7 Things you need to know about SUBITISING...

1. Subitising means instantly seeing how many from a latin word meaning SUDDENLY! A key to teaching subitising is to show a quantity quickly! Children need to understand that they did not count, and a quick flash of the dot value is the only way for them to notice this about their own brain! Subitising is a necessary precursor to counting. Certainly, research with infants suggests that young children possess and spontaneously use subitising to represent the number contained in small sets and that subitising emerges before counting (Klein and Starkey 1988).

2. Perceptual subitising is the ability we all have (along with other mammals) to recognise up to four in terms without having to count these. It is difficult to identify more than four without arranging these into recognisable or iconic arrangements.

3. Conceptual Subitising builds on this knowledge to recognise larger groups. Dice and dot patterns are easily subitised and children should be encouraged to recognise these without ‘counting to check’. These understandings link into important later work combining and partition numbers (Gifford 2018, Early Intervention Foundation 2018).

4. Activities include auditory subitising, or recognising numbers of sounds, such as claps or drum beats, linking with movement and music. Fingers also provide subitisable images for numbers, with the added advantage that they are embodied in muscle memory. Showing all-at-once finger numbers is the key skill here: Marton & Neuman (1990) found that older children with maths difficulties tended to count fingers one at a time, rather than using all-at-once ‘finger numbers’. You can ask young children to first ‘grow’, then ‘show’ and finally to ‘throw’ finger numbers.

5. The spatial arrangement of sets influences how difficult they are to subitise. Children usually find rectangular arrangements easiest, followed by linear, circular, and scrambled arrangements (Beckwith and Restle 1966; Wang, Resnick, and Boozer 1971). Certain arrangements are easier for specific numbers. Take a look at our Subitising Spots .

6. It is not helpful for adults to ask children what they have already subitised, for example: “I can see 4 there and I’m 4” Clements and Samara (Clements 1999, Clements and Samara 2009) have been researching the importance of conceptual and perceptual subitising since the 1990s and yet work with young learners has yet to find it’s way into many early years’ settings and classrooms. subitising is too often a neglected quantifier in educational practice and yet it has been extensively studied as a critical cognitive process.

7. Encourage quick daily practice to help build critical early number sense concepts of conservation (understanding that a quantity does not have to look the same to be equal) and cardinality (‘trusting the count’) become deeply understood. Furthermore, students develop the critical understanding that numbers are not merely a series of ones, but that numbers are composed of/decomposed into other numbers in a variety of ways (Grey & Tall, 2007; Ma, 1999)

References

Clements, D.H. (1999) Subitizing: What is it? Why teach it? Teaching Children Mathematics 5(7) 400-405

Beckwith, Mary, and Frank Restle. "Process of Enumeration." Journal of Educational Research 73 (1966): 437-43

Bobis, J. (1996). Visualisation and the development of number sense with kindergarten children. In J. Mulligan & M. Mitchelmore (Eds), Children’s Number Learning (pp. 17–33). Adelaide: AAMT

Early Spatial Thinking and the Development of Number Sense by Janette Bobis, Australian Primary Mathematics Classroom 13 (1) 2008

Gray, E. & Tall, D. (2007). Abstraction as a natural process of mental compression. Mathematics Education Research Journal 19(2), pp. 23–40.

Klein, A. & Starkey, P. (1988). Universals in the development of early arithmetic cognition. In G. Saxe & M. Gearhart (Eds), Children’s Mathematics (pp. 27–54). San Francisco: Jossey-Bass 

Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. New York, NY: Routledge. 

Marton, F. & Neuman, D. (1990). Constructivism, phenomenology and the origin of arithmetic skills. In L.P. Steffe & T. Wood (Eds.), Transforming children’s mathematics education: international perspectives (pp.62- 75). New Jersey: Lawrence Earlbaum Associates.

Subitising Through the Years by Valerie Faulkner,  North Carolina State University, USA and Jennifer Ainslie, Wake County Public Schools, USA (2017)

Tsao, Y.L. & Lin, Y. C. (2012) Elementary School Teachers' Understanding: Towards the Related Knowledge of Number Sense. US – China Education Review B1. (p 17 – 30) 

Wang, Margaret, Lauren Resnick, and Robert F. Boozer. "The Sequence of Development of Some Early Mathematics Behaviors." Child Development 42 (1971): 1767-78.