A New Approach to Learning Probability in the First Statistics Course

The probability unit in a first statistics course is difficult to teach because there is not much time, the concepts and mechanics are difficult, and the students do not see the relevance of learning it. Research by Cosmides and Tooby (1996) supports our findings that instructors should avoid fractions and decimals and capitalize on students' affinity for counting things. In addition, we avoid the use of normal tables at the beginning of our discussion of continuous random variables by using uniform and triangular distributions. These ideas may be used in traditionally structured classes or in group-based and activity-based classes.

[1]  Pfannkuch Maxine,et al.  Building on and Challenging Students' Intuitions About Probability: Can We Improve Undergraduate Learning? , 1996 .

[2]  Ronald D. Snee,et al.  What's Missing in Statistical Education? , 1993 .

[3]  C. Konold.  An Outbreak of Belief in Independence , 1989 .

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

[5]  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 .

[6]  A. Tversky,et al.  On the study of statistical intuitions , 1982, Cognition.

[7]  Joan Garfield,et al.  Teaching Statistics Using Small-Group Cooperative Learning , 1993 .

[8]  Joan Garfield,et al.  Difficulties in Learning Basic Concepts in Probability and Statistics: Implications for Research. , 1988 .

[9]  J. Laurie Snell,et al.  A Course Called “Chance” , 1992 .

[10]  Donald G. Watts.  Why is Introductory Statistics Difficult to Learn? And What Can We Do to Make it Easier? , 1991 .

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

[12]  George W. Cobb,et al.  Reconsidering Statistics Education: A National Science Foundation Conference , 1993 .

[13]  P Bailey,et al.  Double Edged Sword , 2002 .

[14]  G. Wiggins.  Creating Tests Worth Taking. , 1992 .

[15]  Allan J. Rossman,et al.  Conditional Probability and Education Reform: Are They Compatible? , 1995 .

[16]  Robert V. Hogg,et al.  Statistical Education: Improvements are Badly Needed , 1991 .

[17]  I. W. Kelly.  MUTUALLY EXCLUSIVE AND INDEPENDENCE: UNRAVELLING BASIC MISCONCEPTIONS IN PROBABILITY THEORY , 1986 .

[18]  W. Bart,et al.  The role of an evaluation exercise in the resolution of misconceptions of probability , 1989 .

[19]  A. Tversky,et al.  Subjective Probability: A Judgment of Representativeness , 1972 .

[20]  Fred M. Newmann,et al.  Beyond Standardized Testing : Assessing Authentic Academic Achievement in the Secondary School / , 1988 .

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

[22]  M. Bar-Hillel.  The base-rate fallacy in probability judgments. , 1980 .

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

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

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

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

[27]  Gary Smith,et al.  Learning Statistics by Doing Statistics , 1998 .

[28]  J. Shaughnessy.  The Psychology of Inference and the Teaching of Probability and Statistics: Two Sides of The Same Coin? , 1983 .

[29]  M. Borovcnik,et al.  The Educational Perspective , 1991 .

[30]  John Tooby,et al.  Are humans good intuitive statisticians after all , 1996 .

[31]  I. Ajzen.  Intuitive theories of events and the effects of base-rate information on prediction. , 1977 .

[32]  E. Jacquelin Dietz.  A Cooperative Learning Activity on Methods of Selecting a Sample , 1993 .

[33]  Beth Chance,et al.  Experiences with Authentic Assessment Techniques in an Introductory Statistics Course , 1997 .

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

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

[36]  E. Fischbein,et al.  EFFECTS OF AGE AND INSTRUCTION ON COMBINATORY ABILITY IN CHILDREN , 1970 .

[37]  Paul Cobb,et al.  A Double-Edged Sword@@@Intuition in Science and Mathematics , 1989 .

[38]  A. Tversky,et al.  Judgment under Uncertainty , 1982 .

[39]  L. Resnick,et al.  Tests as Standards of Achievement in Schools. , 1989 .

[40]  Joan Garfield,et al.  How students learn statistics , 1995 .

[41]  G. Gigerenzer.  How to Make Cognitive Illusions Disappear: Beyond “Heuristics and Biases” , 1991 .

[42]  R. Kirk Steinhorst,et al.  Developing Material for Introductory Statistics Courses from a Conceptual, Active Learning Viewpoint , 1995 .

[43]  David Green.  Probability Concepts: Putting Research into Practice , 1987 .

[44]  Ruma Faik,et al.  CONDITIONAL PROBABILITIES : INSIGHTS AND DIFFICULTIES , 2022 .

[45]  Joan Garfield,et al.  Statistics Education, Fin de Siècle , 1995 .

[46]  J. Clement,et al.  Not all preconceptions are misconceptions: finding ‘anchoring conceptions’ for grounding instruction on students’ intuitions , 1989 .

[47]  Alexander Pollatsek,et al.  Understanding conditional probabilities , 1987 .

[48]  Lena Zetterqvist.  Statistics for chemistry students - how to make a statistics course useful by focusing on applications , 1997 .

[49]  David E. Engel.  Pittsburgh's Teacher-Administrator Partnership: A New Relationship. , 1990 .

[50]  Alexander Pollatsek,et al.  Understanding the effects of sample size on the variability of the mean , 1990 .

[51]  R. Todd Ogden,et al.  Interactive Demonstrations for Statistics Education on the World Wide Web , 1998 .

[52]  G. Wiggins.  The Futility of Trying to Teach Everything of Importance. , 1989 .

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

[54]  L. Darling-Hammond.  Performance-Based Assessment and Educational Equity , 1994 .

[55]  R. Kirk Steinhorst,et al.  Using Small Groups to Promote Active Learning in the Introductory Statistics Course: A Report from the Field , 1995 .

[56]  Ruth Beyth-Marom,et al.  A curriculum to improve thinking under uncertainty , 1983 .

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