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Trusting the count

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by

Cora Miller

on 9 December 2015

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Transcript of Trusting the count

Begin by using subitising cards which show values from 1 to 5 with dots represented in traditional dice formations.

As the student's ability to name the values without counting progresses, cards with values up to 10 can be introduced as well as cards with irregular patterns.

Present the student with one flash card at a time and ask "H
ow many dots are there?
"
Students are only given about 1-2 seconds to look at the card and answer, to ensure that they are not counting the dots individually.
Ask the student questions such as "
What do you see?
" "
how do you know that
".
Encourage students to demonstrate their understanding of part-part-whole knowledge. For Example "
I know there is 5 there because there is 2 there and another 3 here
"

Trusting the count
There's more to counting than meets the eye (or the hand)
"One of the main aims of school mathematics is to create mental objects in the mind's eye of children which can be manipulated flexibly with understanding and confidence. A prolonged reliance on inefficient strategies such as 'make-all-count-all' or 'counting-by-ones' is both developmentally dangerous and professionally irresponsible"

Dr Dianne Sieman
Associate Professor of Mathematics education, RMIT
What is 'Trusting the Count' ?
Trusting the count is....
Believing that if you count the same collection again you will get the same result.
Knowing that once you have counted a collection and no changes are made to that collection it stays the same.
Recognising a collection no matter how it is arranged.
Recognising that the last number counted represents the number in the collection.
Recognising collections without counting (subitising).
Developing a mental picture of the numbers 0-9.
Why should we teach students to 'trust the count'?
Even though a student may be able to count to 20 and beyond; recognise, read and write number words and numerals to 10 and count and model small collections of less then 20; they may still be lacking an understanding of which numbers are larger in value when presented in oral or written form and they may struggle to count larger collections of 40 or more. These issue may arise because:
The student has failed to understand that counting is a strategy to determine 'how many' and that the last number counted represents the value of the collection
The student has mismatched between the oral words for numbers and the objects counted
The student has failed to organise the count well enough to avoid counting objects they have already counted
The student has a superficial understanding of the numbers 0 to 10

Why should we teach students to 'trust the count'?
Trusting the count helps students to be able to read, write or hear a number and imagine what it may look like as a collection. For example a student should be able to see the number seven in their minds eye as 1 more than 6, 1 less then 8, 3 and 4 or 5 and 2.
Students who are able to recognise collections of up to 5 objects without counting have formed a mental object in their mind's eye. This means they have learned to subitise. Students with specific learning disabilities may have missed learning these skills in their early years. Being able to visualise these concepts is a crucial basis for future mathematical learning.
How to teach students to trust the count: part 1
How to teach students to trust the count: part 2 Part-part-whole knowledge
In order to understand part-part whole knowledge, students must learn that when adding on to a group eg 5 + 2 they do not need to count the original group of 5 again
Concrete materials such as paddle pop sticks and counters can be used to reinforce the part-part-whole concept.
SNMY activities such as the Zone 1 trusting the count and magic beans activities are useful for teaching this concept.
A deliberate and explicit focus on the development of part-part-whole knowledge is needed to ensure that children move beyond the language and processes of counting to develop mental objects for each of the numbers to ten that they can use flexibly without resource to materials or models.
Useful Resources
Don't use to teach concept but to reinforce and assess understanding.