Download Teaching Statistical Reasoning in Elementary Schools using

Teaching statistical reasoning in
elementary schools using ageappropriate methods
Shrikant I. Bangdiwala, Ph.D.
The University of North Carolina at Chapel Hill
Department of Biostatistics
IASE Statistical Literacy,
Seoul, August 2001
1
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
2
Rationale
• Statistical concepts can be effectively
imparted to elementary school children if
done in an age-appropriate manner
IASE Statistical Literacy,
Seoul, August 2001
3
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
4
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
5
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
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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’
IASE Statistical Literacy,
Seoul, August 2001
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Chaupar
Dice:
• Oblong dice had numbers 1, 3, 4, and 6
Possible
outcomes
2
3
4
5
6
7
8
9
10
11
12
Probability
Distribution
x16
1
0
2
2
1
4
1
2
2
0
1
• Dice of ivory unavailable today except as
antiques
IASE Statistical Literacy,
Seoul, August 2001
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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’
IASE Statistical Literacy,
Seoul, August 2001
9
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
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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
IASE Statistical Literacy,
Seoul, August 2001
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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
IASE Statistical Literacy,
Seoul, August 2001
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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
IASE Statistical Literacy,
Seoul, August 2001
13
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
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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
IASE Statistical Literacy,
Seoul, August 2001
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And for the future …
IASE Statistical Literacy,
Seoul, August 2001
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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
IASE Statistical Literacy,
Seoul, August 2001
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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
IASE Statistical Literacy,
Seoul, August 2001
18
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
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Conclusions
• Keep statistical literacy approaches to
age-appropriate techniques
• Make it fun !!!
IASE Statistical Literacy,
Seoul, August 2001
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