Statistics in the New Curriculum

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Statistics in the New Curriculum

• Jackie Scheiber
• RADMASTE Centre,
• Wits University

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General Education and Training Band (GET)Grades
R to 9
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• Tallies and tables Grade 4 ?
• Stem and leaf displays Grade 7 ?
• Mode Grade 5 ?
• Median Grade 6 ?
• Mean Grade 7 ?
• Measures of central tendency of ungrouped and
  grouped data Grade 8 ?
• Range Grade 7 ?

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• Pictograph Grade 1 ?
• Bar graphs Grade 3 ?
• Histograms Grade 7 ?
• Pie charts Grade 7 ?
• Line and broken line graphs Grade 7 ?
• Scatter plots Grade 8 ?
• Certain, uncertain and impossible events Gr 4 ?
• Lists outcomes Grade 4 ?
• Counts the frequency of outcomes Grade 5 ?
• Determines relative frequency Grade 7 ?
• Determines probability Grade 8 ?

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Maths LiteracyGrade 10, 11 and 12
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Further Education and Training Band (FET)
Grades 10, 11 and 12

• Pages 38 - 43

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Grade 10

• Collect, organise and interpret univariate data
  in order to determine
• Measures of central tendency of grouped and
  ungrouped data
• Measures of dispersion range, percentiles,
  quartiles, interquartile and semi-interquartile
  range
• Represent data effectively, choosing
  appropriately from
• Bar and compound bar graphs
• Histograms (grouped data)
• Frequency polygons
• Pie charts
• Line and broken line graphs

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Grade 11

• Calculate and represent measures of central
  tendency and dispersion in univariate numerical
  data by means of
• A 5-number summary
• Box and whisker diagram
• Ogives
• Calculating the variance and standard deviation
  of sets of data manually and using available
  technology and representing results graphically
  using histograms and frequency polygons
• Representing bivariate numerical data as a
  scatter plot and suggest intuitively whether a
  linear, quadratic or exponential function would
  best fit the data

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Grade 12

• Demonstrate the ability to draw a suitable sample
  from a population and understand the importance
  of sample size in predicting the mean and
  standard deviation of a population
• Use available technology to calculate the linear
  regression function which best fits a given set
  of bivariate numerical data
• Use available technology to calculate the
  correlation co-efficient of a set of bivariate
  numerical data to make relevant deductions

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Grade 10

• Use probability models for comparing the relative
  frequency of an outcome with the probability of
  an outcome
• Use Venn diagrams as an aid to solving
  probability problems, appreciating and correctly
  identifying
• The sample space of a random experiment
• An event of the random experiment as a subset of
  the sample space
• The union and intersection of two or more subsets
  of the sample space
• P(S) 1, where S is the sample space
• P(A or B) P(A) P(B) P(A and B), where A and
  B are events within a sample space
• Disjoint (mutually exclusive) events calculating
  the probability of either of the events occurring
  by applying the addition rule for disjoint
  events P(A or B) P(A) P(B)
• Complementary events calculating the probability
  of an event not occurring P(not A) 1 P(A)

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Grade 11

• Correctly identify dependent and independent
  events (e.g. from two-way contingency tables or
  Venn diagrams) and therefore appreciates when it
  is appropriate to calculate the probability of
  two evens occurring by applying the product rule
  for independent events P(A and B) P(A) . P(B)
• Uses tree and Venn diagrams to solve probability
  problems (where events are not necessarily
  independent)

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Grade 12

• Generalises the fundamental counting principle
  (successive choices from m1 then m2 options
  creates m1.m2.m3 different combined options)
• Solves problems using the fundamental counting
  principle

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Grades 10, 11 and 12

• Identify potential sources of bias, errors in
  measurement, potential uses and misuses of
  statistics and charts and their effects (a
  critical analysis of misleading graphs and claims
  made by persons or groups trying to influence the
  public is implied here)
• Effectively communicate conclusions and
  predictions that can be made from the analysis of
  data

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• Grade 11
• Differentiate between symmetric and skewed data
  and make relevant deductions
• Grade 12
• Identify data which is normally distributed about
  a mean by investigating appropriate histograms
  and frequency polygons

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Grade 10, 11 and 12

• Use theory learned in this grade in an authentic
  integrated form of assessment (e.g. in an
  investigative project)

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The situation out there

• Pretty drastic!
• Very few teachers have any knowledge of data
  handling, let alone probability
• If they have studied statistics at a tertiary
  level, they either have forgotten it, or dont
  have an understanding of school level statistics

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Maths4Stats

• A Stats South Africa Project
• Approximately 45 teachers, with each province
  represented
• Workshops being run by Dr Delia North, Head of
  the Stats Dept at UKZN and myself
• In the process of covering the FET Data Handling
  and Probability content
• Eventually all these teachers will be ready to
  run workshops, in association with AMESA, for
  fellow teachers in their provinces

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Who would be interested in doing something
similar for the Financial Maths Assessment
Standards??