ORIGINAL ARTICLE

Challenges and opportunities for the implementationof inquiry-based learning in day-to-day teaching

Jean-Luc Dorier • Francisco Javier Garcıa

Accepted: 21 May 2013

� FIZ Karlsruhe 2013

Abstract In this paper, we analyse the conditions and

constraints which might favour, or on the contrary hinder, a

large-scale implementation of inquiry-based mathematics

and science education, on the basis of our work within the

PRIMAS project in 12 European countries. As a comple-

ment to the approach through the analysis of teachers’

beliefs and practices (see Engeln et al. in ZDM Int J Math

Educ 45(6), this issue, 2013), we tackle this issue from a

systemic institutional perspective. Indeed, in our approach,

we consider teachers as actors of institutions, representing

some disciplines, embedded in a school system, sharing

some common pedagogical issues, in relation to society.

Our sources of information are easily accessible public

documents. With a theoretical background from Cheval-

lard’s anthropological theory of didactics, we organized

our analysis according to four levels of institutional orga-

nization that co-determine both content and didactical

aspects in the teaching of mathematics and sciences:

society, school, pedagogy and disciplinary. Our approach is

systemic in the sense that we do not focus on teachers as

individuals, nor on the curricula, the organization of

teachers’ training or the textbooks themselves. Rather, we

trace the way the conditions and constraints are operative,

provide the main results of our analysis and draw out a few

perspectives according to our four levels of didactical

determination. Finally, in the conclusion, we reflect on the

limits and potential of our analysis.

Keywords Inquiry-based learning � Ecological analysis �Anthropological theory of the didactics � Didactic

transposition � Scale of levels of didactic determination

1 Introduction

This work is based on our common work in the context of

the PRIMAS European project which aims at promoting

the use of inquiry-based mathematics and science educa-

tion (IBMSE) in everyday practice on a large scale through

the design of actions in terms of professional development

and dissemination to various target groups including par-

ents, school authorities and politicians. This project

involves 14 teams from 12 countries,1 and one of the first

aspects of our work was to analyse the conditions and

constraints which might favour, or on the contrary hinder,

the PRIMAS implementation actions in each country. The

aim of this paper is to give an international overview of the

results of this analysis of the context which in turn facili-

tated the implementation. By contrast with Wake and

Burkhardt (2013), our analysis did not aim at influencing

policy.

Although it is a widely used term, there is no precise,

concise, commonly shared definition of IBMSE. It ‘‘refers

to a student-centred paradigm of teaching mathematics and

science, in which students are invited to work in ways

similar to how mathematicians and scientists work. This

means they have to observe phenomena, ask questions,

J.-L. Dorier

Faculte de Psychologie et des Sciences de l’Education,

University of Geneva, 40, Boulevard du Pont-d’Arve,

1211 Geneva 4, Switzerland

e-mail: Jean-Luc.Dorier@unige.ch

F. J. Garcıa (&)

Departamento Didactica de las Ciencias, University of Jaen,

Campus de Las Lagunillas s/n, Edificio D2, 23071 Jaen, Spain

e-mail: fjgarcia@ujaen.es

1 Cyprus, Denmark, England, Germany, Hungary, Malta, the Neth-

erlands, Norway, Romania, Slovakia, Spain and Switzerland.

123

ZDM Mathematics Education

DOI 10.1007/s11858-013-0512-8

look for mathematical and scientific ways of how to answer

these questions (like carrying out experiments, systemati-

cally controlling variables, drawing diagrams, calculating,

looking for patterns and relationships, making conjectures

and generalizations), interpret and evaluate their solutions

and communicate and discuss their solutions effectively’’

(Dorier and Maaß 2012).

IBMSE, which is clearly related to constructivism

approaches, is a complex and multifaceted notion, which

interacts with different issues. The schema shown in Fig. 1,

produced within the PRIMAS project, visualizes some of

the different dimensions involved.

Nowadays, there is a large consensus about the benefits

of IBMSE (Hiebert et al. 1996; Feldon et al. 2010; King

et al. 2008; Minner et al. 2010). In particular, it is very

often seen as a means to improve poor results in students’

achievement and the decreasing number of students that

choose mathematics or science for university studies by

offering some more attractive and supposedly efficient

teaching methods. This last aspect, in particular, has been

acknowledged in Rocard et al. (2007), which led to support

from the recent European Union Framework programs with

the aim of achieving a wider implementation of IBMSE.

Yet, the main issue is to find ways to promote IBMSE in

order to bring about a change across Europe in the teaching

and learning of mathematics and sciences with teachers

using IBMSE in everyday teaching. Ultimately, the

objective is to have a greater number of students with more

positive dispositions towards further study of these subjects

and the desire to be employed in related fields. Through the

PRIMAS project, IBMSE class materials for teachers’

professional development, as well as supporting activities

for teachers and out-of-school target groups, have been

developed and disseminated. Analyses of educational pol-

icy and of the perception of IBMSE in Europe are also

included in the project (see Wake and Burkhardt 2013).

Finally, an evaluation of the impact of the actions is made

from a quantitative perspective with questionnaires (before,

during, and after the actions) and on more qualitative

perspectives with case studies. The analysis of the contexts

in the 12 countries of the consortium is a key element in

order to ensure maximum potential leverage and impact for

the measures to be taken in the project and the optimal use

of existing structures and materials to make this impact

cost-effective.

2 Theoretical background and methodology

2.1 Theoretical background

The purpose of the present paper, based on this analysis of

the context, is to point to existing factors, structures,

opportunities and obstacles that might help or hinder the

widespread implementation of IBMSE in each country, not

only at the individual or school level, but also on the larger

scale of regions, countries or all across Europe. That means

quite a radical change in teachers’ practices. In this pro-

cess, teachers are the actors and vectors of changes and

consequently play a central role. It is therefore necessary to

uncover their current beliefs and teaching practices (see

Engeln et al. 2013). However, beyond this individual

dimension, teachers are part of a complex system, with its

own dynamics, conditions and rules, affecting and shaping

their actions. It is essential, as a complement to the indi-

vidual approach, to have an institutional one, focusing on

Fig. 1 The multiple dimensions

of IBMSE

J.-L. Dorier, F. J. Garcıa

123

the conditions and constraints that could favour or hinder a

wider implementation of IBMSE. We aim at identifying

some of these conditions, where they come from, and to

analyse to what extent they can be considered as factors

that could be overcome, or as inevitable limiting con-

straints. Following an ecological metaphor, this is a way to

take into account the systemic dimension of education, as

well as the social and cultural background in which it takes

place.

The Anthropological Theory of the Didactic (ATD),

developed in the field of the French ‘‘Didactique des

mathematiques’’ by Chevallard since the 1980s, offered us

a suitable general framework, with some adaptations. It is

not the focus of this paper to present this theory in detail,2

so we only briefly give some key points in order to justify

the methodology we present in more detail below.

ATD originates in the now famous notion of Didactic

Transposition (Chevallard 1985), from which Chevallard

started building a model of the educational system as a

complex structure of different institutions (Chevallard

1992a, b, 2002, 2011).

An individual, as a subject of an institution, is con-

strained by a certain official relation to the objects of

knowledge he/she has to deal with (Chevallard 1992a, b).

Nevertheless, these institutional constraints leave a certain

leeway (marge de manoeuvre): ‘‘persons are the makers of

institutions which in turn are the makers of persons. Gen-

erally, however, institutions come before those persons—

their ‘subjects’—thanks to whom they will continue to

exist and change. So that, in order to understand what

persons are made of, we have to understand how institu-

tions live, develop or recede’’ (Chevallard 2006, p. 4).

Conditions and constraints are determinant factors in

order to understand how a didactic system works. In this

approach, one distinguishes the content of the teaching in

terms of mathematical/scientific organization and the way

it is taught in terms of didactic organization. But these two

aspects cannot be separated: they are co-determined (i.e.

determined in their mutual interaction) by a hierarchy of

institutional levels, which successively condition and

constrain each other.

This hierarchy provided by the ATD helped us in

structuring our analysis of conditions and constraints of the

systems in the various countries of our consortium. For our

purpose, we did not use the whole apparatus of this theory.

The first level we took into account concerns the way the

Disciplines (mathematics, biology, physics, chemistry,…)

are conceived in the curricula and through the didactical

resources at the disposal of teachers. But beyond the dis-

ciplines, there are other non-content-specific constraints

that affect what happens in school. The level of Pedagogy3

is considered here as the general teaching principles

included, explicitly, in the description of the curriculum of

an institution and, implicitly, in teachers’ shared profes-

sional culture. Then the level of School captures conditions

and constraints emerging from school as a social institu-

tion. It takes objective issues into account such as how the

general curriculum is structured, the division into disci-

plines, the time allocated to each, the fact that teachers are

mono- or pluridisciplinary, their initial training, etc.,

reflecting a specific understanding and philosophy of

school as a social institution. The next level deals with

Society, to be considered as a wide and ill-structured

institution where the general debate about education and

schooling takes place. It includes the institutional organi-

zation of the educational system in a country or a region,

the most general level of the curriculum, etc.

This categorization takes into account the various

sources from which we collected the information, but

structures them differently. For instance, the curricula

reflect different layers of influences depending on whether

you look at the levels of discipline (precise contents to be

taught), pedagogy (general teaching principles), school

(curriculum structure), or society (general orientation in

education). All four layers show different types of condi-

tions or constraints for teaching mathematics and sciences

that might hinder or favour IBMSE at different levels, and

are important to sort out in order to optimize the possible

actions within the PRIMAS project and beyond. The same

can be said for the structure of pre- and in-service teachers’

training, and also didactical resources and national

assessments. All of them are conditioned and constrained at

these four various levels. In the following list, we show the

related issues that we identified as relevant to the imple-

mentation of IBMSE in regard to these four levels, and

which provided a structure for our analysis of the data we

collected in the 12 countries of our study:

1. Society level Specific role of mathematics and sciences

in society, tradition or recent changes in education

relevant to IBMSE.

2. School level (global organization) Differentiation

between primary, lower and upper secondary educa-

tion, pre-service and in-service teachers’ training

structures, etc.

2 Some key reports on the ATD can be found at http://yves.

chevallard.free.fr. Also Bosch and Gascon (2006) offer a recon-

struction of the evolution of the theory from the didactic transposition

on.

3 One may be surprised to not see a level devoted to didactics, but

this is included in the level of the discipline and in its interaction with

the level of pedagogy. Within the model of ATD, it is not possible to

separate the knowledge (mathematics or sciences) from the way it is

taught (didactics); they are both sides of a same coin.

Challenges and opportunities for inquiry-based learning

123

3. Pedagogy level Education law, general statements on

pedagogy, tradition in education (transmissive or

constructivist tradition, place of the learner,…), type

and role of national assessments, etc.

4. Disciplinary level Links between mathematics and

sciences in the curricula, integrated science or separate

subjects, etc., mathematics and sciences’ place in the

curricula (number of hours), competence of teachers in

mathematics and sciences (profile of teachers), type of

curricula in mathematics and sciences (signs of

IBMSE?), types of resources for teachers in mathemat-

ics and sciences (textbooks, web, etc.). Are mathematics

and science teachers using IBMSE? Why? Is it a

requisite in the curriculum, or even in the textbooks, and,

if not, why not?

2.2 Methodology

As has been said above, the aim of the analysis of the

context was to (1) facilitate the implementation of the

PRIMAS activities and (2) provide an international

analysis in order to give an overview of the PRIMAS

partner countries. The above-mentioned four levels of

determination help to differentiate between the various

factors in the analyses of constraints and conditions that

characterize the teaching of mathematics and sciences in

different countries regarding the implementation of

IBMSE.

From a methodological perspective, our work is based

on existing information and analysis. Each national team

had to identify relevant and reliable documents, publica-

tions and reports in order to dissect their national context.

The four levels guided the collection and interpretation

process. The information the partners had to look for

consists mainly of facts (such as: Is IBL in the curriculum?

How are teachers educated?). Subsequently, using methods

such as coding was not considered to be necessary in

relation to the aims of the analysis.

As uniformity on each national analysis was needed in

order to be able to extract some conclusions and perspec-

tives at a transnational level, as well as to compare the

situations between countries, we did not claim to have

made a comparative study.

Therefore, the project partners were provided with:

1. A description of the ATD framework, and its speci-

fication to our goal.

2. For each level of co-determination, a set of possible

sources they might use to identify conditions and

constraints coming from each level (Table 1).

3. A structured document, according to the levels of co-

determination, to produce their final report.

Each country used a great variety of resources for

gathering the necessary information. These resources can

be divided into the following categories:

• Official national documents, such as the national

curriculum and other official documents that explain

how the educational system is structured and how the

teaching and learning of mathematics and science is

officially conceived.

• National reports about the teaching of mathematics and

science and, in general, about the educational system

(e.g. from inspection, academic societies, national

organizations, trade unions). These documents can be

useful to get the ‘‘real’’ situation, in contrast with the

‘‘official’’ one, as well as reasons for possible

deviations.

• Research papers, nationally situated, dealing with

topics including the teaching of mathematics and

science, teachers’ initial training and professional

development, school system, assessment, interpretation

and/or reaction to international comparative studies.

These documents complement the previous ones,

helping us to understand the real status and motivations

of mathematics and science teaching.

• European regulations and reports including those

produced by the European Parliament and the European

Commission. They are quite relevant in order to

identify conditions and constraints emerging from

European policies (see also Wake and Burkhardt 2013).

• International reports coming from comparative studies

including PISA, TIMSS, TALIS or TEDS-M, as well as

other OECD reports. These are relevant in order to

dissect both the national reality (students’ achievement,

dominant teaching practices, teacher education,…) and

to understand the impact of the international debate on

the national context.

Each country analysed their relevant documents in order

to explain the conditions and constraints that might affect a

widespread use of IBMSE. Following the aim of facilitat-

ing the implementation of the PRIMAS activities, we did

not seek a detailed comparative analysis, for which rigor-

ous methodological standards of large-scale assessments

would have been necessary. Given the time and budget

constraints, we adopted a pragmatic way of making an

analysis as rich and reliable as possible.

In order to make the data collection as rich, but also as

uniform, as possible across the 12 countries, a working

session during one meeting of the consortium was set up

during the data collection process to share experiences and

discuss difficulties. Moreover, in each country the data

collection was discussed and enriched within each of the

National Consultancy Panels (NCP), which have been set

J.-L. Dorier, F. J. Garcıa

123

up in every country with local groups of teachers, unions,

scientists, teachers’ trainers, researchers in education,

school authorities, policy makers and parents. Therefore,

the panels include actors in each country at various levels

of the educational systems, each one an expert in their field.

Then, the synthesis at the international level was orga-

nized through our general framework with regular

exchanges with the national teams, in order to eventually

address some issues when necessary. From this interna-

tional synthesis, we extract some important ‘‘perspectives’’

for a successful implementation of IBMSE (Sect. 4).

Finally, after 2 years, each country was asked to com-

plement its initial report based on the first 2 years of the

PRIMAS project by highlighting two or three major points

that particularly hindered, or on the contrary favoured, the

realization of PRIMAS objectives, that is, the implemen-

tation of professional development in order to promote the

use of IBMSE. The present paper takes into account the

initial report and these complements.

3 Results

3.1 Society level

The situation in the 12 countries involved in our analysis,

regarding tradition in education and the place of mathe-

matics and sciences in society, is quite varied.

Political, historical, cultural and even religious back-

grounds have been reported to be behind the way mathe-

matics and sciences are conceived within society, as well

as to explain teaching traditions. Differences such as, for

instance, transmissive versus more student-oriented peda-

gogies, or centralized systems with a strong power from

Table 1 Sources to be considered to inform each level of co-determination

Level of

determination

Sources

Civilization/society Historical account of the role of mathematics and science in your country, both in teaching and in general. Influence of

great educators, mathematicians or scientists

Local traditions for teaching mathematics and science

General socio-economical constraints that could have influenced orientations in education

General orientations of teaching at different levels in your country or region (this could be in the introduction of the official

curriculum or in other official documents such as guidelines about how the curriculum should be implemented or about

the role school should play within society,…)

National reports about the situation of the teaching of mathematics and science in your country (from teachers’

professional associations, from the ministry of education, from private institutions, from other projects, from universities,

from groups of experts,…)

Interviews with key actors (for instance, educational authorities, teachers’ associations, parents’ associations…)

General guidelines and structures for pre-service and in-service teacher training. Socio-economic contexts that may

condition the recruitment of teachers

School Official documents about school organization, the distribution of subjects in the school system, time allocated to

mathematics and science education in school, possibility of implementing IBMSE in school, flexibility in the

organization of the teaching at school, possibility of teachers’ training in the school, national assessment,…Structure of pre-service and in-service teachers’ training

Autonomy of school in its organization regarding the national or regional curriculum and regarding professional

development

Interviews with key actors including educational authorities, teachers’ associations, school principals,…)

Pedagogy General pedagogical principles to deliver the curriculum: does it suggest any relation to IBMSE?

Other official documents setting important pedagogical issues that may affect the teaching of mathematics and science at

school as well as the training of teachers

National reports explaining how mathematics/science are taught and professional development is implemented

Sources with information about dominant teaching practices. The official documents may not be sufficient

Interviews with key actors such as teachers’ associations and experienced teachers and trainers

Discipline Official curricula in mathematics and science. Specific instructions for each sub-disciplinary level that might be relevant

for IBMSE. Role of assessment

Textbooks in mathematics and science: are the mathematical, scientific or didactic organizations at stake in textbooks

compatible with IBMSE? What could be an obstacle?

Interviews with experienced teachers. Are they already using IBMSE or something similar? If not, why? And would they

be reluctant to use it?

Challenges and opportunities for inquiry-based learning

123

national or local governments versus decentralized ones

with higher teacher/school autonomy, or the social role of

science education, have been reported as emerging from

these backgrounds and giving rise to opportunities and

challenges for the widespread use of IBMSE.

In spite of all these differences in tradition, which may

have still been quite important in the last decades, in recent

years there has been a common trend in all of the countries

for the promotion of educational paradigms in mathematics

and sciences in which students should be more active,

resulting in sometimes quite radical changes. Therefore,

the curricula are less content-centred and more formulated

in terms of competencies in relation to the outside world.

This movement has been encouraged, in all countries, by

the publication of PISA results. Indeed, the orientation of

PISA towards developing competencies and thinking and

reasoning processes, instead of standard routines and iso-

lated concepts, is creating favourable conditions for the

adoption of IBMSE. It is also a consequence of the influ-

ence of the educational debate at the European level (see

Wake and Burkhardt 2013) and, particularly, of the Euro-

pean framework for key competencies.4 These can be

interpreted as opportunities for spreading IBMSE.

There are also important negative factors appearing in

several countries. One is due to the succession of reforms

in recent years in many countries, resulting in a rejection of

change by teachers and sometimes by parents. In some

countries as well, this has resulted in a resurgence of ideas

defending a return to traditional, pedagogical paradigms

and to fundamental contents such as reading and counting.

Indeed, in several countries, in spite of official new cur-

ricula in favour of IBMSE, the lobbying for a more tradi-

tionalist pedagogy may be very strong.

International studies such as TIMSS5 or TALIS6 have

provided evidence that traditional transmissive practices

predominate in everyday classes in many countries. In the

TALIS report, for instance, what they call structuring

teaching practices are pointed out as dominant. These

include professional gestures such as explicitly stating the

teaching goals, doing a summary of previous lessons,

homework review, checking the exercise book and checking

students’ understanding by questioning. On the other hand,

TALIS showed that teaching practices such as student-

oriented practices (including students working in small

groups to solve a problem or student self-evaluation) as

well as enhanced practices (such as project-oriented work,

making a product or students participating in a debate) are

less used.

Therefore, dominant teaching practices act as a clear

constraint for the implementation of IBMSE, which chal-

lenges teachers’ self-perceived role in the classroom and

forces them to adopt a different position. Even if they are

aware of what their role should be,7 overcoming teachers’

current practices is a major challenge for any action that

foresees a wider use of IBMSE.

3.2 School level

In all 12 countries, in primary schools mathematics is

taught at each level, usually with a rather substantial

number of hours, while science is always taught as an

integrated subject but with a small number of hours.

However, it appears that in many countries, primary school

teachers do not regard mathematics and science as their

favourite subjects, which might be a difficulty for imple-

menting IBMSE at this level.

The organizations of lower secondary schools are more

varied. The lower secondary phase is between three and six

years long, depending on the country. It is usually undif-

ferentiated for all children but may also be selective (for

example in Germany). In most cases, the structure of lower

secondary education is close to that of upper secondary

education. However, in some countries the structure still

reflects primary education (and appears more like upper

primary than lower secondary education) with generalist

teachers (Denmark) or bi-disciplinary teachers (Slovakia

and Hungary). Sciences might be integrated or already

divided into two or three different subjects (not all neces-

sarily taught at each level). The curriculum includes some

mathematics and some sciences in all cases, but the number

of hours is quite different from one country to another.

Teachers are usually mono- or bi-disciplinary specialists.

Upper secondary education is also quite varied. It is

between 2 and 4 years long and is usually differentiated

and selective. Mathematics is taught in nearly all branches,

although not always in non-science and technology bran-

ches at the end of the curriculum. Science education varies

quite considerably depending on the specialty and is usu-

ally divided into two or even three different subjects

(physics, chemistry and biology/geology).

Therefore, the division and distribution of subjects in

primary and secondary schools does not appear as an a

priori restriction for the implementation of IBMSE. Indeed,

the integration of sciences might be seen as an opportunity

for tackling more open problems, which are normally not

restricted to a single school discipline. Also, the later dif-

ferentiation into single-discipline subjects (e.g. physics,

4 OJ L 394, 30.12.2006.5 Data extracted from Hiebert et al. (2003).6 Data extracted from OECD (2009).

7 The TALIS report shows a clear contradiction between teachers’

beliefs about teaching (more constructivist-oriented) and their current

teaching practices (more structured than student-centred).

J.-L. Dorier, F. J. Garcıa

123

chemistry, biology) might have neither positive nor nega-

tive effects on the implementation of IBMSE. However,

the number of hours for which each discipline is taught at

school might be considered as a major constraint, espe-

cially in the case of sciences in both primary and lower

secondary schools. Although the situation varies from one

country to another, it is well known that the lack of school

hours is a barrier to IBMSE very often mentioned by

teachers (Deters 2005).

In relation to the initial teachers’ training, in most

countries primary school teachers are trained at a special

institute or a university for at least 3 years (up to 5). The

training is mainly in educational sciences, but in most cases

it includes courses in didactics of mathematics and sciences

(that may be IBMSE orientated, but this is not the majority

of cases). Didactics of mathematics and sciences usually

represent a small part of the training; in very rare cases,

teachers’ initial training is complemented with mathemat-

ics and/or science courses, while in most countries some

mathematics and/or scientific issues, normally very close to

the primary school syllabus, are included in the courses in

didactics.

Upper secondary teachers, by contrast, usually have at

least a 3-year (up to 5) university degree in mathematics or

one science subject. On the other hand, their pedagogical

training varies from nearly nothing up to 2 years (usually

partly in service) and includes some didactics and some-

times some courses in IBMSE and/or modelling. The

training of lower secondary school teachers is less uniform.

In some countries it is the same as upper secondary, while

in others it is more like primary with a specialization in one

or two subjects.8

Teachers’ initial training might be a significant con-

straint hindering a consistent use of IBMSE. Indeed, most

primary school teachers and some lower secondary school

teachers lack a sufficiently deep and broad understanding

of mathematics and science. This is not the case for most

lower secondary and upper secondary school teachers.

Nevertheless, IBMSE is not dominant in teachers’ initial

training. As a consequence, their relation to subject

knowledge rarely reflects any IBMSE perspective. This

does not favour IBMSE, and may even hinder it in the long

term since initial training may influence teachers’ practices

for their whole career, as teachers’ knowledge and beliefs

(about the nature of science, student learning, and the role

of the science teacher) have a major impact on their

teaching practices (Keys and Bryan 2001).

The issue of in-service teachers’ training and profes-

sional development appears to be a very important one

(Anderson 2002), and particularly so in the case of the

PRIMAS project. It seems to be the one key issue in order

to change teachers’ practices, and all of the national teams

had to find ways to make optimal use of the existing

structures. However, this appeared to be quite problematic

with very different conditions in each country of the

consortium.

The supporting infrastructure for providing in-service

professional development is quite different in each country.

However, it is possible to distinguish between countries in

which professional development is delivered mainly by

institutions directly connected to the national/local gov-

ernments (Romania, Spain, Norway, Slovakia, Switzer-

land) and other countries where another kind of institution

(both public and private) also offers professional devel-

opment (Denmark, England, the Netherlands).

Nevertheless, in both cases PRIMAS partners report that

in-service training is very loosely controlled and the

training mainly consists of one- or two-day sessions mostly

organized by volunteer teachers who do not have a specific

qualification as trainers. In their national analysis, partners

could hardly find any national or local professional

development strategy specifically focused on IBMSE.

Obviously, this does not mean that there are not courses

that promote this approach, but there is not a sustained and

systematic strategy aimed at supporting teachers in their

professional development towards IBMSE. Anderson

(2002) refers to the limited in-service teacher education as

a barrier for the implementation of IBMSE. Indeed, he

argues that preparing IBMSE teaching is more than a

technical matter, and that the political and cultural

dimensions are important as well. Wake and Burkhardt

(2013) also raise some aspects of this issue.

3.3 Pedagogy level

At all levels of education, and in all the PRIMAS countries,

the general education laws (or equivalent) advocate some

type of pedagogy that completely supports IBMSE (which

does not mean that IBMSE is explicitly included in all of

them). Indeed, with different formulations, one finds rec-

ommendations in all countries for developing students’

creativity, supporting open problems with reference to

everyday life in which students can develop their person-

ality in a balanced manner and prepare for social and

professional life. National curricula advocate a construc-

tivist approach where teachers do not lecture, but organize

activities and help students develop their own access to

knowledge with respect to diversity, trying to eliminate

inequalities. One also finds recommendations for less

memorization and more student initiative, development of

analytical and critical skills, and sometimes even project-

based pedagogies.

8 The validity of these statements (both in the case of primary and

secondary teachers) is restricted to the training programs PRIMAS

researchers and NCP members are familiar with.

Challenges and opportunities for inquiry-based learning

123

Moreover, most countries have adopted a description of

the curriculum in terms of competencies rather than just

contents. This results in a tendency to encourage cross-

disciplinary and interdisciplinary activities. Transmissive

practices are condemned, sometimes explicitly, in official

documents. The general idea is to open schools to the

outside world and give students the means to live in a

modern world, characterized by an increasing rate of

change and a necessity for rapid adaptation to new

situations.

Certainly, there is a real homogeneity in the description

of the intended pedagogy in all countries’ official docu-

ments. This clearly reflects an actual international orien-

tation in educational policies, which is a real opportunity

for IBMSE. It also reflects the favourable conditions we

have identified previously at the society level (Sect. 3.1).

Moreover, in some countries IBMSE is a real opportu-

nity to supply the means to fulfil some of the political

requirements by providing support to teachers, parents and

ultimately students.

Yet, beyond this uniformity, there are various situations.

In some countries, this orientation in pedagogy is very

recent (Cyprus, Germany, Hungary, Malta, Romania, Slo-

vakia, Spain). In others, by contrast, there is a long tradi-

tion of constructivist pedagogy (England, Norway, the

Netherlands, Denmark, Switzerland). In some countries,

for example Germany, the change has been quite radical

since the first PISA study results.

However, even if educational policies are in support of

IBMSE, it does not mean that this actually reflects teach-

ers’ practices. This is actually the black spot in all coun-

tries. The reasons evoked vary from one country to another

but are always a mixture of the following, with different

apportioning of weight depending on the national context

(past and recent) and the cultural background: lack of

training for teachers who have usually never experienced

IBMSE as students (related to the constraints identified in

Sect. 3.2); resistance to change; weight of traditions

(related to the conditions identified in Sect. 3.1); and lack

of time (for teachers the first priority is to accomplish all

the contents listed in the program). Moreover, in many, if

not all, countries, the resistance does not only come from

teachers but also from students or maybe even parents and

the society as a whole. This reflects a tension between

intended changes and future perspectives at the society

level promoted by trans-national regulations (see Sect. 3.1;

see also Wake and Burkhardt 2013) and the current state of

our societies.

The situation of course differs from country to country.

For instance, in the countries where the change in policies

is more recent and the tradition of transmissive teaching is

still active, the necessity for change is more radical in order

to achieve the new requirements. This might be positive in

terms of motivation: IBMSE offers effective strategies to

implement the new curriculum coherently with the national

(regional) regulations. By contrast, in those countries

where the change in policy dates back to the 1970s or

1980s and the transmissive tradition has been criticized

since then, IBMSE seems like a reheated pot and old ten-

sions and negative reactions are reactivated from detractors

of constructivism. Nevertheless, the case of the later

countries confirms that changing the curriculum is not

enough for systemic changes to occur. The lesson learnt

from them is that, besides policy changes towards IBMSE,

long-term professional development and continuous sup-

port are necessary for IBMSE to become a reality in

school.

Finally, at the pedagogy level, the issue concerning

national assessment is also important. This undoubtedly

also reflects choices in the pedagogical policies and,

moreover, it may help or hinder the adoption of IBMSE by

teachers. Here as well, in several countries (but not all) the

national policies have evolved in the sense of less tradi-

tional assessment, taking into account the changes in the

educational policies, as well as, in some countries, the

results and spirit of international evaluations such as PISA.

Yet, in many cases the changes are slow and not always

sufficient to really encourage IBMSE.

3.4 Disciplinary level

The programs in all countries of our consortium, with more

or less emphasis, stress the applied dimension of mathe-

matics and science, mainly to daily life and to other dis-

ciplines. References to problem-solving in the case of

mathematics, and the scientific method in the case of sci-

ence, are abundant. Even terms such as modelling and

inquiry are easy to find in most curricula or programs.

Processes such as observing, analysing, planning, explor-

ing, formulating hypotheses, experimenting, constructing,

modelling, setting a work-plan, solving problems, reason-

ing, communicating, developing logical and critical

thinking,… can be found in the official documents we have

analysed in all countries. Therefore, the epistemological

conception of mathematics and science is clearly support-

ive of IBMSE.

An important issue regarding IBMSE concerns the

possibility of building some bridges between different

disciplines. Everywhere, mathematics and science have

traditionally been taught as separate subjects. In most

countries, though, a new tendency is emerging with the aim

of building more coherence between the disciplines. For

instance, in primary education in Germany, they say: ‘‘On

the one hand, mathematics is the tool to answer scientific

questions and solve problems. On the other hand, science

offers the topics for teaching mathematics and allows the

J.-L. Dorier, F. J. Garcıa

123

acquisition of mathematical competencies.’’ In Switzer-

land, the new curriculum regroups mathematics and sci-

ences for all mandatory education in one single domain

with some common goals, even if the core of the

description in the curriculum remains divided. In the

Netherlands as well, a new subject integrates at least two

subjects in thematic learning units. In Spain, the curriculum

has now shrunk, with common competencies to be devel-

oped in all disciplines. The regional curriculum for

Andalusia clearly points out that connections between

school disciplines should be made. In Denmark, the cur-

riculum for secondary school explicitly requires some

interactions between mathematics and the various science

subjects. In Norway, there is a strong emphasis on the

competencies of culture and modelling and general mod-

elling, which include the formulation of mathematical

models based on observed data, the use of technological

tools, mathematical proof and practical experiments.

However, even in these countries, and obviously in the

others, the disciplinary division is traditionally strong. In

regard to science, it is usually taught as a single integrated

subject in primary education, but it breaks into two or even

three different disciplines usually starting from lower sec-

ondary education. It is therefore a challenge for PRIMAS

to provide opportunities to build bridges between the var-

ious disciplines by using IBMSE-orientated common

activities in mathematics and the different science subjects.

As we mentioned above, in most countries the level of

qualification in mathematics and sciences is low for pri-

mary school teachers. In many countries, science education

in primary education in particular seems to be lacking

consistency. Mathematics is usually seen as more impor-

tant, but its teaching is usually traditional and transmissive

in spite of new curricula. In lower secondary education,

teachers’ disciplinary qualification is a bit better, yet in

several countries teachers have to teach two or three sub-

jects while only being properly qualified in one (in some

countries, mathematics may be taught by teachers who

have a university degree in science but not in mathematics,

or physics may be taught by teachers with qualification in

biology,…). In upper secondary education, teachers’ dis-

ciplinary qualification is mostly adequate, sometimes even

excellent. However, their didactical qualification may be

very poor in some cases, and is rarely in IBMSE.

An important issue regarding teachers’ practice con-

cerns the use of resources, especially textbooks, but also

web resources, including didactic literature. In this matter,

the situations in the countries analysed are very different.

In most countries, though, it seems that teachers (especially

in primary and lower secondary education) rely consider-

ably on textbooks. In a majority of countries, these can be

chosen freely either by schools or teachers themselves. In

some countries, however, they are imposed by government

policy or are even specific official documents (Switzer-

land). In most countries, the use of web resources of all

kinds is becoming more and more popular, although not

always with much critical supervision. Textbooks provid-

ing IBMSE opportunities are very rare, with the exception

of the Netherlands, where they are of very good quality,

and Switzerland (in mathematics) where the official

material from the state for compulsory education provides

material with problem-solving and didactic comments (see

Figs. 2, 3).

By contrast, in some countries, for example Romania

and Slovakia, there is a lack of textbooks that meet the new

curricula requirements regarding IBMSE. However, even

explicitly IBMSE or problem-solving orientated documents

can be used by teachers in an inadequate manner, leading

to very poor practice in reality.

4 Perspectives

Following our analysis at the four levels of determination

(see Sect. 3), five main areas have been identified in which

further actions might be needed to support the implemen-

tation of IBMSE: (1) national policies, (2) didactical

resources, (3) national assessment, (4) pre-service teachers’

training, and (5) in-service training and professional

development.

Now, we move on to the perspectives that follow our

analysis, in order to give a general overview of the main

issues that we can highlight for a successful implementa-

tion of IBMSE in the various contexts of our 12 countries,

and more generally in any country. We will go back to a

discussion organized around the main places in which the

conditions and constraints of mathematics and sciences

teaching emerge. With the help of our earlier four levels,

we discuss for each of the above five areas what action is

required and is possible.

4.1 National policies

In all of the countries, we have seen that the most recent

policy regarding the teaching of mathematics and science

supports IBMSE, with some nuances in various countries.

Nevertheless, one has to be careful about historical back-

ground and traditions, which vary greatly from one country

to another and still may be a barrier to making changes

efficiently. Furthermore, there are significant negative

factors emerging in several countries. One is due to the

succession of reforms in recent years in many countries

resulting in a rejection of changes by teachers and some-

times by parents. This has resulted in a resurgence of ideas

defending a return to traditional pedagogical paradigms

and to fundamental contents such as reading and counting

Challenges and opportunities for inquiry-based learning

123

in some countries as well. On the positive side, another

support for IBMSE concerns the fact that, in several

countries, a new tendency is emerging that urges the

development of more coherence between the disciplines,

providing an opportunity for IBMSE common approaches

in mathematics and the science subjects.

At the school level, teachers play a crucial role. Despite

the actions that might be carried out to challenge their

practices and make them evolve, large-scale changes will

be possible only if other dimensions of the school level, as

well as other levels of determination, are also addressed.

Particularly, at the intersection between school and social

levels, attention should be paid to parents and school

authorities.

The situation is of course different in the various

countries. For instance, in the countries where the change

in policies is more recent and the tradition of transmissive

teaching still active, the necessity for change is more

radical, but in a way the novelty of the situation may be a

positive factor for motivation. By contrast, in those coun-

tries where the change in policy dates from the 1970s or

1980s and transmissive pedagogies have progressively lost

relevance, IBMSE may seem less far from actual practices.

Yet, on the other hand, if practices have remained tradi-

tional where changes have been advocated for decades, the

resistance to change is likely to be even stronger. Subse-

quently, any activities aiming at a large-scale implemen-

tation of IBMSE can use the national curricula as a starting

point, but one needs to be aware of a possible resistance

from teachers and maybe also from students and parents,

which needs to be tackled within these activities.

4.2 Didactical resources

Our analysis detected great differences among countries in

the type of resources (especially textbooks) available for

Fig. 2 Task in a Dutch textbook: inquiring about Braille language as a binary code

J.-L. Dorier, F. J. Garcıa

123

teachers and also in the way they use them. It is essential to

develop and make material available for the class that

supports IBMSE where it is missing, or to highlight and

reinforce already-existing material. The use of websites for

resources is of course important, as well as are translations

and adaptations to national contexts. Furthermore, it seems

vital that the material is accompanied by didactical com-

ments on how it can be efficiently implemented in class and

embedded into a device to be used for professional

development. This is particularly necessary in regard to

professional development (see below).

4.3 National assessment

There is obviously an intrinsic difficulty in setting up

assessment compatible with IBMSE, and research work in

this matter is still lacking. Therefore, in most countries,

assessment acts as a powerful restriction that prevents

teachers from adopting IBMSE, especially in those coun-

tries and school levels where national assessment is

important. Indeed, in many countries there is an increasing

pressure on schools due to national ranking or students’

orientation resulting from the national assessment and

Fonctions et algèbre Fonctions et diagrammes

Le diagramme en colonnes ci-dessous indique l’évolution du nombre d’utilisateurs d’Internet, en Suisse et en Inde, entre les années 1990 et 2008.

Unité: M =million

a) Estime par combien le nombre d’utilisateurs d’Internet a été multiplié, en Suisse et en Inde,entre2003 et 2008. Comment, d’après toi, peut-on expliquer cette différence?

b) Sachant que la population de la Suisse est d’environ 7,7 millions d’habitants en 2008, dirais-tuque beaucoup ou peu d’habitants de notre pays ont accès à Internet? Justifie ta réponse.

c) Sachant que la population de l’Inde est d’environ 1,15 milliard d’habitants en 2008, dirais-tu quebeaucoup ou peu d’habitants de ce grand pays d’Asie ont accès à Internet? Justifie ta réponse.

d) En t’aidant des deux diagrammes, imagine le nombre d’utilisateurs d’Internet qu’il y aura en Suisse et en Inde en 2020, en justifiant ta réponse.

FA54Internet

Utilisateurs d’Internet

Suisse

5,7 M

4,6 M

3,5 M

2,3 M

1,2 M

0,0 M90 92 94 96 98 00 02 04 06 0891 93 95 97 99 01 03 05 07

Inde

105 M

84 M

63 M

42 M

21 M

0 M90 92 94 96 98 00 02 04 06 0891 93 95 97 99 01 03 05 07

This diagram shows the evolution of the number of Internet users in Switzerland and

India, between 1990 and 2008

a) Evaluate by what factor the number of Internet users has been multip lied, in

Switzerland and in Ind ia, between 2003 and 2008. How can you explain this

difference?

b) Considering the fact that the population in Switzerland was roughly 7.7 millions

inhabitants in 2008, would you say that many or few inhabitants of our country have

access to Internet in our country? Why?

c) Considering the fact that the population in India was roughly 1.15 billions inhabitants

in 2008, would you say that many or few inhabitants of this Asiatic country have access

to Internet? Why?

d) With the help of the two diagrams, imagine the number of Internet users there will be in Switzerland and in India in 2020. Give some justifications.

Fig. 3 Task in a Swiss textbook: inquiring about the use of the Internet in Switzerland

Challenges and opportunities for inquiry-based learning

123

international evaluations. Thus, if the assessment is not

compatible with IBMSE or just does not benefit from it, the

effect on teachers may be disastrous as they will spend

much time and energy preparing students for the assess-

ment, which will mean avoiding IBMSE. Moreover,

assessment, which is usually content-oriented, puts added

pressure on teachers to cover the program; thus this is a

hindering factor for IBMSE, which is seen as time-con-

suming for little efficiency in terms of assessment results.

Activities aimed at a widespread implementation of

IBMSE need to give teachers support in overcoming

obstacles in relation to assessment, for example by con-

vincing teachers to include IBMSE only once in a while or

by explaining how students learn mathematics and science

when working in an inquiry-based way.

On the other hand, assessment might be seen as a key

lever to make the situation evolve. Finding ways to make

large-scale assessment more compatible with IBMSE would

undoubtedly turn the situation around, changing assessment

from a strong restriction into a powerful driving force.

4.4 Pre-service teachers’ training

In most countries, pre-service primary school teachers (and

some lower secondary school teachers) must be offered

sufficient support in order to overcome their general dis-

inclination towards mathematics and sciences and to dee-

pen their knowledge in these sciences in order to be able to

use IBMSE in class flexibly. Specifically, IBMSE-designed

activities for primary school teachers’ training are needed

that will reactivate students’ interest in these disciplines

and provide good IBMSE material. For secondary school

teachers, the competencies in the discipline are usually

sufficient, therefore the challenge here is to show the

benefits of IBMSE. Pre-service training is also an oppor-

tunity, if necessary, to make students experience IBMSE

activities that they may not have experienced in their

university studies.

4.5 In-service training and professional development

In most countries the typical offering for in-service

teachers’ training and professional development is poor,

not well-structured and, above all, rarely popular. Thus, in

most cases, it seems like a real challenge to find the right

way to present a well-structured and attractive offer when

introducing IBMSE. Some of these national conditions and

constraints are out of reach, since they regard policy issues.

However, at an international level it seems to be important

to develop high quality professional development materi-

als, usable for long-term professional development courses

and adaptable to different national contexts (see Maaß and

Doorman 2013).

One conclusion of this international synthesis is that

professional development is not just a matter of making

materials access and in-service training structure better. It

seems that there is also a need for a change in mentality

and culture regarding the issue of teachers’ professional

learning. This goes beyond the issue of IBMSE and con-

cerns not only teachers, but also the way the society as a

whole takes into account the issue of professional devel-

opment in a profession. It seems that many (teachers and

others) think that good training in the discipline and indi-

vidual pedagogical qualities (not to say vocation) are the

key competencies of teachers, and that only their practice

in class can make them better. In a world where profes-

sional development is recognized and fostered in most

professions, teachers seem be one of the last resisting areas.

5 Conclusion

In this report, we aimed at identifying favourable condi-

tions and limiting constraints for the implementation of

IBMSE in the educational systems of 12 European coun-

tries. As a complement to the approach through the anal-

ysis of teachers’ beliefs and practices (see Engeln et al.

2013) in our approach, we considered teachers not only as

individuals, but as actors of institutions, representing some

disciplines, embedded in a school system, sharing some

common pedagogical issues, in relation to society. Our

sources of information are easily accessible public docu-

ments. With a theoretical background from Chevallard’s

anthropological theory of didactics, we organized our

analysis according to four levels of institutional organiza-

tion that co-determine both content and didactical aspects

in the teaching of mathematics and sciences. Our approach

is systemic in the sense that we do not focus on teachers as

individuals, nor on the curricula, the organization of

teachers’ training or the textbooks themselves. Rather, we

traced the way the conditions and constraints in all these

different places of the institution are operative at the levels

of disciplines, school, pedagogy and society.

The collection of data in the 12 countries was organized

according to our table into the four levels we identified.

One member of the consortium by country, advised by the

NCP in each country, shared the elaboration of our meth-

odology and we kept in constant contact, including a

complement to the first data collection after 2 years.

We recall here that our goal was not to get a precise

overview of each country, but to point to the major types of

conditions and constraints in the various institutional levels

of each country that could favour or hinder a large-scale

implementation of IBMSE. This is how we organized our

conclusions and perspectives that take into account dif-

ferent aspects of the organization of mathematics and

J.-L. Dorier, F. J. Garcıa

123

science teaching in each country, involving higher levels of

the national structures. In this sense, as an echo to Engeln

et al.’s (2013) contribution, in our approach the issue of

how we can make teachers’ practices evolve more towards

IBMSE is not tackled in terms of what needs to be changed

in teachers’ beliefs, but in terms of what needs to be

changed at different institutional levels for teachers to be

able to have a different appreciation of and better access to

IBMSE, not as an individual but as a profession, and acting

in the school system, with children and their parents, as

part of society defending some common cultural values

that concern not only mathematics and sciences and their

teaching, but the role of assessment and the value of pro-

fessional development. Our focus is on giving advice to

future projects and actions about important aspects that

should be considered. It is not restricted merely to policy

(for this, see Wake and Burkhardt 2013), not to teachers,

but encompasses all institutions that influence educational

practices.

Acknowledgments This paper is based on the work within the

project PRIMAS—Promoting Inquiry in Mathematics and Science

Education Across Europe (http://www.primas-project.eu). Project

coordination: University of Education, Freiburg (Germany). Partners:

University of Geneve (Switzerland), Freudenthal Institute, University

of Utrecht (the Netherlands), MARS—Shell Centre, University of

Nottingham (UK), University of Jaen (Spain), Konstantin the Phi-

losopher University in Nitra (Slovak Republic), University of Szeged

(Hungary), Cyprus University of Technology (Cyprus), University of

Malta (Malta), Roskilde University, Department of Science, Systems

and Models (Denmark), University of Manchester (UK), Babes-Bol-

yai University, Cluj Napoca (Romania), Sør-Trøndelag University

College (Norway), IPN-Leibniz Institute for Science and Mathemat-

ics Education at the University of Kiel (Germany). The research

leading to these results/PRIMAS has received funding from the

European Union Seventh Framework Programme (FP7/2007–2013)

under Grant Agreement No. 244380. This paper reflects only the

author’s views and the European Union is not liable for any use that

may be made with the information contained herein.

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