### Why is Mathematisation Important?

By understanding Stages of Early Arithmetical Learning, our aim is for all children to be able to operate at the facile stage (See stages of Early Arithmetical Learning)
For this to happen teachers need to consider the key themes that will enable children to learn just beyond the cutting edge of their number knowledge to develop and refine sophisticated strategies over time. We call this progressive mathemtisation. Themes of progressive mathematisation are:
• Structuring numbers
• Extending the range of numbers
• Decimalising towards Base-ten thinking
• Unitising and not counting by ones
• Distancing the setting of materials
• Notating
• Formalising and generalising
 Mathematisation Theme Addition and Subtraction Multiplication and Division Fractions, Decimals and Percentages Structuring number Understanding the underlying connections between numbers (e.g. 16=10+6,8+8, etc.) Understanding the fairness and equality of multiplication and division Linking and applying knowledge of addition and subtraction to multiplication and division Understand composite and unitary aspects of a quantity Linking and applying knowledge of Multiplication and Division to Fractions, Decimals and Percentages Understand composite and unitary aspects of a quantity Extending the range of numbers Progressively introducing a wider range of numbers to calculate with Introducing multiples and sequences in steps to ensure secure understanding Building on knowledge of fair share and equal parts, sequentially introduce fractions in steps to ensure secure understanding. This leads to a depth of understanding within fractions and this knowledge enables learners to develop a meaningful understanding of decimals and percentages. Decimalising towards Base-ten thinking Developing base ten thinking that exploits using ten as a unit (e.g. conceptual place value and counting in tens) Applying conceptual place value to multiplication and  division Applying conceptual place value to Fractions, Decimals and Percentages Unitising and not counting by ones Regarding a number larger than one as a unit and use this unit to solve a task. Adopting appropriate settings to explore the composite and  unitary aspects of a quantity Unitising, Partitioning, Disembedding and Iterating Distancing the setting of materials Progressively reducing the role of materials Distancing the Setting (Manipulate it àSee itàFlash itàScreen ItàCheck ItàExpress It and Explain It) Distancing the Setting (Manipulate it àSee ità Flash ità Screen Ità Check Ità Express It and Explain It) Notating Progressively formalising mathematical thought in a structured way Notation (Informal JottingsàSemi-Formal Written StrategiesàFormal Written Algorithms) Notation (Informal Jottingsà Semi-Formal Written Strategiesà Formal Written Algorithms) Formalising and generalising Developing arithmetic to involve more formal notation and more formal procedures. Reasoning that involves proceeding from a few cases to many cases Increasing the range of tasks to which children apply their strategies Increasing the range of tasks to which children apply their strategies