What no-one is really telling you about NUMBER SENSE

by Janey Ross

 I'm sharing EMPOWERING, INSPIRING and EDUCATING ways that you can help your learners build that 🌟all important🌟 NUMBER SENSE.   

Don't forget ALL THE IMAGES are clickable DOWNLOADABLE LINKS. 

And the best way to develop fluency with numbers is to develop NUMBER SENSE,  NOT to blindly memorise without number sense.

Number sense - what is it?

Before we even get to addition and subtraction and way before we get to multiplication and division there is so much learning that needs to take place...
 
Early number learning seems to follow a very well-defined pattern, with clear stages. Infants can show surprise when the number of objects in a set changes unexpectedly, which demonstrates very early ability to count (eg Feigenson & Carey, 2003). Young children learn to recite numbers first without understanding their meaning, then they begin to fill this ‘placeholder structure with elaborated concepts’ – known as ‘conceptual boot-strapping’ (Carey, 2009). Young children can directly recognise (subitise) up to three objects, which usually increases to four with adulthood; they must understand the ‘cardinal principle’ – that the last word of a count is the total number of the set – before deeper conceptual number sense occurs (Sarnecka, 2015). Children from lower-income families tend to go through these developmental stages significantly later than children from higher-income families (ibid).
 
 
 
NUMBER SENSE  includes basic counting and comparing skills AND the flexible ability to compute and represent number.
 
Andrews, Sayers and Back, 2013 summarised seven common threads that were evident in studies drawn from a number of different cultures. These were: 
 

 

Having worked with many learners over many years I have realise that when a child starts to struggle along with their mathematics journey, the culprit can almost always be linked  to NUMBER SENSE. Without appropriate intervention, children who start school with limited number sense are likely to remain low achievers throughout their schooling (Aubrey et al., 2006).
 
Good number sense appears strongly linked to high socio-economic status and therefore may also be linked to informal instruction at home; helping some students with specific aspects of number sense like quantity discrimination may help them quickly catch up with peers (Gersten, Jordan & Flojo, 2005). 
 
Effective use of board games with young children before they go to school can enhance early number sense (eg Siegler & Booth, 2004) and in the first years of school helping children make links between verbal and symbolic, digital and analogic representations of number can help develop number sense (Kalchman, Moss & Case,2001).
 
The development of children's NUMBER SENSE is considered "internationally to be an important ingredients in mathematics teaching and learning" (Yang and Li, 2008).
 
If you'd like to support EARLY Number Sense at home or in the classroom, think about trying this:

 

 One of my favourite ways is using this:

 

All @fluencywithnumber resources have been designed to build NUMBER SENSE.  You have instant access to them where ever you are in the world!

Once children have developed a basic sense of the numbers up to ten they need to develop a strong 'sense of ten' as a foundation for both place value and mental calculations. (This is not to say that young children will not also have an awareness of much larger numbers. Indeed, there is no reason why children should not explore larger numbers while working in depth on 'ten-ness'.)

Arguably the best resource for representing ten as a unit is the ten-frame: 

 

Ten-Frames are very useful devices for developing number sense within the context of ten.  The use of ten-frames was developed by researchers such as Van de Walle (1988) and Bobis (1988).
 
Various arrangements of counters on the ten frames can be used to prompt different mental images of numbers and different mental strategies for manipulating these numbers, all in association with the numbers' relationship to ten. These tasks with ten-frames will enable children to build a strong sense of 10.
 
You could try using these populated five/ ten frames to build a strong sense of ten and its subgroups (parts and wholes): 

 

 

If you don't fancy creating your own resources or wasting hours of your life searching the internet for resources like this and impactful ways to help your child  ❤️  Numbers and Maths.... fear not! 
 
Our ULTIMATE SUBITISING SPOTS Print & Play Pack might be just for you! You have instant access to all of these joyful and playful resource (and others) wherever you are in the world.  Start playing and learning straight away! No need to pay for postage or wait for a delivery with a PRINT & PLAY Digital Download. Perfect if you live outside the UK or if you just can't wait to start learning through play! 
 
Where do I go from here?

By the time children leave primary school, we would like them to have a well-developed sense of number and a deep understanding of place value.

 We've discussed what we mean by these two areas of mathematics, outlined relevant research findings and introduced some of the manipulatives which support their early development. 

We have expanded on the key ideas and suggested mathematical activities which will help to develop these important aspects of mathematics.


The  first step towards a deep understanding of number and place value is having a strong sense of the numbers up to ten.  From there, developing children's 'sense of ten' is essential as part of their understanding of place value and this also paves the way for mental calculation.  In addition to this 'sense of ten', place value encompasses three other important ideas:

  • Ordering - comparing numbers with each other
  • Position - understanding how the place of a digit affects its value in any particular number
  • Amount - knowing what the digits represent.

 

 

 If you would like the FREE DOWNLOADS that accompany these games you need to click here: "GIVE ME THE FREE STUFF!"

 

I hope you enjoy working on these important mathematical ideas with your children and that their understanding is enhanced as a result.

Here are some references and resources that might be of interest to you... 

Andrews, P., Sayers, J. & Back, J. (2013) The Development of Foundational Number Sense  in England and Hungary: a case study comparison. Conference Proceedings: CERME 2013.
 

Bobis, J. (1996). Visualisation and the development of number sense with kindergarten children. In Mulligan, J. & Mitchelmore, M. (Eds.) Children's Number Learning : A Research Monograph of the Mathematics Education Group of Australasia and the Australian Association of Mathematics Teachers. Adelaide: AAMT.

Bobis, J. (1991). The effect of instruction on the development of computation estimation strategies. Mathematics Education Research Journal , 3, 7-29.

Case, R. & Sowder, J. (1990). The development of computational estimation: A neo-Piagetian analysis. Cognition and Instruction , 7, 79-104.
 
Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B., & Perlwitz, M., (1991). Assessment of a problem-centred second-grade mathematics project. Journal for Research in Mathematics Education , 22, 3-29.
 
Fischer, F. (1990). A part-part-whole curriculum for teaching number to kindergarten. Journal for Research in Mathematics Education , 21, 207-215.
 
Gelman, R. & Gallistel, C. (1978). The Child's Understanding of Number. Cambridge, MA: Harvard University Press.
 
Hope, J. & Sherril, J. (1987). Characteristics of unskilled and skilled mental calculators. Journal for Research in Mathematics Education , 18, 98-111.
 
Mason, J. (1992). Doing and construing mathematics in screen space, In Perry, B., Southwell, B., & Owens, K. (Eds.). Proceedings of the Thirteenth Annual Conference of the Mathematics Education Research Group of Australasia . Nepean, Sydney: MERGA.
 
Presmeg, N. (1986). Visualisation in high school mathematics. For the Learning of Mathematics , 6 (3), 42-46.
 
Ross, S. (1989). Parts, wholes, and place value: A developmental view. Arithmetic Teacher , 36, 47-51.
  

Sood, S., & Jitendra, A. K. (2007). A Comparative Analysis of Number Sense
Instruction in Reform-Based and Traditional Mathematics Textbooks. Journal of
Special Education, 41(3), 145-157. 

Sowder, J. (1988). Mental computation and number comparison: Their roles in the development of number sense and computational estimation. In Heibert & Behr (Eds.). Research Agenda for Mathematics Education: Number Concepts and Operations in the Middle Grades (pp. 192-197). Hillsdale, NJ: Lawrence, Erlbaum & Reston.
 

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) davidpublishing.com.

Trafton, P. (1992). Using number sense to develop mental computation and computational estimation. In C. Irons (Ed.) Challenging Children to Think when they Compute . (pp. 78-92). Brisbane: Centre for Mathematics and Science Education, Queensland University of Technology.

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