Dissertation by: Paul N. Kustos Presentation by: Nadia Monrose EMS 792 Fall 2011

1. Summary and Critique of: Trends concerning four misconceptions in student’s intuitively-based probabilistic reasoning sourced in the heuristic of representativeness Dissertation by: Paul N. Kustos Presentation by: Nadia Monrose EMS 792 Fall 2011 North Carolina State University

2. Purpose of Study • determine if certain probabilistic misconceptions were related to grade level for middle and high school students • determine if self-efficacy had an effect on student achievement in probabilistic concepts for students in seventh, ninth and eleventh grade

3. Research Questions • What is the relationship between students’ 7th, 9th or 11th grade level and each of the four intuitively-based probabilistic misconceptions of the representativeness misconception, positive and negative regency effects, the distinction between compound and simple events, and the effect of sample size? • What is the relationship between students’ responses in the 7th, 9th or 11th grade levels, to questions involving probability tasks and their perceived self-efficacy in answering those questions? (p. 9)

4. Contents of Literary Review • difficulties of learning probability in grades k-12 • definition of intuition • mathematical intuition and its role in understanding probability, • prior research on probabilistic misconceptions • prior research on mathematical identity and self-efficacy.

5. Methodology • A total of 308 students • 103 7th graders • 101 9th graders • 104 11th graders • Large public school in a suburban city in Alabama were used in this study • 70% of the student population was White, 20% Black, 6% Hispanic and 4% Asian or Pacific Islander. • Used the Spearman Correlations

6. Instrument • Test based on research question used in a 1997 study from Fischbein and Scharch (1997). The four test items were: • A quarter has two sides: heads or tails. On each flip, of the quarter, either heads or tails comes up. If Casey flips a quarter 3 times, and all 3 flips are tails, what would happen on a fourth flip? ____heads ­____tails ____same change of getting heads or tails 2. Which is more likely to happen? ____ you flip a quarter 10 times and get 7 heads ____ you flip a quarter 100 times and get 70 heads ____ both have the same chance

7. Instrument 3. Two six-sided dice have faces numbered 1,2,3,4,5 and 6. If the two dice are rolled together, which is more likely to be rolled face up? ____ one 5 and one 6____ two 6’s ____both have the same chance 4. Draw 4 numbers from a bag which contains the numbers 1 through 30. Which set of numbers would most likely be drawn? ____8, 9, 10, 11 ____4, 28, 17, 19 ____ both sets of numbers are equally likely to be drawn

8. Likert Scale • How certain are you that your answer to question __ is correct? • Not very certain: 1 • Not certain: 2 • Unsure: 3 • Certain: 4 • Very certain: 5.

9. Findings • Question 1: Correct student responses increased as grade level increased. Students with correct answers were more confident • Question 2: Correct answers decreased as grade level increased. 11th graders highly confident in their incorrect answers. • Question 3: Constant across grade levels • Question 4: Constant across grade levels. 7th and 11th graders were highly confident in correct answers.

10. Critique Errors in document • Four misconceptions were examined in this that study arise from this heuristic” (p. ii) • “Intuition is one of those terms with a variety of interpretations. Asked to explain his or her definition of term intuition, chances are that definition will …. (p. 1).

11. Reflection • Know what is expected in terms of quality • Less afraid of the process • More confidence