Creative Education
2013. Vol.4, No.7A1, 33-42
Published Online July 2013 in SciRes (
Copyright © 2013 SciRes. 33
Patterns of Variation: A Way to Support and Challenge Early
Childhood Learning?
—Concluding Reflections from Learning Study Projects Conducted in Swedish Early Childhood Education
Agneta Ljung-Djärf1, Mona Holmqvist Olander Brante1,2, Eva Wennås Brante1,2
1Kristianstad University, Kristianstad, Sweden
2Department of Pedagog i c a l , Curricular and Professional Studies, Universit y of Gothenburg,
Gothenburg, Sweden
Received May 17th, 2013; revised June 16th, 2013; accepted June 23rd, 2013
Copyright © 2013 Agneta Ljung-Djärf et al. This is an open access article distributed under the Creative Com-
mons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, pro-
vided the original work is pr ope rly cited.
The purpose in this article is to elaborate on how the use of patterns of variation designed by variation
theory can challenge and develop the early childhood education (ECE) practice. The analysis is based on
six learning study (LS) projects conducted in Swedish ECE. A LS is a systematical, theoretical based de-
velopment of teacher professionalism, often in close cooperation with researchers. The projects included
17 teachers, 140 children and 7 researchers. The video documented empirical material consists of 16
analysis meetings, 14 interventions and 407 pre-, post-, and delayed posttests. Each project is a concrete
example of the use of patterns of variation to increase early childhood learning. In all cases a tendency of
qualitative changes in children’s ways of discerning the object of learning could be noticed. The purpose
is to search for how this can be understood from a variation theoretical perspective. The main focus is on
changed ways of performing the interventions to search for how patterns of variation were used to create
and capture the learning situations throughout the projects. One of our findings is that we have seen that it
takes more than one intervention for the teachers to capture which aspects of the object of learning are
critical in the targeted group, but as the iterative process allows them to try out the design more than once,
they manage to find them. The second finding is that the teachers changed focus from taken for granted
assumptions of each child to focusing on their own design to facilitate the child’s learning. Finally, the
aspect supposed to be discerned has to vary against an invariant background to be discerned by the chil-
dren, and to separate the principle from the representation is needed to be able to generalize their new
Keywords: Patterns of Variation; Variation Theory; Learning Study; Early Childhood Education
The focus of this article is on how patterns of variation,
based on variation theory (Lo, 2012; Lo & Marton, 2012; Mar-
ton & Booth, 1997), are found to challenge and develop early
childhood learning and development. Early childhood educa-
tion (ECE) in Sweden is organized as pre-school for the 1 -
5-year-olds and a pre-school-class for the 6-year-olds. It is
voluntary to attend but all children have the right to participate.
It is free of charge 15 hours a week, if additional child care is
needed it is coated with a cost. The first curricula, implemented
in 1998 (Ministry of education and research, 1998), was influ-
enced by a pre-school tradition inspired by Fröbel, who advised
the teachers to follow the children’s interests and development
without steering them (see e.g., Fröbel, 1995). There is also a
clear connection between play and early childhood learning.
The implementation of the ECE curriculum gave indeed status
and legitimacy to the ECE practice and work, but, later on, the
educational practice was also criticized not stimulating chil-
dren’s learning systematically (The Swedish national agency
for education, 2004). An ECE “doing culture”—with a main
focus on what to do instead of what to learn—was in focus of
such critique. So, in accordance with governmental suggestions
(Memorandum U2008/6144/S, 2008) a new education act (Ds,
2009: p. 25) and a revised curriculum (The Swedish national
agency for education, 2010) a clarification of the educational
mission were made. The new content and learning objectives
placed emphasis on literacy, mathematics, science, and tech-
nology. ECE practices were also required to conduct systematic
quality work including pedagogical documentation and evalua-
tion. However, the implementation of new learning objectives
has been a challenging task due to e.g. a lack of a ECE tradition
aiming at specific learning objectives as well theoretical tools
on learning to support such new requirements.
The Swedish ECE practice of today is a high quality playful
learning environment based on children’s perspective. It is an
educational practice influenced by a valuable and internation-
ally renowned ECE research approach as well as peddagogical
tradition initiated primarily by professor Ingrid Pramling Sa-
muelsson the, so called, developing pedagogy (se e.g., Pram-
ling, 1994; Pramling Samuelsson & Asplund Carlsson, 2003;
Pramling Samuelsson & Mårdsjö, 2007). A long and wide vari-
ety of studies have been conducted demonstrating its positive
impact on ECE practice and learning. Three main pedagogical
strategies of the developing pedagogy is described as to:
Create and capture situations around which children can
think and speak;
Get children to think, reflect and express themselves ver-
bally and in other ways;
Take advantage of the diversity of children’s ideas.
Further on it is an approach where children’s meaning mak-
ing and variation is central aspects. Variation from this point of
departure implies that teachers illustrate children’s ways of
thinking by focusing on different levels of generality and to
address ways to understand a single learning object—both of
the individual child, and the child group as a whole. Developing
pedagogy takes advantage of children’s intentions and perspec-
tives to capture and challenge the child’s world with the help of
variation. Variation in this sense implies varied views of a
phenomenon. The expressed variation, e.g. different ways of
thinking and talking about the same phenomenon is used as an
asset in making the children aware of a greater number of dif-
ferent ways of understand something (Pramling & Pramling
Samuelsson, 2011: p. 9). During the teaching and learning proc-
ess, variation in this sense is seen as a rich resource at work for
expanding children’s experiences of the world.
However, from a variation theoretical perspective, variation
has been given another meaning. An LS is a systematical plat-
form to help teachers to put variation theory into practice (Lo,
2012; Lo & Marton, 2012). It is a model actualized in concrete
teaching and learning situations by use of this specific theory of
learning as guiding principle. The LS model is used to develop
teacher professionalism; often in close cooperation with re-
searchers (Holmqvist, 2011). During the past few years a proc-
ess of trying out the LS model has been conducted in different
educations settings around the world (Lo, 2012; Lo & Marton,
2012). LS has mainly been used in different primary or com-
pulsory educational setting but has also, as mentioned, been
tried out in ECE practices. Completed ECE LS projects (see
e.g., Holmqvist, Brante, & Tullgren 2012; Holmqvist, Tullgren,
& Brante, 2010; Landgren & Svärd, 2013; Ljung-Djärf, 2013;
Ljung-Djärf & Magnusson, 2010; Ljung-Djärf, Magnusson, &
Peterson, submitted) shows that the LS design may also fit into
the ECE context but needs to be adjusted to suit the early edu-
cation culture and context and young children’s conditions and
needs. Four main features were a school based LS model and
early childhood activity seem to have different points of views,
are the approach to learning, ways of guiding the children, what
content the teachers focus on and ways of assessing learning
outcome (Ljung-Djärf & Holmqvist Olander, 2013). When hav-
ing such features in mind a process of trying out a use of the LS
model in ECE practice have shown that it is possible to apply
and adjust to early childhood settings to deepen the teachers’
understanding about children’s learning (Holmqvist et al., 2010;
Holmqvist et al., 2012; Ljung-Djärf & Holmqvist Olander,
2013) to change focus from doing to learning (Ljung-Djärf &
Magnusson, 2010; Ljung-Djärf et al., submitted) but also an
experienced professional development by participating in a LS
project (Holmqvist Olander & Ljung-Djärf, 2012).
The ECE LS model developed in these projects implies some
similarities compared with development pedagogy but also
some differences. A main similarity is the base of seeing learn-
ing from a learner’s perspective based on a phenomenographi-
cal (Marton & Booth, 1997) point of departure. Both develop-
mental pedagogy and the ECE LS model implemented in the
projects uses interviews as a way to reveal and use children’s
perspectives on their surrounding world when create and cap-
ture learning situations. As a critical difference, though, appears
the view of what variation and discernment entail (Pramling &
Pramling Samuelsson, 2011: p. 9). The purpose in this article is
to elaborate on how the use of patterns of variation designed by
variation theory can challenge and develop the ECE practice i.e.
especially regarding teachers’ readiness to create and stimulate
learning situations. The research question is:
What might patterns of variation designed by variation the-
ory afford ECE practice?
Initially, we will give a brief introduction to the theoretical
point of departure, purpose, and design of the ECE LS model.
The Theoretical Point of Departure of the LS Model;
Variation Theory
From a variation theory perspective learning is always learn-
ing about something. In a LS this something is called the object
of learning. An object of learning consists of many features.
Such features have to be discerned by the learner if the com-
plexity of a phenomenon can be understood. To a young child,
this is obviously a long and extensive process based on con-
tinuous experiences of different kinds and different contexts.
Let us illustrate this with a very simplified example on a possi-
ble object of learning; what is a dog? The phenomenon “dog” is
defined by several features that cohesive defines it as a dog, i.e.
the number of legs, the barking sound and shape of the paws.
To fully understand what a dog is, assumes an understanding of
the whole (“a dog”) as well as the parts (i.e., legs, sound and
paws) and the relation between them. Lo and Marton (2012)
claims that “There must be a whole to which the parts belong
before the parts can make sense to us. We cannot learn mere
details without knowing what they are details of” (p. 26). A
feature, i.e., such as those mentioned above, is critical when not
yet discerned by someone. A small child discerns a variety of
living creatures as “a dog” before having discerned the specific
features that defines a specific animal. Such specific features
are i.e.; it is something that has four legs, barks and has paws.
By that, whether an aspect is critical or not is determined in the
relation between the phenomenon and a learner, or in other
words it is a real critical aspect to that specific person (Olteanu
& Olteanu, 2010). When an aspect is discerned by the learner it
is no longer a critical aspect but an aspect defining the specific
phenomenon. From a variation theoretical approach a way to
experience differences between aspects or values or features of
an aspect is to experience contrast, i.e., what something is and
what something is not. To reuse the dog example this is about
experiencing that a lot of animals have a similar shape of the
body and the same number of legs (i.e., horse, cat and dog). So,
to discern that there is a difference between the horse, cat and
the dog a learner has to focus on something else i.e., the sound
they are making. Such contrast can be discerned by experienc-
ing a barking dog and a mewing cat simultaneously or being
based on a memory of i.e., a mewing cat when hearing the bark
of a dog. When contrasts are experienced it is possible to sepa-
rate the aspect from the object it belongs to and focus on it. All
aspects cannot be in focal awareness at the same time. A varia-
tion of an aspect against a background of sameness can be at-
tained through patterns of variation. Such variations can also be
Copyright © 2013 SciRes.
attained by pointing out what something is by showing what it
is not. The experienced variation enables thus a discernment of
the critical feature from the phenomena, it stands out (Runesson
& Mok, 2003) from the background and we can become focally
aware of it. From a variation theory perspective, this implies to
open a dimension of variation, by which critical aspects are
made possible to discern. If we want to design a learning situa-
tion on the sound of a dog in focus we have to open up a di-
mension of variation that makes this aspect, and no other, pri-
marily stand out against an invariant background. When we put
the sounds of different animals in the foreground by varying
only the sound we have varied sound against a background of
Let us give another example based on the understanding of
the shape of a cylinder. How can a situation that makes the
shape of a cylinder standout be arranged? We can for example
choose to illustrate the shape of by, as in the first example (Ta-
ble 1), the use of cylinders in different sizes, or as in the second
example, differently colored cylinders in the same size, or as in
the third example, a blue cylinder and a blue cubicle in the
same size.
From a variation theoretical perspective is it essential to open
up a dimension of variation that makes a potential critical as-
pect, and no other, primarily stand out against an invariant
background when designing a learning situation. Table 2 sum-
marizes how the use of different aspects to appear as variant or
invariant make different aspects to stand out, or in other words
to appear as background respectively foreground.
To make a feature stand out is from a variation theoretical
point of view, a matter of not originates primarily from same-
ness, but from difference. Learners are usually offered exam-
ples that have the focused meaning in common, but differ oth-
erwise as e.g., in Examples 1 and 2 above. Variation theory
suggests that we turn this pattern around and let the focused
meaning vary, while other things remain invariant as e.g. in
example 3 above. By varying potential critical aspects they will
stand out and afforded to be in focus of a joint discussion (see
also Holmqvist Olander & Ljung-Djärf, 2013).
To summarize, learning can take place when critical aspects
are discerned, which is made possible when a dimension of
variation is opened around that critical aspect by a simultaneous
Table 1.
A summary of used concrete material in the three examples (Holmqvist
Olander & Ljung-Djärf, 2013) .
Example 1 Example 2 Example 3
Table 2.
Example on patterns of variation that makes different aspects to stand
out (Holmqvist Olander & Ljung-Djärf, 2013).
Example 1:
size stands o ut Example 2:
color stands out Example 3:
shape stands out
Size Variant—different
sizes Invariantonly one
size Invariantonly one
Color Invariantonly redVariant—different
colors (green and red) Invariantonly blue
Shape Invariantonly
cubicles Invariantonly
shapes (cubicle
and cylinder)
contrast of the aspects in the dimension of variation. But, how
contrasts are designed for is not possible to tell without know-
ing who the learners are. Lo (2012) highlights how intertwined
critical aspects and features are, it is impossible for a person to
discern a critical feature without knowing which critical aspect
it relates to.
Purpose and De sign of the ECE LS Model
LS is a kind of action research that combines a theory on
learning, variation theory, with the concept of the Asian model
of lesson study (see e.g., Lewis, 2002; Yoshida & Fernandez,
2004). It is a model aiming to get teachers to learn in and from
their own practice. In a LS project researchers and teachers
work together as a team trying to collaboratively generate,
share, develop and implement knowledge about learning with
the aid of variation theory concepts and notion. By that, it is a
process built up by a joint theoretical based reflection on the
educational practice through research ventures. Educational
practice in this context refers to the practice of teaching with
respect to a defined content and in specific institutional settings.
The process is organized in a structured and predetermined
way (see e.g., Holmqvist, 2011; Häggström, Bergqvist, Hans-
son, Kullberg, & Magnusson, 2012). Initially, there are two or
three planning meetings to identifying of the object of learning
and its critical aspects and ways of assess children’s learning.
The object of learning is what the teachers and the children are
supposed to focus on during the forthcoming activities. On one
hand, a distinct object of learning affords an analysis of ways of
discerning that specific object of learning from one delimited
activity. On the other hand it is sometimes found as contradic-
tive to traditional ECE practice. It has even been talked about as
a risk that this way of working will result in a “fragmentatisa-
tion of knowledge quite contrary to the preschool tradition”
(Pramling & Pramling Samuelsson, 2011: p. 9). The identifica-
tion of an object of learning is then followed by a process of
screening, searching for possible stumbling blocks in how
young children might discern this specific object of learning.
The screening could be arranged as interviews, a practical task
or an observation. The screening is aiming to reveal potential
critical aspects (Olteanu & Olteanu, 2010) of the object of
learning, i.e., features of the object of learning that seems to be
difficult to discern. The screening is not a way to search for
overall rules connected to stages of development in a specific
age group but a way to coordinate children’s and the teachers
perspectives related to a shared object of learning, enabling
them to continue with their mutual learning activity. The in-
formation from the screening is used when designing a “test”.
Copyright © 2013 SciRes. 35
As the term test is quite challenging in relation to the ECE
practice it is important to emphasize that the construction and
use of tests not is a way to assess the children based on estab-
lished standards nor it is a way to evaluate and compare one
individual with another. Instead, the term test in this context
implies a way to catch sight of what the children as a group did
seemingly discern related to a specific activity and object of
learning and by that, give the teachers a clue on a possible way
to create and capture challenging learning situations. In line
with Swedish ECE practice and tradition interviews is a com-
mon way to identify children’s ways of perceiving phenomenon
in their surrounding world (se e.g., Doverborg & Pramling,
2000). During the ECE LS projects tests, mainly in the form of
interviews, were used to identifying qualitative changes in how
the children discern the object of learning before and after an
intervention or learning activity. By that the development and
evaluation of qualitative changes at a group level is used as a
methodological tool to reflect on and develop practice further on.
After the initial planning and identifying of the object of
leaning and its potential critical aspects, described above, the
subsequent project comprises commonly three cycles; each con-
taining four specified steps. The cyclic process can be com-
pared with the action research spiral, in which the reflection of
the evaluation of the first action is the point of departure for
further development. A LS cycle is organized as a pre-test, an
intervention, a post-test and an analysis and planning meeting
aiming to reflect on practice to further develop the practice in
the next cycle (see Figure 1). The aim of such a process is to
use teachers’ initial assumptions and existing values as point of
departure to challenge and reconsider it by the use of evidence-
based reflection. In other words, the model is about invention
and re-invention of knowledge on teaching and learning.
A Description of the ECE Learning Study
The analysis is based on six LS projects conducted in Swed-
ish ECE. The projects analyzed in this study have used varia-
tion theory as point of departure; beforehand when planning,
during the interventions and after the interventions in discus-
sions and evaluations. Teachers have thus been introduced to
variation theory in a theoretical way but also by implementing
the theory directly into their educational practice. Table 3 sum-
marizes the objects of learning and participants in the cycles of
each project.
The empirical material is mainly video documented and con-
sists in total of 16 meeti ng s, 14 in terventions, and 407 te sts in the
form of individual pre-, post-, and delayed post-tests (Table 4).
Figure 1.
The design of the LS cycles (L ju ng- Djä rf et al., submitted).
The tests were conducted in different ways. In project 1 and
2 the children were individually interviewed (Holmqvist et al.,
2012). In project 3 all children were individually asked to an-
swer three questions concerning where there were most items in
diffe rent occasions with diffe rent materials (Holmqvist & Tull-
gren, 2009). In project 4 the children were individually given a
pile of wooden blocks and the teacher asked them to sort the
blocks. The intension was to see if the children sorted them
with shapes as a starting point (Landgren & Svärd, 2013). Pro-
ject 5 used individual interviews based on concrete organic
objects in different degrees of degradation (Ljung-Djärf & Mag-
nusson, 2010; Ljung-Djärf et al., submitted). Finally in project
6, the tests had a written form and each child completed it by
itself sitting together with their friends (Ljung-Djärf, 2013). In
all cases qualitative changes in ways of discerning the object of
learning were searched for. As the scoring was based on quail-
tative assessments of the children’s answers, a preliminary as-
sessment was first made of the children’s responses during the
interview. After each session the video documentation was ana-
lysed and the assessments were reviewed separately by two re-
searchers. Table 5 summarizes the material used and how the
tests were scored.
The assessment of children’s learning is summarized quanti-
tatively in Table 6.
Table 3.
Object of learning and participants in the projects.
n = 17 Children
n = 140 Researcher s
n = 7
Project 1: whole
and half 0 3 (4 - 6-yea r- ol ds) A & B
Project 2: numbers
and letters 0 3 (4 - 6-year-olds) A & B
Project 3: more and most
(in Swedish; most by size
or number) 3 39 (4 - 5-year-olds)A & B
Project 4: 3D
geometrical shapes 4 25 (2 - 3-year-olds)A & C
Project 5: organic
decomposition 5 26 (4 - 5-year-olds)D, E & F
Project 6: twice as 5 44 (6-year-olds) D
Table 4.
The empirical material.
n = 16 Interventions
n = 14
delayed p os t t ests
n = 407
Project 1: whole and half 0 1 3/3/0
Project 2: numbers and l etters0 1 3 / 3/0
Project 3: more and most 4 3 39/39/39
Project 4: 3D
geometrical shapes 4 3 25/25/18
Project 5: organic
decomposition 4 3 26/26/26
Project 6: twice as 4 3 44/44/44
Copyright © 2013 SciRes.
Copyright © 2013 SciRes. 37
Table 5.
Used material and ways of evaluate the results.
Material use d for tests Numbers of questions/score per question/m aximum score
Project 1: whole and half Full, half, and quarter circles m ade of paper Open questions to ensure the children’s
understan din g/ not q ua ntif ie d
Project 2: nu mbers and letters 16 cards containing letters or numbers 16/not quantified
Project 3: more and most Logic blocks, potatoes, nuts, sausages, meatballs,
and bottles partially fille d w it h w ater 7/1 point/7 poin ts
Project 4: 3D geometrical shapes Wooden blocks in four different shapes and colours No questions, 1 point if they sorted three blocks alike,
tests were interrupted afte r 10 minutes
Project 5: organic de composition Apple, bread, and leaf in different degrees of
decomposition 9/each 0 - 2 points/18 points
Project 6: twice as Printed booklet with drawn pictures illustrat ing four
different respon se options f o r each question 7/each 0 - 1 point/7 points
Each project has previously been analyzed and published
separately, focusing either on children’s learning and/or teach-
ers learning (see e.g., Holmqvist, 2011; Holmqvist et al., 2010;
Holmqvist et al., 2012; Holmqvist Olander & Ljung-Djärf,
2013; Ljung-Djärf & Magnusson, 2010; Ljung-Djärf et al.,
submitted; Ljung-Djärf, 2013; Landgren & Svärd, 2013), chal-
lenges and possibilities when applying such a school generated
process on pre-school context (Ljung-Djärf & Holmqvist
Olander, 2013), the pre-school teachers views on being co-
participants in a LS project (Holmqvist Olander & Ljung-Djärf,
2012). A joint conclusion from all studies is the positive ex-
perience teachers express of having a mutual understanding of
theoretical concepts. This meta language functions well as a
tool for reflecting together, develop the educational practice
and challenge granted assumptions (Holmqvist Olander &
Ljung-Djärf, 2012; Ljung-Djärf & Holmqvist Olander, 2013;
Ljung-Djärf et al., submitted).
This is a qualitative re-analysis based on six ECE LS projects
conducted by a Swedish research group to find out in what
ways patterns of variation have impact on children’s learn-
ing.The first study was conducted in 2008 and the last in 2011.
Participating teachers and researcher have made an intense and
impressive work, during a process of collective analysis of the
educational practice. In all cases qualitative changes in chil-
dren’s ways of discerning the object of learning could be no-
ticed. The purpose of the meta-analysis is to search for in what
ways the used patterns of variation have been used to make this
change possible. Throughout this process the verbatim tran-
scripts and results of each of the LS projects and the original
video recordings were studied and re-analysed in relation to
each other, rather than individually, to find the important fea-
tures. To be able to grasp the extensive material we have
mainly focused on in what ways aspects of an object of learning
has been offered the children by the use of patterns of variation.
The process of analysis can be described as interplay between
empirical data and the variation theoretical perspective. Such
process of abduction implies an interpretation of data and de-
vise of a theory to explain them. The interventions were de-
signed from a variation theoretical point of departure to high-
light potential critical aspects and to assess qualitative changes
in children’s ways of discerning such critical aspects before and
after the activity. Changed ways of discerning has then been
related to the theoretical intensions.
Each of the six LS projects is seen as evidence based docu-
mentation on how the use of patterns of variation as a peda-
gogical tool developed the ECE practice. From the results of
the conducted LS projects an analysis of the patterns of varia-
tion has been done. The results include a description of the LS
cycles and their patterns of variation.
Analysis of Patterns of Variation: Whole and Half
In this first part of the pilot study three children participated,
aged 4, 5 and 6 years old. The study was aiming at a detailed
study in what ways patterns of variation could be used in
teaching children the object of learning whole and half. By the
use of variation theory, the aspect kept invariant was dividing
an object into two similar parts, halves, and the aspect kept
varying was the items used. By that the children were offered to
discern cutting apples, pears and cakes into halves. The alterna-
tive would have been just cutting e.g. apples into halves as-
suming the children will understand and generalize to other
objects as soon as they have been taught the concept half.
However, the results show that children do not put the same
meaning into the concept half as thought; instead they under-
stood half as something cut into pieces, no matter how many.
By that they were not sure how many halves a whole pear or
cake could be cut into, even if they have discerned that an apple
was cut into two halves. If we have not taken into consideration
the difficulty for children to transfer their experience of cutting
into halves for one representation to another, their understand-
ing that a whole apple which were cut in two halves might only
be right concerning apples and maybe not for any other item.
Analysis of Patterns of Variation: N um bers and
The second part of the pilot study with three children aged 4,
5 and 6, was about the difference between numbers and letters.
This was made to see what patterns the children would notice
by themselves without teaching. They sorted cards in a discus-
sion-like observation. As in the study above, the material used
and the design was based on variation theory. Tolschinsky’s
(2003) results showed that children from several different
Table 6.
The assessment of the children’s learning (mean results, pre-/post-/
respectively delay e d posttest).
Cycle A Cycle B Cycle C
Project 1: whole and half Not quantified Not quantified Not quantified
Project 2: numbers
and letters Not quantifie d Not quantified Not quantified
Project 3: more and most 3.7/4.3/ 4.7 3.5/4.8/ 4.9 5.3/5.9/5.9
Project 4: 3D geometrical
shapes 1.3/2.5/4.5 1.7/1.7/2.2 1.0/1.2/2.6
Project 5: organic
decomposition 7.9/8.9/8.9 6.6/6.8/8.0 8.5/10.9/11.7
Project 6: tw ice as 1.4/1.7/1.4 1.2/1.3/1.8 0.7/2.1/2.2
countries could differ between numbers and letters. The chil-
dren got cards with numbers (single figures or numbers) and
letters (single letters and words) which de were told to sort in
any way they wished. On the number cards, decimal point and
minus were also introduced. The results show that the children
noticed features of both numbers and letters, and could sort
them into two different heaps. However, as they also got cards
with the figure 0 and the letter O, they were confused and made
one heap with cards containing 0 and O. This feature seemed to
be important for them, but the decimal point and minus sign
were not mentioned or noticed at all by any of the three chil-
dren. The pattern of variation used was to keep letters and fig-
ures at different cards, but varying how they were presented as
single letters/figures or words/numbers.
Analysis of Patterns of Variation: M ore and Most
To teach children (n = 39) the difference between more and
most regarding how many, a study including three interventions
in three different groups of children were implemented. The
results show that the third group got the highest scores, based
on how they have responded regarding where there are most
(regarding highest number) in an interview where they have
met e.g. four ordinary sized sausages and five very small sau-
sages, or three filled bottles compared to five empty bottles and
so on. The items were by that designed based on variation the-
ory, as the critical aspect was to separate between how many
and how much which the questions were all about. During the
interventions, the pattern of variation was changed as shown in
Table 7. In the first session, everything varied, such as the ob-
jects used (dolls, wooden blocks, teddy bears and so on), the
size of the obj ect a nd the mat erial (plastic dolls, cloth dolls etc.).
In the second, the objects were the same; teddy bears, but still
the size differed as well as the focused aspects. In the second
session, the teacher also started to talk about if the teddy bears
were friends or not, if they had quarreled and were angry at
each other during the comparison between how many and how
much, which started a discussion about the teddy bears’ human
behaviors instead. To avoid this, the teachers changed pattern
of variation in the third session, and used cotton wool which
could be divided into smaller parts or put together into bigger
parts. In this session, only the size varied at the same time as the
object (cotton wool) and material (cotton wool) was invariant.
Table 7.
Used patterns of variation in project 3 on more and most.
Cycle A Cycle B Cycle C
Objects Variant—dolls,
wooden blocks,
teddy bears etc .
bears Invariant—cotton
Material Variant—plastic,
cloths, wood etc Invariant—cloth Invariant—cotton
Size Variant—different
sizes Variant—different
sizes Variant—different
Analysis of Patterns of Variation: 3D Geometrical
In this project patterns of variation were used to make 3D
geometrical shapes to be in focus. As the children (n = 25) were
quite young (2 - 3-year-olds) this was indeed a challenging task.
Landgren and Svärd (2013) report that the joint discussions,
theoretical reflections and analysis shaped three somewhat
different learning situations. The first one started with teachers
giving each child four blocks of different shapes and different
colors. When the children had all four blocks at the same time it
was hard for them to know what they should focus on (colour
or shape), too much varied, and they saw shapes in general
instead of discerning the critical aspect that separates a cubicle
from a cylinder or cone. Of course the children saw that the
blocks were differed, the aspect shape was not the only one that
At the second learning situation the teachers gave the chil-
dren one shape after another, all of natural wooden. They talked
about the shapes of the blocks, but made no comparison be-
tween the different shapes. The teachers had made four robots
of paper board and tinfoil, one in each shape (as shown in Fig-
ure 2). The robots’ mouths were also shaped as the block; that
is, the cylinder robot had a round hole as mouth and the cubicle
robot had a square as a mouth. Now the teachers told the chil-
dren that the robots could only eat blocks shaped as them, could
the children feed the robots with the right block?
This activity was designed to direct children’s attention to-
wards the shape of the block they held and, actually, to trans-
form a 3D-experience in their hands to a 2D pattern—the
mouths, quite a challenging task for such a young child. The
teachers noticed in their reflection afterwards that they had
talked more about food than discussing why or why not a shape
fitted into a mouth. Their focus had been on the process, feed-
ing the robots and making the robots human-like; and by that
leaving the object of learning (shapes) in the background. They
thus understood that they could improve this situation even
more. The third learning situation started in the same way, each
child got a shape one at a time, but this time, when each child
had all four, teachers initiated a discussion about what differ-
ences and similarities could be found between the blocks. Then
the robots arrived and were fed. Finally, a suitcase was brought
in with empty tins, boxes and things like that. The children and
teachers helped each other to order the objects in front of a
robot; the cans in front of the cylindrical robot and so on. In
this study, the teachers used robots to make the children match
the shape of the cubes with the mouths of the robots. This is an
example of how teachers usually use imagination and play in an
ECE learning situation. However, in this case it can be ques-
tioned if it would not be more featable to do holes in a paper
Copyright © 2013 SciRes.
Figure 2.
The robots used in cycle second and third intervention
(Landgren & Svärd, 2013).
instead of feeding robots. By that the risk of seeing the robots
hunger as main activity will be avoided and more focus kept on
the shapes.
Analysis of Patterns of Variation: Organic
From the initial screening in this project two potential critical
aspects were chosen to be in focus; 1) the decomposers break
down and convert organic matter, and 2) is a perpetually ongo-
ing process. The matter discussed in the LS project group was
how we could design a situation to make such an object of
learning discernible to be used as point of departure in further
discussions. Our first approach was to use a sort of play and
drama frame and from that starting up a discussion and reflec-
tion on what would happen to a bag of waste (fresh, organic as
well as inorganic items) when left in the forest. The children
made suggestions as i.e. it will be eaten by a bird or taken by a
gobbling. As we wanted to direct the attention towards decom-
posers, as e.g. mould, we decided to use different sorts of or-
ganic partly decomposed objects as point of departure during
the next intervention. Nor this illustration seemed to draw chil-
dren’s attention toward the object of learning. In the last activi-
ity we used one sort of organic object in different levels of de-
composition (fresh, mouldy, soil) at a time. This time the chil-
dren seemingly discerned the mould and this could be used as a
point of departure during a joint discussion and reflection. The
used patterns of variation are summarized in Table 8.
When using only fresh items (as in cycle A) or partly de-
composed items (as in cycle B) it was, more or less, taken for
granted that the children would discern the defining features of
decomposers and the on-going process of decomposition by an
abstract reflection in the group. It was also taken for granted
that the children had and could make use of previous experi-
ences of degrees of decomposition of organic items. During this
two cycles the teacher kept the focused features, fresh objects
(cycle A) respectively partly decomposed objects (cycle B)
invariant and varied other out of focus aspects (e.g., different
fresh pic-nic objects and different partly decomposed fruits,
vegetable and sticks). According to variation theory this is not
the best way to do it. During cycle C, the object (e.g., tomato)
was kept invariant and instead the rate of degradation varied,
the on-going process of degradation became in focus. This
group made use of an illustration that did afford an experience
of contrast related to the on-going decomposition process si-
multaneously. When the teachers in intervention C posed the
question “What is the difference between the tomatoes” the
idea was to use simultaneity as a tool to direct focus on contrast
of a the difference between a fresh tomato and a partly decom-
posed one (see Figure 3).
This was then used as basis for joint reflection in the group.
As mentioned above, from a variation theoretical perspective
meaning derives from difference, not sameness. By letting one
value in the same dimension of variation (degradation) was
brought in focus the learners were able to experience such dif-
ference. Even if difference can be discerned by the aid of
memories and earlier experiences it cannot be taken for granted
that a small child has such experiences and are able to remem-
ber and can make such connections all by themselves.
Analysis of Pa ttern s of V ari ation: Twice as
The initial screening showed that the understanding of “twice
as” as “one more” was a common way to make sense of the
concept. Potential critical aspects seemed to be aware of the
relation between the initial amounts to be able to determine
what twice as something is. During the interventions different
representations, appearances of the representations and way of
illustrating the object of learning were made to be variant or
invariant during the three interventions trying to make the con-
trast of the previous identified critical aspects of object of
learning, twice as, stand out in the learning situation. During
the first activity there were examples using natural coloured
wooden blocks as illustrations and there were other examples
using amounts of children to illustrate the initial amount as well
as twice as. The focus was on twice as in the sense of twice as
many. During cycle B the group used wooden blocks and tried
to exemplify twice as by using a variation of examples (twice
as; high, long, and many). Lastly, during the third cycle, they
tried to illustrate and challenge the fact that one has to focus on
the initial qua ntity to be able t o say any thing about if some th ing
is twice as by the use of a variation of appearance (blue and red)
of used representations (pieces of LEGOTM). By that the teacher
could initiate a joint reflection on the initial quantity and twice
as by being illustrated simultaneously. Table 9 summarizes the
used patterns of variation.
In cycle A and B we tried to use a variety of examples of
twice as. During the last intervention (cycle C) it was decided
to use only a few examples but to try to clearly illustrate the
relation between the initial quantity and twice as by using two
Figure 3.
The teacher and the children in group 3, project 4, examine and
discuss the differences between the tomatoes.
Copyright © 2013 SciRes. 39
Copyright © 2013 SciRes.
Table 8.
Used patterns of variation i n p roject 4 on organic decomposition.
Cycle A Cycle B Cycle C
Representations Variant—different sorts of
organic an d inorganic objects Variant—different sorts
of organic objects Invariant—one sort of organic object at a time
Level of degra dation Invariant—all obje cts were freshInvariant—all obje cts were
partly decomposed Variant—different levels of decomposition
(fresh, mouldy, soil)
Table 9.
Used patterns of variation in project 6 on the concept twice as.
Cycle A Cycle B Cycle C
Objects Variant—in some examples
wooden blocks and in some example s
a number of children Invariantonly wo oden blocks Invarianto nly pieces of L EGOTM
Meaning Invarian t — on l y twice as man y Variant—twice as many, long, highInvariant—only twice as many
Appearance of objects
illustrating the initial sum
respectively twice as
Invariant—the appearance of woode n
locks respe ctively childre n w ere the same
illustrating the initial am o unt or twice as
Invariant—the appearance of
the wooden bl ocks was the same
either illustrating the initial amount
or twice as
Variant—blue and red pieces of LEGO™
and a two colored paper were used to
separate the initial amount and twice
as simultaneously
coloured LEGOTM pieces. Relating to what was said before,
such way of arrange the situation could be said to, from a varia-
tion theoretical perspective, confuse the children as both colour
and quantity was varying. But instead it was found to make the
object of learning clear and discernible. How can this be under-
stood from the theoretical perspective?
The first intervention assumed, or even took for granted, that
the children easily or automatically discerned the main prince-
ple of twice as more or less by the teacher using the concept
twice as and showed some examples. By the use of generaliza-
tion the teacher tried to visualize that the same principle is ap-
ply able to different representations (wooden block and chil-
dren). In line with the theoretical perspective the analysis sug-
gests that it is basic to initially focus on differences rather than
sameness as generalization cannot help the learner if they have
not captured what is critical.
Figure 4.
The material used in cycle C.
During the second intervention (cycle B) the natural coloured
wooden blocks were used to make the children to separate an
initial quantity from twice as the initial quantity by discerning
these simultaneously. However, it became quite messy on the
floor when a lot of wooden blocks were placed out in a some-
what unstructured way. It was not easy for the children to
separate which wooden blocks illustrating the initial quantity
and which were illustrating twice as and on the behalf of this
also difficult to discern the contrast between the initial quantity
and twice as. When the teacher were talking about twice as
many, long and high at the same time it also might have con-
fused some of the children. Due to the variation theory it is
crucial to let only one aspect related to the object of learning
vary at the time as more may mess up the possibilities to dis-
cern what is intended to discern.
By using such varied appearance of the pieces of LEGOTM it
was also possible for the teacher to direct the children’s focus
towards the relation between theses quantities by the use of
well-known terms (blue and red). Previously discerned colours
helped this six-year-olds to discern the contrast between the
initial amount and twice as. During this intervention generali-
zation in terms of to generalise what “twice as” means, no mat-
ter of an original amount, is made discernible. According to the
test-results this seemed to be successful. By testing to vary the
representation, and then the meaning of twice as (number, size
and so on) they finally found that to separate the original
amount from twice as by the use of different colours was nec-
essary to make the children discern the relationship between the
original amount and twice as. Thus has also been found in an-
other study about halfing and doubling of numbers (Holmqvist
Olander & Nyberg, in press).
In the third intervention we used both invariation in repre-
sentations (pieces of LEGOTM) and the way of illustrating twice
(only twice as many) but variation in the appearance of the
LEGOTM pieces (blue and red) together with a two coloured
paper to separate the initial quantity from the quantity of twice
possibly to discern simultaneously but also to make the contrast
between the both visualized and clear (see Figure 4).
Patterns of Variation a Way to Support and
Challenge Early Childhood Learning?
The purpose of this article has been to elaborate on how the
use of patterns of variation designed by variation theory can
challenge and develop ECE practice. In summary, patterns of
variation seem to have something to offer when it comes to a
conscious creation and capturing of situations around which
children can think and speak. Instead of focusing on the child’s
individual development, the focus is on the object of learning
and the handling of it to facilitate learning for the child. This
means the teachers do not judge the children’s behavior or
abilities; instead they try to change the learning situation in a
way making all children discern what is going to be taught or
developed. By that, the way of using patterns of variation, the
teachers professional development gain by giving them a tool to
use in future learning situations with other children as it is re-
lated mainly to the object of learning and minor to a specified
child. The analysis has shown that a joint reflection on used
patterns of variation shows qualitative changes in the children’s
ways of discerning the object of learning before and after an
intervention. The teachers seem to have a developed ability to
sharpen the use of illustrations to make a potential critical as-
pect to “stand out”. This has been noticed in all projects, for
example project 3, cycle A, when the project group strived
against not letting everything vary simultaneously as, from a
variation theory perspective, all aspects cannot be in focal
awareness at the same time. Or in project 4 when the illustra-
tions in cycle C made the degradation process as on-going
stood out from the illustrations of organic objects in different
degrees of degradation. In this case, the experienced variation
enabled a discernment of a potential critical aspect, or in other
words it stood out from a background of sameness and the
children became focally aware of it. The need of a conscious
use of simultaneity in the concrete situation has also been high-
lighted. From a variation theoretical perspective contrast can be
used to make the children experience what something is and
what something is not by offering aspects that are in some kind
of relation to each other simultaneously (Lo, 2012; Lo & Mar-
ton, 2012). Such an example is to let the children see the origin-
nal amount together with the new amount when learning how to
double, instead of letting the original amount disappear during
the instruction (see Figure 4). This can be done in the concrete
situation or based on a previous experience and memory, if the
teacher really knows that the child really has such experience.
When analyzing the initial intervention of the projects it was
clear that the te achers in many cases took for grante d and base d
on a presumption of previous experiences of these young chil-
dren. This could be seen i.e. in project 4 when only fresh ob-
jects (cycle A) respectively only partly decomposed objects
(cycle B) were used as illustrations. On behalf of this we will
argue on the need of the teacher taking the responsibility to
afford experiences of “critical features simultaneously” (Lo,
2012: p. 61) and use such experiences afforded in the concrete
situation as basis for discussions instead of leaving to the chil-
dren to create simultaneity by her- or himself. Further on, the
projects have also pointed at the need to challenge the chil-
dren’s learning by a conscious use of separation to make the
child able to generalize as a way to contribute to create a pur-
poseful educational practice. This was intentionally used in the
first study by the use of different representations (apple, pear,
cake) to make the children aware of that half is not related to a
specific object, no matter what object a whole always become
two identical halves. To understand this, the child has to sepa-
rate what half is from the object and develop a general idea
instead. In the sixth study, the children got several different
amounts to work with, to make them separate what twice as
many are from the amount. No matter what the amount is, they
have to generalize the assumption that it takes the same amount
once and once again to get twice as much.
The analysis have highlighted and exemplified how the par-
ticipating teachers’, as the ECE LS projects progressed, created
and captured ECE learning situations in a new and, seemingly,
more carefully considered way at least regarding the design of
the patterns of variation. This new way was not about “using
variation between one particular object of learning and another
as a means of helping the learner discern and hence understand
this object of learning in a particular and singular way” (Pram-
ling & Pramling Samuelsson, 201 1: p. 9) but to use such knowl-
edge when creating and capturing learning situations might
challenge, and a joint reflection on a potential critical aspect
can make great differences. While creating patterns of variation
in this way, they supported the children to discern something
potential critical in this joint reflection rather than focused at
the child’s behavior as such. By that, they sharpened their focus
on learning content and consciously used children’s meaning
making as an indicator of potential critical aspects when creat-
ing and capturing learning situations. As far as we have found,
this is a substantial contribution to coordinate the children’s and
teacher’s perspective to a shared object of learning, enabling
them to continue with their mutual learning activity. One of our
findings is that we have seen that it takes more than one inter-
vention for the teachers to capture which aspects of the object
of learning are critical in the targeted group, but as the iterative
process allows them to try out the design more than once they
manage to find them. The second finding is the teachers chan-
ged focus from taken for granted assumptions of each child to
focusing on their own design to facilitate the child’s learning.
Finally, the aspect supposed to be discerned has to vary against
an invariant background to be discerned by the children, and to
separate the principle (e.g., to half or double) from the repre-
sentation is needed to be able to generalize their new knowl-
edge. However, the results is limited to the six studies reported
in this article, and the findings need to be supported in further
projects focusing more on the explicit use of patterns of varia-
tion to further on expand the knowledge of what the use might
afford early childhood learning and development.
We would like to thank the participating teachers who gen-
erously shared their time and teaching, and our research team
Learning Design (LeaD) at Kristianstad University, Sweden,
for encouragement and support.
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