INTO Numeracy in the Primary School
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“Understanding place value is important to
achieving good number sense, estimating and
using mental mathematical skills, and
understanding multi-digit operations” (Ross
2002, 423).
INTO Numeracy in the Primary School
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Hindu-Arabic influence
All numbers can be represented by the digits
0-9
0 as a placeholder (added around 500a.d. in
India)
Groups of ten
Position of digit determines its value
INTO Numeracy in the Primary School
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Make groups of 10, count each group as one
Grouping by tens, hundreds, thousands
Counting by tens, hundreds, thousands
Multiplicative and additive principles
Importance of zero as a place holder
Record pictorially on abacus, notation board,
number line and with blocks, coins, etc.
Represent using digits and words
Column Value & Quantity Value
Canonical/non-canonical value
Apply to compare numbers, partition numbers
and do calculations
INTO Numeracy in the Primary School
Research from around the world on
children’s understanding of place value
and the factors that may influence it.
 Seminal work in the 80’s and 90’s by
Resnick, Ross, Kamii, Fuson, Jones et al.
to
 Recent work from Australia (ENRP & CMIT),
New Zealand (NDP), & U.S.A. (Murata &
Fuson, Chandler & Kamii)
INTO Numeracy in the Primary School
The following topics have been researched:
 Influence of Language
 Stages of Development
 Teaching Methodology
 Curricular Placement
 Use of Materials
 Textbook Presentations
INTO Numeracy in the Primary School
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Difficulty of English number words compared
with many other languages
Especially teen numbers
No consistency/Pattern
Different names for ten
Decade numbers
INTO Numeracy in the Primary School
Gaelic word
Literal
Meanin
g
Japanes
e word
Literal
Meaning
English Word
10
deich
10
Ju
Ten
Ten
11
aon dheug
1 + 10
Ju-ichi
Ten-one
Eleven
12
dà dheug
2 + 10
Ju-ni
Ten-two
Twelve
13
trì deug
3 + 10
Ju-san
Ten-three
Thirteen
14
ceithir deug
4 + 10
Ju-shi
Ten-four
Fourteen
15
cóig deug
5 + 10
Ju-go
Ten-five
Fifteen
16
sia deug
6 + 10
Ju-roku
Ten-six
Sixteen
seachd deug
7 + 10
Jushichi
Ten-seven
Seventeen
ochd deug
8 + 10
Juhachi
Ten-eight
Eighteen
19
naoi deug
9 + 10
Ju-kyu
Ten-nine
Nineteen
20
fichead
20
Ni-ju
Two-ten
Twenty
17
18
Is there a
consistent pattern
in English
vocabulary ?
Do the number
names 11-20 link
to number names
1-10?
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Stage I -Whole Numeral (25 as 25 units)
Stage II- Positional Property (2t and 5u)
Stage III- Face Value (2 ten blocks and 5
unit blocks)
Stage IV- Construction Zone (2 tens and 5
units)
Stage V-Understanding (2t 5u, 1t 15u, 25
units) (Ross)
INTO Numeracy in the Primary School
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Rote learning and textbooks
Moving into structured materials too quickly
Moving away from materials too quickly
Ignoring place value aspect when teaching
algorithms
Unstructured →structured →visual→
abstract
INTO Numeracy in the Primary School
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Too Early
Deal with numbers up to twenty before
dealing with place value
Not until end of second class
INTO Numeracy in the Primary School
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Move into structured materials too early
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Inconsistency of language
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Representations limited
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Rote learning encouraged
INTO Numeracy in the Primary School
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Small Scale – 100 children interviewed
4th class
Semi-structured interviews
Questions linked to PSC-Mathematics
objectives for number at 3rd/4th class level
INTO Numeracy in the Primary School
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Children in this study demonstrated a good
understanding of certain aspects of place
value.
Regrouping, connecting column value to
quantity value and estimation proved difficult
for many children.
Prevalence of counting by ones when
counting a quantity of objects (25- 100).
Use of the standard algorithm for mental
maths.
Children showed limited estimation
strategies.
INTO Numeracy in the Primary School
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- grouping & counting in twos, threes, fours,
etc.
- creating groups of tens from a variety of
objects
- quantity & column value and to make
connections between them
- ideas about numbers through discussion
and writing
- estimation strategies
INTO Numeracy in the Primary School
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Mathematical language used in textbooks was
not consistent with language of curriculum or
consistent even within the textbooks.
Counting strategies rarely appeared in any of
the fourth class textbooks other than skip
counting used for multiplication and number
sequences.
Number lines rarely used in textbooks and
rarely to show adding on or subtracting by
ones, tens or hundreds.
INTO Numeracy in the Primary School
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Move away from text books
Replacement Units as a transition (Maths
Recovery, First Steps in Mathematics, Ready
Set Go Maths, Math Solutions, Family Maths,
TERC, NZmaths)
Develop your own whole school activities to
meet the needs of your children
(Croke Park hours??)
INTO Numeracy in the Primary School
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Whole numbers
Read, write & order
Expanded form
Significance of zero in place value
Rounding up and down to nearest 10, 100,
1000
Identify Place Value
INTO Numeracy in the Primary School
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Grouped Objects
Dienes Blocks (Base 10 materials)
Abacus
Notation Board
Money
Arrow Cards
Number Lines (used in every class JI-6th )
Hundred Chart (0-99/1-100, up or down)
INTO Numeracy in the Primary School
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Place Value Game
Place Value Ordering Game
Washing Line/Person Line
Circle Game –count on by 10, 100, 1000
Calculator Game
Race to 100, 1,000, 10,000
101 and out, 1001 and out
Applying to everyday life (children’s interests)
INTO Numeracy in the Primary School
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Arrow Cards
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Calculator
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Partitioning (see InTouch L.Harbison article)
INTO Numeracy in the Primary School
Rounding up & down
 Estimation Bingo
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Rounding Dice
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Follow me
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Number Line
INTO Numeracy in the Primary School
Materials: spinner or dice 0-9, pen and place value sheet for
each player
 Players: At Least 3 Players to Whole Class
 Objective: Read, write and order whole numbers.
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The teacher/caller spins spinner and calls out a number. The
players write the number in one of the place value boxes. The
caller repeats four times. The players can discard one of the
numbers. The object of the game is to have the
highest/lowest number.
The discussion of possible numbers and ordering along a
number line as well as strategies used is an important part of
this activity
INTO Numeracy in the Primary School
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Materials: Game sheet, 2 dice (0-9)
Players: 2 – Whole Class
Objective: Read, write and order whole
numbers.
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Throw dice and decide which number
represents tens and which number represents
units. Write the numbers in the blank boxes.
At the end of the game all boxes must be
completed in order from 0 –100. Winner is
first person to fill all boxes in correct order.
INTO Numeracy in the Primary School
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Material: game sheet, 0-9 die or spinner, pencils
Players: 2 to whole class
Objective: Explore and identify place value in whole
numbers
The dice is thrown 5 times and each time the
players have to decide to put the digit in either the
tens or units place. Once chosen the position
cannot be changed. A zero is put in the position
not chosen. At the end of the five throws each
player adds up their five numbers. The object of
the game is to have a total as close to, but not over
100.
INTO Numeracy in the Primary School