Improving Mathematics Teaching in Kindergarten with RealisticMathematical Education

Stamatios Papadakis1 • Michail Kalogiannakis2 • Nicholas Zaranis2

� Springer Science+Business Media New York 2016

Abstract The present study investigates and compares

the influence of teaching Realistic Mathematics on the

development of mathematical competence in kindergarten.

The sample consisted of 231 Greek kindergarten students.

For the implementation of the survey, we conducted an

intervention, which included one experimental and one

control group. Children in the experimental group were

taught Realistic Mathematics according to the principles of

Realistic Mathematics Education. The control group was

taught mathematics following the basic pedagogical prin-

ciples of curriculum for kindergarten students. In order to

evaluate the mathematical performance of children we used

the Test of Early Mathematics Ability (TEMA-3). The

results showed that the teaching technique with the use of

Realistic Mathematic Education contributed significantly

to the development of mathematical competence of young

children. Moreover, factors such as gender, age and non-

verbal cognitive ability, did not seem to differentiate the

development of mathematical competence of children.

Keywords Realistic Mathematics Education �Mathematics � Early childhood education � Kindergarten �TEMA-3

Introduction

Interest in early childhood and especially in kindergarten

mathematical education is constantly increasing. Kinder-

garten education is away to counteract mathematical illit-

eracy, which nowadays is considered as detrimental as

linguistic illiteracy (Doliopoulou 2007; Clements and

Sarama 2013; Ginsburg 2004; Linder et al. 2011). A

number of research findings confirms that the teaching of

mathematical concepts in kindergarten education, as it

facilitates the transition to formal mathematical knowledge

(Nunes and Bryant 1996) by laying cognitive foundations

in children’s ability to master the systematic teaching of

‘‘real’’ mathematical concepts in later educational steps

(Balfanz et al. 2003). According to recent perceptions in

the area of mathematical teaching, in order for the above

transition to be achieved, the mathematical concepts and

ideas must be approached with the use of ‘‘context’’

problems (Van Den Heuvel-Panhuizen 2003, 2008) that are

meaningful for children and relevant to their experiences

(Ginsburg 1999; Ginsburg et al. 2004).

Researchers dealing with mathematical education

emphasize the importance and contribution of Realistic

Mathematical Education (RME) in the teaching of mathe-

matics (Treffers 1991). In contrast with the mechanistic

teaching approach for mathematics, RME ‘‘invests’’ in the

solution of a problem through children’s preexisting

informal knowledge (Van den Brink 1991). However,

while the positive influence of RME on the teaching of

mathematical concepts even in the area of preschool edu-

cation (Van den Heuvel-Panhuizen 1996, 2008) is

acknowledged, there is little research on the teaching of

Realistic Mathematics in preschool children.

The purpose of the current research is to compare the

influence of a teaching didactic approach based on RME,

& Stamatios Papadakis

stpapadakis@gmail.com

1 Secondary Education Teacher, Crete, Greece

2 Department of Preschool Education, Faculty of Education,

University of Crete, Crete, Greece

123

Early Childhood Educ J

DOI 10.1007/s10643-015-0768-4

on the development of mathematical ability of kindergarten

children.

Theoretical Background

Importance of Mathematical Training

in Kindergarten

In recent decades, there have been short periods of rein-

forcement and long periods of devaluation of mathematical

training during early childhood and particularly in kinder-

garten (Clements and Sarama 2009). Educators, under the

influence of Piaget’s views, have been forming curricula in

kindergarten, based on the perception that young children

cannot comprehend important mathematical meanings

(Ginsburg 2004). For decades, preschool and early school

age was approached as the age during which children were

engaged in childish activities without any particular ori-

entation and direction (Perry and Dockett 2002; Ginsburg

2004).

In recent years, there is a continuously increasing

international interest for kindergarten mathematical edu-

cation, as kindergarten education is identified as a high

priority target for tackling mathematical illiteracy, which

nowadays is considered as important as linguistic illiteracy

(Clements and Sarama 2013; Linder et al. 2011). Aspects

of children’s informal mathematical knowledge, such as

initial counting and problem solving, recognition of sym-

metries and geometric knowledge, are growing quite

impressively during the preschool and early childhood age,

thus forming the prerequisites for the acquisition of typical

mathematical knowledge in school (Clements et al. 2003).

On the other side, deficient teaching of mathematics in

kindergarten hinders the consolidation of basic mathemat-

ical knowledge, which is useful to children during their

following school course and the absence of which,

according to many researchers, is responsible for the extent

failure of students in mathematics. The phenomenon of

children handling mathematics very well in the classroom

while handling the same mathematics poorly in everyday

life, is common place in education (Nunes and Bryant

1996). At the same time, several international research

efforts reveal that schoolchildren cannot approach basic

mathematical concepts and problems (Chard et al. 2008;

Gersten et al. 2005; Jordan et al. 2006).

Often, teaching in kindergarten devalues children’s prior

knowledge and imposes mathematical knowledge that has

no meaning to them (Copley 1999). Mathematics will

attract children’s interest when children themselves realize

that mathematics is a tool for solving real world problems.

One way that kindergarten teachers can achieve this is by

utilizing problems from children’s everyday life as a means

of teaching mathematics. Consequently, mathematical

learning should not take place in a neutral and abstract

world in which children’s experiences have no place.

Mathematics attracts children when they can connect their

mathematical knowledge to realistic meanings, through

which they can comprehend why and how certain calcu-

lations are made for the solution of a problem (Nunes and

Bryant 1996). A modern preschool mathematical education

is not interested in imposing premade ideas and meaning-

less procedures in the minds of children. It is oriented

towards a complete multifaceted development of children

as students and as persons enabling them to think and act in

a mathematical way (Clements and Sarama 2007, 2009;

Jacobi-Vessels et al. 2014; Jordan et al. 2009; Locuniak

and Jordan 2008). Additionally, the interactions between

teachers and students in learning settings, make it a suit-

able measure for examining the quality of mathematics

teaching in kindergarten settings (Kilday and Kinzie 2009).

Realistic Mathematics Education

Realistic Mathematics Education (RME) is a mathematics

teaching theory, which was developed by the Freudenthal

Institute in the Netherlands as a reform movement that

challenged the traditional, mechanistic approach mathe-

matical education (De Lange 1996; Van den Heuvel-Pan-

huizen and Wijers 2005). On one hand, the term RME

implies the connection between mathematics and reality

and on the other hand, the fact that the teaching aims that

are set while teaching mathematics do not exceed the

ability of teachers and schoolchildren to carry them out.

The theoretical approach to RME advocates that mathe-

matical learning is a constructive activity within the social

environment, in which teachers and schoolchildren interact

and cooperate with the aim of a progressive knowledge

acquisition by children (Streenfland 1993). The desired

processes are carried out with the use of suitable instruc-

tions or ‘‘context problems’’ while, necessary ‘‘course

adjustments’’ are achieved through social interaction (Van

den Brink 1989). RME emphasizes on careful, long-term

planning of educational processes, highlighting at the same

time the value and significance of schoolchildren’s ideas,

selecting problems that quite possibly reflect their potential

experiences or/and personal interests (Shiakalli and

Zacharos 2011).

In RME, the kindergarten educational approach follows

certain paths that allow children to develop spontaneous

strategies when confronting various situations while aiming

always towards generalization (Zaranis et al. 2013). The

goal is for children to understand that the usefulness of

mathematics lies on solving problematic situations that

they model through the process of gradual mathematization

(Gravemeijer 1994). Despite their frequent vagueness and

Early Childhood Educ J

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boundary overlapping, we can distinguish two phases

during mathematization (Freudenthal 1991): horizontal and

vertical mathematization. Freudenthal (1991) briefly states

that horizontal mathematization contains a children’s

transition from the world of life to the world of symbols,

while vertical mathematization means that children tra-

verse the world of symbols. She distinction between these

two forms is not always clear because often one world can

expand in expense of the other in the favor of the educa-

tional process (Freudenthal 1983, 1991). Horizontal

mathematization practices are mainly met in the first

classes of primary school as well as in kindergarten. The

same mathematical process takes place during vertical

mathematization, as the learner faces each problem through

mathematical tools, namely with the use of abstract con-

cepts and symbols (Freudenthal 1983).

Specifically, in kindergarten, according to RME, an

elementary number sense is developed in three general

levels (van den Heuvel-Panhuizen 2008). A child conducts

in a particular level, if it ‘‘functions’’ effectively in that

level, in most cases with its participation in relatively

difficult examples. In these three levels, prior knowledge

that children ‘‘bring’’ with them when entering kinder-

garten, can be incorporated (Buys 2008). In conclusion, the

RME identifies four different levels of number sense

(ground or zero, first, second and third), which characterize

the knowledge of children about numbers, knowledge that

they have or may develop while attending kindergarten

(Fig. 1).

The relatively variable initial state, in which children,

with all their diversity, enter kindergarten, could be

described as the ground or zero level. In the first level,

basic numerical concepts such as counting calculations,

based on specific context, take place in meaningful, related

to the problem situations, in which questions like ‘‘how

many?’’ or questions in the form of comparisons may be

placed under appropriate form. The object-bound mea-

surement and calculating of the second level appears in

problem situations that focus directly on the quantitative

aspect. Unlike the first level, in this level questions like

‘‘how many?’’ are set and understood. However, children

can understand this type of problems only if the relevant

questions relate to specific objects such as ‘‘how many

pencils are in the box?’’ or ‘‘how many balloons are

there?’’ etc. (Treffers 2008; van den Heuvel-Panhuizen

2008).

Therefore, a key question that arises has to do with, how

the transition from the first (context connected) to the

second level (object connected) will be facilitated in the

most effective manner. The answer seems to lie in the

gradual push of the context to the background. The

teaching benefit from the gradual shift of the context is that

the initial condition associated with the context remains

essentially available for children who may still need it. In

this way, the context serves as a model in which children

are able to acquire the foundation they need in order to be

able to interpret and respond to the question ‘‘how?’’. This

leads them into efficient counting and calculating of

specific objects. Once the child has reached the second

level, he or she is able to work in a diverse and wide range

of measurement and calculation operations. Using pure

enumeration and calculating of the third level, a question

such as, ‘‘how many remain if I get three out of seven’’ is

understood and answered properly by the children using

their fingers. In this manner, counting ceases to be bound to

objects and it is transferred to physical or mental repre-

sentations of objects. These representations can be partic-

ularly helpful in understanding different abstract levels,

including the use of ‘‘net’’ figures. An example is the

activity in which one asks children to determine a child’s

age at a birthday party (Treffers 2008).

Study Overview

From the above theoretical context, one can deduce that it

is important to study influences on the development of

kindergar ten children’s mathematical competence, inves-

tigate a teaching practice in kindergarten based on RME

principles, and compare traditional methods of teaching

mathematics with the RME instructional approach. For this

reason, this research aims to comparing the influence

exerted on the development of the mathematical ability of

kindergarten children, by using a didactic method based on

Fig. 1 The four levels of basic

number sense (van den Heuvel-

Panhuizen 2008)

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RME. A co-examination of the effect of various other

factors, such as gender, age, and nonverbal cognitive

ability was conducted while assessing the impact of

teaching technique on the development of mathematical

ability.

Based on the literature review, we make the following

hypotheses:

H1. The initial mathematical ability performance of the

experimental group and the control group will increase

significantly after the intervention.

H2. The mathematical ability performance of children

taught mathematics with the traditional method will be

significantly lower than the mathematical ability of chil-

dren taught mathematics with the RME.

H3. The mathematical ability performance of children

taught mathematics with the traditional method is signifi-

cantly lower than the mathematical ability of children

taught mathematics with the RME, and will not be affected

by various other factors such as nonverbal cognitive ability,

gender and the age of children.

Method

Sample

Sample selection took place in October 2013. The tech-

nique of multistage or two-stage sampling—which com-

bines simple stratified sampling and cluster sampling—was

selected in order to achieve this goal (Cohen et al. 2007).

The research sample consisted of 231 kindergarten children

(116 boys, 155 girls). The age of the children ranged

between 4 and 6 years (M = 66.0 months, SD = 5.2

months). The children attended classes in public and pri-

vate kindergartens in Greece during the school year

2013–2014. The sample was homogeneous in terms of

demographics such as ethnicity and language. In addition,

before initiation of the first phase of research, all necessary

permissions were taken from the Greek Institute of Edu-

cation Policy (IEP) (No. Orig. U15/976/162735/C1).

Research Design

For the verification of the research hypotheses, an experi-

mental procedure was designed, in which the sample was

divided into two groups, the control and the experimental

group. The experimental design included three phases:

(a) the pre-experimental control phase, during which the

measurement of the dependent variable was performed;

(b) the experimental phase, during which the manipulation

of the independent variable took place and (c) the post-

experimental control phase, during which the post-control

of the dependent variable was performed. Before the

experimental procedure, the pre-research procedure took

place, in which the Greek version of the criterion TEMA-3

was tested. The Institutional Review Board (IRB) of the

University of Crete reviewed the scientific merit of the

research, the validity of the research strategy and the

adherence to the accepted practices in the respective field

of study for human subject research protocols.

Pre-research Procedure

Given that the original TEMA-3 criterion is in the English

language, in this research the researchers used a version of

the criterion TEMA-3, translated into the Greek language.

However, the simple translation or adaptation of a weigh-

ted test in the Greek language is not sufficient to transfer its

psychometric properties in the Greek reality. Therefore,

before the start of the first phase of the research, the

researchers conducted pilot implementations of the Greek

version of the TEMA-3 criterion in kindergartens not

included in the research sample. The aim was to assess

possible difficulties and misunderstandings by young

children, which possibly related to the translation of the

criterion in Greek language, the use of the supporting

material and particularly the administration of the exami-

nation. The assessment of the findings of the pilot imple-

mentation did not lead to significant changes and

modifications to the structure of the instrument or to

changes in the examination procedures.

Research Procedure

The research procedure lasted from November 2013 until

May 2014 and included the pre-experimental procedure,

the experimental intervention and post-experimental pro-

cedure. The pre-experimental procedure, which was com-

mon to all groups, took place during November and

December of the school year 2013–2014. In this phase,

children were asked to tackle questions-activities of two

different tests. The first test presented to children was the

Raven’s Colored Progressive Matrices (CPM) and the

second test was the Test of Early Mathematics Ability

(TEMA-3). The evaluation in each test lasted for

10–30 min, depending on the performance of each child.

All first phase meetings were completed prior to the start of

the teaching of mathematics in order to check the sys-

tematic mathematical teaching, which could exert a posi-

tive effect on children’s mathematical knowledge. Children

who were absent on the days the tests were administered

were not included in the sample.

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The experimental intervention took place between Jan-

uary and April of the school year 2013–2014. The activities

of the interventionist-experiential approach included

experiential games, stories and mathematic scenarios. They

were based on the RME approach and on the prior

knowledge and experiences of young children, resulting in

familiar and rich stimuli and a learning environment that

encouraged their creative imagination. The teaching aids

contained original everyday life objects and were designed

carefully to meet the daily reality of children (everyday

products, coins). Each week’s teaching intervention was

associated with a different level of number sense in pre-

school education (ground, first, second and third level)

according to the RME (Van den Heuvel-Panhuizen 2008).

In the control group, the teacher of each kindergarten in

accordance with the thematic approach conducted mathe-

matics teaching, as the Greek Curriculum of Studies for

kindergarten education defines it. Children who were

absent in more than two teaching interventions were

excluded from the survey. The second phase of the research

was completed by the end of the teaching intervention.

The post-experimental procedure was carried out in May

of the school year 2013–2014. During this phase, there was

a meeting with every child of the three groups. At this

meeting, each child was examined once again using the

TEMA-3. Testing followed the same procedure as that used

during the pre-test phase.

The ethical considerations and guidelines concerning the

privacy of individuals and other relevant ethical aspects in

social research were carefully taken into account through-

out the whole research process. Requirements concerning

information, informed consent, confidentiality and usage of

data were carefully met, both orally and in writing, by

informing the preschool staff, children and guardians on

the purpose of the study and their rights to refrain or

withdraw from participation.

Organization of Activities During the Teaching

Intervention Phase

Description of Activities in the Control Group

The objective of mathematical education in modern Greek

kindergarten is no longer the formal learning of concepts

and procedures but the development of a thinking that

exploits features of mathematics. It is intended that chil-

dren will begin to think in mathematical ways, realizing the

value of the use of mathematics in real life. Children,

through daily actions and their interaction with the envi-

ronment, gradually explore all five axes whose trajectories

are developed in the program of mathematics, such as

numbers and operations, space and geometry,

measurements, stochastic mathematics and introduction to

algebraic thinking. This management of mathematical

concepts in kindergarten education can only be approached

through interdisciplinary approaches. Interdisciplinary

unification will directly connect the school with the real

life of children in order to fully take advantage of chil-

dren’s interests, ideas, and experiences in the learning

process (Helm and Katz 2011). To achieve this aim,

teachers provide children with a well-organized learning

environment, rich in discrete and continuous materials, in

order for children to approach the mathematical ideas in

various ways, such as playing, observing, discovering

properties etc.

Description of Activities in the Experimental Group

The interventional teaching of each day, which was part of

the daily teaching routine, was devoted to the teaching of

realistic mathematics through a thematic approach. With

the term ‘‘thematic teaching-approach’’, we mean the

theme-based approach of knowledge and not the teaching

of discrete objects (Endsley 2011). The teaching inter-

vention was aimed at developing the logical-mathematical

thinking of children. The intervention activities were

designed according to the RME. They were based on prior

knowledge of children in numbers and tried to an extended

it in an entertaining way through contexts familiar to them.

The problems which children were asked to solve were

presented in the form of stories and daily activities familiar

to them, such as visiting a grocery store or a museum.

Particular attention was given to the numbers used in order

to reflect reality (tickets, commodity prices, money).

Activities were organized into four distinct levels of

increasing difficulty. For each teaching level, digital

activities followed respective experiential activities of the

same level.

With these activities, children extended their knowledge

and developed their own mental models for the mathema-

tization of problems. The activities were organized into

four levels (Van den Heuvel-Panhuizen 2008). In every

level, there was an introduction of a new learning com-

ponent, which increased the difficulty of each activity.

Figure 2 illustrates some of the experiential activities of

children.

Data Collection Instruments

Nonverbal Cognitive Ability Measurement Test

For the evaluation of children’s nonverbal cognitive ability,

the nonlinguistic Coloured Progressive Matrices (CPM)

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test was used (Raven 1956; Wright et al. 1996). This is a

nonverbal test, which was developed to assess the cognitive

ability of children between the ages of 5–11 years, and

consists of 36 questions of graded difficulty. In this test, the

oral instructions are kept to a minimum because the test

includes only visuospatial exercises with shapes following

a standard pattern or formation.

Test of Early Mathematics Ability (SELA-3)

For the evaluation of children mathematical ability per-

formance before and after the teaching intervention, the

Test of Early Mathematics Ability, third edition (TEMA-

3) was administered. The TEMA-3 was developed by

Ginsburg and Baroody (2003) and is the most updated

version of the Test of Early Mathematics Ability (TEMA)

developed by the aforementioned researchers in 1983

(Ginsburg and Baroody 2003). The TEMA-3 can be used

as a norm-referenced measure or as a diagnostic instru-

ment to determine specific strengths and weaknesses in

math skills for children between the ages of 4 years and

0 months (4–0) and 8 years and 11 months (8–11). In

short, the concepts examined by the TEMA-3 are the

identification and writing of numbers, coiunting, com-

parison of sets and sorting of numbers as well as arith-

metic operations (numbering skills, number-comparison

facility, numeral literacy, mastery of number facts, cal-

culation skills, and understanding of concepts). Each of

these abilities is represented by a set of trials and/or

questions distributed across the test and are related to the

level of knowledge which the children should have ideally

achieved at a specified age.

Results

Equivalence Checking of the Experimental Groups

Initially, the equivalence of the experimental and the

control group in terms of the children’s gender was tested.

The application of the Chi-square statistical criterion

showed that the experimental and the control group did not

differ significantly in the number of boys and girls inclu-

ded, X2(2) = .59, p[ .05. Subsequently, an analysis of

variance (ANOVA) showed that the experimental and the

control group were equivalent as to children’s age, F(1,

229) = 1.70, p[ .05 in the performance of children in the

nonverbal cognitive ability test (RAVEN), F(1,

229) = .88, p[ .05. Additionally, according to the results

of the ANOVA analysis, both groups revealed a non-sta-

tistically significant difference in terms of the performance

of children in the test of Early Mathematics Ability

(TEMA-3) before the start of the teaching intervention,

F(1, 229) = .64, p[ .05. Taking into consideration the

aggregated results concerning the formation on the

research teams, we concluded that the experimental and the

control group were equivalent in terms of: (a) age,

(b) gender, (c) nonverbal cognitive ability and (d) mathe-

matical ability, as expressed by children’s performance in

the TEMA-3 criterion.

Influence of the Experimental Intervention

in the Development of Mathematical Competence

of Children

The main purpose of this study was to investigate whether

the performance of children in mathematical ability

Fig. 2 Illustrations from the experiential activities of children

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increased significantly, after applying the techniques of

teaching using RME. According to the results of using

correlated t test there was, both in the experimental and in

the control group, increased performance of the children in

their mathematical ability, after the completion of the

experimental intervention (Fig. 3).

The difference between the performances of children in

each group during the two measurements is statistically

significant (Table 1).

Review of the Impact of the Experimental

Intervention in Performance Improvement

of Children in TEMA-3 Criterion

In addition to the final performance, it was considered

useful to investigate the effect of the experimental inter-

vention on the degree of improvement in the performance

of children in mathematical ability. For this purpose, we

calculated the difference in children’s performance in their

mathematical ability performance between the first—be-

fore the start of intervention—and the second measure-

ment—immediately after the intervention. According to

the results, the greatest improvement in the performance in

mathematical ability was demonstrated by children of the

experimental group (M = 5.94, SD = 4.43), followed by

children of the control group (M = 2.19, SD = 2.43). The

statistical control of the difference between the effects of

the experimental intervention on the degree of improve-

ment in the performance of children in TEMA-3 criterion

was performed using the ANOVA. The results indicated

that the intervention had a statistically significant effect on

the degree of improvement in the performance of children

in mathematical ability, in the experimental group, F(1,

229) = 61.52, p\ .01.

Effect of Cognitive and Other Factors

on the Development of Mathematical Ability

of Children

A key question in this study was whether the effect of the

experimental intervention in the performance of the chil-

dren in mathematical ability were affected and thus dif-

fered due to initial differences in cognition. The results of

using Pearson product-moment correlation coefficient

indicated that there was no correlation between the age of

children, r(231) = .11, p[ .05 and the nonverbal intel-

lectual ability, r(231) = .01, p[ .05, in the improvement

of their performance in mathematical ability. Respectively,

to investigated the effect of the gender of the children as a

differentiating factor in the extent of improvement in per-

formance in mathematical ability, a t test for independent

samples was applied. The results of the test showed that the

effect of gender in the improvement in the performance of

children’s mathematical ability was not statistically sig-

nificant, t(229) = -1.13, p[ .05, namely, gender did not

seem to be an influence on children’s performance in

mathematical ability.

Additionally, through the criterion of factorial variance

analysis there was a study of the effects of more than one

independent variable on the dependent variable, improve-

ment in the performance of children’s mathematical ability

and the interactions between them. The results indicated

that in all cases the only main significant effect in the

extent of improvement in children’s performance in

mathematical ability was the experimental intervention.

Table 2 summarizes the results of the effects of the main

independent variables, as well as of the interactions with

the independent variable of the experimental intervention

in the extent of the improvement in children’s final per-

formance in mathematical ability, which emerged from the

present study.Fig. 3 Initial and final performance of children groups in mathemat-

ical ability

Table 1 Means (M), standard deviations (SD) children’s mathe-

matical ability

L SD t test (df = 121)

Experimental group

Mathematical competence

Pre-test 20.74 7.20 -14.82, p\ .01

Post-test 26.68 7.97

L SD t test (df = 108)

Control group

Mathematical competence

Pre-test 21.45 6.22 -8.23, p\ .01

Post-test 23.48 6.27

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Confirmation of Research Hypotheses

The purpose of this study was to investigate and compare

the influence exercised on the development of mathemat-

ical ability in kindergarten students, by a didactic approach,

according to the principles of RME, which was applied in

the teaching of mathematics to young children. In addition,

the main purpose of this study was to examine whether the

effect exerted by the didactic approach according to the

principles of RME was affected by various other factors.

The first hypothesis (H1) was verified, as statistical

analysis showed that the mathematic didactic approach,

according to the principles of RME contributed signifi-

cantly in the improvement of children’s performance in the

criterion of mathematical ability assessment.

The second hypothesis (H2) was verified too, as that, the

performance of the experimental and the control group in

children’s mathematical ability differ significantly after the

intervention, depending on each didactic approach. In the

intervention, where teaching according to RME was

applied, children showed a higher final performance and a

significantly greater improvement in their mathematical

ability after the intervention, in comparison to the control

group.

The third hypothesis (H3) was also verified. The per-

formance of the experimental and the control group in

mathematical ability differed significantly after the inter-

vention, depending on the didactic approach, even after the

control of various other factors related to the development

of mathematical ability such as age, gender and nonverbal

cognitive ability. Additionally, the effect of the experi-

mental intervention on the improvement of children’s

performance in mathematical ability was not differentiated

by the age of children, their gender, and their nonverbal

cognitive ability.

Conclusions

Holistically, our results suggest that teaching of realistic

mathematics is a didactic approach with a positive effect,

on the development of mathematical competence in

kindergarten. Children acquire mathematical knowledge

through teaching approaches that emphasize experiential

activities and realistic problems. The active participation of

children in the resolution of those problems is considered

as an important element of a teaching environment suit-

able for the conquest of basic mathematical concepts. In

this context, the current research is consistent with other

international research (Bowman et al. 2001; Clements

2001; Sarama and Clements 2004; Jordan et al. 2006),

which indicate active involvement of children in the

learning process as the most important factor in designing

effective teaching interventions aiming at the development

of children’s mathematical ability.

This result accords well with earlier literature showing

that when the mathematical activities that take place in a

school, are meaningful and help children approach the

mathematical knowledge and discover mathematical con-

cepts through various kinds of stimuli, can effectively help

them develop their mathematical ability (Balfanz et al.

2003; Clements et al. 2003; Clements and Sarama 2013;

Ginsburg 2004; Nunes and Bryant 1996; Clements and

Sarama 2009).

Additionally, our data suggest that gender, age, and

nonverbal cognitive ability are not important influencing

factors on children’s performance with regard to the cri-

terion for the assessment of mathematical ability. The

results of the study regarding gender, are also supported by

international research (Aunola et al. 2004; Jordan et al.

2006), which shows that there is no gender differentiation

in math performance in kindergarten. The influence—at a

non–statistically significant level—of the nonverbal cog-

nitive ability on children’s performance during the last

administration of TEMA-3, is not in line with the results of

previous studies (Pascale et al. 2010; Shelton et al. 2010),

which highlight the close relationship between the working

memory and intelligence. It seems that the didactic

approach, which was used in the experimental group,

helped children who had weak memory mechanisms to

improve their mathematical ability significantly. Finally, as

far as age is concerned, the non-statistically significant

effect of children’s age contrasts the findings of other

studies that indicate age as a significant predictor of the

Table 2 Results of the effects

of the main independent

variables and their interactions

Main effects—interaction Improvement in mathematical ability

Gender F(1, 227) = 1.67, p[ .05

Gender * teaching intervention F(1, 227) = .06, p[ .05

Age F(19, 192) = .84, p[ .05

Age * teaching intervention F(18, 192) = .98, p[ .05

Nonverbal cognitive ability F(21, 195) = 1.12, p[ .05

Nonverbal cognitive ability * teaching intervention F(13, 195) = 1.07, p[ .05

The asterisk signifies interaction between the variables

Early Childhood Educ J

123

overall performance in number sense when they leave

kindergarten (Jordan et al. 2006).

Discussion: Perspectives

The low math performance of children internationally

reflects the need for a different approach to teaching math

concepts, which is distinct from the traditional approach to

learning and teaching mathematics. Kindergarten children

arrive at school with informal numeracy knowledge which

can be expanded, enriched, an developed through appro-

priately designed learning activities. Consequently, it

would be interesting for kindergarten educators during

mathematics teaching to emphasize creating a different

learning environment. More specifically, it requires the

design of learning approaches that will be linked to the

experiences of children, will attract their interest and

gradually will lead them to the construction of formal

numeracy. The didactic approach, which is based on the

principles of RME, is not particularly interested in the

instrumental aspect of knowledge. Instead, it is based on

the idea of building knowledge by the children themselves,

and is considered highly fruitful for teaching mathematics

by an increasing number of researchers. As part of this

approach, kindergartners can derive the most benefit from

their informal mathematical knowledge and use it as a

foundation for further mathematical development.

The current research has some limitations. For its pur-

poses, a teaching intervention that lasted 14 weeks was

carried out. Although the length of the instructional inter-

vention can be considered satisfactory for the experimental

verification of the effects of various teaching approaches, it

is not always found sufficient to cover the range of the

learning objectives in the teaching of mathematics in

kindergarten. For this reason, it is necessary to design and

implement instructional interventions in kindergarten

education which would be longer in duration in order to

investigate extensively the effect of various teaching

techniques on the development of the wider mathematical

competence in kindergarten.

An important extension of this study would be the

implementation of a longitudinal research in order to study

the effects of the teaching technique of Realistic Mathe-

matics Education on the development of children’s math-

ematical ability during their first grade in primary school. It

is also important to extend the investigation through a

subsequent post-control of the performance of children in

the criteria of TEMA-3 in order to investigate whether the

effects of the teaching technique using RME is maintained

over time and if the technique has contributed to a long-

term growth in children’s mathematical ability.

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