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2023 Swiss Journal of Educational Research 45 (3), 307-319
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DOI 10.24452/sjer.45.3.7 ISSN 2624-8492
This article is licensed under the Creative Commons Attribution 4.0 International License.
There is a paucity of research on Montessori Education’s impact on learning, especially in France. In this article, we
present a study comparing the development of early number learning in preschoolers through Montessori Education
with “conventional” education in France. Using a cross-sectional design and random assignment of children, we
evaluated 131 French preschoolers (aged 5-6) enrolled at the same public school following either Montessori Education
or conventional education over three years. Students were evaluated with the Woodcock-Johnson III (WJ-III) Applied
Problems sub-test and a test designed by researchers in math education. The Montessori curriculum was associated
with outcomes that were comparable to the conventional curriculum on math.
According to recent reviews, studies into the impact of the Montessori Education method on development and
learning are rare, and for the most part, conducted in the United States (Lillard, 2012; Marshall, 2017). Among
the few existing studies, some show the results of the Montessori method to be superior to other methods (e.g.
Besançon & Lubart, 2008; Denervaud et al., 2020; Lillard et al., 2017; Lillard & Else-Quest, 2006; Reed,
2008). Others show similar or even unfavorable results of the method compared to other methods (e.g. Ansari
& Winsler, 2014; Lopata et al., 2005). These contradictory results could be due to two categories of limitations,
the first being methodological limitations such as variations in the quality of implementing the Montessori
method, the absence of “active control groups” (i.e., benefiting also from an different type of intervention than
the experimental group), or inadequate sample sizes, or the second category relating to Montessori’s conception
of development, such as ignoring the role of language (Gentaz & Richard, 2022).
Our research team investigated the impact of the Montessori method during the preschool years (3 to 6
years old), as defined by the French system. In a previous article (Courtier et al., 2021), we focused on evalu-
ating executive control (such as inhibition and flexibility), social competencies (such as understanding the
knowledge, beliefs, and desires of the other) and academic achievements (especially in language and mathe-
matics). In this article, we review the results concerning academic achievement only in mathematics. Our study
used a cross-sectional design and random assignment of children, with a sample of public-school students aged
5-6 from disadvantaged backgrounds. We compared the mathematical performance of preschoolers who had
received 3 years of Montessori pedagogy with those of students who had not, using two tests: a psychometric
test, and a test specific to the study, developed by our team and based on a didactic theoretical framework.
This test enables a detailed assessment of the skills mobilized when the preschooler constructs the concept of
number.
1. Theoretical Background
1.1. Montessori Method
The Montessori Method of education was developed during the first half of the 20th century by an Italian
doctor, Maria Montessori. She first became interested in the role of sensorimotor education in the devel-
opment of children with intellectual disabilities. Eventually she began working with underprivileged children
with typical development. In 1907, she set up her own preschool classroom in Rome and applied her teaching
methods; it became her laboratory, where she established the basics of the Montessori Method (Montessori,
2015, 2016). From her observations, Maria Montessori defined and proposed her guiding principles for child
development, which she used as a basis for her philosophy and educational method.
Her first principle claimed that children are born with an “absorbent mind” (Montessori, 2015, p. 48), and
a motivation to learn. Second, she posited that the child passes through “sensitive periods”, during which they
are particularly receptive to understanding specific learning domains easily and rapidly. Finally, she asserted that
The impact of the Montessori education on early
number learning in french pre-schools
Marie-Caroline Croset, Université Grenoble Alpes
Philippine Courtier, Éducation Nationale – Académie de Créteil
Marie-Line Gardes, Haute école pédagogique du canton de Vaud
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not all children progress at the same speed through these sensitive periods, therefore each child must be allowed
to activate their sensitive period at the most appropriate time for them.
In the classroom, these principles translate into various specifications concerning the environment available
to the children and the role of the teacher. First, classrooms have mixed age groups; for example, in the preschool
environment, children range from 3 to 6 years old. Second, children move from one self-chosen activity to
another, they choose how long they spend on each activity, who they would like to work with, and where
they would like to work. A child can repeat each activity as many times as they wish during the three years of
Montessori Education. Third, the material has some specifications; materials automatically provide feedback,
and only one set of each activity is available per classroom. The materials are laid out on small shelves in
the classroom, organized according to level of difficulty and grouped by educational domain. These domains
include practical life, sensorial, language, mathematical, geography, biology, music and visual arts (Montessori,
1934a, 1934b). Fourth, the role of the educator is to present each activity to the children and ensure that the
students choose activities of an appropriate level of difficulty. Finally, the activities are presented almost exclu-
sively in small groups or one-on-one.
1.2. Studies Investigating the Impact of the Montessori Method on Learning
Mathematics in Kindergarten
The effects of Montessori pedagogy on child development may be contradictory or moderate, but Deman-
geon’s recent meta-analysis of 33 studies (Demangeon et al., 2023) shows that, in terms of academic success,
this pedagogy appears to produce significant and positive effects. Only a few studies have specifically compared
the mathematical advancement of children in Montessori programs with children in conventional educational
programs in preschool, and their results showed mixed outcomes (e.g., Laski et al., 2016; Lillard & Else-Quest,
2006; Mix et al., 2017; Reed, 2008; Wexley et al., 1974). As our study focuses on math and preschool, we
present a few studies on the impact of Montessori pedagogy on success in math before 2nd grade, and try to
highlight their limitations.
In 1974, Wexley and colleagues compared children aged 3 to 5 from disadvantaged backgrounds in a
Montessori program with children in a conventional day care program. They used a matched pairs design,
considering age, sex, race, socio-economic status, number of parents in the home, and number of years spent
in an educational context. These groups were also compared to two control groups (one group of children
from an advantaged background and the other from a disadvantaged background) who were not enrolled in
any program. Cognitive development was evaluated using the Weschler Preschool and Primary Scale of Intelli-
gence (WPPSI) (Weschler, 1967) and other cognitive tests. This study showed that the students enrolled in the
Montessori program had better results in arithmetic than the control group (not enrolled in any program) from
a disadvantaged background. However, the Montessori group was no different from the children in the daycare
program, or the control group (not enrolled in any program) from an advantaged background.
In 2006, Lillard & Else-Quest conducted an evaluation of the Montessori Method by using a lottery-based
allocation system. All parents who participated in this lottery were interested in enrolling their child in a
Montessori program. The families not drawn from the lottery were enrolled in other education systems and
assigned to a control group. In total, American children of 5 years old– and 12 years old – were compared on a
series of cognitive measures. For the measure of mathematics knowledge, the group used the Applied Problems
subtest from Woodcock-Johnson III (Woodcock et al., 2001). They observed a significant difference in favor of
the Montessori group for the 5-year-old children, but not the 12-year-olds.
In 2008, Reed compared understanding of calculation and place-value concepts among children in 1st grade
through 3rd grade enrolled in Montessori schools and conventional schools. The students in the Montessori
classrooms performed better than the students in the conventional classrooms on the two tasks concerning
place-values of a digit. This was particularly true for the 1st grade group, where 71% of Montessori classroom
students succeeded in one of the tasks, as compared to 13% of conventional classroom students. In the addition
tasks, presented by line to the students, the students in the Montessori program used more sophisticated
techniques. No significant difference was found for the addition tasks completed in columns. The author
interpreted the results as demonstrating a superior utilization of the principles of order of operations among the
students enrolled in Montessori programs.
More recently, Lillard (2012) conducted a study on children aged 3-6, questioning the importance of
Montessori implementation fidelity. In this research, she observed the impact of pedagogy on various skills;
in terms of mathematics, she showed that children from high fidelity schools perform better than those from
lower fidelity schools (offering materials other than those promoted by the Montessori pedagogy). In this
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study,
however, it is worth noting that the sample sizes were quite small and there was no randomization of
children.
Laski et al. (2016) obtained similar results in a longitudinal study investigating understanding of place-
values and arithmetic in 150 children enrolled in Montessori and non-Montessori educational contexts. The
children were tested (time point 1) at the end of kindergarten for a first cohort, and at the end of 1st grade for
a second cohort. The same students were tested again two years later (time point 2), either in 2nd grade for the
first cohort, or 3rd grade for the second cohort. At time point 1, the students were tested on their understanding
of the place-value system and on their performance of calculating addition problems. At time point 2, they
were evaluated on their performance of resolving comparison problems in symbolic writing and various math
problems. The authors found that at time point 1, the children in Montessori programs had better results on the
task evaluating understanding of the place-value system, but no differences were visible two years later.
Mix et al. (2017) evaluated students aged 5 and 7 enrolled in Montessori or conventional programs from
the age of 3. There were no significant differences between these two groups on the decimal numeral system
or division at the age of 5. However, the students enrolled in the Montessori program fared better than the
students in the conventional group at the age of 7. No differences were found between the groups at age 5 or 7
in a number line estimation task (i.e., ability to place numbers on a physical line). It should be noted that the
teachers in the Montessori group had been trained by the AMI (Association Montessori Internationale).
Finally, Denervaud et al. (2020) evaluated scholastic development in a cross-sectional study of kindergarten.
They showed that Montessori kindergarteners outperformed children from traditional schools in academic
outcomes. A single competence was used to assess the numeracy skills of kindergarteners, solving 10 arithmetic
word problems. In terms of these skills, the Montessori Education groups produced positive results. One of the
limitations of this study is that the Montessori classes were all in private schools, whereas the traditional schools
were public.
In conclusion, these studies seem to indicate that compared to conventional methods of education, the
Montessori Method generally leads to better performance in tests of certain mathematical competencies in
primary school. However, these results should be interpreted with caution. There have been few studies, all
of which have multiple methodological limitations. For example, the assignment to experimental and control
groups in most of these studies was not randomized (except for Lillard & Else-Quest, 2006). Even in this study,
all parents were supportive of their children’s enrollment in the Montessori system, which limits the external
validity of the study to the general population of public school students. Some of the papers cited give no infor-
mation about how well the schools included in the studies adhered to the principles of the Montessori method
(Laski et al., 2016; Reed, 2008). Furthermore, some studies tend to overgeneralize the results of tests that
measured a limited range of mathematical competencies (Denervaud et al., 2020). Finally, apart from Dener-
vaud’s research, all these studies were conducted in one world region only, namely the United States. Therefore,
in the following section, since our study was conducted in France, we will specify the unique characteristics of
early childhood education in France.
1.3. French school system
In France, primary school (for 3- to 10-year-olds) includes the stages of preschool (for 3- to 6-year-olds) and
elementary school (for 6- to 10-year-olds) (Figure 1). Preschool, as understood in France, is free, attended by
nearly all children from the age of 3, and has recently become mandatory as of the 2019 school year. In other
words, all children in France between the age of 3 and 6 years old are expected to attend school. Preschool
(ages 3-6) is therefore an integral part of the education system in France: teachers working in preschools have
received the same training as teachers at elementary level. A preschool teacher teaches all disciplines of study
and is responsible for a single class consisting, on average, of 25 students. This class may include multiple levels
or groups. Every teacher refers to the educational program, which is set by a board of academics, researchers,
education specialists, and elected representatives of the country and wider society (Ministère de l’Éducation
Nationale et de la Jeunesse [MEN], 2023).
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Figure 1
Primary School in France
This compulsory “preschool” - equivalent to pre-school, pre-kindergarten and kindergarten in the United
States, and reception and year 1 in the United Kingdom - is a characteristic of the French system. The French
government, bolstered by low rankings of French students in international assessments such as the PIRLS and
the PISA, is prioritizing school attendance in preschool years as essential for student achievement. These aspects
of the French system - mandatory school attendance at the age of 3, the same training program for preschool
and elementary school teachers, and the existence of an educational program establishing nationwide expec-
tations of students – mean that our research group can study children as young as 3 years old in a classroom
setting. Indeed, since children in other countries rarely attend school from the age of 3, it is quite rare for
educational research to be carried out in real-life learning conditions.
1.4. Teaching numbers in France
During the preschool years in the French public school system, the objective of the mathematics curriculum is
for each child to understand that a number can express both a quantity of a set and a rank in a list. Learning
numbers is based on understanding quantity, both written and spoken codification, oral number sequencing,
and counting (MEN, 2023). The French mathematics curriculum is based on research in mathematics education
and recommends a balance between a concrete approach with manipulative and conceptual understanding of
numbers. It is similar to the Common Core State Standards for Mathematics (CCSSM) in early childhood in
the US, which are based on a “balanced approach that includes both understanding and fluency and generally
moves in each math domain from meaning making and supporting understanding of concepts to a focus on
practice to gain fluency to prepare for the next level of conceptual learning” (Clements et al., 2019, p. 13). Like
CCSSM in early childhood, learning numbers in French preschool precedes the introduction of the decimal
number system. Students are not given learning activities centered on place value; the topics of grouping and
exchange, recognizing the connection between the position of a digit, and the number of groupings are first
tackled in elementary school, not preschool (Margolinas & Wozniak, 2014). No time is dedicated at this stage
to mathematical operations.
In a didactic study, Croset and Gardes (2020, 2020) mapped the early understanding of numbers. This
study is based on various research results in math education (Fayol & Seron, 2005; Fischer, 1990; Fuson,
1988; Margolinas & Wozniak, 2012, 2014). Eleven types of tasks were identified to test the different areas of
knowledge necessary for early understanding of numbers. These task types were categorized into three groups
based on the use of the number in the given setting; the use can be cardinal, meaning the number is used as a
measure of quantity, ordinal, meaning the number is used as a measure of position, or the number can be used
out of a practical context (i.e., without support of magnitude). For each type of use, tasks can require coding
or decoding actions (Fayol & Seron, 2005), association of numbers, comparison of numbers, or anticipation of
the result of an action. Examples are given in Figure 2. These eleven types of tasks characterize the mathematical
field we consider in this study, henceforth referred to as ‘number construction’. We will use this conceptual
framework to describe what we have assessed as competencies in this study. The advantage of this framework -
over that of the National Research Council (2009) or the National Council of Teachers of Mathematics (2023)
- is that it is adapted to the French school system and, by virtue of its construction, gives a complete overview
of the skills involved in learning the concept of number.
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Figure 2
Map of number construction development in preschool (Croset & Gardes, 2020)
2. Present study
In summary, various features distinguish our study from previous studies in this field. First, the present study was
conducted in a French public school, in a disadvantaged area. Second, students enrolled in the study followed
the same type of education for three years, both in the Montessori classrooms as well as the conventional class-
rooms. Children were assigned to one of these classrooms on entering school at age 3. All children included in
the analyses of this article followed the same pedagogical approach during the three years of schooling, and their
teachers were trained to teach the entire age range, from 3- to 6-years-old. In studies on monitoring learning
achievement, there is generally some attrition of students (moving, absence during assessments (see below),
etc.). For this reason, we collected data on 3 cohorts of students; each cohort followed the same pedagogy for
3 years and was tested at the end of this period, in June 2017, 2018, and 2019 respectively. Third, the control
group and the experimental group were in the same school and the group assignment was randomized. Finally,
the educational and didactic competencies and perspectives of the research team allowed us to clearly outline
the specific tasks used to understand the concept of numbers in each pedagogical approach. In this article,
we aim to closely analyze what skills are learned, and to investigate the following research question: Are there
differences between the Montessori and conventional teaching methods concerning the completion of each type
of task described in Figure 2?
3. Method
3.1. Participants and procedure
We evaluated 131 French preschoolers enrolled at the same public school: 53 children were taught according to
the Montessori method (27 girls), and 78 children in a control group (40 girls) were taught with the conven-
tional method used in French public schools. Three cohorts of students were tested in June 2017, 2018, and
2019 respectively. The data were collected over 5 years to increase the number of participants in the same school
(see Figure 3). The experiment was approved by the local school board and conducted in accordance with the
ethical standards established by the Declaration of Helsinki.
Initially, 160 students were eligible to be included in the study. Of these 160 students, 29 were excluded
because parental consent was not given (n = 10), they changed education program (n =12), were not fluent in
French (n = 3), had a diagnosed disability (n = 3) or were related to a staff member (n = 1). All the children
retained for the study followed three years of the same type of education, either Montessori or conventional.
Furthermore, of the 131 students who remained, two students were excluded from certain tasks because of
absence or refusal to complete the task.
Code
Decode
Associate
Compare
Order
Anticipate
How many tokens?
Give me four tokens
Go nd as many garages
as there are cars
Which group has more
tokens in it?
How many tokens
are in the box?
What position is the blue pearl in?
Show me the 7th pearl
Place a rabbit in the same wagon
as the one on the model train
Who is the closest
to the nish line?
What will the next
position of the pawn be?
How do you write
the number three?
Which number is
larger?
How much is 7 + 5?
Cardinal use Ordinal use Out of practical context
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Figure 3
Chronology of the study
The school is in a disadvantaged area (the school comes under the French ‘Reinforced Priority Education
Network’) and has multiple classrooms of children aged 3 to 6. There are two types of classrooms in the same
school: multi-age Montessori classrooms (3-, 4- and 5-year-olds), and conventional classrooms with maximum
of one or two age groups (3- and 4-year-olds or 4- and 5-year-olds).
Some teachers already occupied their post in the school at the start of the research, and therefore stayed for
the five years of the experiment, while others were in the post for just one year. Also, some teachers worked in
their classrooms full-time, and others part-time (so that some classes, whether Montessori or conventional, had
two teachers each week). In addition, three teachers were on maternity leave over the course of the project and
were therefore replaced for part of the year. None of the teachers in the Montessori classrooms were trained in
an AMI (Association Montessori Internationale) center at the beginning of the experiment. They held a degree
from a conventional teacher’s college (minimum requirement in France), and initially were largely self-trained
in Montessori Education only. By the end of the study, however, one teacher in the Montessori-public group
had completed AMI training.
To ensure that our findings would be reproducible and generalizable to other contexts, we quantified the
fidelity of implementation of the Montessori pedagogy in the preschool of our study using a scale based on
the characteristics and activities of both Montessori and conventional classrooms (see Courtier et al., 2021).
Overall, the Montessori group scored relatively high on the characteristics (above 80% fidelity) and activities
scales (above 86% fidelity), whereas the conventional classrooms scored relatively low (above 20% fidelity on
characteristics and above 5% fidelity on activities scales). For information, an accredited Montessori School
obtains 92% on characteristics and 83% on activities scales. We therefore obtained a high fidelity of the imple-
mentation, and ensured that the two groups were very different from the point of view of applied pedagogy.
The teachers randomly assigned the children to their classrooms on enrollment in the school. The students
were tested individually at the end of preschool, after three years of one type of education (conventional vs.
Montessori). At the time of testing, students in the Montessori classes were on average 5.94 years old (SD =
0.28), while students in the conventional classes were on average 5.98 years old (SD = 0.29). The ages of the two
groups did not differ significantly, t(129) = -0.65; p = 0.52. For more information, see Courtier et al. (2021).
3.2. Measures
The students were evaluated with the Woodcock-Johnson III (WJ-III) Applied Problems sub-test (Woodcock
et al., 2001). This subtest was translated by our team into French. The test consists of 63 items of increasing
difficulty; one point was awarded for each item successfully solved therefore the score could range from 0 to
63. After six consecutive errors, the test was stopped. This test was chosen because of its use in prior studies,
especially Lillard & Else-Quest (2006), Lillard (2012) and Lillard et al. (2017). The accompanying manual states
that the test is a measure of quantitative reasoning, or mathematical knowledge and competencies (Woodcock
et al., 2001). However, matching items on the test to the concepts on the map in the theoretical background
of this paper (Figure 2) allows us to determine that the first 30 items of the test only evaluate coding/decoding
(11 tasks) and additive problem solving (11 tasks). There are no items which test comparing numbers, ordinal
use of numbers, or construction of an equivalent collection. This test does not consider the complexity inherent
in mathematical skills, as described in Figure 2. This ties in with the results of Peteers (2020) who analyzed
this and other tests designed to evaluate basic mathematics skills with various theoretical frameworks, such as
Zareki-R (Dellatolas & Von Aster, 2005) and Tedi-Math (Van Nieuwenhoven et al., 2001). Using didactical
analysis criteria, the authors highlight the shortcomings of numerical cognition tests in relation to what is
taught and knowledge of mathematics education.
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Therefore, in addition to this test, we created the Mathematical Didactic Diagnosis Test (Appendix 1), based
on the map of the development of number construction in preschool (Figure 2) to evaluate the expectations of
a French public preschool. The first task, essential for counting, asks the student to recite their numbers as far
as they can (T1). This task is a continuous variable, as compared to the other tasks presented below. Seven other
types of tasks were chosen from the eleven presented in Figure 2. Tasks related to comparisons and anticipation
of positions, or calculation of numbers out of context were not retained for the assessment because they fell
outside the expectations of the program of national education in France. The tasks included in this assessment
are concrete, using tokens that the children can manipulate themselves. We present the tasks below, showing in
brackets their connection with the elements presented in Figure 2 (see appendix 1 for details).
Determine the cardinal (number of elements) of a set (T2)
Construct a set with a given cardinal (T3) [Code/Decode, cardinal use]
Solve simple arithmetical problems (addition or subtraction of an element from a set) (T4) [Anticipate,
cardinal use]
Construct a set of the same number of elements as another set (T5) [Associate, cardinal use]
Compare the cardinal of two sets (T6) [Compare, cardinal use]
Name written numbers (T7) [Code/Decode, use numbers out of context]
Identify the rank of a given element in a list (T8) [Code/Decode, ordinal use]
Identify a rank in a list and reproduce it in another list (T9) [Associate, ordinal use]
For tasks T2, T3, T4, T5, T6, and T9, we proposed varying subtasks of increasing difficulty. For example, in
task T2, the children first identify the cardinal of a set of 3 tokens, then 7 and finally 11. At the end of these
subtasks, a child’s score can range from 0 to 3, based on their success in identifying the cardinals. The score is
then averaged to achieve a minimum score of 0 and a maximum score of 1. In total, the children were tested on
33 subtasks divided into 8 tasks, giving them a total score between 0 and 8.
Children were tested individually in a quiet room at their preschool. The tests were administered by different
testers (graduate students, research assistants, and undergraduate students) over five sessions of approximately
15 to 20 minutes. The order of sessions was randomized on a child-to-child basis. No feedback was given to
children during testing, and children, teachers, and parents were not informed of the results for the duration
of the study. Teachers and parents were unaware of the test content until data collection had been completed.
3.3. Analyses
The data were analyzed using both frequentist and Bayesian inference tests. First, we compared the total scores
on the two tests (Applied Problems and Mathematical Didactic Diagnosis Test) and on each of the tasks in the
Mathematical Didactic Diagnosis Test using frequentist independent t-tests or Chi squared tests. We used a
significance threshold of p = .05. The effect size was quantified using Cohen’s d.
However, since frequentist statistical methods do not allow us to invalidate the presence of a difference
between the two groups of students when the effect is not significant, we also completed the analyses using
Bayesian statistical methods. These allowed us to evaluate the measure of strength of evidence using the Bayes
factor (BF) in favor of the alternative hypothesis of a difference between these groups (H1), as compared to the
null hypothesis of an absence of a difference between the groups (H0) for each test.
We used Jeffreys (1961) guidelines for interpreting BFs: a BF < 3 is considered anecdotal evidence, a 3 <
BF < 10 is considered substantial evidence, a 10 < BF < 30 is considered strong evidence, a 30 < BF < 100 is
considered very strong evidence, and finally, anything above 100 (100 < BF) is considered extremely strong
evidence. The BF is indicative of the likelihood that the data are more probable under the alternative hypothesis
than the null hypothesis (i.e., BF10), or under the null hypothesis than the alternative hypothesis (i.e., BF01).
Given the contrasting information found in the literature on the impact of the Montessori Method, these
Bayesian tests were completed using default priors. The analyses were performed with Jamovi software (Jamovi
Project, 2019).
4. Results
4.1. Applied Problems test
53 students in Montessori classrooms and 77 students in conventional classrooms were tested with the WJ-III
Applied Problems subtest. The students in the Montessori classroom had a mean score of 16.74 (SD = 3.14)
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and the students in the conventional classroom had a mean score of 16.66 (SD = 3.67). A Student’s t-test
showed substantial evidence for the null hypothesis, t(128) = 0.12, p = 0.91, d = 0.02, BF01 = 5.26 (Figure 4).
Figure 4
Score out of 63 on the Applied Problems test by pedagogical method
4.2. Mathematical Didactic Diagnosis Test
52 students in Montessori classrooms and 76 students in conventional classrooms were tested with the Mathe-
matical Didactic Diagnosis Test. Of the 131 students who remained, two were excluded from this Didactic Test
because of absence or refusal to complete the task. The counting knowledge score (T1, continuous variable) was
dissociated from the quantitative knowledge score (T2-T9) to facilitate interpretation.
Regarding the first task (T1), which evaluated the stable capacity to count, the mean was 46.38 (SD = 44.73)
for students in the Montessori classroom and 50.08 (SD = 113.84) for students in the conventional classroom.
A Student’s t-test showed substantial evidence for the null hypothesis t(126) = -0.22, p = 0.82, d = -0.04,
BF01 = 5 (Figure 5).
Figure 5
Score of counting knowledge by pedagogical method.1
1 Six data points greater than 100 do not appear on the figure to ensure it remains legible. The data points are at 102, 201, and
256 in the Montessori group, and 121, 201, and 999 in the Conventional group.
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The Montessori group obtained a total mean score of 5.82 (SD=1.17) out of 8 for tasks 2 through 9, while
the conventional group obtained a total mean score of 6.08 (SD=1.11) out of 8. A Student’s t-test showed
anecdotal evidence for the null hypothesis, t(126) = -1.27, p = 0.21, d = -0.23, BF01 = 2.5.
Since the results of T2 through T9 contributed individually to the total score reported above, the individual
results for each of these tasks are reported below (Table 1).
Table 1
Results by task on the Mathematical Didactic Diagnosis Test
Task Mean Hypothesis test BF
Montessori Conventional
T2
T3
T4
T5
T6
T7
T8
T9
0.79 (0.27)
0.84 (0.29)
0.73 (0.29)
0.26 (0.36)
0.95 (0.15)
0.98 (0.12)
81%
0.46 (0.33)
0.78 (0.26)
0.87 (0.26)
0.71 (0.29)
0.35 (0.38)
0.97 (0.12)
0.97 (0.10)
86%
0.57 (0.31)
t(126) = 0.30, p = 0.77 , d = 0.05
t(126) = -0.78, p = 0.44, d = -0.14
t(126) = 0.32,p = 0.75, d = 0.06
t(126) = -1.32, p = 0.19, d = -0.24
t(126) = -0.62, p = 0.53, d = -0.11
t(126) = 0.51,p = 0.61, d = 0.09
χ²(1 ; N = 128) = 0.51, p = 0.48
t(126) = -1.92, p = 0.06 , d = -0.35
BF01=5
BF01=4
BF01=5
BF01=2,38
BF01=4,35
BF01=4,55
BF01=2,44
BF10=1.01
In conclusion, the Student’s t-tests and the Chi squared test indicated substantial evidence for the null hypothesis
between the means for tasks 2, 3, 4, 6, and 7. Meanwhile, t-tests and Chi squared tests for tasks 5, 8, and 9 did
not allow us to draw conclusions about the presence or absence of a significant difference between the means of
the two groups (they showed anecdotal evidence for the null or alternative hypothesis).
5. Discussion
This study shows that there is no evidence of a difference in mathematics test performance at the end of the
preschool years between the groups of students who were taught using the Montessori Method compared with
conventional pedagogical methods. These results are consistent with the results of Ansari & Winsler (2014)
who tested a large sample of pre-schoolers from low-income backgrounds on cognitive tasks such as counting.
The same is true of the study by Lopata et al. (2005) on a large sample of children which shows no significant
difference in favor of Montessori pedagogy on mathematical skills.
These results were obtained with an experimental protocol, with the presence of a control group. First, we
have a randomized group distribution, without any parental intervention. The parents chose the school for
its location, and not for its pedagogical practices. In addition, children were randomly assigned to one of the
pedagogies. In Lillard & Else-Quest’s study (2006), parents entered their children in a lottery for their children
to attend a Montessori school. The parents were therefore clearly invested in school choice for their child, and
most likely in their child’s education in general as well. Thus, parental involvement could explain the difference
in results between the Montessori students from this study as opposed to our study. Secondly, interventions
into real-life learning context inevitably raise questions about the fidelity of implementation of educational
programs (Fixsen, 2005). Lillard (2012) outlined that implementation could vary greatly from one class to
another. In our study, we quantified the fidelity of implementation of the Montessori pedagogy as described
above. Since the experiment was conducted in the same school, contamination effects could have occurred. This
was not the case: Montessori classrooms were still far more faithful to Montessori Education than the conven-
tional classrooms, which scored very low on our fidelity scale. Both groups (Montessori vs. conventional) seem
to be therefore quite distinct. Third, we carried out didactic analysis on the mathematical skills expected by the
French school system. Studies comparing the skills of students in Montessori and conventional education do
not always consider this complexity inherent in mathematical abilities. For instance, in their longitudinal study,
Lillard et al. (2017) showed a global improvement in learning: ‘[The results] show significantly greater growth
in academic achievement across preschool for children enrolled in Montessori preschool [...] than waitlisted
controls.’ (p. 9-16). However, the authors grouped the results of the language tests (vocabulary and reading)
and mathematics (problem solving and calculations) in the same measure, under academic competencies’. In
our study, we have chosen to use a test that, according to our theoretical framework, exhaustively assesses the
skillset involved in number construction.
2023 SJER 45 (3), DOI 10.24452/sjer.
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To summarize, with a randomized distribution of participants, an accurate implementation of Montessori
pedagogy, and a didactical analysis of the skills involved, we found that the Montessori method in public
preschool leads to gains in math skills that are similar to a conventional preschool curriculum.
Nevertheless, our study has limits. First, teachers were not randomly assigned to the test conditions. This
might have introduced some bias. The sample size was also constrained by the number of children attending the
schools for the duration of the study. This influences the generalizability of results. Secondly, only one teacher
in the Montessori group completed Association Montessori Internationale (AMI) training and the others were
self-trained in Montessori Education. This may have had an impact on the results. Even if the implementation
of the pedagogy seems correct, the training of teachers could be improved. A third limit could be related to the
evaluated content. In our study, we chose to use a test that, according to our theoretical framework, exhaustively
assesses the skillset involved in number construction. However, the two mathematical evaluations we used do
not provide any information on certain skills targeted by the Montessori method, such as understanding the
decimal system or calculations. As mentioned, recent studies (Laski et al., 2016; Mix et al., 2017) have shown
that students in Montessori classrooms show higher success rates than students from conventional classrooms
on tasks evaluating understanding of the decimal system.
In future, studies with larger sample sizes, randomized selection of participants, high rigor for implemen-
tation of the Montessori program, and didactic approaches towards mathematical abilities are necessary to
further explore this question and confirm these preliminary results on precise mathematical performance.
6. Conclusion
The goal of the study presented here was to evaluate the impact of the Montessori Method on mathematical
competencies in a disadvantaged preschool. Specifically, we focused on the competencies necessary to under-
stand number construction as defined by Croset & Gardes (2019, 2020). The methodology was a randomized,
cross-sectional study of a sample of children enrolled in the same school for three years. We showed that
the students in a Montessori classroom exhibit no differences in performance compared with students in a
conventional classroom in the Applied Problems sub-test of Woodcock-Johnson III, with a substantial level of
evidence. Similar results were obtained in a test made up of nine tasks that allow for the evaluation of a range
of crucial competencies in number construction. At a time when both critics and committed supporters of the
Montessori educational approach are working to determine the true effectiveness of its methods, and the French
government is in the process of reviewing teaching objectives in mathematics (Villani & Torossian, 2018), an
analysis of this kind appears particularly pertinent and timely.
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Keywords: Early numerical abilities; Montessori education; didactical analysis; preschool; disadvantaged area
2023 SJER 45 (3), DOI 10.24452/sjer.
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Marie-Caroline Croset, Philippine Courtier et Marie-Line Gardes
Varia
Auswirkungen der Montessori-Pädagogik auf das frühe Zahlenlernen in
Französischen Vorschulen
Zusammenfassung
Es gibt nur wenige Untersuchungen über die Auswirkungen der Montessori-Pädagogik auf Lernergebnisse,
insbesondere in Frankreich. Wir stellen eine randomisierte kontrollierte Querschnittsstudie vor, welche das
frühe Zahlenlernen bei französischen Vorschulkindern, die drei Jahre lang eine Montessori-Pädagogik durch-
laufen haben, mit der von Kindern vergleicht, die eine “konventionelle” Pädagogik durchlaufen haben. 131
Kinder (5-6 Jahre) wurden mit dem Untertest “Applied problems” des Woodcock-Johnson-III-Tests (WJ-III)
und mit einem in der Mathematikdidaktik entwickelten Test beurteilt. Die Schülerinnen und Schüler, die
nach der Montessori-Pädagogik unterrichtet wurden, erzielten in Mathematik vergleichbare Ergebnisse wie die
Schülerinnen und Schüler des “herkömmlichen” Lehrplans.
Schlagworte: Frühe numerische Fähigkeiten; Montessori-Pädagogik; didaktische Analyse; Kindergarten;
benachteiligtes Umfeld
Impact de la pédagogie Montessori sur l’aptitude numérique précoce à l’école
maternelle française
Résumé
Il existe peu de recherches de l’impact de la pédagogie Montessori sur les apprentissages, en particulier en
France. Nous présentons une étude transversale contrôlée randomisée qui vise à comparer le développement du
concept de nombre chez des enfants de maternelle française ayant suivi pendant 3 ans une pédagogie Montessori
à celui d’enfants ayant suivi une pédagogie « conventionnelle ». 131 enfants français de grande section (5-6 ans)
d’une même école publique ont été évalués avec le sous-test « Applied problems » du test Woodcock-Johnson III
(WJ-III) et avec un test conçu en didactique des mathématiques. Les élèves ayant suivi la pédagogie Montessori
obtiennent des résultats comparables à ceux du programme « conventionnel » en mathématiques.
Mots-clés : Aptitudes numériques précoces ; pédagogie Montessori ; analyse didactique ; école maternelle ;
milieu défavorisé
L’impatto della pedagogia Montessori sull’apprendimento precoce dei numeri nelle
scuole materne francesi
Riassunto
Esistono poche ricerche sull’impatto della pedagogia Montessori sull’apprendimento, soprattutto in Francia.
In questo articolo, presentiamo uno studio trasversale, randomizzato e controllato che mira a confrontare lo
sviluppo dell’apprendimento precoce dei numeri in bambini in età prescolare provenienti da un’educazione
Montessori e da un’educazione “convenzionale” in Francia. Nell’ambito dello studio, sono stati valutati
131 bambini in età prescolare (5-6 anni) iscritti alla medesima scuola pubblica che hanno seguito l’educazione
montessoriana o quella convenzionale per tre anni. I bambini sono stati valutati sia con il sottotest Woodcock-
Johnson III (WJ-III) sui problemi applicati, sia con un test progettato da ricercatori nel campo dell’educazione
matematica. I bambini che hanno seguito la pedagogia Montessori hanno ottenuto risultati paragonabili a
quelli che hanno frequentato il programma «convenzionale» in matematica.
Parole chiave: Abilità numeriche precoci; pedagogia montessori; analisi didattica; scuola dell’infanzia; ambiente
svantaggiato
2023 SJER 45 (3), DOI 10.24452/sjer.
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Marie-Caroline Croset, Philippine Courtier et Marie-Line Gardes
Varia
Marie-Caroline Croset is an associate professor in the field of didactics of mathematics and a mathematics
teacher trainer in Grenoble (France). Her current research focuses on learning and teaching numbers from
nursery school to high school, using a combination of qualitative and quantitative research methods.
Université Grenoble Alpes, Bât. IMAG, 700 av. Centrale CS 40700 - 38058 Grenoble CEDEX 9 - France
E-mail: Marie-Caroline.Croset@univ-grenoble-alpes.fr
Philippine Courtier is a psychologist of the French Education Nationale in Paris. She defended her PhD in
developmental psychology at the Lyon Neuroscience Research Centre in 2019. Her work focused on the impact
of Montessori pedagogy on the cognitive, social and academic development of disadvantaged kindergarteners.
Éducation Nationale – Académie de Créteil, 4 Rue Georges Enesco, 94000 Créteil
E-mail: philippine.courtier@gmail.com
Marie-Line Gardes is a full professor at the Haute École Pédagogique in Lausanne. She is a teacher trainer
at primary and secondary level and a researcher in the didactics of mathematics. Her research focuses on
teaching and learning of mathematics through problem-solving and on learning difficulties and disorders in
mathematics. She is also interested in the links between research in the cognitive sciences and in the didactics
of mathematics.
HEP Vaud, Avenue de Cour 33 - 1014 Lausanne
E-mail: marie-line.gardes@hepl.ch
Appendix 1
Description of the Mathematical Didactic Diagnosis Test
Skill Description Items Maximum score
T1 Counting Knowledge The child was asked to count as high as possible.
She/he was asked to do the task twice.
Highest number
reached
T2 Code. Determine the
cardinal of a set (“How
many” task)
The child was asked to count and say how many
elements there were.
3, 7, 11 3
T3 Decode. Construct
a set with a given
cardinal (“Give n” task)
The child was asked to put an amount of tokens
into a cup.
5, 12 2
T4 Arithmetical trans-
formations problem-
solving
The child was presented X arithmetical problems
that involve transformation (i.e., “There are x
tokens in my hand. If I add y tokens, how many
tokens will there be?” or “There are x tokens in my
hand. If I take away y tokens, how many tokens
will there be?”)
3 + 1 = ?, 3 + 2 = ?,
3 - 1 = ?, 3 - 2 = ?, 6 +
1 = ?, 6 + 2 = ?, 6 - 1 =
?, 6 - 2 = ?)
8
T5 Construct a set of
the same number of
elements as another set
The child was asked to match a set of the same
number of elements as another set (i.e., “In one
trip, get just enough red tokens to put on top of
the blue tokens. You must take that many and you
can’t go back for more”).
5, 12 2
T6 Compare the cardinal
of two sets
The child was asked to compare the cardinal of
two sets (i.e., “Which pile has the most tokens?”)
(2 vs. 3, 8 vs. 9) 2
T7 Name written numbers The child was presented 9 flashcards with numbers
on them. (i.e., “What number is this?”)
1, 3, 2, 5, 4, 6, 8, 9, 7 9
T8 Identify the rank of
a given element in a list
The child was presented seven tokens. 1st, last, 3rd 3
T9 Reproduce a rank of a
given element in a list
in another list
The child was asked to match a rank of a list
with another list (i.e., “Here’s a model train with
wagons. There is a token in a wagon. Now I hide
this model train. Here’s another train. Can you
place the token in the same place as the one in the
model train?”).
3, 7, 13 3
