ZDM Mathematics Education (2013) 45:823–836 DOI 10.1007/s11858-013-0507-5

ORIGINAL ARTICLE

Inquiry-based learning in mathematics and science: a comparative baseline study of teachers’ beliefs and practices across 12 European countries Katrin Engeln • Manfred Euler • Katja Maass

Accepted: 27 April 2013 / Published online: 15 May 2013  FIZ Karlsruhe 2013

Abstract In the European educational context, reports by expert groups have identified the necessity of a renewed pedagogy in schools to overcome deficits in science and mathematics teaching and to raise the standards of scientific and mathematical literacy. Inquiry-based learning (IBL) is considered the method of choice. However, it remains open to what extent IBL is actually used in day-today teaching. In the study presented here we elaborate— from the perspective of teachers—the current status of IBL in day-to-day teaching. Further, we explore what problems teachers anticipate when implementing IBL. In order to gain insight into the wide spectrum of practices in mathematics and science teaching in relation to IBL, a baseline study using teacher questionnaires was carried out in the 12 participating countries. We present selected results from this study that for the first time provides an overview of teachers’ beliefs and their reports on the current use of IBL practices in a European context. The results facilitate a cross-cultural comparison on the potentials and challenges of implementing IBL from the perspective of practicing teachers. Furthermore, the study reveals considerable differences between the teaching of mathematics and science subjects. The findings of the baseline study can serve as a reference line against which the impact of interventions to improve the quality of teaching and learning can be evaluated. K. Engeln
M. Euler Leibniz-Institute for Science and Mathematics Education, Olshausenstraße 62, 24098 Kiel, Germany e-mail: [email protected] K. Maass (&) Institute for Mathematical Education, University of Education Freiburg, Kunzenweg 21, 79117 Freiburg, Germany e-mail: [email protected]

Keywords Inquiry-based learning
PRIMAS
Teachers’ beliefs
Subject differences
Cultural differences

1 Introduction Over the past decades, serious concerns have been raised about the status and the impact of mathematics and science education in many developed countries. There is a generally accepted consensus that a lack of basic competencies and interest in mathematics and science subjects will hinder young people in becoming active citizens and contributing adequately to the development of society. Furthermore, the present uptake of science and technologyrelated studies is considered insufficient to keep up the pace of innovation and to react adequately to the economic, ecological and social challenges of a rapidly changing world (Gallup Organization 2008). In this context, the quality of teaching and learning in mathematics and science is considered crucial and requires considerable improvements in order to comply with growing societal needs. As a consequence, a variety of new educational programs and projects are being launched to improve the quality of science and mathematics education. Engaging students in inquiry-based learning (IBL) is seen as a means of improving education—especially in science and mathematics—both on a global and on a European level (Abd-el-Khalick et al. 2004; Rocard et al. 2007). IBL implies a shift from traditional, mainly deductive, teaching styles towards more appealing and activating forms of teaching and learning. On a European level most educational documents, such as educational policy documents or curriculum guidelines, support and require an introduction of IBL to school subjects (Dorier and Garcia 2013). Accordingly, many projects focus on

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various ways to foster inquiry-based approaches in mathematics and science education. Among them is the EUproject PRIMAS (http://www.primas-project.eu/en/index. do). In this project 14 universities from 12 different countries1 are working together to further promote the implementation and use of IBL in mathematics and science. Within the PRIMAS project a baseline study of teachers’ beliefs on the status of IBL, factors hindering the implementation of IBL and their current teaching practice across 12 European countries has been carried out with the help of a questionnaire. Especially, in this paper our research on the status of IBL with respect to teachers’ orientations and routine use in daily practice is reported, and different lesson patterns regarding IBL are introduced. Furthermore, we investigate the problems teachers anticipate when implementing IBL.

2 Theoretical background In this section a short introduction to the concept of IBL in mathematics and science is given in order to provide a theoretical framework for devising the baseline study. For a more detailed discussion of IBL in the context of mathematics see Artigue and Blomhoej (2013). Furthermore, the relevance of teachers’ beliefs for their teaching practice and also for any change in teaching practice is discussed. 2.1 Inquiry-based learning and the IBL concept of PRIMAS Inquiry-based science education has a long history and there are many approaches to teaching and learning science as inquiry (Barrow 2006; Prince and Felder 2007). In the USA the tradition of IBL goes back to Dewey (1859–1952) (Dewey 1910), whereas in Germany, for example, inquiry learning was introduced within the reformist pedagogy in the 1920s (cf. Wagenschein 1962). In discussions on improving education, the word ‘‘inquiry’’ is used in different ways and contexts. Not only is the term IBL used without clarifying connections and distinctions, but also terms such as inquiry-based teaching, inquiry-based method, inquiry-based education and inquiry-based pedagogy are widespread. Furthermore, IBL is often conflated or used interchangeably with other terms that describe similar learning and teaching approaches such as anchored instruction, hands-on, problem-based, projectbased, student-centered, inductive and dialogic approaches (Anderson 2002; Hayes 2002). For example, the Rocard

K. Engeln et al.

Report (Rocard et al. 2007) identifies problem-based learning as the method of choice for mathematics education and IBL for science education, but it is not clear whether problem-based learning and IBL can be used interchangeably. The failure to give a concrete definition has led to misunderstandings and is one reason for discussions about the effectiveness of IBL. For example, Kirschner et al. (2006) characterize inquiry learning, inquiry-based teaching and problem-based learning as minimal guidance approaches and conclude that these approaches do not work. In a direct response Hmelo-Silver et al. (2006) argue that problem-based learning and inquiry learning are not minimally guided approaches but rather provide extensive scaffolding and guidance. In a narrow sense, IBL refers to learning that takes place following the processes that are involved in scientific inquiry. Students are encouraged to pose questions, to formulate assumptions and hypotheses, to gather and analyse data and to construct evidence-based arguments. Due to the different understandings of IBL as discussed above and due to the different perspectives of the countries involved in PRIMAS, the project used a much broader definition of IBL (Fig. 1), which we also followed in the study reported here. According to this definition, IBL is seen as a multi-faceted teaching and learning culture which sees the process of inquiry central for learning but also emphasizes that: • • • •

students construct meanings, meaningful learning takes place in a social context, learning is supported by meaningful contexts (situated cognition) and learning is a dialogic process (e.g. Cunningham and Helms 1998; Duit and Treagust 1998; Mortimer and Scott 2003).

Students take responsibility for their own learning as they learn to work individually as well as in groups. The

1

Cyprus, Denmark, Germany, Hungary, Malta, Netherlands, Norway, Romania, Spain, Slovak Republic, Switzerland, United Kingdom.

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Fig. 1 A multi-faceted approach to IBL

Inquiry-based learning in mathematics and science

covered topics are relevant to the students and their prior experience is adequately taken into account. Thus, by engaging students actively in the construction, evaluation and reflection of knowledge, inquiry-based education promotes competencies that are relevant for lifelong learning and for a successful orientation in a complex world. On the teachers’ part, orchestrating and facilitating learning processes, for example through modelling and coaching, is a subtle skill that is critical in making IBL function well (Barrow 2006; Colburn 2006; Hmelo-Silver 2004; Prince and Felder 2007). Nevertheless, we have to be aware that even within this definition of IBL, the spectrum of interpretation is wide. There is room for a diversity of views and practices because the precise meaning given to the different features can vary. Furthermore, the respective importance given to these features can also vary. For example, IBL can be differentiated according to the type and the complexity of the problems, the degree of student-centered learning and also to the order of problem and information presentation (Walker and Leary 2009). In addition, Staver and Bay (1987) distinguish three different levels of guidance: structured inquiry, guided inquiry and open inquiry. In structured inquiry activities students are given a problem to solve, a method for solving the problem, and also the necessary materials. In guided inquiry, students have to choose themselves a method for solving the problem given. Finally, in open inquiry, students must also formulate the problem they will investigate. It is reasonable to hypothesize that all these variants of IBL are not equally effective in the same teaching and learning situation. Subject-specific differences in the understanding and the implementation of IBL also exist. These differences can be related to the nature of the subject in question that is transformed to a certain degree to the school subject. For instance, mathematics teachers tend to see their subject much less related to empirical findings, and at the same time more axiomatically oriented, more deductive and sequential and more structured, than science teachers see their subjects (e.g. Stodolsky and Grossman 1995). Experiments are more prominent in science than in mathematics and serve a spectrum of purposes, for instance in gaining knowledge, in grounding knowledge in experience and in testing hypotheses. In spite of their central role in the scientific method the actual practice of experimental work in school has been critically discussed; in particular, the so-called cookbook exercises where students follow recipes to reach particular, pre-determined outcomes have been subject to criticism for different reasons. They give an inadequate picture of scientific inquiry and they fail to motivate students. The resulting tension between inquiry in classrooms and the scientific inquiry process and related

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problems are discussed elsewhere (e.g. Chinn and Malhotra 2002; Hodson 1996; Hodson and Brencze 1998; Hofstein and Lunetta 2004; Kirschner 1992; Lunetta 1998). Even though there is a strong belief that science and mathematics education can be improved through the implementation of IBL, its effectiveness is not yet firmly established (Bruder and Prescott 2013). It is difficult to obtain reliable evidence from empirical studies because the spectrum of IBL is vast and the research findings are highly contextual (e.g. Alfieri et al. 2011; Anderson 2002; Trundle et al. 2010). Furthermore, a straightforward comparison with more structured teaching approaches is complicated, because these approaches often emphasize different teaching objectives. Meta-analyses have to be read carefully because they depend on the model, and in particular on the operationalization of the specific type of IBL in question (Seidel and Shavelson 2007). Despite these limitations the results of recent metaanalyses affirm the benefits of inquiry-based education from empirical research (Maass and Artigue 2013). Seidel and Shavelson (2007) conclude that domain-specific activities such as mathematics problem solving and science inquiry had the highest effect on learning outcome. In their meta-analysis, Minner et al. (2010) find that ‘‘instruction within the investigation cycle’’ has a positive effect on student content learning. In his meta-analysis Hattie (2009, pp. 209–210) concludes: ‘‘Overall, inquiry-based instruction was shown to produce transferable critical thinking skills as well as significant domain benefits, improved achievement and improved attitude towards the subject.’’ However, these meta-analyses also indicate that it is not only the use of IBL making the difference with respect to improving students’ performance. Teachers, for example, need to be directive and give frequent feedback (Hattie 2009, p. 243). These findings clearly show that, in spite of its expected benefits, a widely accepted and successful implementation of inquiry-based mathematics and science education is far from trivial. Teachers’ professional competences are of crucial importance for keeping a proper balance between efficient instruction on the teachers’ part and autonomous construction on the learners’ part in the teaching and learning of mathematics and science: ‘‘[…] there’s no such thing as a teacher-proof curriculum, and there are lots of times when inquiry-based instruction is less advantageous than other methods. It’s up to you to find the right mix of inquiry and non-inquiry methods that engage your students in the learning of science’’ (Colburn 2000, p. 44). 2.2 Teachers’ beliefs To promote IBL it is essential not to focus solely on teachers’ competences because the ‘‘task of preparing teachers for inquiry teaching is much bigger than the

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technical matters…the matter must be addressed…at a level that includes central attention to beliefs and values’’ (Anderson 2002). Teachers’ beliefs about mathematics, science and their education are thought to have a major influence on the way in which innovative ways of teaching are implemented in day-to-day mathematical lessons (Bishop et al. 2003; Chapmann 2002; Gellert 1998; Llinares 2002; Ponte et al. 1994). The importance of taking a closer look at teachers’ beliefs is highlighted by the results of research. Kaiser (2006) shows that innovations required by the curriculum can be interpreted by the teacher in such a way that they fit into their belief system, and only the parts that are compatible with the existing belief system are implemented successfully. The same holds true for the tasks chosen. Additionally, Lloyd (2002) found that teachers’ beliefs about mathematical education have a strong connection to the mathematics lessons they themselves experienced as children. However, different definitions of beliefs and different concepts are used within the discussion about mathematics education (Op’t Eynde et al. 2002; Pehkonen and To¨rner 1996). Following Pehkonen and To¨rner (1996), the term ‘‘beliefs’’ will be used here. Accordingly, beliefs will be defined as follows: ‘‘Beliefs are composed of a relatively long-lasting subjective knowledge of certain objects as well as the attitudes linked to that knowledge. Beliefs can be conscious or unconscious, whereby the latter type are often distinguished by an affective character’’ (p. 6). One of the main stumbling blocks for implementing IBL in the classroom is teachers’ beliefs about teaching and learning. Numerous educational researchers argue that any effort of implementing innovative teaching practices has to consider teachers’ beliefs from the beginning (Harwood et al. 2006; Simmons et al. 1999; Wideen et al. 1998). Furthermore, the relationship between classroom practices, student learning outcomes and teachers’ beliefs and attitudes is highly complex, influencing each other in both directions (Guskey 2000, 2002). When, for example, a teacher strongly believes that teaching is good and effective when a rule is first explained to students and students afterwards do exercises then such a belief is contrary to the implementation of IBL. 2.3 Aims and research questions Following on from the theoretical discussion, the aim of this study is to investigate teachers’ beliefs on the current status of IBL in the different teaching cultures and collect challenges of implementation in 12 European countries. The findings inform the members of the PRIMAS consortium and contribute to optimizing the ongoing professional development programs about IBL. In order to tailor the interventions to the teachers’ needs it is important to

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get a deeper insight into their beliefs in relation to IBL across all participating countries. Furthermore, the results of the PRIMAS baseline study can be used as a reference to monitor changes due to the teacher training measures within the project. The following research questions will be addressed in this paper from the perspective of teachers: • • •

What is the status of IBL with respect to teachers’ orientations and routine use in daily practice? What problems do teachers anticipate when implementing IBL? What are the lesson patterns regarding IBL described by the teachers?

The findings on these three questions are presented here with a special focus on differences due to the teaching cultures in the participating countries and due to subjectspecific belief-systems of the teachers.

3 Methodology of the baseline study In this section an overview of the methodology of the baseline study is given. In particular, the design of the employed questionnaire is introduced. 3.1 Design of the questionnaire In order to fulfill the aim of the baseline study, a teacher questionnaire was designed that takes the introduced multifaceted view on IBL (see below) into account. This questionnaire contains collected data on information on personal data, on views about professional development, on beliefs about IBL and on the description of current classroom practice (Euler 2011). Four-point Likert-type items are used whenever suitable, the applied categories reflecting frequencies or agreement (never or hardly ever, in some lessons, in most lessons, in almost all lessons; and strongly disagree, disagree, agree, strongly agree). In order to take the potential multi-faceted views on IBL into account, we introduced IBL at the beginning of the questionnaire in the following way to the teachers: Inquiry-based learning (IBL) is a student-centered way of learning content, strategies and self-directed learning skills. Students develop their questions to examine, engage in self-directed inquiry (diagnosing problems—formulating hypothesis—identifying variables—collecting data—documenting their work—interpreting and communicating results) and collaborate. The aim of IBL is to stimulate students to adopt a critical inquiring mind and develop an aptitude for problem solving.

Inquiry-based learning in mathematics and science

The following section consists of items to inquire into teachers’ orientation towards IBL and their actual use of IBL (Table 1). The items about orientation towards the use of IBL ori and about self-reported actual use of IBL rou are influenced by the Concern-Based Adoption Model (Hall et al. 1977; Loucks and Hall 1979), which gives attention to two facets of the individual development: Stages of Concern (What concerns does a person have in relation to a suggested change?) and Levels of Use (In which way does a person use a suggested change?). The items regarding problems teachers expect to face with a broader implementation of IBL (Table 2) are based on the literature (e.g. Colburn 2000; Walker 2007). Furthermore, teachers are asked to respond to items describing their current teaching practice with reference to a particular subject. Altogether, 32 items have been adapted in this section in accordance with the multi-faceted understanding of IBL (see Sect. 2.1) (Brandon et al. 2009; OECD 2009; Swan 2006). Ten of these items were modified from the scales about science learning and teaching used in the PISA 2006 student questionnaire (OECD 2009, pp. 333–336).

827 Table 2 Item describing problems teachers anticipate when implementing IBL Scale

Item I have difficulties in implementing IBL, because…

res Resources

I don’t have adequate teaching materials IBL is not included in textbooks I use I don’t have access to any adequate CPD programs involving IBL I don’t have sufficient resources such as computers, laboratory

cla

I worry about students’ discipline being more difficult in IBL lessons

Classroom

I don’t feel confident with IBL

Management

I worry about my students getting lost and frustrated in their learning I think that group work is difficult to manage

syr

The curriculum does not encourage IBL

System

There is not enough time in the curriculum

Restrictions

My students have to take assessments that don’t reward IBL The number of students in my classes is too big for IBL to be effective

Scale: 1, strongly disagree; 2, disagree; 3, agree; 4, strongly agree

3.2 Sample Members of the PRIMAS consortium in all participating countries asked teachers to complete the questionnaires. Teachers from Cyprus, Denmark, Germany, Hungary, Malta, Netherlands, Norway, Romania, Slovakia, Spain, Switzerland and the UK are in the sample. The participating teachers in each country are not randomized; therefore, the sample is not representative for the whole country. In most cases the members of the consortium contacted secondary schools in their area. For example, in Switzerland only teachers from the French-speaking region around Geneva are in the sample. In Germany, only teachers from the area around Freiburg, Baden-Wu¨rttemberg took part in the survey. Therefore, with the exception of Cyprus and Malta the sample consists of secondary Table 1 Item describing teachers’ orientation towards IBL and their actual use Scale

Item Please indicate to what extent you agree with the following statements

ori

I would like to implement more IBL in my lessons

Orientation

I would like to have more support to integrate IBL in my lessons

rou

IBL is important for my current teaching practice

Routine

I already use IBL a great deal

use

I regularly do projects with my students using IBL

Scale: 1, strongly disagree; 2, disagree; 3, agree; 4, strongly agree

teachers representing a specific region of each country. Most countries used a paper and pencil approach while Denmark and the UK administered online questionnaires. A complete set of questionnaires from 917 teachers is available, representing all the 12 countries of the PRIMAS consortium. Of the teacher sample, 36 % are male and the average age is 40 (Table 3). Most of them teach children 12 years and older (80 %). Furthermore, 57 % of the teachers refer to maths while the remaining 43 % refer to physics, chemistry, biology or general science. For the purpose of this paper comparing mathematics and science teachers in different European countries, this latter group is labeled ‘‘science teacher’’. Due to the composition of the sample in the different countries this group is not further differentiated between the subjects, even though considerable differences between the subjects do exist.

4 Results In the following, selected results of the PRIMAS baseline study are presented. 4.1 Status of IBL The two scales ori ‘‘Orientation towards IBL’’ and rou ‘‘Routine use of IBL’’ are constructed. Cronbach’s alphas for the two ori and the three rou items were 0.57 and 0.81,

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Table 3 Overview of the sample of the PRIMAS baseline study Country

Size

Cyprus Denmark Germany Hungary

Male proportion

Average age

46

0.35

32

47

0.55

45

58

0.42

44 41

53

0.15

101

0.35

35

40

0.36

43

Norway

61

0.53

40

Romania

121

0.41

44

Slovakia

110

0.19

40

Malta Netherlands

Spain

47

0.47

42

Switzerland UK

162 71

0.30 0.38

41 37

All

917

0.36

40

respectively. The results indicate that all over Europe there is a positive orientation towards IBL. Routine use can be found in all countries at least at a rudimentary level. Regarding both scales the country has a significant influence (Fig. 2). A one-way ANOVA was used to test for orientation differences among the 12 participating countries. Orientation towards IBL differed significantly across the 12 countries, F(11,863) = 10.29, p \ 0.01. The assumption of homogeneity of variance was violated; therefore, the Brown–Forsythe-F-ratio is also reported F(11,641.33) = 11.25, p \ 0.01. As Fig. 2 and Table 4 indicate, Tamhane post hoc comparisons of the 12 countries confirm that especially Romania and Switzerland differ significantly from the remaining countries. Teachers in Romania [M = 3.40, 95 % CI (3.31, 3.50)] are significantly more positively orientated towards IBL than the teachers in all other countries except Denmark. Moreover, teachers in Switzerland [M = 2.71 95 % CI (2.61, 2.82)] are significantly less oriented towards IBL than teachers in all other participating countries except Germany. Another one-way ANOVA was conducted to compare the routine use of IBL in the 12 countries. There was a significant effect of the country on the routine use, F(11,862) = 8.83, p \ 0.01. Again, the assumption of homogeneity of variance was violated. The significant effect of the country on the routine use of IBL was sustained using the Brown– Forsythe-test, F(11,586.18) = 8.73, p \ 0.01. Post hoc comparison using the Tamhane-test indicates that the countries can be grouped. The mean scores for Malta, Slovakia, Cyprus and Romania are each significantly different from the scores of the UK, Norway, the Netherlands and Hungary (Table 4). The first group reports a significantly higher use of IBL in their daily practice. The effect size for comparing these two groups is r = 0.48.

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Fig. 2 Scatter plot of variables ori (orientation towards IBL) and rou (routine use of IBL) differentiating the European countries (1, strongly disagree; 2, disagree; 3, agree; 4, strongly agree)

Therefore, the effect is large. Germany, Spain and Switzerland are between these two groups. Comparisons between Spain or Switzerland and any other country were not statistically significant at p \ 0.05. For German teachers only the comparison with Romanian teachers was significant. Taken together, these results suggest that—from the perspective of teachers—there are cultural differences regarding the orientation towards IBL and the implementation of IBL in daily practice. Any professional development course and any evaluation of implementation will have to consider this fact. 4.2 Problems anticipated with integrating IBL A three-factor structure for 12 out of the 15 items which are asking for problems when implementing IBL was evident, based on a principal components exploratory factor analysis with an oblimin rotation. The three factors are named system restrictions (syr) (4 items; Cronbach’s a = 0.70), classroom management (cla) (4 items; Cronbach’s a = 0.76), and resources (res) (4 items; Cronbach’s a = 0.74) (see Table 2). These three factors are also found in the answers of open questions regarding difficulties that hinder the implementation of IBL. A teacher from Malta gave the following answer: My major stumbling block is time. I cannot leave out whole chunks of the syllabus to implement IBL, therefore I am using an inquiry-based approach but collaborative group work is at the bare minimum, e.g. once a month or less frequently.

Inquiry-based learning in mathematics and science Table 4 Orientation towards IBL (ori) and routine use of IBL (rou)

Country

N

ori

rou

Mean ori

SD

95 % CI Lower

Upper

Mean rou

SD

95 % CI Lower

Upper

Cyprus

46

3.12

0.32

3.02

3.21

2.76

0.40

2.64

2.88

Denmark

44

3.19

0.43

3.06

3.33

2.71

0.76

2.48

2.94

Germany

58

2.88

0.60

2.72

3.05

2.37

0.75

2.17

2.57

Hungary

51

3.00

0.40

2.89

3.11

2.33

0.57

2.17

2.49 2.81

Malta

Judgments were on a 4-point scale (1, strongly disagree; 2, disagree; 3, agree; 4, strongly agree)

829

100

3.11

0.50

3.01

3.21

2.71

0.55

2.60

Netherlands

40

2.99

0.65

2.78

3.19

2.30

0.69

2.08

2.52

Norway Romania

60 96

3.06 3.40

0.37 0.47

2.96 3.31

3.15 3.50

2.26 2.77

0.46 0.55

2.14 2.66

2.37 2.88

Slovakia

109

3.08

0.58

2.97

3.19

2.74

0.52

2.64

2.84 2.58

Spain Switzerland UK

47

3.09

0.42

2.96

3.21

2.40

0.62

2.22

155

2.713

0.65

2.61

2.82

2.50

0.67

2.40

2.61

68

3.02

0.66

2.86

3.18

2.22

0.56

2.08

2.35

A member of the Hungarian PRIMAS team commented: …The opinions here can be divided into two main clusters: (1) lack of PD programs about IBL, and even more frequently (2) lack of resources and equipment. Maybe people from the Western part of the river Elbe can hardly believe that even pencils, pens, cardboard and other very simple equipment are missing from the school or are bought by parents and brought to the school by the children. Analysing the data of the questionnaires indicates that teachers see the three factors classroom management, system restrictions and resources as relevant. While the average of classroom management is only 2.3, the other two are rated more important: system restrictions and resources both have an average of 2.8 (1, strongly disagree; 2, disagree; 3, agree; 4, strongly agree) (Fig. 3). To have a comparative look at the results, several analyses were carried out to give an insight into differences between the countries. One-way ANOVA was used to test for differences in the three factors among the 12 participating countries. All three factors, classroom management (cla), resources (res) and system restrictions (syr) differed significantly across the 12 countries. The F-ratios were F(11,868) = 3.90, p \ 0.01, F(11,869) = 13,212, p \ 0.01 and F(11,870) = 13,838, p \ 0.01, respectively. The assumption of homogeneity of variance for cla was violated; therefore, the Brown–Forsythe-F-ratio is also reported: F(11,608.50) = 4.12, p \ 0.01. These results show that significant differences exist amongst the groups. Pairwise comparisons give a more profound insight. In all countries actual classroom management is seen as the least significant problem out of the three reviewed problems. Except for the United Kingdom and the

Netherlands, all countries have values between 2.1 and 2.4. The Netherlands has the smallest value and the United Kingdom the highest. Post hoc analysis using the Tamhane-test to test for significance differences of cla among the 12 countries indicates that only a few significant differences exist. Out of all pairwise comparisons only five are significant; four of them involve the UK. Teachers in the UK report significantly more problems related to classroom management when implementing IBL than their colleagues in Germany, the Netherlands, Hungary and Cyprus (r = 0.46). As Table 5 indicates, Tukey post hoc comparisons showed that the relevance of resources as a hindrance for implementing IBL is rated significantly different. Pairwise comparison showed, for example, that teachers in Romania, Slovakia and Hungary gave significantly higher ratings than teachers in Denmark, Germany, Malta, Norway and Switzerland (0.22 \ r \ 0.48).

Fig. 3 Problems with implementation of IBL: classroom management (cla), resources (res) and system restrictions (syr) (1, strongly disagree; 2, disagree; 3, agree; 4, strongly agree)

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830 Table 5 Resources and system restrictions as a problem hindering the implementation of IBL

Judgments were on a 4-point scale (1, strongly disagree; 2, disagree; 3, agree; 4, strongly agree)

K. Engeln et al.

Country

N

res Mean res

syr SD

95 % CI Lower

Upper

Mean syr

SD

95 % CI Lower

Upper

Cyprus

44

2.92

0.58

2.74

3.09

3.10

0.084

2.92

3.26

Denmark

38

2.48

0.56

2.29

2.67

2.32

0.086

2.15

2.50

Germany

56

2.45

0.57

2.29

2.60

2.51

0.087

2.33

2.68

Hungary

52

2.97

0.54

2.82

3.12

2.80

0.056

2.69

2.92

Malta

97

2.58

0.53

2.48

2.69

2.94

0.051

2.84

3.04

Netherlands

40

2.87

0.54

2.70

3.04

2.56

0.074

2.42

2.70

Norway Romania

60 118

2.58 3.10

0.45 0.56

2.46 3.00

2.69 3.20

2.39 3.13

0.065 0.051

2.26 3.03

2.52 3.23

Slovakia

110

3.11

0.77

3.00

3.26

2.98

0.075

2.83

3.13

Spain Switzerland UK

47

2.89

0.49

2.74

3.03

2.96

0.074

2.81

3.10

153

2.58

0.58

2.50

2.68

2.83

0.042

2.74

2.91

66

2.78

0.58

2.64

2.92

2.75

0.065

2.62

2.88

The Tukey post hoc comparison of the 12 countries indicates the relevance of system restriction and is rated prominently different (Table 5). Twenty-seven pairwise comparisons are significant at p \ 0.05. For example, teachers in each of the countries Denmark, Norway, Germany and the Netherlands see system restrictions as less of a hindrance than their colleagues in Malta, Slovakia, Cyprus and Romania (0.32 \ r \ 0.54). Taken together, the results indicate that classroom management is not seen as a major problem, especially not in the UK. Examining responses on the two other categories (system restrictions and resources) shows that teachers in Denmark, Germany and Norway see fewer problems with the implementation of IBL than in the other countries. Teachers in Slovakia and Romania have the greatest worries about implementation. In these countries, system restrictions and lacking resources are rated nearly equally obstructively. With the remaining five countries it is striking that in Switzerland and in Malta teachers see system restriction clearly as more of a hindrance than the availability of resources (Fig. 4).

model simpler and having at least one item from each scale ensures that no information is lost. The scales investigation and hands-on-activities both refer to different forms of inquiry, therefore a second item was chosen from the interactive scale to give this scale an equal weight. All five items have been adapted from the PISA 2006 study (Table 6) (OECD 2009). These items have been selected because they describe aspects of IBL in accordance with the explicated multi-faceted understanding of

4.3 Description of current practice In the last section of the questionnaire teachers answered 32 items about their teaching practice. The items cover various aspects of the multi-faceted view of IBL. We measured the following scales: the frequency of interactive teaching, of hands-on activities (strongly guided inquiry), of investigation and of focus on application. Out of these four scales measuring teachers’ reports on their current teaching practice, five items were chosen for conducting a latent class analysis (LCA) to analyse different lesson patterns. Choosing only five items makes the

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Fig. 4 Scatter plot of system-related problems versus resourcesrelated problems (1, strongly disagree; 2, disagree; 3, agree; 4, strongly agree)

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IBL. Item own ideas (ST34Q01) and item discussions (ST34Q13) describe the activity of the students and the corresponding classroom atmosphere. These items are chosen even though they belong to the same scale because one of them is clearly more student-centered than the other. Item outside (ST34Q12) is connected with the type of problems being used in an IBL learning and teaching culture. The items instruction (STQ14) and own experiments (ST34Q08) both deal with the process of inquiry students are involved in. Both items are chosen because they clearly distinguish between teacher-centered strongly guided inquiry and student-centered more open inquiry. Figure 5 shows the mean and the SD of the selected items. From the perspective of the teachers, they use their subject to explain the world outside school and give students opportunities to explain their own ideas. Teachers report less frequently on discussions among students and students doing experiments following instructions. Finally, designing their own experiments is an activity which students are rarely allowed to carry out. Most teachers state that guided inquiry (experiments following instructions) is only part of some lessons and that investigations (own experiments) are conducted even less. This leads to the conclusion that primarily those IBL elements are visible which still give the teachers a certain degree of control. Elements which are more student-centered and/or focus on inquiry still play a secondary role in the lessons. All five reported variables depend significantly on the country. Except for the two variables related to classroom atmosphere ideas and discussion, they also depend on the subject. ANOVA testing with the country and the subject revealed a main effect of the country and the subject on the items outside (F(11,850) = 5.67, p \ 0.01, g2p = 0.068, F(1,850) = 22.22, p \ 0.01, g2p = 0.025), instruction (F(11,815) = 4.10, p \ 0.01, g2p = 0.052, F(1,815) = 20.51, p \ 0.01, g2p = 0.025) and experiments (F(11,823) = 7.85, p \ 0.01, g2p = 0.095, F(1,823) = 4.53, p = 0.03, g2p = 0.005). Science teachers report significantly higher frequency of outside, instruction and experiments (Table 7). Interestingly, for the items instruction and experiments the interaction of the variables country and subject is also significant, F(11,815) = 2.21, p = 0.01, g2p = 0.029,

Fig. 5 Mean and SD of five selected variables describing IBL-related elements of lesson patterns (1, never or hardly ever; 2, in some lessons; 3, in most lessons; 4, in almost all lessons) Table 7 Mean and SD of five items describing teaching practice Item Outside Own ideas Discussions Instructions Own experiments

Subject

N

Mean

SD

Science

359

3.16

0.719

Mathematics

515

2.67

0.758

Science

361

2.92

0.729

Mathematics

508

2.88

0.712

Science

355

2.70

0.752

Mathematics

505

2.54

0.761

Science

353

2.37

0.667

Mathematics

486

2.09

0.743

Science

355

1.93

0.733

Mathematics

492

1.80

0.778

F(11,823) = 2.37, p \ 0.01, g2p = 0.031. Regarding the implementation of experiments, differences between the subjects depend on the country. As an example, Fig. 6 shows a scatter plot of the items experiments and outside. It illustrates that both items depend on the country and the subject. Math teachers help students less frequently to understand the world outside school in their lessons than science teachers do. Moreover, they use experiments less frequently. Interestingly, this is

Table 6 Overview of the five items adapted from PISA 2006 used to describe IBL-related lesson characteristics Name PISA2006

Scale

Item

ST34Q01

Interactive

My students are given opportunities to explain their own ideas

ST34Q08

Investigation

My students are allowed to design their own experiments

ST34Q12

Focus on application

I use science/mathematics to help students understand the world outside school

ST34Q13

Interactive

My students have discussions about the topics

ST34Q14

Hands-on-activities

My students do experiments by following my instructions

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country-dependent. It becomes evident that in some countries the subjects have different teaching and learning cultures while in others they are more similar. In the German sample, for example, strong differences between mathematics and science can be identified, while in the sample from other countries such as Hungary and Slovakia these differences are clearly smaller. A LCA using the program Mplus (Muthe´n and Muthe´n 1998–2010) was conducted with the described five variables to get a more precise picture of the lesson patterns. In an LCA ‘‘objects are assumed to belong to one of a set of K latent classes, with the number of classes and their sizes not known a priori. In addition, objects belonging to the same class are similar with respect to the observed variable’’ (Vermunt and Magidson 2002). Therefore, an LCA identifies unobservable subgroups within a population. Here an LCA was used to cluster the teachers according to their lesson pattern. A three-class model was identified to be most appropriate using the information criteria BIC, the Vuong–Lo–Mendell–Rubin-Test and considering that the number of classes should be as small as possible (Geiser 2011, p. 270). Consequently, three teacher profiles have been identified (Fig. 7) on the basis of the LCA. Class 1 is the smallest of the three constructed classes, with only 8 % belonging to it. Teachers in this class have the highest means in all five variables. In almost all lessons, students have the opportunity to explain their ideas and to discuss them among themselves. In addition, the subject is used to explain the world outside school. Students have the opportunity to do experiments following instructions and designing them themselves. From the presented

Fig. 6 Scatter plot of the items experiments and outside depending on the subject and the country (the samples of Romanian and UK science teachers are too small to be analyzed) (1, never or hardly ever; 2, in some lessons; 3, in most lessons; 4, in almost all lessons)

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Fig. 7 LCA 3-class solution: profiles of science teaching and learning (1, never or hardly ever; 2, in some lessons; 3, in most lessons; 4, in almost all lessons)

information, the teachers of class 1 seem to apply IBL in their daily lessons. Here, this class can be labeled student and activity oriented style of teaching. Class 2 has 41 % of the teachers belonging to it. The lesson patterns of these teachers are characterized by students being actively involved. Reference to real life is made. Experiments play a minor role; the frequencies of hands-on activities and investigations are quite low. Therefore, this pattern is called student-oriented. Teachers of class 2 already use some elements regularly that are an important part of IBL. Concerning practical work, including investigations, they still have a desideratum. Class 3, with 51 % of the teachers, is the largest class. For obvious reasons, this class is labeled teacher-oriented. The elements of IBL which are directly connected to experiments play a subordinated rule. Furthermore, there is not much room for students to explain their ideas or discuss among themselves. In addition, a reference to the real world outside school does not exist. IBL is not part of the daily teaching of these teachers. In the following, the allocation of the teachers to the three generated classes is analyzed with respect to the 12 different PRIMAS countries. The focus is on teachers referring to their mathematics classes to eliminate the influence of the subject (see above). The samples of the other subjects are too small for a separate statistical analysis. Figure 8 presents the scatter plot of the percentage of mathematics teachers belonging to the student-oriented and the teacher-oriented class depending on the country. Differences and similarities between the PRIMAS countries become visible, showing remarkable variations between the countries. The proportion of teachers belonging to the teacher-oriented class 3 is between 40 % (Cyprus) and 90 % (Germany). Noticeably, the Western European countries the Netherlands, the UK and especially Germany have the highest proportion of teachers belonging to the

Inquiry-based learning in mathematics and science

Fig. 8 Scatter plot of percentage of student-oriented lesson patterns versus percentage of teacher-oriented lesson patterns for PRIMAS math teachers (1, never or hardly ever; 2, in some lessons; 3, in most lessons; 4, in almost all lessons)

teacher-oriented class, whereas the Eastern European countries and Cyprus have the smallest proportion of teachers belonging to that class. The results of the LCA indicated that teachers can be assigned to three different groups. These groups have different lesson patterns regarding the implementation of IBL. The probability of being in a certain class depends not just on the subject but also on the country.

5 Discussion and conclusions 5.1 Summary The results of the PRIMAS baseline study give an insight into teachers’ perspectives on IBL in 12 European countries. Generally, it has been shown that at least within the PRIMAS sample the status of IBL in Europe depends significantly on the country and also on the subject. The PRIMAS baseline study highlights some aspects the PRIMAS interventions have to take into consideration. First, there seem to be relevant country-specific differences in relation to IBL which make cultural adaptations of the common international concept (see Maass and Doorman 2013) necessary. Also, the restrictions for the implementation of IBL perceived by teachers need to be addressed. We can conclude from the responses that in all 12 countries teachers report a positive attitude towards IBL. This is a valuable prerequisite for its implementation. The results indicate that the implementation into daily practice depends significantly on the country (respectively the region explored in the country) and therefore on the

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existing school system. However, so far our sample indicates that IBL does not seem to have a noticeable presence in all countries. Interestingly we can identify two groups of four countries each which differ significantly regarding the reported regular use of IBL, and more detailed microstudies are needed to explain these differences between the countries. According to the data, classroom management is perceived as the least important restriction for the implementation of IBL by teachers as opposed to systemic restrictions and resources. Classroom management also shows the least variance among the countries. A closer look reveals that systemic restrictions and resources are external factors while classroom management strongly depends on the teachers’ competences. On the one hand, one interpretation might be that it is much easier for teachers to ‘‘complain’’ about external factors than admit difficulties relating to their own performance. On the other hand, it might well be that teachers only perceive minor problems with classroom management and are troubled by restrictions. To clarify this, more research would be necessary. The relevance of resources and particularly of system restrictions differs significantly among the countries. These results are important for they highlight two aspects. First, the precondition for implementing IBL is different in the learning cultures. In countries such as Slovakia, Cyprus or Romania, where teachers perceive greater problems because of unavailable resources and also due to existing system restrictions, efforts to implement IBL will be more difficult. Second, the importance of systemic restrictions highlights that any effort to change teaching practice has to take organizational support and change into account. This requires involvement and cooperation with school authorities and policy makers. This question has to be addressed during implementation. Concrete elements of the school system which are most likely to hinder the uptake of IBL and ways to change them have to be identified. Further results which may be considered as striking can be seen in Figs. 6 and 8. Figure 8 shows that teachers in Germany, UK and the Netherlands consider their teaching as teacher-orientated whilst, for example, teachers in Hungary, Romania and Slovakia consider their teaching as more student-orientated. The same holds true for Fig. 6. Whilst mathematics teachers in Germany, the UK and the Netherlands seem to do very few experiments and have no focus on explaining the world outside, teachers in Hungary, Romania and Slovakia see their teaching differently. (The differences in science are smaller.) This perception may depend on what tradition teachers come from. On the one hand, teachers in the western countries may know about the expectations of the curriculum in relation to student-orientated teaching and that they do not fulfill them, whilst teachers from the eastern countries may have a tradition of

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very teacher-orientated teaching and any change from this may be considered as student-orientated. On the other hand, it may well be that in the atmosphere of change in the east, teaching has changed very much towards studentorientated teaching. These findings have still to be verified with further research. Enriching the quantitative data through, for example, interviews would be very useful. In some countries, notably in Germany, mathematics teaching is strongly teacher-centered and the difference between mathematics and science teaching is much greater than in other countries. This may be explained by the teaching traditions in these subjects and on the teachers’ beliefs of what IBL is. In many cases science teachers allow students to work on hands-on experiments in some lessons—and thus have experience with more open ways of teaching which they may consider to be IBL. In contrast to this, many mathematics teachers do not have these experiments and may stick to more traditional ways of teaching. This may also be the reason why more science teachers report doing IBL than do mathematics teachers. When running the professional development courses, teacher educators need to be aware of the differences between mathematics and science teachers. As to the different possibilities of interpreting the perceptions of teachers as discussed above, the PRIMAS evaluation will give a more profound insight into what goes on in classrooms. 5.2 Limitations of the study The results of our study are limited through the sampling procedure within the 12 countries. Due to external reasons we were not able to standardize this procedure, therefore we are not able to say how comparable the samples are and how representative they are for a specific region or even a certain country. Furthermore, it has to be investigated whether the given multiple-faceted definition of IBL interferes with the existing belief system and therefore leads to different understandings of IBL. 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 Gene`ve (Switzerland), Freudenthal Institute, University of Utrecht (The Netherlands), MARS—Shell Centre, University of Nottingham (UK), University of Jaen (Spain), Konstantin the Philosopher 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-Bolyai University, Cluj Napoca (Romania), Sør-Trøndelag University College (Norway), IPN-Leibniz Institute for Science and Mathematics Education at the University of Kiel (Germany). PRIMAS has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under Grant Agreement No. 244380.

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K. Engeln et al. This paper reflects only the authors’ views and the European Union is not liable for any use that may be made of the information contained herein.

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