Teaching Uncertaint to High School Students教学不确定性的高中学生.pptVIP

Teaching Uncertainty to High School Students Roberta Harnett MAR 550 Current curriculum Only 2% of college-bound H.S. students had statistics courses (1988)? 160 statistics courses in 13 departments at one university Biology Physics Math NCTM Principles and Standards for School Mathematics (/standards) Uncertainty is part of NYS math standards for all grades Nature of Science Science is a search for the ”right” answer Authoritative, objective, and factual Uncertainty in science is counterintuitive, and often not expressed explicitly in problems The “true” value of something can be measured, deviations from this are errors caused by students Point reasoning vs. set reasoning More students in point than set reasoning category Misconceptions Marble task: Two bags have black and white counters Bag J: 3 black and 1 white Bag K: 6 black and 2 white Which bag gives the better chance of picking a black counter? A) Same chance B) Bag J C) Bag K D) Dont know Why?________________________ Answer Correct answer: A (? vs 6/8 = ? black counters)? 50% chose C because there were more blacks in bag K (39%)? Ratio concept in probability Little improvement with age Randomness Students asked to identify which distribution of snowflakes and which sequences of 0s and 1s were random Students expected patterns in randomness Sequence of coin tosses Can the teacher guess which is random, and which is designed by the student? Kahneman and Tversky Representativeness Even small samples should reflect distribution or the process which produced the random event you’re looking at Neglect of sample size Chance of getting 7 out of 10 heads is same as chance of getting 70 out of 100 heads Sequence of children born BGGBGB vs. BBBBGB vs. BBBGGG Representativeness Assume that the chance of having a boy or girl baby is the same. Over the course of a year, in which type of hospital would you expect there to be more days on which at least 60% of the babies born were boys? A) In a large hospital