West Melton Numeracy and Basic Facts Workshop
The
Number Framework:
¨ Strategy-creates
new knowledge through use
¨ Knowledge-
provides the foundation for the strategies
¨ Operational
Domains-addition and subtraction, multiplication and division, proportions and
ratios
The Numeracy Project:
¨ The
Numeracy Project aims to raise the level of student achievement in Number and
Algebra and in the other strands of the mathematics and statistics learning
area.
¨ It
is based on careful research about how children learn and is designed to teach
children to think mathematically.
¨ There
is an emphasis on children developing a sense of number that they can apply
rather than learning by rules.
You can
support your child’s learning in mathematics:
¨ Being positive and enthusiastic about
maths yourself
¨ Discuss mathematical experiences with
your family
¨ Recognising the stage of development
your child is at
¨ Don’t feel you have to know
everything. Get your child to show you how. They will love having you ask and
will learn from explaining
Numeracy
Stages:
¨ Emergent-learning to count
¨ Stage 1 One-to-one counting-counting objects
up to ten
¨ Stage 2 Counting from One on Materials- add
and subtract using their fingers or objects
¨ Stage 3 Counting from One by using
Imaging-no materials in front of child-they need to picture what it will look
like-see objects in their mind rather than using real objects
¨ Stage 4 Advanced Counting-counting on-using
maths equations-when adding 4 + 3 they will count on from four
¨ Stage 5 Early Additive – part-whole - can
separate numbers into units to solve addition and
subtraction-part-whole-separate numbers into useful units to solve addition and
subtraction i.e. 7 + 8 can be done as 7 + 7 + 1
¨ Stage 6 Advanced Additive – part-whole -
separate numbers into useful units in a variety of ways to solve addition and
subtraction, and are beginning to solve multiplication and division problems
¨ Stage 7 Advanced Multiplicative – can choose
from a range of strategies to solve problems involving multiplication and
division, including problems with fractions
¨ Stage 8 Advanced Proportional – can make use
of a variety of complex strategies to solve problems involving fractions,
proportions and ratios
Basic Facts:
¨ Children need to be able to make
sense of addition and multiplication before they try to memorise their tables.
When they do understand it is important that they learn these basic facts and
recall them instantly. Each of the basic facts families are linked to the
stages of the Numeracy Project.
Previous
Approaches:
¨ In the past teaching of basic facts
was focused on memorisation without a firm foundation of number sense
¨ Current international research supports
the importance of developing a conceptual understanding (comprehension of mathematical concepts,
operations, and relations) to enable future success in mathematics
¨ Conceptual understanding also
improves numerical reasoning, procedural fluency and accuracy
¨ Overreliance on memorised procedures
prevents students from using mathematical reasoning
Importance
of Basic Facts:
¨ Learning basic facts involves
developing an understanding of the relationship between numbers e.g. 7 is 3
less than 10 and 2 more than 5, leading into these relationships developing
strategies for solving equations in a meaningful and logical manner
¨ Alongside knowledge of the Numeracy
project, basic facts enables children to develop the ability to extend their
number strategies and understanding of number to multidigit problems 23 + 38 =
Developing
Understanding:
¨ Begins at the counting on stage with
children developing their sense of the representations of numbers
¨ Also central in developing their
basic facts understanding is learning facts in a problem-solving context. By
solving problems, children develop a richer understanding of the relationship
between problems and number facts. When students are given a problem, encourage
them to develop and share a strategy with their peers, encouraged to work
flexibly with different strategies, they are further developing their
understanding of number operations
¨ Students develop a strong
understanding of operations (addition, subtraction, multiplication and
division) and of number relationships by solving problems
¨ Most students can learn basic facts
accurately, although their speed may vary
¨ Students should have many experiences
modelling the facts using concentrate and pictorial representations i.e.
counters and paddocks, egg cartons
¨ Students should be encouraged to look
for patterns and relationships between the operations and the numbers in the
facts
¨ Students need strategies that help
them reason their way to the solutions for the facts, rather than strategies
for memorising the facts
¨ Students need their foundational
knowledge of how to count from 1 – 10, connection to objects being counted,
each number represents a network of connections, that numbers can be acted on,
magnitude of numbers increases as students count on and decreased as they count
back
¨ Part-whole concepts-Numeracy Project
To practice
your child can:
¨ Discuss the related family
¨ Flashcards
¨ Chanting
¨ Games
¨ Family
of facts i.e. 7 + 3 = 10, 10 – 7 = 3
¨ Quick
ten
The role
of games:
Play is a significant medium through which students
acquire informal mathematical knowledge by forming links between the known and
the new or unfamiliar and making sense of their new information.
¨ Students
practice sets of facts that can be solved by a similar strategy, giving them
the opportunity to match strategies to facts to assist in the development of
recall.
¨ At
the point of recall, students can retrieve the answer to a fact equation
quickly and efficiently.
¨ Playing games provides good
opportunities for children to learn about logic and strategies. For example
playing cards and board games are good ways to encourage and develop children's
numeracy ability. Playing, listening, watching and talking about games and
activities helps develop, reinforce, and consolidate children's mathematical
understandings.
¨ As you read through an activity or
game, think about how it could be made easier or harder to suit the needs of
the children. A simple activity can be made harder by changing a few numbers.
