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Tag: Number Sense

Subitising

Subitising refers to being instantly and automatically able to recognise small numerosities without having to count (Clements, 1999; Jung et al., 2013; Moeller et al., 2009; Clements & Sarama, 2009).
 
‘Some suggest that subitising may well be the developmental prerequisite skill necessary to learn counting. If so, we should examine subitising more closely and determine if reinforcing this skill in children will help them learn counting easier’ (Sousa, 2008). There are also ‘strong suggestions that all later mathematics is built on the ability to subitise (Baker, 2015).
 
Clements (1999) describes two types of subitising: perceptual and conceptual.

Perceptual Subitising

Perceptual subitising involves recognising a number without using other mathematical processes. It assists children to separate collections of objects into single units and connect each unit with only one number word, thus developing the process of counting.
 

Conceptual Subitising

Conceptual subitising allows one to know the number of a collection be recognising a familiar pattern, such as the spatial arrangement of dots on the faces of dice or on domino tiles. Other patterns may be kinesthetic, such as using finger patterns to figure out addition problems, or rhythmic patterns, such as gesturing out one “beat” with each count.
 

What Does Research Tell Us?

Subitizing: What Is It? Why Teach It? Douglas H. Clements (1999)

A seminal article which is often referred to!!

Subitizing: A Critical Early Math Skill Subitizing Paula Hartman, Myoungwhon Jung and Greg Conderman, Northern Illinois University (2012)
 
An easy to read article that contains activities and apps.
 
 
Again, an easy to read article that contains activities to support children in learning to subitize.
 

Activities to Support Perceptual Subitising

Dice games – simply playing board games with a 6-sided subitised die will assist children in developing perceptual subitising.

Making Patterns – show a quick image or flash card of a subitised pattern. Children then use counters or coloured glass stones to replicate the pattern. This activity assists children to visualise patterns and embed the image in their minds.

PowerPoint of Quick Images

Display each dot pattern for only 3 seconds. Click ‘enter’ to go to a blue screen then click again to reveal the answer.

Domino: Games with Dots from Lessons Learnt Journal

Printable Dominoes from First-School.ws

Printable Dominoes from Helping With Math

Subitizing with Dot Plates from Mathematics for the Curious Pre-K-K  Click on the owl to download

Flower and Flower Pot Match from Lovely Commotion

1-6 Playing Cards for Go Fish and Concentration

Monster Dice Match from The Measured Mom

Ladybug, Ladybug Roll and Cover from Oceans of First Grade Fun

Ice Cream Count and Match from The Measured Mom

Subitizing – Laying the foundations for number sense – yes, there is a cost involved but this book by Ann and Johnny Baker provides activities and games, problematized situations and mental routines. The mental routine includes closed, open and flipped questions, that encourage a deeper level of thinking.  great resource!!

 

Until next time,

Carole

Stable-Order-Principle -Saying the Number Names in the Same Order Every Time

The stable-order-principle is one of the most basic principles of number and parents often think that this is the only concept a child needs to know. 
 
It is the simple concept that the sequence for how we count always stays the same. 
 
For example, it is always 1, 2, 3, 4, 5, 6, 7, 8, 9, etc. 


NOT 1, 2, 5, 7, 3, 4, 6, 9, 8!

Activities that employ the stable-order-principle are most useful when they are simultaneously employed with the one-to-one principle. Children need to understand that one word is said as one object is touched or action is completed. To be able to count also means knowing that the list or sequence of words used must be in a repeatable order.  

 

Source: Origin One

Number language is complicated as it involves rote learning of words that do not have a recognisable pattern.
Initially children may just be chanting words memorised through rhymes and stories with it not
having much meaning. Increasingly, the order of words takes meaning and children will begin to
realise that the order of counting words is always the same and must always be said in this order:
the stable order principle (Montague-Smith and Price, 2012).

Difficulties

Decade Numbers

  • For children who speak English, learning number words greater than ten is difficult (Fuson & Kwon,
    1991; Miller & Stigler, 1987). This is because the number words for values up to the hundreds are often irregular and do not assist children by NOT relating to the base-10 number system.

 

  • Many of these confusions are avoided in East Asian languages, because of a direct one-to-one relation between number words greater than ten and the underlying base-10 system (Fuson & Kwon, 1991; I. Miura, Kim, Chang, & Okamoto, 1988; I. Miura, Okamoto, Kim, Steere, & Fayol, 1993). The Chinese word for twelve is translated as “ten two.” Using ten two to represent 12 has two advantages. First, children do not need to memorise additional word tags, such as eleven and twelve. Second, the fact that twelve is composed of a single tens value and two units values is obvious.

Teen Numbers

  • Usually I talk to children about the numbers after ten, explaining that it would be easier if we said ‘ten and one’ rather than eleven or ‘two tens’ rather than twenty. Introducing the numbers in this way seems to develop some understanding of the structure of numbers.

 

  • Some researchers have suggested that we introduce the numbers eleven, twelve, and the ‘teen’ numbers after they learn to count to 100. I understand why they suggest this but have never been able to reconcile as to how we would teach this way when we have groups of objects above ten!!!!

Activities

Count Around the Circle  The teacher/adult sets what the children will count to. Children can say either 1, 2 or 3 numbers, for example, child 1 says, “1, 2”, the next child “3” and the next child, maybe “4, 5, 6”. It is up to the child. When the target number is reached that child sits down and the next child starts from 1 again.

Counting books, singing simple number songs, repetitive counting and consistent modelling help students develop this concept of number sense and correct errors that may occur.

Counting Dinosaurs from FUSE Education

Curious George – flowers online game

Curious George – bubbles online game

Counting Videos

Until next time,

Carole