1 Introduction

We are currently witnessing an explosion of international interest in mathematics teacher education, fuelled partly by the desire to make mathematics accessible to all (Adler, et al. 2005) and also by a growing concern to reverse the decline in students’ enthusiasm for mathematics and the consequent drop in the numbers of students pursuing scientific careers (Mullis, et al. 2008; Rocard 2007). In response, many initiatives have appeared in order to support teachers in moving away from traditional transmission-based approaches towards ‘inquiry-based’, ‘student-centred’, collaborative pedagogies, such as those currently commissioned by the EU. One such project is the project PRIMAS: Promoting Inquiry-based learning in Mathematics and Science (PRIMAS 2012).

In the context of this reform agenda, the design of replicable professional development models is an increasingly important focus for research. Most teacher education research is conducted with pre-service or practicing teachers with whom researchers normally work and is not ‘scaled up’ (Adler, et al. 2005). In our work, we are engaged in a design-research process that seeks to progressively design, analyse and refine professional development processes and products that may be used to help stimulate PD led by others. In this paper we describe the design of a professional development (PD) intervention program for mathematics teachers, describe its impact on the beliefs and practices of the participants and the pedagogical issues that arise.

The PD program was intended to support the investigation by teachers of effective inquiry based-learning (IBL) pedagogies. In the ideal IBL classroom, students are active participants. They observe and formulate questions; if problems are too complex, they simplify or model; they make reasoned assumptions, collect and analyse data, make representations, and make connections with what they already know. They interpret findings, check that they are sensible and share them with others. The teachers’ role is not to stand back and expect students to discover everything for themselves; it is rather to scaffold the processes of inquiry through the use of carefully designed tasks and structured lessons (Artigue & Blomhoej 2013).

Inquiry-based learning is a complex, multifaceted construct. The PD program was designed to help teachers study and synthesise effective component teaching strategies. These include: choosing substantive tasks that are extendable, encourage decision-making, creativity and higher order questioning (Ahmed 1987; Watson & Mason 1998); working collaboratively and developing dialogic talk (Alexander 2008; Mercer 1995); building on students’ prior knowledge (Black & Wiliam 1998); encouraging students to critically examine alternative approaches and achieve consensus (Inoue 2011). It is not the purpose of this paper, however, to evaluate IBL or attempt to answer its critics. Suffice it to say that following an international report (Rocard 2007), the promotion of IBL is currently a priority area for science and mathematics education in the European Union.

In this paper, we seek insights into two research questions:

  1. 1.

    How might PD resources be designed to foster pedagogies supporting IBL?

  2. 2.

    What impact might such resources have on the practices and beliefs of teachers, and what pedagogical issues arise as they use them?

The first question will be addressed through a discussion of the theoretical basis for the PD (Sects. 2 and 3) and its iterative development (Sects. 4 and 5) using a design research paradigm. The second question will be addressed by considering empirical evidence for the effects of the PD during its design and subsequent take-up as part of the PRIMAS project (Sects. 6 and 7).

2 A theoretical approach to designing PD

Our work may be characterised as one of ‘design research’. Design-based research is a formative approach to research, in which a product or process (or ‘tool’) is envisaged, designed, developed and refined through cycles of enactment, observation, analysis and redesign, with systematic feedback from end-users (Barab & Squire 2004; Bereiter 2002; Cobb, et al. 2003a; DBRC 2003, p. 5; Kelly 2003; Swan 2006a, 2011b; van den Akker, et al. 2006). Its goals are to create innovative tools for others to use, to describe and explain how these tools function, account for the range of implementations that occur and develop principles and theories that may guide future designs. In this case, the tools are a PD process and associated resources.

The design of the PD drew on social constructivist and socio-cultural theories of learning. From this perspective, teachers learn just as students do; they participate in social practices and through active engagement develop and internalise new ways of speaking and thinking. Goal-directed and tool-mediated activity are fundamental to this process and these are influenced by the rules (e.g. the curriculum goals); the communities within which teachers play a part (within the PD events and within schools) and the roles of participants within these communities (Engestrom 1999; Jaworski 2008; Vygotsky 1978; Wertsch 1991).

The goals of the PD design were to support the collaborative investigation by teachers of effective IBL pedagogies. Conceptual and physical resources (the tools) were found necessary to stimulate activity toward these goals. These included novel ‘genres’ of classroom activity, illustrated with classroom videos, and sample lesson plans. The design was planned to work at two levels; activities for the PD events were designed to mirror the intended classroom experiences of students. Rules and communities have a profound influence on the impact of PD. Teachers must integrate IBL into the culture of the school with its own curriculum goals, and they are expected to interact with and justify their actions to colleagues. As for roles, the power relations within PD are important. We do not want to appear authoritarian, telling teachers how to teach and limiting their creativity; neither do we want to deprive teachers of the wisdom of well-researched models. We see our role as PD designers, as selecting and suggesting potentially powerful stimuli and tools (e.g. PD structures, lesson plans) leaving it for teacher educators and teachers to adapt, apply and evaluate in local contexts. These tools should enable teacher educators and teachers to be challenged and to act reflectively in new ways.

Our PD is intended to allow cycles of discussions of pedagogical issues, classroom challenges, and reflective feedback (Even 2005; Müller, et al. 2011; Swan 2011a). First, teachers work on collaborative classroom activities that illustrate the pedagogical challenges of IBL. Second, they watch other teachers using these same activities on video. These are expected to provide a ‘challenge’ to existing practices. Third, teachers are encouraged to adapt and try the activities in their own classrooms, supported by sample lesson plans. Fourth, teachers meet together to share their classroom experiences, discuss the pedagogical implications and reflect on the growth of new practices and beliefs. This cyclical process is repeated at successive PD events, as new pedagogical issues are addressed. This process has resonances with Japanese Lesson Study (with its pattern of investigation, planning, research lesson and reflection (Lewis, et al. 2009; Stigler & Hiebert 1999)) though there are also major differences. Teachers are given sample lesson plans to adapt and it is not assumed that teachers are able to observe each other’s lessons nor that an outside expert is available to support the extensive analysis of all lessons. These differences we hope increase support and scalability in a European context.

3 Characterising teachers’ beliefs and practices

Ultimately, PD attempts to influence the beliefs and practices of teachers. Research has shown that teachers hold on to their beliefs and practices tenaciously, and attempts to dislodge or replace them through rational argument and persuasion are usually unsuccessful (Kagan 1992; Nespor 1987). In our PD, rather than seeking to persuade teachers to change beliefs so that they will behave differently, we invite teachers to take risks and adopt new practices so that they have cause to reflect on and perhaps modify their beliefs (Fullan 1991). As Guskey (1986) noted, professional development programmes are mostly unsuccessful in modifying beliefs, but when teachers are encouraged to adopt a procedure and find that it improves student motivation and achievement, significant changes in attitude may be attained. The design of our PD thus attempts to offer teachers opportunities ‘to doubt, reflect and reconstruct’ IBL pedagogies in an unhurried, ‘safe’ environment (Wilson & Cooney 2002). In evaluating our trials of the materials we therefore sought to develop a framework for describing the evolution of beliefs and practices.

Our description of the beliefs of teachers are based on characterizations described by Ernest (Ernest 1991a, 1991b) and Askew (1997), elaborated in Table 1.

Table 1 Beliefs about mathematics, teaching and learning
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Ernest suggests that a teacher’s belief system has three components; the teacher’s conception of the nature of mathematics as a subject, of the nature of mathematics teaching and of the process of learning mathematics. Askew characterized the orientations of teachers towards each of these components as transmission, discovery or connectionist. These categories are ‘ideal types’ and an individual teacher’s beliefs may combine elements of each of them, even where these appear to conflict. These categories were originally derived from studies of primary teachers and we recognize that they take on different interpretations in other settings. For example, we have found secondary and further education teachers attended particularly to the individual learning and collaborative learning aspects of the ‘discovery’ and ‘connectionist’ orientations respectively. It may further be noted that both discovery and connectionist orientations may foster IBL, however both empirical and theoretical analyses would suggest that connectionist orientations are more effective (Askew, et al. 1997; Kirschner, et al. 2006).

Many researchers report inconsistencies between what teachers say they believe about teaching and learning and what they do in practice (Fang 1996). Beliefs may be compromised in practice by day-to-day realities of classroom management, student expectations, available resources and so on. One must also be suspicious of self-reporting by teachers as they commonly claim changes that appear exaggerated to an outsider. Often cited is the case study of Mrs Oblier (Cohen 1990), who reported revolutionary shifts to her practice yet, when observed closely, these were revealed to be cosmetic. In evaluative trials of the PD material, where opportunities for direct classroom observation was often limited, we therefore sought students’ views of teachers’ practices as well as teachers’ self-reported practices. The evolution of the questionnaires used is described more fully in Swan (2006b).

4 Structure and purpose of the PD units

The PD units were designed to support the investigation by teachers of effective IBL pedagogies. The units are activity-based; and are built around the development and analysis of real lessons. Each unit includes a PD session guide for a facilitator (who may be a teacher) and handouts for participants, as well as sample classroom activities and lesson plans. The video sequences show teachers trying these materials with their own classes for the first time. Their status is not to exemplify ‘best practice’ but rather to illustrate the issues that arise as teachers attempt to modify their own practice. They invite participants to share in a learning process.

Moving towards an inquiry-based learning (IBL) approach raises many pedagogical issues for teachers: How can I encourage my students to ask and pursue their own questions? How can I help students to follow up these questions in profitable ways? How can I teach students to work cooperatively and to learn from each other? The PD is structured in a way that systematically tackles such questions in seven units (Table 2). These units are freely available online (Swan & Pead 2008, 2011) and are intended to provide a cumulative experience, and the gradual integration of the pedagogical challenges are illustrated by lesson plans.

Table 2 The PD units for PRIMAS
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We illustrate the activity sequence with one unit, Asking Questions that Promote Reasoning.

  1. 1.

    Make existing beliefs and practices explicit. Teachers are asked to identify the different types of questions they ask, the different functions served, the frequency they use them, and the most common mistakes they make when asking questions.

  2. 2.

    Consider ‘contrasting practices’. Teachers are asked to reflect on the types of questions that are most likely to encourage student inquiry, and are offered principles, drawn from research, for effective questioning (Watson & Mason 1998). Participants are shown a video of a teacher attempting to put such principles into practice, are invited to identify occasions where the teacher employs each principle and then consider the effects of such questioning.

  3. 3.

    Develop a lesson plan. Teachers are offered a situation and are asked to prepare an introduction, ground rules for interaction (e.g. ‘think, pair, share’), intervention strategies, and specific questions that may be asked at different points in the lesson. To support this, they are offered a lesson plan showing a possible structure for a 1-h lesson. An outline of this is shown in Table 3. The full lesson plan is more detailed, offering sample questions teachers might ask at various stages of the lesson and typical student responses.

    Table 3 A generic lesson plan for a 1-h lesson
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  4. 4.

    Teach a lesson. Teachers use their collaborative lesson plan incorporating the questioning strategies they have considered. They are encouraged to audio record some of the questions they use to share in the post-lesson discussion.

  5. 5.

    Analyse the lesson. After teaching the lesson, participants meet again to share experiences of questioning and reflect further at how students may be made more aware of the value being placed on reasoning. Further strategies for making reasoning more ‘visible’ are discussed.

The important role of the teachers in the development of these units must be mentioned. During early drafts of the units, groups of teachers were invited to use them. Each group met for 1 h to reflect on existing practice and discuss the pedagogical focus of the unit. Teachers then taught their own adaptations of the sample lesson plan, paying particular attention to its pedagogical focus. Finally they met up again to discuss what they had learned. This process was videotaped and analysed. The issues raised by teachers, their enacted lessons and their reflections were then incorporated into the revised, now video-enhanced PD resources. Thus the teachers’ own interpretations of the pedagogical ideas were systematically built into the resources.

5 The historical development of the PD units

The PD units evolved slowly over several years and have now been adapted for different contexts. When opportunity and funding has allowed, empirical data have been collected to evaluate the impact of the PD and lesson plans on teachers and students. In this section we describe some data gathered from three early cycles of the design. These involved a study with 44 teachers of low-attaining 16–19 year old students, a study with 24 teachers of adult numeracy classes and a study with 30 secondary school teachers (Table 4). Later in the paper, we report on more qualitative data from later trials of the material as they have been used more widely. At each stage of development, the content of the PD was adapted to incorporate issues raised by teachers.

Table 4 Three formative trials of the PD development
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The PD programs during the trials in Table 4 each consisted of an initial two-day residential workshop, followed by a number of 1-day follow-up meetings. In between, teachers were invited to use the lesson plans in their own classrooms.

The first version of the PD resources was constructed in a limited domain: the use of collaborative learning activities in the teaching of algebra to low-attaining students aged 16–19. A series of algebra lesson plans were developed with eight teachers over 1 year. These teachers were filmed using and discussing the lessons and this was incorporated into the PD. The lessons included specific ‘genres’ of classroom activities that were designed to engage students’ concept development: classifying mathematical objects, interpreting multiple representations, evaluating mathematical statements, creating and solving students’ own problems, and generalizing existing problem situations. In the second year the resource was used within a four-day course for 44 teachers spread over 6 months. In between meetings, teachers tried a variety of classroom tasks within each genre. The results of this empirical study are summarized below (Swan 2006a, 2007). The resulting resources were published and copies were sent to all Further Education Colleges in England by the Learning and Skills Development Agency, a government body (Swan & Green 2002).

Subsequently, government funding (from the then DfES Standards Unit) permitted us to develop a second version of the PD resource and make this freely available to all post-16 providers in England (Swan 2005). This was developed over 2 years, and expanded the content from algebra to relate to other content. Over 50 lesson plans were written and piloted with 90 teachers. Again videos were made and incorporated into the PD materials. Unfortunately, however, no systematic study of the effects of this PD was made. During regular inspections of post-16 education institutions, however, OfstedFootnote 1 came across these resources in use and they noted their use in their report:

These materials encouraged teachers to be more reflective and offered strategies to encourage students to think more independently. They encouraged discussion and active learning lessons. While some colleges were just dipping into the resources, a few had used the full package to transform teaching and learning across an entire mathematics team.

(Ofsted 2006 paras 32, 33).

Then a third UK government agency (the Department for Education and Skills), embarked on a further program (Maths4Life) to improve the teaching of adult literacy and numeracy. We were offered funding to develop PD resources for this and used this as an opportunity to further develop the resources. This time, a formal evaluation was conducted (Swain & Swan 2007, 2009; Swan & Swain 2010) and some of the results from this are shown below.

Up to this point, the emphasis in the PD resources had been concerned with the pedagogical skills necessary for teaching mathematical concepts. A further project, funded by an independent charity, Bowland Maths, allowed us to further extend this work to consider the development of mathematical processes with lower secondary classrooms. These processes included those involved in mathematical modelling: simplifying and representing, analysing and solving, interpreting and evaluating, communicating and reflecting. This was the first version of the resources that incorporated the IBL units in Table 2 (Swan & Pead 2008). This was evaluated with funding from one local district in England (Somerset). The results are summarized below (previously unpublished). Currently, the PD materials are being adapted for secondary classrooms around Europe as part of the PRIMAS project (Swan & Pead 2011). This adaptation involves removing specific cultural content (such as references to the English National Curriculum) and including some emphasis on science learning. We are currently redeveloping the resources to support the development of the mathematical practices (or processes) in the common core state standards in the US (Swan, et al. 2012). Evaluation of the use and impact of these is still in its early stages.

6 The impact of the trials of the PD units on teachers

Teachers were asked to rate their own beliefs by assigning weightings to each of nine descriptive categories (Table 1). These were cross-validated with more qualitative descriptions which showed remarkable consistency, when checked by independent researchers. The results concerning changes in beliefs of the teachers in England during the pilot studies (averaging over Mathematics, Learning and Teaching) are given in Table 5.

Table 5 Trajectories of changes in predominant beliefs (%)
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The FE teachers and the secondary teachers both began with predominantly transmission views. Both groups were focused on getting students through the examinations. The adult numeracy teachers, on the other hand, had lower expectations, and worked with much smaller classes that included students with severe learning difficulties. These teachers had a different profile, and the discovery orientation was more evident in this group.

Generally speaking, in the post-questionnaire in all three studies, teachers reported a shift away from transmission orientations (see Table 4). Initially the percentages of teachers expressing overall preferences for Transmission, Discovery, Connectionist were respectively 44:22:23. After the PD these ratios were 16: 21:53.

In Table 5 we have aggregated each of the 71 teachers’ reported orientations and allocated them to the most predominant one.

The trajectories of these changes are particularly interesting. Some of the transmission teachers claimed little change in their beliefs. These beliefs had been long-held and were associated with a need to be “in control” and a belief that students could not cope with IBL pedagogies:

Students are more confident with an imitation approach. Only stronger students can cope with non-linear dialogue.

(FE teacher).

Others blamed examination pressures for an unwillingness to change:

I feel that these (lessons) are very good for learning breakthroughs, but I don’t think they are going to get the bulk of my students through their exams. I think you need a ‘crammed’ approach. This is the big issue for me. I’d be quite happy to use these materials every lesson, the time went ‘like that’ and it’s great to see people not yawning and actually enjoying themselves. You don’t have discipline problems. But, I feel that for an exam, I’ve got to feel that I am giving them the knowledge that they need to pass that exam and I feel that I can do that through the traditional approaches and a bit of bullying.

(FE teacher)

Some teachers moved from ‘transmission’ towards ‘discovery learning’ orientations. These teachers clearly recognized the shortcomings of transmission methods and that ‘telling’ was not an effective way of helping learners to develop concepts and processes. In reaction to this, it appeared that they moved to a position in which they seemed uncertain of their own role in the classroom, beyond that of ‘facilitator’:

It is allowing them to make discoveries for themselves rather than you writing it up on the board […] It is their discovering, not mine; it is nothing to do with me really. I have just to keep an eye on it.

(Adult numeracy teacher).

Three-quarters of the teachers that began with a discovery orientation moved towards a connectionist orientation. These teachers appear to have adopted a more interventionist role, and were prepared to challenge and discuss concepts and approaches with groups of students in a collaborative manner.

These and other qualitative data suggested to us that many teachers may follow a transmission to discovery to connectionist trajectory as they at first withdraw support from students and then recognise the need to redefine their own role in the classroom. If, as some researchers assert (Askew, et al. 1997; Kirschner, et al. 2006), discovery approaches are less effective than transmission-based ones, this may have the consequence that teachers at first become less effective, before they become more effective as they develop along this trajectory.

6.1 The impact on practices

We further examined both teachers’ and students’ perceptions about the changes that had occurred in teachers’ practices. Both open and closed response questionnaires were used. These were given by the researchers to teachers during the PD sessions and by the teachers to students in the classrooms. The rationale and design of these questionnaires is given in Swan (2006b). On pre- and post-questionnaires, teachers were asked to describe how frequently they now displayed 25 classroom behaviours on a 5-point scale: 1 = almost never to 5 = almost always.

The results (Table 6) are ranked in order of the overall changes in means. Teachers described their own practices as mostly ‘teacher-centred’ at the outset of the PD and reported that these had changed towards more ‘student-centred’ practices by the end. This is reflected in the table by the S statements increasing in frequency, while the T statements decreased in frequency (these labels did not appear on the questionnaire). Teachers reported more collaboration and discussion (including the discussion of mistakes) giving more choice about the questions to tackle, fewer graded exercises, students were encouraged to be more creative, lessons were more responsive to student needs and less predictable.

Table 6 Changes in teachers’ practices (self-reported)
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As we have said, self-reporting is unreliable, so to confirm teachers’ accounts, we asked students to describe their teachers’ behaviours. In the FE project, this was only done on one occasion as the course was short and at the beginning students were unable to comment on teachers’ practices. We also found it difficult for the adult education teachers to administer questionnaires to students of very limited attainment. The results from the secondary schools are reported below in Table 7. The student statements were derived from the teacher statements by excluding those that refer to a teacher’s motivation for behaving in particular ways and strategic issues such as curriculum design and coverage. It was felt that students would be unable to respond to these. Noyes (2012) also used these items in a large survey with over 2,900 11-year-old students in state-funded comprehensive schools in the Midlands of England and the means from this data are presented for comparison.

Table 7 Changes in teachers’ practices (student-reported)
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The rank order of teaching behaviours reported in the pre-questionnaires for the Noyes data and the secondary schools is almost identical. The most predominant style, according to students, appears to be worksheet or textbook-led; the teacher selects the questions, demonstrates the method, expects students to practice this intensively, working mostly on their own.

Comparing the pre- and post-questionnaire data, there is evidence that the incidence of pair and group work, discussion and making connections between topics have all increased, and teachers are beginning to discuss multiple ways of doing questions. Comparing with the Noyes data, in these schools, there is perhaps less emphasis on following textbooks and imitating procedures than in other schools. A factor analysis was conducted on these statements and this showed that they do not form a uni-dimensional scale. The S statements taken alone, however, are acceptably consistent (Cronbach alpha = 0.72Footnote 2) and the pre-post changes using this measure are statistically significant (Table 8).

Table 8 Changes in the ‘Student-centred’ mean rating
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7 Issues arising for teachers

In the above projects, and as the PD resources have been disseminated more widely across the EU as part of the PRIMAS project, we have had many opportunities to observe and interview teachers. In this section we draw together and exemplify some of the major findings that have emerged in the United Kingdom and in the Netherlands. In order to preserve the relationship between the findings and the contexts involved (adult education, school education; UK, Netherlands), we present these issues study by study rather than in a thematic manner. We then synthesise the common issues that have emerged.

The principles underlying IBL are complex and teachers’ appropriation of them is often gradual, and at first, partial. In the UK-study involving adult numeracy teachers (Swain & Swan 2009), for example, 49 semi-structured teacher interviews and 110 classroom observations were carried out, and each teacher was observed between 3 and 6 times. These findings showed that some teachers had initially adopted superficial understandings of IBL pedagogies, seeing IBL as merely adding ‘fun’ or ‘enrichment’ to an otherwise dull curriculum. Others, as noted above, confused IBL with ‘discovery learning’ and did not support students sufficiently in their learning. This study also attempted to identify aspects of IBL pedagogy that appear to be more accessible for teachers and those that appear more problematic. By the end of the PD, a majority of the adult education teachers were observed effectively and consistently using unstructured, collaborative tasks, organising co-operative group work and using more probing questions to assess and promote reasoning. Teachers, however, found it much more difficult to develop connections and build on students’ prior knowledge. These aspects require sound content knowledge and an ability to flexibly adapt teaching to students’ needs ‘in the moment’. They also found it particularly difficult to focus on teaching process skills for problem solving.

The issues arising from the secondary school study were distilled from both oral and written responses made during structured debriefing sessions with the 30 teachers. A variety of issues emerged, which we list below. Teachers consistently expressed surprise at increased levels of student engagement and creativity when engaging in IBL activity. They reported that the lesson plans were shifting the emphasis from ‘answer-getting’ to analysing and reasoning, particularly when students were encouraged to assess the work of others (in units 6 and 7). A few claimed that this revealed misconceptions of which the teachers themselves had been unaware. Some began to recognise the need to reduce their expectations of what they might ‘cover’ in a lesson. Rather than completing lists of questions, they were exploring fewer, richer tasks in multiple ways. They began to recognise the power of giving formative feedback; rather than ‘correcting’ answers, asking follow-up questions to cause further reflection.

These teachers also reported many anxieties and struggles. Their main fears concerned the introduction of collaborative learning. They commented that discussions reduced the ‘pace’ of lessons and made it more difficult to ‘cover’ the required curriculum content. Several reported that their students did not want to discuss or explore mathematics. Many students had difficulty turn-taking, listening and elaborating each other’s reasoning, and talked in ‘disputational’ rather than ‘exploratory’ ways (Mercer 1995). This led to concerns about maintaining classroom control. Teachers were also concerned with accountability issues and frequently referred to the ephemeral nature of discussions and the lack of individual written outputs. “What hard evidence will I have of learning?”

In the Netherlands, the PD materials were taken up and used as part of the PRIMAS project. Twenty teachers from two secondary schools joined a PD program based on the resources, from different disciplines. In one school the teachers chose to join the program (they were allowed to choose from a school-selected offer of PD-activities). The teachers from the other school were asked to join by their school authority as part of their obligatory professional development. The teachers varied in level of experience. Teachers were paired, so that they were able to support each other in planning and observing lessons. They were asked to report on lessons through structured feedback forms (including topic, plans, experiences and new insights). Initially, teachers were sceptical of letting the students pose their own questions and follow their own lines of inquiry, but they nevertheless agreed to try. They met with mixed success. The examples below are drawn from this work.

A mathematics teacher created a worksheet for experimenting and explaining parallax in a ninth grade class. The teacher hoped that the students could find explanations within small groups. The questions on the worksheet were open and the students did not get any guidance during the process of searching proofs or explanations. The teacher ran from group to group to solve small questions or misunderstandings. She reported that: “these kind of activities might be suitable for better students, but not for whole class group work”.

(Researcher notes)

When asked to report about their experiences with new pedagogies the teachers also reported that some students felt uncomfortable with the new approaches. Without careful guidance and scaffolding of their inquiry process they became lost and unclear about the purpose of their activity. This example illustrates again the danger of equating IBL with ‘discovery’ approaches. One cannot expect minimal guidance to result in learning ‘unless students have sufficiently high prior knowledge to provide internal guidance’ (Kirschner, et al. 2006). Our lesson plans, however, do not advocate minimal guidance throughout the lesson, but rather strategic support at times of need. Teachers that used these plans met with greater success:

A physics teacher took an existing, highly structured, “cookbook”, practical assignment from his own curriculum and created a less guided version. The original task led students step-by-step to deduce a conclusion about the formula for converging lenses. The teacher revised his pedagogical approach, following the lesson plan from the video. At first the students were asked to think what they could investigate with the material they had been given. Students made suggestions concerning the relationship between the distance between the object and the lens and the size of the image obtained. After five minutes the teacher discussed students’ suggestions, prioritised possible questions to investigate, invited students to choose a research question and then continue with their investigation. The teacher monitored groups and restricted feedback to those relating to process. During the final discussion students’ findings were presented. While no student had discovered the formula, they had become more aware of the relationships with lenses when compared to the traditional cookbook approach. The teacher was happy with the increased motivation of the students, their creativity in trying to find a formula, and wanted to change practical assignments more often into this approach.

(Researcher notes)

From an analysis of the feedback from teachers, we found that when the teacher used the lesson plans provided to scaffold the students’ inquiry processes, or modelled their own planning on these examples, the lessons were consistently reported as more successful. Sixteen of the 18 feedback forms supported this pattern. In summary, the Dutch teachers removed the structure from textbook activities for experimenting with IBL-related pedagogies. The success of their reported experiences was related to the care with which they prepared lesson plans to structure student activity. It is important to note here that we are not talking about simply replacing the structured guidance embedded within textbook tasks with similar structured guidance given by the teacher. The structure within the lesson plans refers not so much to cognitive features, but rather to structuring the order and type of interaction that students engage in. Thus a structured plan may include periods for individual work, pair work, group discussion, reporting back, evaluation and so on. It also attempts to anticipate student difficulties and organise planned responses that lead to students further engaging in reflection and discussion. The provision of adaptable sample lesson plans that incorporate such features appear to be valuable resources for developing new pedagogies for inquiry-based learning.

We are currently undertaking further design research into the use of lesson planning to address the issues that have emerged from this paper. Only one example will be given. As we have noted, many teachers found it difficult to anticipate student approaches to open, unstructured tasks. In consequence, they struggled to respond appropriately and strategically to student learning needs as they arose in lessons. In response to this, we are now studying the effect of sample lesson plans that include the use of assessment tasks that students complete, individually, before lessons, together with a list of difficulties that students typically experience with these tasks and sample strategic questions that might move students’ thinking forward. In the PD, teachers are invited to assess their own students’ work on the assessment tasks, identify issues that are pertinent and use the sample questions as models for their own questioning. These questions may then be written into the teachers’ own lesson plans. These approaches are being trialled in current PD materials supporting the introduction of mathematical practices in the US (Swan, et al. 2012).

8 Concluding comments

At the start of this paper we set ourselves two research questions. We first set out to study how PD resources may be designed to foster pedagogies that support IBL. Our discussion illustrates something of the complexity and difficulty in designing and researching such resources in an authentic context. The PD exhibited many features that are reported to be ‘effective’: it was sustained, related to local contexts (Cobb, et al. 2003b), involved teachers in active and collective participation (Garet, et al. 1999), focused on teachers’ knowledge of content, pedagogy and principles (Hammerness, et al. 2005) and offered support for translating new ideas into everyday practice (Lee & Wiliam 2005). The ‘tools’ that were devised stimulated reflection and discussion on key pedagogical issues and the difficulties noted have provided ideas that will be incorporated into subsequent designs. The design process is continually evolving. Teachers are involved in the design, particularly in providing examples of their practice, for other teachers to scrutinise.

The second question set out to study the potential impact of such resources and the pedagogical issues that arise for teachers. The teachers claimed changes to their beliefs and practices, and that students also confirmed changes to teachers’ practices, but to a lesser degree. This may be due to a combination of the teacher unconsciously adopting a ‘melange’ of old and new practices (Cohen 1990), and the delay between a teacher first adopting and reporting a new practice and students’ noticing it being used in a sustained, embedded manner.

Teachers frequently reported to us that their understanding of the new pedagogies developed slowly, and that they continued to struggle with embedding and sustaining them. The most significant broad issues for teachers may be summarised as: confusing IBL with ‘discovery’ learning, fostering the development of processes, developing and managing collaborative cultures within the classroom and planning lessons that adapt to the emerging needs of learners.

We recognise many limitations of the work reported. While we have paid some attention to the culture within the PD events themselves, we have paid little to the various school-based cultures in which teachers work. In future designs we will need to give greater attention to this. In particular, we are beginning to recognise the importance of designing resources that teachers can use with colleagues and senior managers to help inform and evolve these local cultures.

Finally we note that, with the international effort being poured into PD that promotes inquiry-based learning there is an urgent need for design research to provide more efficient products and processes for PD. We hope that the products and processes described here and available on the websites will be a modest, but valuable contribution to this work.