Mathematical Thinking and Fluency

Mathematical Thinking

NCETM, The 5 Big Ideas of teaching for Mastery 

"when children are engaged in mathematical activity (thinking), they are involved in manipulating one or more of these four key components of mathematical experience:  concrete materials, symbols, language and pictures”

 

Derek Haylock and Anne Cockburn (2008), Understanding Mathematics for young children 

Structure ⇔ mathematical relationship between elements 


Emergent structure (involving analyzing/forming/ seeing local relationships) 


Mathematical structure (involving analyzing/forming/ seeing general relationships) 

ARCHITECTURE OF MATHEMATICAL STRUCTURE 

HAMSA VENKAT, MIKE ASKEW, ANNE WATSON, JOHN MASON

The research suggests that mathematical thinking occurs when students are thinking about mathematical structure.

Fluency


Fluency also demands the flexibility to move between different contexts and representations of mathematics, to recognise relationships and make connections and to make appropriate choices from a whole toolkit of methods, strategies and approaches.

NCETM, The 5 Big Ideas of teaching for Mastery