Wednesday, 17 July 2013

Early Number Sense - Stages of Development

I have been reading Developing Efficient Numeracy Strategies Stage 1 to help me to plan my math lessons better.

EDIT: You can read the entire book here!

As I mentioned in an earlier post, I am researching the stages of development that learners progress through. I attempted to compare the Stages in this book with the more recent research in First Steps in Mathematics: Number

Developing Efficient Numeracy Strategies
(Count Me in Too) Developmental Stages
First Steps in Mathematics
 Number Map of Development
“The student knows some number words but cannot count visible items. The student either does not know the correct sequence of number words or cannot coordinate the words with items.” DENS p.8
These students recognise that numbers may be used to signify quantity. They use words like smaller and bigger and same.
(FS states that this typically occurs between age 3-5. DENS does not give an age/grade level)
“The student can count perceived items but not those in concealed collections. Perceptual counting includes seeing, hearing or feeling items.” DENS p.8

Children at this stage “consistently apply the one-to-one principle of matching one number word to each item … they rely on counting by ones and always begin at one”. DENS p. 75.
Matching Phase
This students use one-to-one relations to share and count out.
They use numbers as adjectives to describe amounts of physical objects.
Can orally count to 10 or more.
“The student can count concealed items but counts from one rather than counting on. Has a “figurative” notion of numbers and does not need to count perceived items, but counts from one to construct a number in additive situations”. DENS, p. 8
 (no similar stage)
Counting On
“The student can use advanced count-by-one strategies. Counts on rather than counting from “one”, to solve addition tasks or tasks involving a missing addend.” DENS p.8.
Quantifying Phase
These students use part-part-whole relations for numerical quantities. (decomposing)
Counting on and various strategies are used. Students don’t need to count from one.

What do you think, wise teacher friends? Does this look right to you?

Each day I am going to focus on one stage and post some teaching ideas! Please comment and share your ideas too! (Maybe I will attempt my first linky! What do you think??) 

Tomorrow I will blog about the EMERGENT stage. 


  1. Hi Liz,

    I found your blog through Kylie's Aussie bloggers list. I teach Prep in Queensland and am your newest follower. I love the book Developing Efficient Numeracy Strategies - I got it for a uni subject over 10 years ago and still use it. I actually brought it home from school this weekend to help with my maths plans for next week. :)

    I'd love you to stop by my blog.

    Love, Laughter and Learning in Prep!

    1. thanks Lauren! Nice to "meet" you!!
      I'll come visit your blog now.