Konold,et al.  Making Sense of Randomness " Implicit Encoding as a Basis for Judgment , 1997 .

[35]  E. Fischbein,et al.  The Evolution with Age of Probabilistic, Intuitively Based Misconceptions. , 1997 .

[36]  Cynthia W. Langrall,et al.  Students' Probabilistic Thinking in Instruction. , 1999 .

[37]  Carmen Batanero,et al.  The Meaning of Randomness for Secondary School Students. , 1999 .

[38]  C. Wild,et al.  Statistical Thinking in Empirical Enquiry , 1999 .

[39]  Dave Pratt,et al.  Making Sense of the Total of Two Dice , 2000 .

[40]  Joan Ferrini-Mundy,et al.  Principles and Standards for School Mathematics: A Guide for Mathematicians , 2000 .

[41]  Donald Gillies,et al.  Varieties of Propensity , 2000, The British Journal for the Philosophy of Science.

[42]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[43]  Randomness , 2001, ArXiv.

[44]  Pre-Service Teachers' Use of Computer Simulation to Explore Probability , 2001 .

[46]  Alexander Pollatsek,et al.  Data Analysis as the Search for Signals in Noisy Processes. , 2002 .

[47]  D. Kahneman,et al.  Representativeness revisited: Attribute substitution in intuitive judgment. , 2002 .

[48]  D. Kahneman,et al.  Heuristics and Biases: The Psychology of Intuitive Judgment , 2002 .

[49]  Hollylynne Stohl,et al.  Developing notions of inference using probability simulation tools , 2002 .

[50]  Literature survey and children's perception on risk , 2003 .

[51]  Marja van den Heuvel-Panhuizen,et al.  The International Commission on Mathematical Instruction [ICMI]: The Fifteenth ICMI Study: The Professional Education and Development of Teachers of Mathematics , 2004 .

[52]  Carmen Batanero,et al.  Training Teachers to Teach Probability , 2001, Statistics Literacy- Material From Some of the Talks IASE Satellite Conference.

[53]  Joan Garfield,et al.  The challenge of developing statistical literacy, reasoning and thinking , 2004 .

[54]  Michel Henry,et al.  The Nature of Chance and Probability , 2005 .

[55]  Graham A. Jones,et al.  An Overview of Research into the Teaching and Learning of Probability , 2005 .

[56]  J. Engel,et al.  On middle-school students' comprehension of randomness and chance variability in data , 2005 .

[57]  Iddo Gal,et al.  TOWARDS "PROBABILITY LITERACY" FOR ALL CITIZENS: BUILDING BLOCKS AND INSTRUCTIONAL DILEMMAS , 2005 .

[58]  Hollylynne Stohl,et al.  Probability in Teacher Education and Development , 2005 .

[59]  Graham A. Jones,et al.  Exploring Probability in School , 2005 .

[60]  Edward S. Mooney,et al.  Characteristics of Elementary School Students' Probabilistic Reasoning , 2005 .

[61]  Manfred Borovcnik,et al.  PROBABILISTIC AND STATISTICAL THINKING , 2005 .

[62]  Geoffrey C. Phelps Content knowledge for teaching reading. , 2005 .

[63]  Ian Hacking,et al.  The Emergence of Probability: Duality , 2006 .

[64]  James E. Tarr,et al.  AN EXAMINATION OF THE LEVELS OF COGITIVE DEMAND REQUIRED BY PROBABILITY TASKS IN MIDDLE GRADES MATHEMATICS TEXTBOOKS , 2007, STATISTICS EDUCATION RESEARCH JOURNAL.

[65]  Per Nilsson,et al.  Different ways in which students handle chance encounters in the explorative setting of a dice game , 2007 .

[66]  C. Batanero,et al.  The Meaning and Understanding of Mathematics , 2007 .

[67]  MODELING SCATTERPLOT DATA AND THE SIGNAL-NOISE METAPHOR : TOWARDS STATISTICAL LITERACY FOR PRE-SERVICE TEACHERS , 2008 .

[68]  Robyn Pierce,et al.  Teaching statistics at the primary school level: beliefs, affordances, and pedagogical content knowledge , 2008, Joint ICMI/IASE Study: Teaching Statistics in School Mathematics IASE Roundtable Conference.

[69]  Cliff Konold,et al.  Reconnecting Data and Chance , 2008 .

[70]  Dor Abrahamson,et al.  Bridging Theory: Activities Designed to Support the Grounding of Outcome-Based Combinatorial Analysis in Event-Based Intuitive Judgment—A Case Study , 2008 .

[71]  Laura Martignon,et al.  Hands-On Activities for Fourth Graders: A Tool Box for Decision-Making and Reckoning with Risk , 2009, International Electronic Journal of Mathematics Education.

[72]  Egan J. Chernoff Sample space partitions: An investigative lens , 2009 .

[73]  Dor Abrahamson,et al.  Please Scroll down for Article Cognition and Instruction Orchestrating Semiotic Leaps from Tacit to Cultural Quantitative Reasoning—the Case of Anticipating Experimental Outcomes of a Quasi- Binomial Random Generator , 2022 .

[74]  Per Nilsson,et al.  Conceptual variation and coordination in probability reasoning , 2009 .

[75]  Hollylynne S Lee,et al.  Reasoning about Probabilistic Phenomena: Lessons Learned and Applied in Software Design , 2009 .

[76]  Rolf Biehler,et al.  A MODEL FOR TEACHER KNOWLEDGE AS A BASIS FOR ONLINE COURSES FOR PROFESSIONAL DEVELOPMENT OF STATISTICS TEACHERS , 2010 .

[77]  Evolution de l'enseignement secondaire français en statistique et probabilités , 2010 .

[78]  J. E. Tarr,et al.  MAKING COMPARISONS BETWEEN OBSERVED DATA AND EXPECTED OUTCOMES: STUDENTS’ INFORMAL HYPOTHESIS TESTING WITH PROBABILITY SIMULATION TOOLS , 2010, STATISTICS EDUCATION RESEARCH JOURNAL.

[79]  Dave Pratt,et al.  Re-connecting probability and reasoning about data in secondary school teaching , 2011 .

[80]  J. Godino,et al.  Models for Statistical Pedagogical Knowledge , 2011 .

[81]  Randall E. Groth,et al.  Preparing Teachers Through Case Analyses , 2011 .

[82]  Michel Henry,et al.  Frequentist Approach: Modelling and Simulation in Statistics and Probability Teaching , 2011 .

[83]  Karen Hollebrands,et al.  Characterising and Developing Teachers’ Knowledge for Teaching Statistics with Technology , 2011 .

[84]  Manfred Borovcnik,et al.  Strengthening the Role of Probability Within Statistics Curricula , 2011 .

[85]  Rina Zazkis,et al.  From personal to conventional probabilities: from sample set to sample space , 2011 .

[86]  D. Kahneman Thinking, Fast and Slow , 2011 .

[87]  Phillip Kent,et al.  Role of Context in Risk-Based Reasoning , 2011 .

[88]  Dave Pratt,et al.  The Role of Technology in Teaching and Learning Statistics , 2011 .

[89]  Egan J. Chernoff Recognizing revisitation of the representativeness heuristic: an analysis of answer key attributes , 2012 .

[90]  M. Borovcnik Multiple perspectives on the concept of conditional probability. 'Perspectivas múltiples sobre el concepto del probabilidad condicional' , 2012 .

[91]  Egan J. Chernoff,et al.  The Fallacy of Composition: Prospective Mathematics Teachers’ Use of Logical Fallacies , 2012 .

[92]  Theodosia Prodromou,et al.  Connecting experimental probability and theoretical probability , 2012 .

[93]  Randall E. Groth,et al.  Mapping the structure of knowledge for teaching nominal categorical data analysis , 2013 .

[94]  La statistique dans l’enseignement secondaire en France , 2013 .

[95]  Bharath Sriraman Probabilistic Thinking: Presenting Plural Perspectives , 2014 .

[96]  Egan J. Chernoff,et al.  Commentary on Probabilistic Thinking: Presenting Plural Perspectives , 2014 .

[97]  Dave Pratt,et al.  Chance Re-encounters: ’Computers in Probability Education’ revisited , 2014 .

[98]  Laura Martignon,et al.  Fostering Children’s Probabilistic Reasoning and First Elements of Risk Evaluation , 2014 .

[99]  Theodosia Prodromou Developing a Modelling Approach to Probability Using Computer-Based Simulations , 2014 .

[100]  The cognitive demands of understanding the sample space , 2014 .

[101]  Manfred Borovcnik,et al.  A Historical and Philosophical Perspective on Probability , 2014 .

[102]  Per Nilsson,et al.  Experimentation in Probability Teaching and Learning , 2014 .

[103]  Pedro Arteaga,et al.  Prospective Primary School Teachers’ Perception of Randomness , 2014 .

[104]  Markus Vogel,et al.  Three Approaches for Modelling Situations with Randomness , 2014 .

[105]  M. Borovcnik,et al.  From Puzzles and Paradoxes to Concepts in Probability , 2014 .

[106]  Teaching and Learning of Probability , 2015 .

[107]  C. Batanero UNDERSTANDING RANDOMNESS: CHALLENGES FOR RESEARCH AND TEACHING , 2015 .

[108]  R. Hertwig,et al.  Heuristics: The Foundations of Adaptive Behavior , 2015 .

[109]  A. D. Moivre The Doctrine of Chances , 2016, The Doctrine of Chances.