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

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

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Rationale

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

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

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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 ones
  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
Probability Distribution 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 MM 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 MM 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 MMs 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 MM 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

• Childrens 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 !!!