Early Numeracy in the Transition
from Kindergarten to
Primary School –
Supporting Children’s Development
in Mathematics by Individual
Learning Plans
Meike Grüßing
University of Oldenburg, Germany
(meike.gruessing@uni-oldenburg.de)
17th EECERA Annual Conference, Exploring Vygotsky’s Ideas
Prague, 29th August – 1st September 2007
Background
• Results of longitudinal studies (e.g.
Krajewski, 2003) show that knowledge
about quantities and numbers can be
seen as an important pre-competency
for mathematical learning
• The findings suggest that it is possible
to predict and minimize potential
mathematical learning difficulties of
‘children at risk’ prior to them starting
school
Mathematics Learning in
Early Childhood Education
gifted children / children with
special interests in mathematics
based on
mathematical
situations in
everyday life and
play
individual
assistance
children potentially at
risk in learning
mathematics
Aims of the Study
The study seeks to
• investigate young children‘s mathematical
understanding in the transition from
Kindergarten to primary school
• to evaluate appropriate assessment
instruments
• to explore how young children can be
supported effectively in terms of their number
concept development in early childhood
education.
Sample:
• in 2005/2006:
850 Kindergarten children (five-year-olds)
The Study
Effects of early interventions for preschoolers at risk in learning
mathematics –
A three year longitudinal study
Year 1:
Kindergarten
Tests and
interviews
(Sept/Oct
05)
Early
intervention
program
(Jan – June
06)
Year 2: Year 3:
Grade 1 Grade 2
Tests and
interviews
(June 06)
Tests and Tests and
interviews interviews
(June 07) (June 08)
(funded by the EWE-Foundation)
Instruments
standardized
 OTZ / Utrecht Early Numeracy Test
 Culture Fair Intelligence Test (CFT 1)
 German test of mathematical abilities for the 1st
grade (DEMAT 1+)
 German test of mathematical abilities for the 2nd
grade (DEMAT 2+)
not standardized
 Elementarmathematisches Basisinterview (EMBI)
(basis interview on elementary mathematics)
• Tasks on visual perception
Instruments
The data collection in kindergarten is
based on two different instruments:
• OTZ / Utrecht Early Numeracy Test
(van Luit, van de Rijt & Hasemann, 2001):
– a standardized test aiming to measure
children‘s development of number concept
Instruments
• EMBI (ElementarMathematisches BasisInterview) including a preschoolers’
interview
– A task-based one-on-one interview which
allows children to articulate their developing
mathematical understanding through the use
of specific materials provided for each task
– This interview is based on the ENRP-Interview
developed by the research team of the
Australian Early Numeracy Research Project
(e.g. see Clarke, 2001)
P1: Simpler Counting Tasks – More or
Less – Conservation
Place a pile of 20 teddies in front of the child in a scattered
pattern, made up exactly by 4 yellow teddies, 5 red teddies,
3 green teddies, and 8 blue ones
Please put the yellow teddies together.
How many yellow teddies are there?
Put a group of 3 green teddies together near the 4 yellow
teddies (giving two different small groups)
Are there more green or more yellow teddies?
Push the yellow and green teddies aside.
Please get five blue teddies...
Now put them in a line. (If the child has already put them
in a line, ask the child to “move them together now“.)
… Tell me how many blue teddies there are.
P3: Subitizing – Matching Numerals to Dots
I‘m going to show you some cards quite quickly.
Tell me how many dots you see.
Show each flashcard for 2 seconds only, in the following
order and orientation.
Now put the dot cards all down in the order shown here.
Spread out the 0 – 9 cards randomly, face up, in front of
the child, between the child and the dot cards.
Find the number to match the dots.
(If the child seems puzzled that there are more numeral
cards than sets of dots, explain that “you won’t need to
use all the numbers.”)
Results of the OTZ
(September/October 2005)
Results of the OTZ
(September/October 2005)
Results of the OTZ:
Mean of correct answers (max. 5 per aspect) in groups with different test results
Concepts of
comparison
Classifi Correspond Seriation
cation ence
Using
counting
words
Counting
Resultative
synchronously Counting
and
Structured
counting
Knowledge of Total
numbers
Complete
Sample
4,48
4,21 3,50
2,57
2,74
2,59
1,85
2,88
24,84
Upper
Quartile
Lower
Quartile
4,81
4,69 4,51
4,09
4,24
3,98
3,22
4,29
34,03
3,92
3,41 2,22
1,13
1,05
0,94
0,56
1,51
14,74
Bottom 10%
3,44
2,98 1,69
0,82
0,57
0,54
0,25
1,13
11,40
Results of the EMBI Preschoolers’
Interview (Sept/Oct 2005)
Results of the EMBI
Preschoolers’ Interview
(September/October 2005)
Results of the ENRP FYSMI
Mean of correct answers (max. 1 per aspect) in groups with different test results
Small
sets
Language Pattern
of Location
Compete
Sample
0,91
0,91
Upper
Quartile
Lower
Quartile
0,99
Bottom
10%
Ordinal
Number
Subitizing Matching Ordering
numerals numbes
to dots
Part-part- Number
whole
before
/after
One-toone
Corresp.
Ordering
Total
0,69 0,70
0,76
0,74
0,53
0,47
0,51
0,93
0,75
0,98
0,91 0,97
0,86
0,96
0,98
0,74
0,84
1,0
1,0
10,2
0,75
0,77
0,46 0,27
0,62
0,37
0,08
0,22
0,16
0,79
0,34
4,8
0,59
0,59
0,32 0,08
0,55
0,21
0,07
0,11
0,07
0,67
0,17
3,4
7,91
Findings
• Based on interviews with 850 kindergarten
children (five-year-olds), a range of number
skills that most pre-schoolers demonstrated
especially in the material based interviews,
were identified.
• However, around 10 % of the children clearly
struggled with certain areas relevant to the
development of number concept such as
seriation, part-whole-relationships, ordering
numbers and counting small collections. They
were identified as ‘children at risk’ with respect
to their later school mathematics learning.
Intervention Program
 Group 1: individual intervention program
conducted by preservice teachers during weekly
individual sessions
 Group 2: Intervention program conducted by the
kindergarten teachers within their groups
(supported by the researchers)
 Group 3: no further support
Intervention Program
 Group 1: individual intervention program
conducted by preservice teachers during weekly
individual sessions
 Group 2: Intervention program conducted by the
kindergarten teachers within their groups
(supported by the researchers)
 Group 3: no further support
Early Mathematics Learning
 ... should focus on important
mathematical ideas
 ... should be connected to children‘s
everyday life and play
 ... should be based on lots of experiences
with all senses
 ... should be based on appropriate
assessment
A questionable example:
Personified numbers
Mathematics and Play
Which number do
you need to win?
Mathematics learning with all senses
Can you jump in
steps of two?
Role of the teacher
• In order to support children in their
mathematics development, teachers
need to be able to identify children‘s
current individual knowledge and skills
• They need to have knowledge about
certain “milestones” or growth points
with respect to the mathematics
development
• This knowledge is needed to be able to
lead children into their “zone of
proximal development”
Name
Finn
5 Y 8 M
V1a V1b V1c
  
V1d V1e V2a
 
V2b V2c
Ordering numbers: 1 – 9
V3a
V3b
V3c V3d V3e V3f
(–) (–)

4 Pencils
V3g V3h
Ordering
3 Pencils
One-to-one
correspondence
Numbers before
Numbers after
Part-part-whole
0-9
Matching numerals to dots
V2d V2e V2f
Subitizing
Ordinal number
Explain pattern
Continue pattern
Match pattern
Pattern
Name colours
Location
Conserve number
Make a set of 5
Identify one group as „more“
Count a collection of 4
Small Sets
Sort by colour
Development of individual learning plans
V3i
V3j
Example: Individual learning plan for Finn
Focus
Contents and activities
Material
One-to-one
correspondence
Co-ordinating number words with
the objects to be counted
Teddies, pencils, wooden
cubes, etc.
One-to-one correspondence
Counting activities
Counting collections
Making sets
Reading numbers
Subitizing
Ordinal numbers
Various materials
Dice
“Mice race“
Cards with numerals and dots
“Number road”
Games: Bingo, Memory,
Domino
Comparison and
seriation
Comparison of sets
Ordering objects
Teddies, pictures, pencils
Mathematical language
Language of location
Teddies
“Number road”
„Numbers Road“
„Mice Race“
Finn builds a juice factory
Finn writes numbers
Results of the EMBI
Preschoolers’ Interview
Preschoolers' Interview
1
0,8
Autumn 2005
0,6
Summer 2006
0,4
0,2
0
g
in
er
rd
r
O
ne
fte
-o
/a
-to
e
ne
or
O
ef
rb
be
le
um
ho
N
w
rts
er
pa
b
ts
rtdo
um
Pa
n
to
g
s
in
al
er
er
rd
m
O
nu
in
ch
at
M
g
in
r
ti z
bi
be
m
Su
nu
al
in
rd
O
rn
t te
Pa
n
tio
ca
Lo
s
et
lS
al
Sm
Evaluation of the Enhancement
Program: First Results
EMBI
1
0,8
Whole group 2005
0,6
Whole group 2006
"Children at risk" 2005
0,4
"Children at risk" 2006
0,2
0
Sm
all
s
Lo
Pa
ca
tte
t io
rn
n
ets
Su
Or
Or
Pa
On
Or
Ma
Nu
de
d in
bit
de
rt-p
e -t
mb
thi
rin
izin
r
al
o
i
a
n
n
e
g
g
r
on
gn
rs
nu
t-w
g
nu
e
b
mb
um
ho
m
e
for
er
e ra
le
be
e/
rs
ls
aft
to
er
do
ts
Name
Finn
5 Y 8 M
Finn
6 Y 4 M
V1a V1b V1c
  
   
V1d V1e V2a
V2b V2c
Ordering numbers: 1 – 9
V3a
V3b
V3c V3d V3e V3f
 
(–) (–)
  
 () ()

(–)(–)(–) 
4 Pencils
V3g V3h
Ordering
3 Pencils
One-to-one
correspondence
Numbers before
Numbers after
Part-part-whole
0-9
Matching numerals to dots
V2d V2e V2f
Subitizing
Ordinal number
Explain pattern
Continue pattern
Match pattern
Pattern
Name colours
Location
Conserve number
Make a set of 5
Identify one group as „more“
Count a collection of 4
Small Sets
Sort by colour
Results of the Second Interview
V3i
V3j
First Results of the DEMAT 1+
Finn‘s
score: 23
First Results of the DEMAT 1+
Finn‘s
score: 23
Identified as
„Children at Risk“
Findings and implications
• Especially the results of the EMBI-Interview
provide the teachers with valuable information
about the mathematical thinking of children
and they are useful to develop learning plans.
• The children who took part in the intervention
program generally made progress in their
mathematics learning
• There is evidence to suggest that it is possible
to minimize potential mathematical learning
difficulties of ‘children at risk’ prior to them
starting school
• Further data analysis is needed! (study in
progress)