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| Counting and Number Operations. |
In this article, Counting and
Number Operations will be discussed.
Teaching Counting
Counting is vital because it
helps children understand the base-ten system, which includes the numbers from
0 to 9, do number operations, and problem-solve, so children learn to count
easily and accurately while figuring out the quantity of objects
There are two types of
counting, namely rote counting, where number names are recited from memory, and
rational counting, where a number name is matched to an object in a collection
These are the following
counting opportunities, namely knowing number name sequence, one-to-one
correspondence, cardinality, stability, relative size, making connections
between number names, quantities and symbols, counting forwards, backwards, or
middle, and base-ten structure
The Big Ideas for Counting are
firstly that counting is used to find out the quantity in a collection, and
secondly, it also has rules that apply to any collection
Big Idea #1 of Counting
Firstly, counting is used to
find out the quantity in a collection. This Big Idea recognises counting as
related to number sense, where the main purpose of counting is the cardinal use
of numbers, which then allows children to use number operation activities or
even to do subitising
Big Idea #2 of Counting
Secondly, counting has rules
that apply to any collection. This Big Idea has the following four key
principles: stable order, one-to-one correspondence, order irrelevance, and
cardinality
Stable order refers to always
starting from one when counting, so if a child has not mastered this principle,
he will use random numbers during counting, and this is not just important for
number sequence memorisation but each number is bigger than the one that
precedes it and smaller than the next, and because the number system is
base-10, every number that ends with 9 will go back to 0
One-to-one correspondence
happens when children say each number that corresponds to an object in the
group
Order irrelevance builds on
stable order and generalises one-to-one correspondence, because no matter which
object the counting starts from, the result will remain the same, and the fact that
number words do not change the objects themselves but are only used during
counting, but then this affects reality, so when objects are counted, they
should be set aside to avoid confusion
Cardinality is knowing that
the last number used is the quantity of objects, and cardinality serves two
purposes: children use numbers to apply to objects, and children use the last
number to represent the quantity of objects
Teaching Number Operations
Number Operations are tools
that need a foundation of understanding that every operation tells a story
The Big Ideas for Number
Operations are firstly that sets can be changed through joining or separating,
secondly, sets are compared using numerosity and are ordered by more than, less
than, and equal to, and thirdly, a quantity can be decomposed into equal or
unequal parts, and the parts can be composed to form a whole
Big Idea #1 of Number Operations
Firstly, sets can be changed
through joining or separating. Sets can change when objects are added or
removed, so children need to know the definitions of adding and taking away, and
there are strategies like counting all, where a child counts a set of objects
from the first object whenever there is a change, and counting on, which is
when new objects are added, but the number continues from the last counted
object
Big Idea #2 of Number Operations
Secondly, sets are compared
using numerosity and are ordered by more than, less than, and equal to. Children
will naturally know to use visual comparison to tell if a set has more objects,
and they use matching where sets are placed next to each other with one-to-one
correspondence to determine the quantities, and even if the objects vary in
size, children know that they are only focusing on the number of objects
Ordering is about ordinal
numbers of first to last or most to fewest, thus the order of number sequences
tells the relationship between sets, in which sets are then determined whether
which has more than, less than, or equal to each other
Big Idea #3 of Number Operations
Thirdly, a quantity can be
decomposed into equal or unequal parts, and the parts can be composed to form a
whole. The concept of subitising is required as children learn that there are multiple
ways to get a certain quantity, and they can add and subtract automatically,
but this differs from rote thinking, as it is an understanding of part/whole
relationships
Role of the teacher
So what does the role of a
teacher look like? A classroom should have mathematically rich resources like
tools, materials, and manipulatives, and also utilise space well
Teachers can also implement
strategies that include intentional lessons and activities, learning centres,
or provocations where children’s thinking is triggered as the teacher
encourages a new direction of play, though the children do not necessarily have
to follow the teacher’s guidance
Therefore, as simple as
counting and number operations may seem to adults, these ideas are more
relevant and enlightening for children to learn more about the world around
them.
References
Brownell, J., Chen, J.-Q., Ginet, L., &
Hynes-Berry, M. (2013). Big Ideas of Early Mathematics. US: Pearson
Education.
Chaillé, C. (2021). ECE314 Facilitating children's mathematical thinking (study guide). Singapore: Singapore University of Social Sciences.
Novakowski. (2015). Counting.
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