iase statistical literacy, seoul, august 20011 teaching statistical reasoning in elementary schools...

IASE Statistical Literacy, Seoul, August 2001

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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


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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


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Rationale

• Statistical concepts can be effectively imparted to elementary school children if done in an age-appropriate manner


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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


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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


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Chaupar / soktabaji

Played by the Emperor Akbar I of the 16th century Mogul Empire

Lead to the Western games of Ludo and Pachisi


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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’


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Chaupar

Dice:• Oblong dice had numbers 1, 3, 4, and 6

• Dice of ivory unavailable today except as antiques

Possible outcomes

2 3 4 5 6 7 8 9 10 11 12

ProbabilityDistribution x16

1 0 2 2 1 4 1 2 2 0 1


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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’


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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


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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


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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


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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


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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


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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


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And for the future …


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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


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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


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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


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Conclusions

• Keep statistical literacy approaches to age-appropriate techniques

• Make it fun !!!

iase statistical literacy, seoul, august 20011 teaching statistical reasoning in elementary schools...

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