Intuitive Conceptions of Probability and the Development of Basic Math Skills

[1]  Diana Sommer,et al.  The Origin Of The Idea Of Chance In Children , 2016 .

[2]  J. Fuhrmann.  The Psychological Foundations Of Culture , 2016 .

[3]  Leslie P. Steffe,et al.  Transforming Children's Mathematics Education : International Perspectives , 2013 .

[4]  ames Hiebert and Diana Wearne.  Procedures Over Concepts: The Acquisition of Decimal Number Knowledge , 2013 .

[5]  Edward A. Silver.  Using Conceptual and Procedural Knowledge: A Focus on Relationships , 2013 .

[6]  David William Carraher.  Learning About Fractions , 2013 .

[7]  Karen Wynn,et al.  Tracking and quantifying objects and non-cohesive substances. , 2011, Developmental science.

[8]  Hulya Kilic.  Preservice Secondary Mathematics Teachers’ Knowledge of Students , 2011 .

[9]  David Barber,et al.  Learning as inference , 2011 .

[10]  Carlos Castillo-Garsow,et al.  Teaching the Verhulst Model: A Teaching Experiment in Covariational Reasoning and Exponential Growth. , 2010 .

[11]  Michael Long,et al.  Secondary Pre-Service Teachers' Content Knowledge for State Assessments: Implications for Mathematics Education Programs. , 2010 .

[12]  Peter Sedlmeier,et al.  Are Judgments of the Positional Frequencies of Letters Systematically Biased Due to Availability ? , 2010 .

[13]  Andreas Nieder,et al.  Notation-Independent Representation of Fractions in the Human Parietal Cortex , 2009, The Journal of Neuroscience.

[14]  Gary L. Brase.  Pictorial representations in statistical reasoning , 2009 .

[15]  Carmen Batanero,et al.  TRAINING SCHOOL TEACHERS TO TEACH PROBABILITY: REFLECTIONS AND CHALLENGES , 2009 .

[16]  Michael C. Frank,et al.  Number as a cognitive technology: Evidence from Pirahã language and cognition , 2008, Cognition.

[17]  V. Steinle.  Changes with Age in Student Misconceptions of Decimal Numbers , 2008 .

[18]  Fei Xu,et al.  Intuitive statistics by 8-month-old infants , 2008, Proceedings of the National Academy of Sciences.

[19]  Gary L. Brase,et al.  Frequency interpretation of ambiguous statistical information facilitates Bayesian reasoning , 2008, Psychonomic bulletin & review.

[20]  D. Ansari.  Effects of development and enculturation on number representation in the brain , 2008, Nature Reviews Neuroscience.

[21]  The Evolutionary and Developmental Foundations of Mathematics , 2008, PLoS biology.

[22]  Stanislas Dehaene,et al.  Distinct Cerebral Pathways for Object Identity and Number in Human Infants , 2008, PLoS biology.

[23]  Rina Zazkis,et al.  What makes a counterexample exemplary? , 2008 .

[24]  T. Matsuzawa,et al.  Working memory of numerals in chimpanzees , 2007, Current Biology.

[25]  Elizabeth M Brannon,et al.  Basic Math in Monkeys and College Students , 2007, PLoS biology.

[26]  Andreas Nieder,et al.  Semantic Associations between Signs and Numerical Categories in the Prefrontal Cortex , 2007, PLoS biology.

[27]  D. Geary,et al.  An Evolutionary Perspective on Learning Disability in Mathematics , 2007, Developmental neuropsychology.

[28]  Gary L. Brase.  Omissions, conflations, and false dichotomies: Conceptual and empirical problems with the Barbey & Sloman account. , 2007 .

[29]  S. Sloman,et al.  Base-rate respect: From ecological rationality to dual processes. , 2007, The Behavioral and brain sciences.

[30]  Elizabeth S. Spelke,et al.  Symbolic arithmetic knowledge without instruction , 2007, Nature.

[31]  Maxwel Roberts,et al.  Integrating the Mind , 2007 .

[32]  Avishai Henik,et al.  Notation-Dependent and -Independent Representations of Numbers in the Parietal Lobes , 2007, Neuron.

[33]  S. Dehaene,et al.  A Magnitude Code Common to Numerosities and Number Symbols in Human Intraparietal Cortex , 2007, Neuron.

[34]  Michael J Beran,et al.  Rhesus monkeys (Macaca mulatta) enumerate large and small sequentially presented sets of items using analog numerical representations. , 2007, Journal of experimental psychology. Animal behavior processes.

[35]  Katherine D. Kinzler,et al.  Core knowledge. , 2007, Developmental science.

[36]  Helen De Cruz,et al.  Why are some numerical concepts more successful than others? An evolutionary perspective on the history of number concepts , 2006 .

[37]  J. Cantlon,et al.  Shared System for Ordering Small and Large Numbers in Monkeys and Humans , 2006, Psychological science.

[38]  E. J. Carter,et al.  Functional Imaging of Numerical Processing in Adults and 4-y-Old Children , 2006, PLoS biology.

[39]  Gerd Gigerenzer,et al.  Children can solve Bayesian problems: the role of representation in mental computation , 2006, Cognition.

[40]  E. Spelke,et al.  Core Knowledge of Geometry in an Amazonian Indigene Group , 2006, Science.

[41]  Stephen C. Levinson,et al.  Evolution and culture: A Fyssen Foundation Symposium , 2006 .

[42]  Kelly S. Mix,et al.  Do we need a number sense ? , 2006 .

[43]  Daniel Ansari,et al.  Neural correlates of symbolic number processing in children and adults , 2005, Neuroreport.

[44]  V Menon,et al.  Cerebral Cortex doi:10.1093/cercor/bhi055 Developmental Changes in Mental Arithmetic: Evidence for Increased Functional Specialization in the Left Inferior Parietal Cortex , 2005 .

[45]  D. Everett.  Cultural Constraints on Grammar and Cognition in Pirahã , 2005, Current Anthropology.

[46]  Nicole M. McNeil,et al.  Why won't you change your mind? Knowledge of operational patterns hinders learning and performance on equations. , 2005, Child development.

[47]  Heather C. Hill,et al.  Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement , 2005 .

[48]  Daniel Casasanto.  Crying "Whorf" , 2005, Science.

[49]  Yujing Ni,et al.  Teaching and Learning Fraction and Rational Numbers: The Origins and Implications of Whole Number Bias , 2005 .

[50]  Guershon Harel,et al.  Advanced Mathematical-Thinking at Any Age: Its Nature and Its Development , 2005 .

[51]  P. Gould.  Year 6 students' methods of comparing the size of fractions , 2005 .

[52]  R. Bibace,et al.  Science and medicine in dialogue : thinking through particulars and universals , 2005 .

[53]  G. Gigerenzer,et al.  Understanding the results of medical tests : why the representation of statistical information matters , 2005 .

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

[55]  Graham Alfred Jones,et al.  Exploring Probability in School: Challenges for Teaching and Learning , 2005 .

[56]  K. Wynn,et al.  Large-Number Addition and Subtraction by 9-Month-Old Infants , 2004, Psychological science.

[57]  P. Gordon.  Numerical Cognition Without Words: Evidence from Amazonia , 2004, Science.

[58]  S. Vosniadou,et al.  Understanding the structure of the set of rational numbers: a conceptual change approach , 2004 .

[59]  J. Pilcher,et al.  Evaluating Evidence of Psychological Adaptation: How Do We Know One When We See One? , 2004, Psychological science.

[60]  K. Stacey,et al.  PERSISTENCE OF DECIMAL MISCONCEPTIONS AND READINESS TO MOVE TO EXPERTISE , 2004 .

[61]  E. Spelke,et al.  Language and Conceptual Development series Core systems of number , 2004 .

[62]  Kc Stacey,et al.  A Longitudinal Study of Students' Understanding of Decimal Notation: An Overview and Refined Results , 2004 .

[63]  Fei Xu,et al.  Numerosity discrimination in infants: Evidence for two systems of representations , 2003, Cognition.

[64]  Jeffrey M. Stibel,et al.  Frequency illusions and other fallacies , 2003 .

[65]  Jim Albert,et al.  College Students' Conceptions of Probability , 2003 .

[66]  P. Thompson,et al.  Fractions and multiplicative reasoning , 2003 .

[67]  Barbara J. Dougherty,et al.  Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education , 2020 .

[68]  Gary L. Brase.  Which Statistical Formats Facilitate What Decisions? The Perception and Influence of Different Statistical Information Formats , 2002 .

[69]  Gary L. Brase,et al.  Ecological and evolutionary validity: comments on Johnson-Laird, Legrenzi, Girotto, Legrenzi, and Caverni's (1999) mental-model theory of extensional reasoning. , 2002, Psychological review.

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

[71]  G. Gigerenzer,et al.  Representation facilitates reasoning: what natural frequencies are and what they are not , 2002, Cognition.

[72]  C. Allen,et al.  The Cognitive Animal: Empirical and Theoretical Perspectives on Animal Cognition , 2002 .

[73]  Masaki Tomonaga,et al.  Enumeration of briefly presented items by the chimpanzee (Pan troglodytes) and humans (Homo sapiens) , 2002, Animal learning & behavior.

[74]  Susan C. Levine,et al.  Quantitative Development in Infancy and Early Childhood , 2002 .

[75]  George W. Bright,et al.  Making Sense of Fractions, Ratios, and Proportions: 2002 Yearbook , 2002 .

[76]  S. Carey,et al.  The Representations Underlying Infants' Choice of More: Object Files Versus Analog Magnitudes , 2002, Psychological science.

[77]  Gary L. Brase.  “Bugs” built into the system: , 2002 .

[78]  Lynn Hasher,et al.  Frequency processing: A twenty-five year perspective. , 2002 .

[79]  Elizabeth M. Brannon,et al.  The evolution and ontogeny of ordinal numerical ability , 2002 .

[80]  Duane M. Rumbaugh,et al.  "Constructive" enumeration by chimpanzees (Pan troglodytes) on a computerized task , 2001, Animal Cognition.

[81]  D E Over,et al.  Contingency, causation, and adaptive inference. , 2001, Psychological review.

[82]  B. Rittle-Johnson,et al.  Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process. , 2001 .

[83]  V. Girotto,et al.  Solving probabilistic and statistical problems: a matter of information structure and question form , 2001, Cognition.

[84]  The (Mis)organization of Psychology , 2001 .

[85]  X. T. Wang,et al.  Social cues and verbal framing in risky choice. , 2001 .

[86]  J. Confrey,et al.  Helping students build a path of understanding from ratio and proportion to decimal notation , 2001 .

[87]  E L Grigorenko,et al.  Unified psychology. , 2001, The American psychologist.

[88]  Gerd Gigerenzer,et al.  Communicating Statistical Information , 2000, Science.

[89]  C. Sophian.  From objects to quantities: developments in preschool children's judgments about aggregate amount. , 2000, Developmental psychology.

[90]  E. Spelke,et al.  Large number discrimination in 6-month-old infants , 2000, Cognition.

[91]  Robert E. Reys,et al.  The Decimal Dilemma. , 2000 .

[92]  R. Siegler,et al.  The rebirth of children's learning. , 2000, Child development.

[93]  H S Terrace,et al.  Representation of the numerosities 1-9 by rhesus macaques (Macaca mulatta). , 2000, Journal of experimental psychology. Animal behavior processes.

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

[95]  Mary K. Hoard,et al.  Numerical and arithmetical cognition: patterns of functions and deficits in children at risk for a mathematical disability. , 1999, Journal of experimental child psychology.

[96]  Brian Butterworth,et al.  The Mathematical Brain , 1999 .

[97]  J. Moss.  Developing Children's Understanding of the Rational Numbers: A New Model and an Experimental Curriculum , 1999 .

[98]  Tommy J. Bryan.  THE CONCEPTUAL KNOWLEDGE OF PRESERVICE SECONDARY MATHEMATICS TEACHERS : HOW WELL DO THEY KNOW THE SUBJECT MATTER THEY WILL TEACH ? , 1999 .

[99]  P. Todd,et al.  Simple Heuristics That Make Us Smart , 1999 .

[100]  Chris Donlan,et al.  The Development of Mathematical Skills , 2021 .

[101]  Gerd Gigerenzer,et al.  Are judgments of the positional frequencies of letters systematically biased due to availability , 1998 .

[102]  Martin A. Simon,et al.  Educating Teachers to Teach Multiplicative Structures in the Middle Grades , 1998 .

[103]  Colin Allen,et al.  The evolution of mind , 1998 .

[104]  Karen Wynn,et al.  Numerical competence in infants. , 1998 .

[105]  S. Dehaene,et al.  The Number Sense: How the Mind Creates Mathematics. , 1998 .

[106]  Kaye Stacey,et al.  Changes with age in students’ conceptions of decimal notation , 1997 .

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

[108]  Rina Hershkowitz,et al.  Relative and absolute thinking in visual estimation processes , 1997 .

[109]  D. B. Aichele.  Middle School Students' Understanding of Number Sense Related to Percent. , 1997 .

[110]  Judith T. Sowder.  Place Value as the Key To Teaching Decimal Operations. , 1997 .

[111]  Wang.  Framing Effects: Dynamics and Task Domains , 1996, Organizational behavior and human decision processes.

[112]  X. T. Wang.  Domain-specific rationality in human choices: violations of utility axioms and social contexts , 1996, Cognition.

[113]  L. Cosmides,et al.  Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty , 1996, Cognition.

[114]  M. Glassman.  The argument for constructivism. , 1996 .

[115]  Leslie P. Steffe,et al.  Theories of Mathematical Learning , 1996 .

[116]  Patrick W Thompson,et al.  Talking about rates conceptually, Part II: Mathematical knowledge for teaching , 1996 .

[117]  Gaea Leinhardt,et al.  Percent: A Privileged Proportion , 1995 .

[118]  Victor S. Johnston,et al.  Perceived social context and risk preference: A re‐examination of framing effects in a life‐death decision problem , 1995 .

[119]  Nancy K. Mack.  Confounding whole-number and fraction concepts when building on informal knowledge. , 1995 .

[120]  Gerd Gigerenzer,et al.  How to Improve Bayesian Reasoning Without Instruction: Frequency Formats , 1995 .

[121]  David C. Geary,et al.  Reflections of evolution and culture in children's cognition: Implications for mathematical development and instruction. , 1995 .

[122]  Jere Confrey,et al.  The Development of multiplicative reasoning in the learning of mathematics , 1995 .

[123]  Beatriz S. D'Ambrosio,et al.  Children's Constructions of Fractions and their Implications for Classroom Instruction , 1994 .

[124]  Patrick W Thompson,et al.  Talking about Rates Conceptually, Part I: A Teacher's Struggle. , 1994 .

[125]  Gernot D. Kleiter,et al.  Natural Sampling: Rationality without Base Rates , 1994 .

[126]  Patrick W Thompson,et al.  The development of the concept of speed and its relationship to concepts of rate , 1994 .

[127]  Gerhard H. Fischer,et al.  "Contributions to Mathematical Psychology, Psychometrics, and Methodology" , 1993 .

[128]  Nancy K. Mack.  Learning rational numbers with understanding: The case of informal knowledge. , 1993 .

[129]  Gerd Gigerenzer,et al.  The superego, the ego, and the id in statistical reasoning , 1993 .

[130]  Thomas A. Romberg,et al.  Rational numbers : an integration of research , 1993 .

[131]  C. Gallistel,et al.  Preverbal and verbal counting and computation , 1992, Cognition.

[132]  N. Sanders,et al.  Journal of behavioral decision making: "The need for contextual and technical knowledge in judgmental forecasting", 5 (1992) 39-52 , 1992 .

[133]  Patrick W Thompson,et al.  Images of Rate , 1992 .

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

[135]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning , 1992 .

[136]  L. Cosmides,et al.  The Adapted mind : evolutionary psychology and the generation of culture , 1992 .

[137]  L A Real,et al.  Animal choice behavior and the evolution of cognitive architecture , 1991, Science.

[138]  J. Hiebert,et al.  Fourth Graders' Gradual Construction of Decimal Fractions during Instruction Using Different Physical Representations , 1991, The Elementary School Journal.

[139]  Leen Streefland,et al.  Fractions in Realistic Mathematics Education , 1991 .

[140]  Karen C. Fuson,et al.  Conceptual Structures for Multiunit Numbers: Implications for Learning and Teaching Multidigit Addition, Subtraction, and Place Value , 1990 .

[141]  Nancy K. Mack.  Learning Fractions with Understanding: Building on Informal Knowledge , 1990 .

[142]  C. Gallistel.  The organization of learning , 1990 .

[143]  John Beatty,et al.  The Empire of Chance: How Probability Changed Science and Everyday Life , 1989 .

[144]  G. Berntson,et al.  Numerical competence in a chimpanzee (Pan troglodytes). , 1989, Journal of comparative psychology.

[145]  L. Resnick,et al.  Conceptual Bases of Arithmetic Errors: The Case of Decimal Fractions. , 1989 .

[146]  R. Bolles,et al.  Evolution and learning , 1988 .

[147]  Harold L. Schoen.  Estimation and Mental Computation. , 1987 .

[148]  J. Hiebert.  Conceptual and procedural knowledge : the case of mathematics , 1987 .

[149]  P. Nesher,et al.  Shifts in reasoning , 1986 .

[150]  T. Caraco,et al.  RISK AND FORAGING IN STOCHASTIC ENVIRONMENTS , 1986 .

[151]  James Hiebert,et al.  A Model of Students' Decimal Computation Procedures , 1985 .

[152]  Francois Léonard,et al.  Intermediate Cognitive Organizations in the Process of Learning a Mathematical Concept: The Order of Positive Decimal Numbers , 1985 .

[153]  Tetsuro Matsuzawa,et al.  Use of numbers by a chimpanzee , 1985, Nature.

[154]  Richard Lesh,et al.  ORDER AND EQUIVALENCE OF RATIONAL NUMBERS: A CLINICAL TEACHING EXPERIMENT , 1984 .

[155]  R. Shepard.  Ecological constraints on internal representation: resonant kinematics of perceiving, imagining, thinking, and dreaming. , 1984, Psychological review.

[156]  James Hiebert,et al.  Children's Mathematics Learning: The Struggle to Link Form and Understanding , 1984, The Elementary School Journal.

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

[158]  A. Tversky,et al.  Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment , 1983 .

[159]  Thomas E. Kieren,et al.  Recent Research on Number Learning , 1982 .

[160]  M. C. Thornton,et al.  How do college students solve proportion problems , 1981 .

[161]  A. Tversky,et al.  The framing of decisions and the psychology of choice. , 1981, Science.

[162]  K. Hart,et al.  Children's understanding of mathematics: 11-16 , 1981 .

[163]  L. Hasher,et al.  Automatic and effortful processes in memory. , 1979 .

[164]  Ian Hacking,et al.  The Emergence of Probability. A Philosophical Study of Early Ideas about Probability, Induction and Statistical Inference , 1979 .

[165]  W. Casscells,et al.  Interpretation by physicians of clinical laboratory results. , 1978, The New England journal of medicine.

[166]  John Seely Brown,et al.  Diagnostic Models for Procedural Bugs in Basic Mathematical Skills , 1978, Cogn. Sci..

[167]  Douglas L. Hintzman,et al.  Contextual variability and memory for frequency. , 1978 .

[168]  Richard Lesh,et al.  Number and Measurement. Papers from a Research Workshop. , 1976 .

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

[170]  Ken Hale.  Gaps in grammar and culture , 1975 .

[171]  Daniel Kahneman,et al.  Availability: A heuristic for judging frequency and probability , 1973 .

[172]  A. Tversky,et al.  On the psychology of prediction , 1973 .

[173]  A. Tversky,et al.  BELIEF IN THE LAW OF SMALL NUMBERS , 1971, Pediatrics.

[174]  Charles R. Day,et al.  Studies in developmental psychology , 1968 .

[175]  W. R. Garner,et al.  Operationism and the concept of perception. , 1956, Psychological review.

[176]  H. Simon,et al.  Rational choice and the structure of the environment. , 1956, Psychological review.