Thank you to all the parents who attended the Maths Evening on Tuesday 6th May. It was a wonderful opportunity for all the parents to hear and see what we do in maths. Parents were asked to put themselves in their children's shoes to solve maths problems. Year 2 mathematics program consists of Mathematics Investigations, where children are given the opportunity to explore mathematical games and puzzles. The children also participate in maths workshops and maths target groups. There were many robust discussions about maths.
Thank you for a successful evening.
Maths Information
A
context
It is a central belief of mathematics
education that learning occurs through the construction of ideas, processes and
understandings in a social setting rather than by the transfer of pre-formed
knowledge from teacher to student. Consequently two factors are important in
the development of mathematical understanding
·
The use of materials that
assist children in the construction of these understandings
·
The use of a consistent
language that is appropriate to the capabilities and needs of each child.
Sequences of development that build on well
understood prior knowledge are necessary. But even well designed games and
activities are not enough on their own. Learning situations need to have a
context that encourages discussion in order to elicit emerging understandings.
Talking about what is happening, and reflecting on the concepts being
constructed enables concepts to take shape in the learner’s mind.
Children often have beliefs and methods
which can appear very different from accepted mathematical practice. Ill-formed
ideas and inappropriate generalisations need to be challenged, using activities
that require children to revise former ways of thinking. The challenge is to
lead children to understand and accept the new way of thinking as their own
rather than to get them to learn another person’s method by rote. Evidence from
children who have experienced difficulty in learning mathematics has shown that
those who simply acquire teacher-taught techniques by rote are often unable to
apply this knowledge outside of the situation it is taught in. By contrast
children who participate actively in their own learning are more able to apply
knowledge and understanding and to maintain future use and adaption.
At Princes Hill Primary the following four
ideas underpin all mathematical learning and these exist at all year levels. It
is the complexity and the sophistication of these ideas that develop as
children progress in their mathematical learning. Not all children progress at
the same pace which is why teachers differentiate the learning.
‘Really big ideas’:
- Representation – numbers can be modelled and represented in
many different ways (e.g., materials, diagrams, number charts,
partial/open number lines)
- Enumeration – whole numbers are used to count
collections, counts can be achieved in multiple ways, and different units
can be used to say how many or how much
- Equivalence – numbers can be renamed in many different
but equivalent ways, renaming is a special type of representation
- Relationships – numbers can be used to compare and order;
relationships between numbers lead to different number sets (e.g.
fractions, ratios, per cents, etc
The evening focused on introducing
the concept of place value. Place value is an essential concept to learn
because it underpins computation processes. It involves much more than
recognising place value parts. Place value is a system of assigning values to
digits based on their position (a base 10 system of numeration, positions
represent successive powers of 10)
Big
Ideas for Place Value
·
Whole numbers can be recognised
as cardinal numbers as well as composite units, that is, as numbers that tell
how many in a set (e.g. 6 ones) or as units in their own right (e.g. 1 six)
·
A sense of numbers beyond 10 as
‘a ten and some more’ is necessary to appreciate the two-digit place-value
pattern.
·
Two patterns underpin
place-value understanding at this level of schooling: ’10 of these is 1 of
those’ and ‘1000 of these is 1 of those’.
·
Place value knowledge is
developed by making (representing) numbers in terms of their place value parts,
naming and recording
·
Place value knowledge is
consolidated by comparing, ordering, counting forwards and backwards in place
value parts, and renaming
Before they are ready to meet the ‘big
ideas’ of place value, children need to be able to:
·
Count fluently by ones using
the number naming sequence to 20 and beyond
·
Model, read and write numbers
to 10 using materials, diagrams, words and symbols
·
Recognise collections to 10
without counting
·
Trust the count for each of the
numbers to 10 without having to model or count by ones
·
Demonstrate a sense of numbers
beyond 10 in terms of 1 ten and some more
·
Count larger collections by
two’s, fives, and tens
Key
Language
Cardinal
number – a specific number name for how many in a
given collection of objects
Composite
unit – a unit made up of other units ( when
children understand 6 as one 6 rather than a collection of 6 ones.
Conceptual
understanding – understanding that is made between
new and existing ideas ( eg: a conceptual understanding of area allows students
to apply this knowledge to an unfamiliar problem such as determining the
dimensions of a garden given the length of the fencing around it)
Context – the situation or
circumstances that require the application of numeracy skills
Renaming
– writing a number in an equivalent form, usually
in terms of its place value parts (eg 365 is 3 hundreds 6 tens and 5 ones but
it can be renamed as 36 tens and 5 ones or 3 hundreds and 65 ones
and
renaming when adding/multiplying or
subtracting/dividing (eg 5 tens and 8 tens is 13 tens, it is regrouped for
recording purposes as 1 hundred and 3 tens but when subtracting 28 from 45 the
8 ones can only be taken if 1 of the 4 tens is renamed as 10 ones)
