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Student Learning of Probabilistic Concepts and their Misconceptions

Student Learning of Probabilistic Concepts and their Misconceptions. Presented by: Nadia Monrose EMS 792X November 28, 2011. Introduction Intuition and Probabilistic Learning Epistemology of Probabilistic Development Misconceptions Instructional Practices Discussion/Implications.

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Student Learning of Probabilistic Concepts and their Misconceptions

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  1. Student Learning of Probabilistic Concepts and their Misconceptions Presented by: Nadia Monrose EMS 792X November 28, 2011

  2. Introduction • Intuition and Probabilistic Learning • Epistemology of Probabilistic Development • Misconceptions • Instructional Practices • Discussion/Implications Outline

  3. Integration of Probability and Statistics in Schools • Relatively new discipline • NCTM • Why early exposure? • Reduce misconceptions • Develop sound intuitions • Build experiences (Jones, Langrall & Mooney, 2007, NCTM) • Mathematical Reasoning different from Statistical and Probabilistic Reasoning • Grounded in real-world context • Predicting uncertainty versus deterministic structure • Separate from Mathematics Introduction

  4. Focus of Literary Review

  5. Student learning of probability concepts and their misconceptions • Intuitions • Brief overview • How intuition affects learning of probability concepts • Epistemology of probabilistic development • Brief overview • Early work: Piaget and Inhelder (1951) • Later work: replications with modifications of Piaget and Inhelder • Misconceptions • Present research qualitative and quantitative • Focus on representativeness, positive/negative recency, compound and simple events and the effects of sample size • Effect of instruction and technology on these misconceptions • Focused on studies that use instruction and technological environments as interventions • Discussion/Implications Focus of Literary Review

  6. Origin of studies in intuition • Began with philosophers, then psychologists and mathematics researchers • Type of cognitive thinking drawn from previous experiences and personal truths (Kustos, 2010) • Many different definitions for intuition (Fischbein, 1999; Kustos, 2010) • All definitions consists of two key elements (Kustos, 2010) • “Immediate answers with little or no reasoning • “Perception of obviousness resulting from the thought process employed through self-efficacy beliefs” (p. 3 ) Intuition

  7. Contribution of Piaget and Inhelder (1951) • Development of chance begins in the concrete-operational stage (7 to 10 years) • Proficiency in probabilistic reasoning occurs in formal operational stage (age 11) • Research criticized and replicated • Small sample size, needed verbalization, underestimated children’s ability • Other Research • Davies (1965) used 112 students aged 3 to 9 years, conclusions in support of Piaget and Inhelder, used non-verbal tasks found that some students may be able to understand probabilistic concepts in non-verbal settings • Green (1978)supported the findings • Summary • The findings of Piaget and Inhelder holds given the verbal tasks • Students may be able to understand probability if given non-verbal tasks • Misconceptions attributed to linguistic difficulties (Fischbein, 1991) Epistemology of Probabilistic Development

  8. Representativeness • Decreased with age (Fischbein & Schnarch, 1997; • Correct responses (Sharma, 2007; Quinn, 2004) • Negative recency • Decreased with age (Fischbein & Schnarch, 1997; Kustos, 2010;) • Compound and Simple Events • Stable across ages (Fischbein & Schnarch, 1997, Kustos, 2010 • Effects of sample size • Increased with age (Fischbein& Schnarch, 1997, Kustos, 2010 • Inconsistent based on context of problem (Morsanyi, 2009) • Increased with instruction (Morsanyi, 2009 • Decreased with logical instruction (Morsanyi, 2009 • Correct responses (Sharma, 2007) Misconceptions

  9. Representativeness • Performance decreased after instruction (Cox & Mouw, 1992) • Prominent in student reasoning using Chance-Makers (Pratt, 2000) • Not consistent and prominent (Vahey, 1997) • Positive Recency effect • Improved with instruction (Fischbein& Gazit, 1984) • Effect of Sample Size • Performance decreased after instruction (Fischbein & Gazit, 1984; Cox & Mouw, 1992) • Not consistent and prominent (Vahey, 1997) Instructional Practices

  10. Early research • Conducted primarily by psychologists • Study intuition • Children development • Later Research • Focused on Misconceptions • Present Research • Links instructional practices and technology to student learning • How these interventions affect misconceptions • Probability simulations using Excel, Probability Explorer (Lee, 2000) • More research needed • Types of experiences needed to decrease misconceptions • Curriculum design and implementation • Longitudinal study on instruction based on technology Discussion/Implications

  11. Questions and Comments

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