Statistical literacy

Statistical literacy

1. Importance / relevance

   • Shortage of graduates (Carmichael)
   • Declining trend in higher level maths courses (Carmichael)
   • ABS difficulty in obtaining graduates
   • Important for adults in everyday life (Carmichael)
   • Belief amongst some teachers that because statistics is new to the curriculum it cannot be as important as more traditional topics (Watson, Chapter 1)
   • For most students statistical understanding will be more essential than trigonometry or algebra (Watson, Chapter 1)
     • Most students will not study higher level maths
     • All students enter a society where everyday decisions are argued and made based on statistical analysis
   • Relevance to other subject areas through collaboration with other faculties (Watson, Chapter 1)
   • "Democratization" of mathematics, making it available to rich & poor (Watson, Chapter 1)
     • Problem if two different tracks created: trigonometry, alegebra & calculus for the elite, college-bound, & quantitative literacy for the poor
       • Argument that including more statistics does a disservice to the college-bound, by reducing calculus in the maths course
       • However, teaching mathematics for reasoning, rather than mastery of algorithms alleviates the problem
   • Statistics & statistical literacy should be complementary & integral aspects of the mathematics curriculum in the same way as mathematics & numeracy (Watson, Chapter 1)

2. Reasons for decline

   • Lack of interest and liking for middle school mathematics (Carmichael)
   • Previous achievement in mathematics (Carmichael)
   • Mathematics self-concept (Carmichael)
   • Perceptions regarding usefulness (Carmichael)
   • Difficulty of mathematics (Carmichael)

3. Models of statistical literacy

   • Gal (2002)
     • Dispositional component
       • Readiness to criticise messages containing statistical elements
       • Is a result of self-belief in capabilities, & interest & willingness to engage in statistical thinking
     • Knowledge Elements (Gal, 2002)
       • Literacy Skills
       • Mathematical knowledge
       • Statistical knowledge
       • Context knowledge
       • Critical questions
     • Dispositional elements (Gal, 2002)
       • Beliefs and attitudes
       • Critical stance
   • Watson (2006)
     • Dispositional component
       • Scepticism
       • Imagination
       • Curiosity

4. Dispositions developed by positive learning experiences (Carmichael)

   • Formally commence in school, reaching necessary levels of sophistication by the end of middle school
     • Positive affect in middle school has a bearing on senior subject choices (Carmichael)
   • Early adolescence (middle school years) critical stage for affective development
     • Decline in positive affect as student progresses through school
       • Minimum in year 10
       • Strongest correlation between attitude & achievement in years 8 - 10

5. Concept of "interest" (Carmichael)

   • Situational interest
     • Pedagogical practices
     • Social climate of the classroom
       • "Situational collective interest"
         • Students motivated to join problem-solving activity as peers become involved
     • Classroom management strategies used by teachers
       • Outline class rules
       • Monitor student progress
     • Views of significant others
       • Parents
       • Teachers
   • Individual interest
     • Prior knowledge
     • Competency-based beliefs
       • Link between conceptions of competency and level if interest
       • High achieving students grouped with even higher achieving students reported low levels of interest
       • Low achieving students grouped with even lower achieving students reported high levels of interest
     • Link between achievement and interest
       • Achievement in mid adolescence does not predict subsequent lack of interest
       • Achievement in early adolescence (year 7) predicts interest in mid adolescence (year 10)
     • Younger adolescents are more sensitive to achievement feedback
   • Interest in statistical literacy develops as expertise increases
     • Early stages - low levels of interest and learners rely on situational interest
     • As expertise is gained, situational interest becomes less important as individual interest takes over
     • Silvia (2001) - "Collative" variables in shift from situational to individual interest
       • Novelty
         • Low level & student won't engage
         • Too high & student won't engage
         • Optimal level invokes curiosity
           • Learner motivated to resolve the conflict created by the variable
       • Uncertainty
       • Complexity
   • May occur as a result of engaging individual's unique set of interests
     • May prove problematic in a classroom setting
   • Tertiary context
     • Innovative practices promoted a positive attitude towards class or teacher, not necessarily the field of statistics

6. Gap in literature (Carmichael)

   • Interest in a mathematics education context
   • Positive affect in a tertiary context
   • Only one study (Mitchell, 1997) interest in a secondary school context

7. Statistics a distinct field from mathematics (Moore, 1988) in Carmichael

8. History (Watson Chapter 1)

   • Rationale first proposed in 1975 by Radhakrishna Rao
   • Framework proposed by Peter Holmes, 1980
     • Data collection
       • Use of a census
       • Types of data
       • Sampling
       • Obtaining data
     • Data tabulation and representation
       • Tabulation
       • Pictorial representation
     • Data reduction
       • Measures of location
       • Measures of dispersion
       • Other summarising statistics
       • Regression and correlation
     • Probability
       • Assigning probabilities
       • Manipulating probabilities
       • Modelling & probability distributions
     • Interpretation & inference
       • Inferring from tables & diagrams
       • Trends & projections
       • Data comparisons
       • Parameter estimates
       • Variability estimates
       • Test statistics
       • Type I & II error
   • Wild & Pfannkuch's four-dimensional model, 1999
     • Based on the way statisticians work
     • Investigative cycle
       • Defining the problem, planning for what is needed
       • Collecting & managing the data
       • Analysing the data
       • Interpreting and communicating conclusions
     • Types of thinking required
       • Strategic (planning, anticipating)
       • Seeking explanations
       • Modelling
       • Applying techniques
       • Recognising the need for data
       • Transnumeration (changing representations)
       • Consideration of variation
       • Reasoning with statistical models
       • Integrating the statistical and contextual
     • Interrogative cycle
       • Generate plans, explanations, models
       • Seek internal and external information
       • Interpret by seeing, translating, comparing and connecting
       • Criticise by checking reference points
       • Judge in making decisions
     • Dispositions required
       • Scepticism
       • Imagination
       • Curiosity and awareness
       • Openness
       • A propensity to seek deeper meaning
       • Being logical
       • Engagement
       • Perseverance

9. Thesis: working knowledge of statistics is more relevant to the majority of students than trigonometry, algebra & calculus