Teaching statistical reasoning in elementary schools using age-appropriate methods

1. Teaching statistical reasoning in elementary schools using age-appropriate methods Shrikant I. Bangdiwala, Ph.D. The University of North Carolina at Chapel Hill Department of Biostatistics IASE Statistical Literacy, Seoul, August 2001

2. Issue • In the USA, children in elementary school are taught arithmetic and mathematics, but not statistics • Teaching the concepts and principles of statistics is fundamental for developing an understanding of • Uncertainty • Variability • Probability • Risk IASE Statistical Literacy, Seoul, August 2001

3. Rationale • Statistical concepts can be effectively imparted to elementary school children if done in an age-appropriate manner IASE Statistical Literacy, Seoul, August 2001

4. Methods • In the USA, parents are allowed to actively participate in the instruction in public schools • I personally volunteered to teach “math classes” for my two children  teachers were more than happy to have a guest instructor teach a class IASE Statistical Literacy, Seoul, August 2001

5. Second grade – ages 7 & 8 Children love games and have learned to count  • Teach goodness-of-fit, composition bar graphs • Using an ancient game from India with oblong dice – chaupar or soktabaji • Concepts: ‘fairness’ – probability and expected outcomes  variability, uncertainty IASE Statistical Literacy, Seoul, August 2001

6. Chaupar / soktabaji Played by the Emperor Akbar I of the 16th century Mogul Empire Lead to the Western games of Ludo and Pachisi IASE Statistical Literacy, Seoul, August 2001

7. Chaupar Rules: • Each of four players moves his/her pieces (soktas) around the path of squares while avoiding being ‘caught’ and forced to re-start • Advance is based on roll of 5 cowry shells or two oblong dice • Objective is to be the first to get all one’s pieces safely ‘home’ IASE Statistical Literacy, Seoul, August 2001

8. Chaupar Dice: • Oblong dice had numbers 1, 3, 4, and 6 • Dice of ivory unavailable today except as antiques IASE Statistical Literacy, Seoul, August 2001

9. Strategy • I made several dice out of hard acrylic, cut to the correct size and labeled – discussed “how do we know which dice are fair?” • Children were enlisted to pick a die during ‘math center’ and in teams, roll it 100 times • They counted off squares in a data form – visually constructing a ‘bar chart’ • I produced summary charts after all dice were thrown 1000 times (several weeks) – and the class determined the dice that were ‘fair’ IASE Statistical Literacy, Seoul, August 2001

10. Fourth grade – ages 9 & 10 Children love candy and have learned fractions  • Teach sampling distribution of the mean, estimating proportions • Using colored M&M plain candy bags • Concepts: variability, sample size, estimating probabilities IASE Statistical Literacy, Seoul, August 2001

11. M & M candy • Candy sold in packages of various sizes • Marketing campaigns by the M&M Mars Company have focused on the distribution of colors IASE Statistical Literacy, Seoul, August 2001

12. Strategy • Focused on the ‘fraction’ of candies in a bag that were RED • Children got a partner and were placed in tables of 4 • Each child received a small package of candy • Children made bar charts with their ‘data’ and calculated their fraction – special forms • Estimates charted on the blackboard • Each team of two calculated a pooled-data fraction – charted on same blackboard just below previous chart • Each table calculated a pooled-data fraction – charted on same blackboard just below previous charts IASE Statistical Literacy, Seoul, August 2001

13. Discussions • Variability in the number of M&Ms per same size bag – very important to the children! • Do not ‘tamper’ with your data until the end of the study – Do not eat your data ! • Variability of the estimated proportions • Central tendency of the estimated proportions • How larger sample sizes (double and quadruple) got less variability of the estimated proportions, but same central tendency • Bell-shaped distribution of the sample of estimated proportions is better for larger sample sizes IASE Statistical Literacy, Seoul, August 2001

14. Sixth grade – ages 11 & 12 Children fascinated by probability  • Teach sampling techniques • Using sampling demonstrator of 10,000 colored balls of various colors, sampling ‘palettes’ • Concepts: sampling variability, precision of larger samples IASE Statistical Literacy, Seoul, August 2001

15. Strategy • Basically similar to the M&M exercise, but children are older and do not need ‘candy bribe’ • Concept of sampling from a population to give equal chance of selection and not introduce selection biases • mixing of balls • palettes with holes for objectivity • Sampling palettes of sizes 10, 25, 50 and 100 illustrate the reduced variability and increased accuracy in samples of larger sizes IASE Statistical Literacy, Seoul, August 2001

16. And for the future … IASE Statistical Literacy, Seoul, August 2001

17. Eight grade – ages 13 & 14 Children’s bodies are changing and they are able to cook  • Teach experimental design in biology class or chemistry class • Having them conduct small experiments • growing small plants under different conditions, or • Cooking under different variations of ingredients • Concepts: uncertainty in outcome, likelihood and relative risk IASE Statistical Literacy, Seoul, August 2001

18. Tenth grade – ages 15 & 16 Children noticing their bodies  • Teach measurement error and summary measures • Having them create their own data by measuring their heights, weights, skinfolds, and other anthropometric values • Concepts: variability, representativeness of the classroom IASE Statistical Literacy, Seoul, August 2001

19. Twelfth grade –ages 17 & 18 Children more interested in the World  • Teach utility of statistics in daily life • Use examples from politics, media, Census, medical research • Concepts: utility of statistics in everyday life, relative risk of their behaviors IASE Statistical Literacy, Seoul, August 2001

20. Conclusions • Keep statistical literacy approaches to age-appropriate techniques • Make it fun !!! IASE Statistical Literacy, Seoul, August 2001