Numeracy, mathematics and number sense

1. Numeracy, mathematics and number sense

2. Give working definitions of number sense and numeracy • NUMERACY • Knowing and understanding mathematics (Curtin University, 2011a). • Using knowledge of mathematics to form an opinion (Curtin University, 2011a). • Recall and utilise mathematical content (Curtin University, 2011a). • Apply mathematical content to everyday situations (Curtin University, 2011a). • The ability to pose and solve mathematical problems in a variety of contexts (Curtin University, 2011a). • The inclination to pose and solve mathematical problems in a variety of contexts (Curtin University, 2011a). • ‘Numeracy is intelligent, practical mathematical action in context’ (Sue Willis, 2000 as cited in Curtin University, 2011a). • ‘A person is more or less numerate with respect to particular contexts, not numerate or innumerate’. (Sue Willis, 2000, as cited in Curtin University, 2011a). • ‘The content of numeracy is derived from five strands of the mathematics curriculum – space, number, measurement, chance and data, and (pattern and) algebra – as described in the National Statement and Profiles’ (Curtin University, 2011a). • ‘Numeracy is a cross-curriculum matter’ (Curtin University, 2011a). • NUMBER SENSE • ‘Number sense is a person’s general understanding of numbers and operations along with the ability and inclination to use this understanding in flexible ways to make mathematical judgements and to develop useful and efficient strategies for dealing with numbers and operations’ (McIntosh, Reys & Reys, 1997, as cited in Curtin University, 2011b). • ‘Children with good number sense thoroughly understand number meanings’ (National Council for Teachers of Mathematics, 1989, as cited in Curtin University, 2011b). • ‘Children with good number sense have developed multiple relationships among numbers’ (NCTM, 1989, as cited in Curtin University, 2011b). • ‘Children with good number sense recognise the relative magnitude of numbers’ (NCTM, 1989, as cited in Curtin University, 2011b). • ‘Children with good number sense know the relative effect/s of operating on numbers’ (NCTM, 1989, as cited in Curtin University, 2011b). • ‘Children with good number sense develop referents for measures of common objects and situations in their environments’ (NCTM, 1989, as cited in Curtin University, 2011b). • Number sense is illustrated in a child’s ability to recognise patterns, perform simple calculations mentally, select the correct mathematical formula to use in a given situation, estimate and use mathematics in everyday situations (Curtin University, 2011b). • ‘Recognition of links and connections between processes’ (Curtin University, 2011b). • ‘Emphasise ‘relational understanding’ instead of ‘instrumental understanding’ (Curtin University, 2011b).

3. Give examples of ‘number sense’ and examples of activities to promote the development of number sense while also being able to explain/justify their examples

5. List and justify modern, research-based strategies and principles for the effective teaching of mathematics related to constructivism and diagnostic assessment practices.

6. References Curtin University. (2011a). 18 Definitions of Numeracy. Retrieved from http://lms.curtin.edu.au/@@EAC4FEF21ECD733ACE8F97697B33459C/courses/1/312566-Vice-Chancello-811022391/content/_1861839_1/embedded/18%20Definitions%20of%20Numeracy.doc Curtin University. (2011b). Number Sense Summary. Retrieved from http://lms.curtin.edu.au/@@EAC4FEF21ECD733ACE8F97697B33459C/courses/1/312566-Vice-Chancello-11022391/content/_1861839_1/embedded/Number%20Sense%20Summary.doc Booker, G., Bond, D., Sparrow, L. & Swan, P. (2010). Teaching primary mathematics (4th Ed.). Frenchs Forest, NSW: Pearson Australia Clements, D.H. & Battista. (1990). M.T. Constructivist learning and teaching. Arithmetic teaching. 38 (1), pp 35-35.