1. Diagrammatic Representation of the Competency Classes
Mathematical literacy
Reproduction and routine (no mathematisation)
Mathematisation
Standard
Original and/or complex
Competency Class One
     Standard representations and definitions
     Routine computations
     Routing procedures
     Routine problem solving
Competency Class Two
     Modelling
     Standard problem solving
     Interpretation, reflection
     Multiple well-defined methods
Competency Class Three
     Complex problem solving and posing
     Reflection and insight
     Original mathematical approach
     Multiple complex methods
     Generalisation
Key words for this class: Standard problem solving (making connections and using integration) involving: reasoning, reflection, interpretation

2. Number, proportionality and operations Quantity
Relationships between OECD/PISA 2003 Big Ideas and Curriculum Content Strands
Curriculum strands
NAEP
PISA Big Ideas
Number
Number, proportionality and operations
Quantity
Measurement
Geometry
Geometry and spatial sense
Space and shape
Algebra
Algebra and functions
Change and relationships
Functions
Probability and statistics
Data analysis, statistics and probability
Uncertainty
Statistics
Discrete mathematics
(not included)
Space and Shape, and Change and relationships

3. Horizontal and Vertical Mathematisation
Real-world problem
Problem in mathematics world
Mathematics world
Real world
Horizontal
Mathematisation
Problem structured and formalised
Vertical Mathematisation