Designing effective continued professional development for primary teachers during curriculum reform in mathematics

ABSTRACT

Mathematics curriculums worldwide are being refined to prepare students for the twenty-first century by focusing on developing students’ higher-level thinking skills. As a result, teachers need to adjust their pedagogical approaches to enact new curriculums, which is frequently facilitated through continued professional development (CPD). During curriculum change, the challenges to fostering effective CPD are often exacerbated, signalling a necessity to understand better how CPD can be structured during reform. This research study aims to design a curriculum resource that acts as a form of CPD, seeking to enhance teachers’ use of higher-level thinking questions in mathematics lessons while also gaining a greater understanding of what constitutes effective CPD during curriculum reform. Six Irish primary school teachers in an urban school collaborated for one year with the primary researcher to develop a curriculum resource. Analysis of data collected from observations, focus groups, and researcher field notes guided the iterative design of the curriculum resource. Design characteristics of the curriculum resource and their impact on teachers’ practice are discussed. Finally, suggestions for designing and facilitating CPD during periods of change and implications for further research are proposed.

KEYWORDS:

• Mathematics education
• continued professional development
• design
• curriculum reform

1. Introduction

To ensure students are equipped to overcome twenty-first-century challenges in the future, they must possess critical thinking skills such as analysing, innovating, and synthesising (Geisinger, 2016). Although trends in mathematics achievement worldwide show an increase in students’ mathematics abilities, their critical thinking abilities remain weak (Eivers & Clerkin, 2011; Schleicher, 2019). Mathematics education is undergoing periods of change globally to address these deficiencies. As a result, mathematics curriculums are being rewritten to incorporate pedagogical approaches that support students’ critical thinking skill development. Many recently released mathematics curriculums encourage teachers to use dialogue to increase students’ abilities to analyse, synthesise, and predict (Australian Curriculum Assessment and Reporting Authority, 2022; Ministry of Education, 2020; National Council of Curriculum and Assessment, 2023). Using cognitively demanding questions when teaching mathematics is integral to student dialogue (Boaler & Brodie, 2004; Imm & Stylianou, 2012). This pedagogical skill is complex and often challenging to use effectively in classrooms. Teachers often resort to asking less cognitively demanding tasks of students (Hiebert et al., 2005) or, if they do ask higher-level questions, are unsure how to respond to students’ responses (Moyer & Milewicz, 2002). Teachers must possess the required pedagogical knowledge and skills to deliver reformed curriculums effectively. Continued professional development (CPD) aids in preparing teachers to enact new curriculums as written.

An essential component of teachers’ professional growth is CPD. Unfortunately, delivering impactful CPD during curriculum reform can be problematic. Barriers to effective CPD, such as time, capacity, connection to practice, and school culture, can be exacerbated during periods of change (Porcenaluk et al., 2023). Although research on CPD is extensive, the characteristics of effective CPD during curriculum change at the primary level have not been thoroughly examined. There is a lack of studies examining whether a curriculum resource may act as a form of CPD during curriculum reform and its potential impacts on teacher practice. Therefore, additional research is needed to evaluate how CPD can be designed to overcome these barriers to ensure teachers are growing their knowledge skills to deliver new curriculums as intended.

This paper discusses a project aimed at designing a form of CPD which addresses the challenges to teachers’ professional growth during curriculum reform. The project adopted a DBR methodology integrating collaboration with six Irish primary school teachers in an urban city school over an academic year. The curriculum resource aimed to teach the importance of higher-level thinking, questioning and dialogue in mathematics lessons and how to incorporate questioning into mathematics lessons. The following research questions are discussed in this paper:

1. Can a curriculum resource be designed as a form of effective continued professional development during curriculum reform?

2. How did the developed curriculum resource impact teachers’ professional learning?

The research project was guided by relevant teaching and learning theories in the developed MACE (motivation, autonomy, community, and autonomy) theoretical framework discussed in this paper. These key concepts informed the curriculum resource's design and the analysis conducted through observations, focus groups, and researchers’ field notes.

2. Literature review and background

Education systems worldwide are examining their mathematics curriculums and identifying how they can better prepare students with skills to develop innovative solutions for twenty-first-century challenges. Ireland has recently joined other countries in revising their mathematics curriculums to address unfortunate trends indicating a weakness in student’s critical thinking abilities (Eivers & Clerkin, 2011; Schleicher, 2019). The Irish Primary Mathematics Curriculum (IPMC) was released to all primary and special schools at the start of the 2023 academic year, with full implementation starting in September 2024 (O'Connor, 2023). The IPMC changes little of the mathematics content taught but instead transforms how to facilitate students’ development as mathematicians with a productive disposition towards mathematics (National Council of Curriculum and Assessment, 2023). Teachers are encouraged to be facilitators of student learning and support student agency in learning mathematics. This constructivist approach to teaching and learning mathematics is linked to developing students’ higher-level thinking skills, such as analysing, predicting, synthesising, and problem-solving (Leinwand et al., 2014). One substantial change within the IPMC is the focus on incorporating dialogue into teaching mathematics. Structuring meaningful conversations that are cognitively engaging for students in mathematics can be a challenging pedagogical skill for teachers as numerous sub-skills are necessary for effective implementation.

2.1. Encouraging productive dialogue with effective questioning methods

Effective questioning integrated into mathematics lessons benefits teachers and students and is essential to enacting new mathematics curriculums. Asking questions of students has always been a component of teaching mathematics. However, teachers often stick to asking questions that require less cognitive demand from students (Black, 2001; Desli & Galanopoulou, 2015). These questions often require students to recall information, restate it, or provide a specific response. Although low-cognitive level questions are beneficial to inform teachers of a student’s understanding and guide the lesson, in isolation, they fail to develop students’ critical thinking skills adequately. Teachers who do ask higher-level questions often reserve these conversations for students already proficient in grade-level skills (Leinwand et al., 2014). All students, however, need exposure to high-level mathematics instruction and the opportunity to engage with cognitively demanding tasks.

To successfully enact new curriculums, such as the IPMC, teachers must incorporate all levels of questions into mathematics lessons to use dialogue in teaching effectively. The National Council of Teachers of Mathematics (2014) provides a framework which identifies four types of questions beneficial for teaching mathematics: ‘gathering information, probing thinking, making mathematics visible, and encouraging reflection and justification’ (pp. 36–37). Asking questions from all categories is paramount in helping all students learn mathematics at high levels. However, questioning is a complex skill for teachers to learn and implement. Effectively incorporating questioning requires teachers to understand the purpose of questions in teaching mathematics, plan appropriate questions of all levels related to the mathematical content, and generate potential student answers (Chapin et al., 2009). As there is no way to predict student responses perfectly when planning for instruction, teachers must also be comfortable providing impromptu responses to students, highlighting the complexity of this pedagogical skill. Therefore, it is vital to understand how to support teachers’ pedagogical knowledge and skill development to ensure students receive rigorous and quality mathematics instruction.

2.2. Importance of continued professional development during curriculum reform

To increase a curriculum’s chance of successful implementation, teachers must fully understand its aims, desired learning outcomes, and rationale while possessing the necessary pedagogical skills to teach students (Cheung & Man Wong, 2012; Darling-Hammond & McLaughlin, 2011). Throughout the world, CPD has comprised an essential component of curriculum change (Darling-Hammond & McLaughlin, 2011; Handal & Herrington, 2003; Roehrig & Kruse, 2005). Unfortunately, barriers to effective CPD often limit teachers’ ability to develop knowledge and skills. During periods of change, such as curriculum reform, these challenges, such as time, teacher capacity, school culture, and choice in CPD, may be exacerbated (Porcenaluk et al., 2023). Without addressing these potential barriers to CPD, teachers may fail to advance their skills and enact new curriculums fully.

In order to furnish students with an opportunity to develop critical thinking skills in mathematics, teachers must be prepared with the pedagogical skills which can be gained through effective CPD. However, designing CPD that compliments curriculum reform may require a reimagined approach. CPD should not only teach the skills necessary to deliver new curriculums but also consider the barriers to CPD that may be exacerbated during periods of change. This research builds on this viewpoint, examining how a curriculum resource designed as a form of CPD might address these obstacles.

3. Theoretical framework

CPD can be defined as activities that aspire to alter teachers’ beliefs, knowledge, and skills to affect students’ academic achievement positively (Guskey, 2002). Numerous frameworks exist for guiding the design, implementation, and analysis of CPD (Desimone, 2011; Guskey, 1999; Kirkpatrick & Kirkpatrick, 2023). At the time of this paper, no theoretical framework explicitly focuses on CPD during curriculum reform. Therefore, it was critical to identify theories to direct this project to develop a curriculum resource as a form of CPD. What follows is a brief overview of four concepts, motivation, autonomy, community, and efficacy and their corresponding theories, which support the development and analysis of CPD within this research.

3.1. Motivation in continued professional development

Motivation is a component of effective teacher CPD and is interwoven throughout all the concepts discussed in this theoretical framework. Ryan and Deci theorise that intrinsic motivation is required for an individual to learn and develop to their highest potential (2000). An individual’s desire for happiness and to satisfy their curiosity about a particular area are the foundations for intrinsic motivation (Ryan & Deci, 2000). On the other hand, a lack of intrinsic motivation can hinder an individual’s learning progression. Extrinsically motivated behaviours can result in individuals feeling disengaged with learning, lacking a sense of control over their lives, or even resenting the origin of extrinsic motivation (Deci & Ryan, 1985).

Teachers must feel intrinsically motivated to fully engage with CPD and integrate learning into the classroom environment, thus changing their approach to teaching mathematics over time. Although extensive research has been conducted on motivation as a psychological construct, how it supports teachers’ engagement with CPD has been studied very little (Appova & Arbaugh, 2018). Therefore, this research aims to contribute to filling this knowledge gap and better understand the role motivation plays in teachers’ willingness to participate in CPD during curriculum reform.

3.2. Autonomy in continued professional development

Autonomy plays a role in distinct ways when designing and facilitating CPD. Within CPD, a teacher takes the role of a learner but also retains their role as a teacher within the classroom. Therefore, it is necessary to identify how autonomy in both learning and teaching influences the success of CPD. Autonomy is closely related to the first concept of motivation. Ryan and Deci (2000) identify autonomy as one of the basic psychological needs that support the development of intrinsic motivation. Autonomous learners are more likely to engage in learning, successfully obtain new skills, and experience positive emotions (Niemiec & Ryan, 2009). In addition, autonomy is essential when considering how pedagogical skills and knowledge are displayed within the learning environment. Teachers desire autonomy when making instructional decisions. As curriculums change, teachers are more apt to develop buy-in towards the changes, increasing their likelihood of implementation if provided autonomy throughout the process (Briggs et al., 2018). In developing CPD, teachers must be provided with autonomy during the learning and when implementing new pedagogical skills.

3.3. Community in continued professional development

Developing and supporting a community of learners within CPD can guide teachers’ professional growth and implementation of new pedagogical skills. Vygotsky (1978) posits that the interactions between the teacher and student are critical to students’ learning. Structuring learning to meet the needs and preferences of each teacher during CPD is incredibly important, even though it is exceptionally challenging. The zone of proximal development is often attributed to children’s learning; however, it applies to adults as learners (Blake & Pope, 2008). Vygotsky (1978) writes that understanding the learners’ current understanding and the next logical step in the learning progression with the teacher's assistance is valuable to meeting each student’s needs. Scaffolding learning by providing adequate support to teachers that allows productive struggle to occur can help bridge that knowledge gap (Wood et al., 1976). CPD experiences must meet teachers where they are in their learning progression to aid their professional growth. By establishing meaningful relationships or communities of learning within schools, teachers may benefit more from the CPD they undertake.

3.4. Efficacy in continued professional development

Teacher efficacy supports teachers in developing pedagogical skills during CPD and implementing them into their practice. Bandura’s (1997) self-efficacy theory emphasises the importance of believing in one’s abilities to carry out a learned behaviour or skill. Self-efficacy is a complex concept that can manifest within individuals differently. Concerning CPD, self-efficacy can be supported by persevering through challenges, modelling oneself after colleagues’ success, and being encouraged verbally by peers or authority figures (Bandura, 1997). In addition to external individuals playing a role in CPD, the resources available to teachers can affect their self-efficacy. Eden (2001) theorises that means efficacy can significantly impact one’s self-efficacy. Means efficacy refers to the ability of available external resources to contribute to one’s success on a task (Eden et al., 2010). Therefore, the resources provided to teachers during CPD to supplement their learning or teaching are pivotal in advancing their pedagogical skills.

As a result of identifying theories to guide this research, the MACE theoretical framework was developed. The MACE framework provided a foundation for developing the curriculum resource, implementing it with teachers, and analysing the effects on teachers’ pedagogical knowledge and skills.

4. Method

4.1. Research design

An educational design-based research (DBR) methodology was adopted, which provided a method for iteratively designing and creating interventions to solve relevant issues in education while also contributing to the theories underpinning the research (Plomp, 2010). A repeated critique in educational research is that it is often too far removed from real-world classrooms, resulting in outcomes that fail to progress education adequately (van den Akker, 2006). DBR aims to offer a different approach to educational research to address this criticism. Stemming from the work of Brown (1992) and Collins (1992) on design experiments, DBR involves purposefully affecting the learning environment under observation to create evidence-based outcomes from the research. As the IPMC was being introduced in classrooms almost parallel with this project, there was a sense of urgency for developing a potential solution to a real-world problem aided by DBR. Although varying models exist for utilising DBR, they overlap in countless ways, defining distinct characteristics of DBR, including flexibility in design, an iterative design process, close collaboration with participants, and being conducted in a real-world environment (Collins, 2012). McKenney and Reeves (2012) also postulate that DBR should act as a form of professional learning for participants as a third outcome. In our research, we use the model McKenney and Reeves (2018) put forward on utilising DBR as a methodology.

Figure 1 depicts an overview of this project’s design, influenced by McKenney and Reeves (2018) during the first two years of execution. The arrow signifies reversibility in the process, signalling that the process was not necessarily linear, and portions of each phase were revisited throughout. The project began in June 2022 by exploring existing problems in teaching primary mathematics through policy review and focus groups. As a result, the problem of teaching critical thinking skills was identified. Following this phase, three design cycles took place from September 2022 to June 2023, in which the researchers collaborated with six primary school teachers to develop a potential solution to the identified problem.

Figure 1. Overview project phases guided by McKenney and Reeves’ (2012) model for conducting educational design research.

4.2. Research participants

Participants were recruited by contacting all primary schools within the area accessible to the primary researcher. The project design required participants to develop, use, and analyse a solution to a real-world issue developed in collaboration with the primary researcher. It was also critical for the school environment to support this research project as teachers would contribute time, capacity, and resources to the project throughout an entire academic school year. In following the concept of community in the MACE framework, it was a goal for the teachers participating in the project to work at the same school and preferably teach the same grade level to allow for a community of learners to form. In addition, as relationships and trust are essential to DBR (Cobb et al., 2003), the project aimed to recruit a group of teachers willing to work closely with the primary researcher. An urban city school was ultimately chosen after discussing the project and requirements with the principal, support staff, and teachers to gain buy-in from all involved. The school consists of teachers of third through sixth class of mainstream students. In addition, four special classes are present at the school, including a class for students with specific language impairments, dyslexia, general learning disabilities, and one for students who are deaf.

The project included two separate cohorts of teachers: (1) the six fourth-class teachers, which consisted of four classroom teachers, one special education teacher, and one special-class teacher, and (2) the remaining teachers at the school from third-class through sixth-class. The first three design cycles focused on working alongside cohort 1 to develop a solution to the agreed-upon issue of developing students’ higher-level thinking skills. Design cycle 4, in progress at the time of this paper, called for cohort 2 to use the developed solution and report their experiences to further analyse its usefulness and effectiveness.

Ethical approval was obtained from the relevant research committee board before data collection began. Participants were informed with written consent to be part of the study.

4.3. Models of continued professional development

The design and subsequent analysis of the curriculum resource developed in this project were guided in part by CPD models from Ball and Cohen (Ball & Cohen, 1996), Guskey (Guskey, 1999), Kirkpatrick and Kirkpatrick (Kirkpatrick & Kirkpatrick, 2006), and Main and Pendergast (Main & Pendergast, 2015). A summary of the models and their application to the project are provided in Table 1.

Table 1. Models of designing and evaluating CPD utilised in the project and their corresponding applications.

Model and Author(s)	Application to Research
Utilising curriculum materials as methods of professional learning (Ball & Cohen, 1996)	Informed the decision to develop a curriculum resource that guides teachers through using questioning effectively in mathematics lessons, aiming to consider the barriers to CPD during reform.
Evaluating Professional Development (Guskey, 2002)	Guided evaluation of the developed curriculum resource as a form of effective continued professional development and its subsequent analysis.
Evaluating Training Programs (Kirkpatrick & Kirkpatrick, 2006)	Informed the evaluation of the curriculum resource in terms of participants’ reactions, learning, behaviour, and results.
Evaluating features of CPD (Main & Pendergast, 2015)	Provided a validated questionnaire for evaluating the final version of the curriculum resource implemented with Cohort 2 of teachers.

4.4. Data collection

Data collection within the first three design cycles with the first cohort of teachers consisted of three forms of data collection: focus groups, observations of instruction by the primary researcher, and informal individual conversations with teachers documented by field notes.

After each eight-week design cycle, focus groups were conducted with cohort one teachers. The primary researcher conducted the focus groups using a semi-structured format to allow teachers to feel comfortable guiding the conversation (Harrell & Bradley, 2009). Focus groups allowed a deeper look into teachers’ perspectives, experiences, and beliefs about the curriculum resource (Cohen et al., 2017). In addition, the focus groups aimed to analyse design features of the curriculum resource concerning the teachers’ professional learning to inform changes necessary before the subsequent design cycle.

As part of the research project design, the primary researcher visited the school a minimum of once per week. Guided by DBR methods, which recommend developing relationships with the participants, the primary researcher supported teachers through modelled lessons or assisted students during the lesson. Throughout these weekly visits, the primary researcher recorded notes about teachers’ lessons, student work, and teachers’ use of the curriculum resource. These observations included photos of student work or resources used to teach mathematics concepts. The researcher recorded these reflections during and after each classroom visit.

During the weekly visits to teachers’ classrooms, informal conversations occurred throughout the school day. These conversations between individual teachers and the primary researcher allowed the teachers to ask questions or provide insight into using the curriculum resource related to their unique classroom. The primary researcher took notes of these discussions, which helped inform the following focus group sessions and the iterative design of the curriculum resource. These conversations gave a more individualised perspective on using the curriculum resource that may not be uncovered in focus group conversations.

4.5. Data analysis

After each design cycle, focus groups were transcribed. Transcriptions were analysed using guidance from Galletta and Cross (2013) on qualitative data analysis from interviews and Birks et al. (2008) on memoing to make sense of data through conceptual means. This process incorporated becoming familiarised with the data, generating codes through multiple iterations, developing themes and sub-themes based on the text, and finally synthesising these codes into categories (Galletta & Cross, 2013). The data was input into a spreadsheet linking direct teacher quotes or field notes to each code to ensure that evidence supports codes and themes. A sample of this process is provided in Figure 2. Initial codes were then reviewed to combine those of a similar nature. Finally, the codes were combined into broad themes, reviewed in this paper's results and discussion sections. The MACE theoretical framework was utilised throughout the initial coding of the data and the generation of themes and categories. This process entailed reviewing the data and identifying where motivation, autonomy, community, and efficacy themes were evident. Figure 2 provides insight into how the analytic memos were analysed using the MACE framework.

Figure 2. Data analysis of transcribed focus group interviews showing links between direct quotes, memos, and codes.

5. Results

The results of the first three design cycles and emerging themes from the analysis are presented in the following sections, centred around the two research questions addressed in this paper. Data from observations and focus groups is provided to support the findings.

5.1. RQ1: can a curriculum resource be designed as a form of effective continued professional development during curriculum reform?

This project first entailed the development of a curriculum resource as a form of CPD. After three phases of iterative development, a curriculum resource was developed that was deemed a form of CPD and addressed challenges to professional growth during reform. The concerns of time and connection to practice are focused on within this paper to allow for a more in-depth review.

5.1.1. Time’s impact on ideal versus realistic design components

The curriculum resource was designed for teachers to use independently in their classrooms as they saw fit. Therefore, it was essential to examine if teachers were driven to use the resource by intrinsic motivation, as identified in the MACE framework. Focus groups indicated that time was a primary influence on motivation. Teachers agreed that the curriculum resource helped teach mathematics. Unfortunately, from teachers’ perspectives, it was unrealistic for them to read through the entirety of the curriculum resource due to the time constraints they were under. One teacher commented during the first design cycle.

It takes time for a teacher to read through, ehh, read through the leaflet, and when you’re in class, you don’t have that time, and it’s very much at the moment.

Teachers agreed that the curriculum resource needed to be designed to allow them to glance at potential questions to ask in a lesson. The lengthy four pages of the resource’s first design deterred teachers from doing this. Teachers agreed that having a one-page resource developed and on hand for each mathematical concept they teach would allow for a scan for questions to ask during that day’s lesson. Teachers suggested that the curriculum resource be designed as a one-page sheet for each mathematical concept that could be easily stuck into a textbook. Another teacher commented in response.

Pages like that from the PDST, I used to stick on my board. And they were my glance cards, keeping me on track.

Other teachers agreed that they often lost resources provided during CPD workshops or filed them away and forgot about them. Therefore, the curriculum resource needed to be physically accessible. As a result, the curriculum resource was printed on cardstock, laminated, and placed on a binder ring so teachers could easily organise and store it.

The curriculum resource contained introductory pages explaining how to use it, the rationale behind questioning (Figure 3), and a two-page resource for each mathematical concept (Figure 4). While one teacher replied that this feature contained ‘good to know’ information, another recommended that it be included ‘in the first one’. As a result, the design for the second and third design cycles incorporated a one-sided page resource for each mathematics topic they taught (Figures 5 and 6). The information sheet was provided once as a reference if teachers needed it.

Figure 3. Initial design incorporated a two-page overview of how to utilise the curriculum resource.

Figure 4. Example of initial curriculum resource with a two-page design.

Figure 5. Example of design cycle two’s design as a one-page curriculum resource, which includes a QR code for additional resources and guidance.

Figure 6. Example of the curriculum resource after design cycle 3.

Interestingly, one teacher recommended that an additional resource be developed that suggested what concrete manipulatives could be used alongside the questions. Other teachers agreed that they do not often remember or know how to use various manipulatives alongside probing questions, such as pattern blocks or base-ten blocks. It was agreed upon that this reference sheet should be external to the curriculum resource on questioning. Therefore, the second design cycle included a QR code teachers could scan to access a recommended list of manipulatives, both physical and virtual, to use when asking questions for each mathematics concept being taught (Figure 5). Focus groups from design two concluded that although the external resource seemed beneficial in content, it was not used by any teacher during design cycle two. One teacher commented.

I haven’t scanned your QR code at any time.

In response, the other teachers added their agreement, even laughing as they admitted the suggestion they made from design cycle one was used by none of them.

Data suggests that ignoring the requested resource was partly because it was not easily and quickly accessible, further emphasising the importance of a curriculum resource being initially designed with simplicity as a focus. Teachers recommended that future resources with additional information beyond the questioning guidance be developed as separate physical resources that teachers can use if necessary.

5.1.2. Utilising the curriculum resource alongside a textbook

As part of the data collection, the primary researcher observed teachers’ mathematics lessons and co-taught alongside each of them on average four times throughout the academic year. The primary researcher was in at least one classroom per week. During all three design cycles, all observed lessons utilised a textbook. The SET teacher did not rely on the mathematics textbook for every lesson, instead incorporating other resources and sometimes not using a textbook. The special class teacher rarely used a textbook, as observed by the primary researcher and instead focused on using online resources or real-world mathematics tasks found from sources other than a textbook.

The focus groups also showed teachers’ reliance on using a textbook to teach mathematics. During the first design cycle’s focus group, one teacher explained their use of the textbook, indicating their use of it as almost problematic, stating.

You can get tied to the book. You know you gotta get through this page, gotta do this chapter. And you’re goin’ okay, well, who does this serve at the end of the day? Is it just to be able to say that’s all been done?

Other teachers agreed with the teacher’s comment on textbooks, stating that they often ‘get caught up in the book’ and that lessons often focus on ‘racing to finish the pages for the day’. Field notes indicated that teachers often utilised the resource primarily at the start of a lesson, followed by students completing work in a textbook without integrating more questions from the resource. As the purpose of the curriculum resource was to guide teachers’ knowledge building and use of questioning rather than change their textbook use, it was decided that the curriculum resource should complement the textbooks they were using. As a result, the second iteration of the curriculum resource closely followed the lessons in the textbook used by the four primary classroom teachers. The rationale was that it would strengthen the curriculum resource’s connection to practice and increase the likelihood of using it.

In the subsequent focus group after design cycle 2, the subject of textbook use was brought up again. Like before, teachers expressed their tendency to be attached to the textbook while, at the time, identifying issues resulting from strict textbook use. One teacher commented.

I think, in my opinion, the book is a million miles from perfect. You know, they have question 1, 2, 3. And 1 might be one concept, and 2 may be a completely different concept and 3 is the same as 1. And they’re all over the shop.

Despite the criticisms of the textbooks used daily in their classrooms, teachers agreed that they provided a structure for teaching the content throughout the year. There was a consensus that without that structure, they might overlook a particular concept or not spend the appropriate time teaching it. These issues relate closely to the theme of time as a barrier to effective CPD. One teacher stated,

And again, going back to the time thing. If there isn’t the structure of the book, you do end up kind going down a rabbit hole on a topic and going, oh, this is great and we’re having a great time, jeez, that two weeks is gone on something that should have taken half an hour

As a follow-up to these comments, the primary researcher asked the teachers whether the curriculum resource pairing with their textbooks was important to them. The teachers all indicated that they thought this was a beneficial design characteristic that should continue into subsequent designs of the curriculum resource.

The primary researcher modelled lessons using the curriculum resource without a textbook. In reflecting after these lessons with teachers, they commented that it was valuable for them to observe conversations with students centred on students’ thinking and understanding, which they claimed can be hindered with strict textbook use. Interestingly, even after these modelled lessons and positive teacher feedback, the textbook remained the primary use of mathematics lessons. These observations may indicate the necessity for curriculum resources to be provided with lessons or easily used alongside textbooks to increase the likelihood of their use.

In answering the first research question, results from the first two design cycles indicate that curriculum resources as forms of CPD should be designed to fit the teachers’ current practice while integrating the targeted pedagogical skills. It was essential, for example, that the curriculum resource did not require an abundance of planning to be used. A simple design may encourage teachers to use the resource. Teachers also wanted a resource aligned with the lessons and resources already used, such as textbooks. Although teachers were willing to learn new pedagogical skills through curriculum resources, they seemed to desire the comfort of using lessons they had previously taught and were familiar with using.

5.2. RQ2: How did the developed source impact teachers’ professional learning?

The study's second aim was to analyse how the developed resource affected teachers’ professional learning. Two identified themes concerning this research question emerged and are discussed below, supported by data collected throughout all three design cycles. The data below was analysed using guidance from Guskey and Kirkpatrick, and this paper focuses on the evaluation through the teachers’ reactions and their learning.

5.2.1. Reactions to the curriculum resource as a form of continued professional development

Within focus groups, teachers expressed that the curriculum resource reminded them of best practices they had learned previously. The school's principal participated in the focus group in the first design cycle. She commented that all the teachers participating in the project were, as she stated, ‘very experienced class teachers’ and posed the following question to the other teachers.

I think it’s interesting to hear their perspectives, because, you know, some of these methodologies, it might have been a while since we engaged with them. And we would … have maybe done them in the past, but I’m just wondering, from your own perspective, was it like almost like a CPD, nearly, or a reminder?

In response, the teachers agreed that the curriculum resource was a form of CPD. In discussing teachers’ professional learning, numerous mentions were made regarding lessons the primary researcher modelled to show the use of the curriculum resource. The teachers responded that seeing the curriculum resource be used in a modelled lesson with their students was highly beneficial for them and more effective than traditional CPD. One teacher stated.

I think that, the lessons that you modelled for me, in my class, Jane, I think, I really enjoyed them the most. Cause you know sometimes when you’re at CPD, you kinda go to, some seminar and you’re given all this information. But to see something modeleled, done with the children that you teach and see. You know, it’s definitely hits home better.

As the teachers pointed out the importance of modelled lessons, it was essential to understand whether modelling lessons were a valuable component of the curriculum resource or a necessary one. Therefore, the primary researcher who moderated the focus groups inquired about how the curriculum resource could be modified to be successful without using modelled lessons. Teachers immediately jumped at the idea of accessing online videos that modelled instruction. However, they quickly pointed out that modelled lessons are far less valuable than watching someone teach in their classroom. One teacher pointed out.

I think you need to see the person in your class, dealing with the personalities in your class. You know dealing with the students you find most difficult to get the information across. And I think there is nothing that beats in-class support.

Other teachers agreed with that sentiment and indicated that while videos of lessons are the ‘next best thing’, it was less impactful than modelled instruction in person. The teachers went on to recommend that accompanying videos to the curriculum resource needed to be in an Irish classroom and show different levels of students, including students who are both bored because they have mastered the content being taught and students who are multiple levels behind.

Although teachers mentioned the benefits of watching another teacher, they were less willing to open up their classrooms to other teachers or even watch another teacher at their school. After a modelled lesson, a teacher stated how much they had learned from the primary researcher, even in a thirty-minute lesson. Upon hearing this, the researcher offered to schedule time for the fourth-class teachers to watch each other. Immediately, the teacher declined the offer, stating that they were not an expert.

Through these discussions, it was evident that modelled instruction using the curriculum resource and showing the pedagogical skill of questioning was a suitable use of teachers’ time and progressed their questioning skills. This discussion led to the addition of a fourth design cycle, in progress during the publication of this paper, which has teachers utilise the finalised curriculum resource without support from the primary researcher. The aim is to understand better if modelling was essential to the success of the curriculum resource.

5.2.2. Teachers’ ability to identify stages of their professional learning

While using the curriculum resource, teachers began to identify areas in their teaching that they wished to develop and the additional support necessary for that continued growth. Throughout informal discussions during observations and focus groups, teachers began to express how their perspectives on questioning in mathematics shifted to recognising the pedagogical skill as critical to teaching mathematics. As this occurred, teachers began to recognise the need to learn more about integrating this practice. During the second design cycle’s focus group interview, one teacher commented on how their practice had gradually shifted due to using the curriculum resource. They commented on the use of questioning in the classroom.

Well I know that I’m more conscious of talking about it and trying to talk through. Now, not massively, but we do try and discuss what we’re doing a little bit more you know. And that has helped.

Other teachers also recognised how their teaching practice had changed, referencing incorporating more discussion in their lessons. They also witnessed students’ increased willingness to participate in those conversations compared to the start of the school year. Teachers identified the next step in learning to ask higher-level questions and respond to student responses. One teacher recommended the following for the curriculum resource’s third design.

What would be helpful, I think, just thinking off the top of my head now, would be, a response you get back from a child, or an answer. And you are saying this mean that they don’t get step three. Rather than this means they don’t get any of it, you know.

The conversation then shifted toward teachers’ struggles with using the curriculum resource, referencing time as the continued challenge. One teacher recognised questioning was beneficial in teaching mathematics but stated.

Well, two questions given, if you ask those two questions and you get six responses and you get 12 responses, and that’s … 

To which another teacher cut in with their response,

Time.

The discussion then shifted toward how the teachers would want that information presented in the curriculum resource. The primary researcher recommended a separate sheet with the potential student responses and how to respond. Teachers, however, were hesitant to agree that another sheet would be utilised as the additional resource developed per teachers’ request was ignored.

The results of design cycles one and two indicate that teachers’ professional learning was positively impacted by utilising the curriculum resource. At times, teachers continued to develop skills they had previously learned. In addition, teachers began integrating new strategies for teaching mathematics into lessons, such as questioning and effective dialogue. In addition, teachers reported that they learned how better to integrate questions into lessons and saw the positive impacts of such a pedagogical approach. However, discussions with teachers indicated that although they saw the value in questioning in mathematics lessons, it uncovered additional challenges to this teaching approach. Successfully meeting students’ individual needs when facilitating discourse through questioning is complex, and teachers desired additional training.

In connection with research question one, although the curriculum resource developed as a form of CPD, data indicates there may be limits to teachers’ professional growth from such a resource. As indicated by the teachers in focus groups, they desired to understand more clearly how to respond to students’ answers after questions were posed. However, adding this guidance into the curriculum resource seemed unmanageable for teachers and was unlikely to be utilised. Overall, the data in this project's first two design cycles indicate that there may be limits to how much pedagogical knowledge and skills can be covered in a curriculum resource acting as CPD and, therefore, limits the extent to which teachers’ professional learning is affected. This deduction suggests that curriculum resources as forms of CPD may be most beneficial when they focus on one specific subskill of a pedagogical approach and are supplemented with other forms of CPD.

At this point, the complexity of CPD in terms of individual teacher needs should also be noted. Although these themes were present in this data, more research is necessary to determine how these findings transcend other populations of teachers and students. In addition, it is worth pointing out that due to teachers’ individual preferences, beliefs, and past experiences, there is likely not a one-size-fits-all approach to CPD. Offering multiple outlets for professional development during curriculum reform is likely the optimal approach.

6. Discussion

This DBR research project aimed to develop a curriculum resource to aid primary teachers in learning about and implementing effective questioning into mathematics lessons to be used during periods of curriculum reform. As a result of three design cycles, a curriculum resource was developed in coordination with six primary school teachers.

The outcomes of this research resulted in a design for a curriculum resource as a form of CPD that other teachers can use by adapting the questions to match the mathematical content. Valuable design characteristics of the developed curriculum resource can also be translated to other resources in development. In addition, this research provides insight into how a curriculum resource can be designed to contribute to teachers’ professional growth. Designing a curriculum resource that allows teachers to use it with their current practice can motivate teachers to use it without feeling overwhelmed or needing to change vast swaths of their practice simultaneously. Instead, a curriculum resource that encourages small yet powerful adjustments to teaching over a sustained period may increase buy-in from teachers.

In examining the results in combination with the potential barriers to CPD during curriculum reform: time, connection to practice, school culture, and choice, it is evident that teachers’ desire to learn and grow professionally can be thwarted by the structure of the CPD and support provided. Guided by the MACE framework, the themes of motivation and community stood out within the data discussed in this paper.

6.1. Motivation for using curriculum resources as forms of continued professional development

A key component of the MACE framework is how motivation might impact the usefulness and effectiveness of a curriculum resource as a form of CPD. Without intrinsic motivation to participate in professional development opportunities, teachers may fail to adequately benefit or fully integrate new learning into their practice (Ryan & Deci, 2017). The data discussed from the first two design cycles of this project reveals that teachers are motivated to use curriculum resources that consider the time and capacity of teachers and are in part aligned with the resources and pedagogical approaches they already have in place.

The overall aim of this project’s designed curriculum resource is that it can be a form of CPD that does not require teachers to attend training outside of the school day or rely on CPD facilitators to reap its benefits. It was evident through the data that motivating teachers to utilise the curriculum resource depended in part on the physical design of the curriculum resource. It was essential for teachers that the curriculum resource allowed them to extract information efficiently immediately before or during a lesson. Too much information or lengthy steps teachers must perform could result in the resource being ignored altogether. This finding potentially indicates that the structure of the curriculum resource is as vital as the content for initially engaging teachers in its use. Teachers want to engage in more CPD (Mullis et al., 2020), although the time available for professional learning poses a significant barrier (OECD, 2019). If teachers are learning a new curriculum, time will likely become even more sparse, emphasising the need to design resources and CPD that teachers can easily and quickly digest.

Another element affecting teachers’ motivation to use a curriculum resource as a form of CPD relates to designing it to fit within their current practice. Research on CPD indicates that teachers value CPD that connects to their current practice rather than being generalised (Owens et al., 2018). In this project, teachers used mathematics textbooks almost daily. Designing the curriculum resource to complement the textbook motivated teachers to utilise the tool. However, during observations, it was noted that teachers rarely referenced the resource when having discussions with individual students as they worked on textbook pages. Teachers focused on guiding students to correct responses to textbook problems, indicating that merely pairing the resources together may not fully motivate teachers to use the resource at all times.

The data also indicates that the curriculum resource as a form of CPD should target one specific skill, potentially simplifying that skill to a few simple actions teachers can take to implement it into a lesson. Teachers recognised there was more to questioning than simply choosing and asking questions. However, adding these subsequent steps to effective questioning of the resource did not result in teachers utilising the additional steps. This research indicated that teachers would be more motivated to use the curriculum resource and integrate a new pedagogical skill if they could quickly and easily implement it. Curriculum resources aimed at providing CPD to teachers may benefit teachers more if they concentrate on a subskill of a more extensive complex skill.

6.2. How community impacts the use of curriculum resources as forms of continued professional development

The theme of community from the MACE framework also appeared throughout the analysis. The curriculum resource aimed to be a tool that teachers could use independently. However, due to the nature of DBR, the primary researcher was frequently present in teachers’ classrooms. As relationships were formed, teachers asked for additional support in using the curriculum resource through modelled instruction and in-class support. Throughout every focus group interview, teachers referred back to the value of watching a lesson be modelled using questioning techniques. Teachers reiterated that nothing can substitute watching an expert implement a pedagogical skill in their classroom with their students. Relating to connection to practice, the data indicates that teachers greatly benefit from seeing how a pedagogical skill, curriculum resource, or CPD opportunity relates to their classroom environment. The literature supports the importance of learning communities in teachers’ professional development (Admiraal et al., 2021).

Interestingly, although teachers valued modelled instruction from the primary researcher, they were vehemently against watching one another teach, viewing themselves as non-experts. Observing peers can significantly help teachers refine their approaches to teaching mathematics (Sjöblom et al., 2023). Teachers who opt out of opportunities for modelled instruction may miss out on learning new skills. In this project, teachers reported greatly benefitting from using the curriculum resource. However, this was done in coordination with modelled instruction centred around the importance of social interactions arising from the community component of the MACE framework. It is critical to understand further the role individualised support from peers or experts plays in curriculum resources as forms of CPD to conclude whether they can stand alone as effective forms of professional development. Research indicates that teachers must feel a sense of trust and appropriate levels of challenge when learning alongside others (Bolam et al., 2005). However, suppose teachers feel uncomfortable watching their colleagues or opening up their classrooms to model lessons, as they did in this study. In that case, schools may need to examine who can provide this critical component of CPD. There is also a need to identify further how modelled lessons can be integrated into CPD during curriculum reform while being mindful of teachers’ time and capacity.

6.3. The role of curriculum resources in continued professional development during mathematics curriculum reform

Curriculum reform often requires teachers to develop the pedagogical skills necessary to implement new curriculums. Evident worldwide in updated mathematics curriculums, teachers are being asked to implement approaches to teaching mathematics that may require a shift in beliefs and skills, which can require significant support and time to develop (Dooley, 2019; McGatha et al., 2009). This research supports the literature in classifying dialogue and questioning in mathematics lessons as complex skills to learn and integrate into lessons. Although teachers in this project requested additional support in using questioning, they also indicated professional growth due to using the curriculum resource. In coordination with curriculum reform, curriculum resources may play a vital role in supplementing teachers’ professional development; however, they will likely need to be supplemented with other methods of CPD.

Finally, it is critical to mention that throughout the data, it was indicated that meeting the individual needs of teachers was crucial to the success of the curriculum resource. Teachers want to learn professionally to meet the needs of their students better. However, CPD should be approached in a way that considers the context in which it takes place (Loucks-Horsley et al., 2009). Therefore, the design and implementation of CPD during curriculum reform may benefit from a collaborative approach with teachers. Ensuring CPD meets the individual teachers’ needs is common throughout the literature. However, what is particularly interesting from the data in this study is that even the suggestions made by teachers were later not implemented. Further research on whether helping teachers reflect on CPD that they desire while also being mindful of the design of CPD that fits their real-world experiences may help to increase CPD’s effectiveness. What is clear is that the involvement of teachers in developing, implementing, and reflecting on CPD should be considered a key component to advancing teachers’ pedagogical skills and knowledge.

7. Conclusion

CPD is critical to equipping teachers with the necessary pedagogical knowledge and skills to implement mathematics curriculums effectively (Darling-Hammond & McLaughlin, 2011). As curriculums are reformed to prepare students for twenty-first-century challenges, effective CPD must be integrated to increase the likelihood of successful implementation. Unfortunately, challenges such as time and connection to practice can be intensified during curriculum reform, calling for the need to examine how CPD should be examined during these periods of change.

The primary focus of this study was to determine whether a curriculum resource can be developed as a form of effective CPD that can address challenges to professional learning during periods of change. This study concluded that curriculum resources designed as a form of CPD can successfully guide teachers through implementing new or forgotten pedagogical skills, in this case, using higher-level questions in mathematics lessons. However, the design of the curriculum resource should be streamlined to allow teachers to quickly scan the resource immediately before or during a lesson to incorporate the skill. The curriculum resource should also connect to teachers’ current practice. Both design elements can increase teachers’ likelihood of using the curriculum resource and potential for developing pedagogical skills. It is recommended that developers of curriculum resources with a CPD component consider targeting a particular component of a pedagogical skill.

The curriculum resource also aimed to be used independently by teachers, requiring minimal support. Due to the DBR methodology utilised in designing the curriculum resource, teachers developed relationships with the primary researcher and asked for guidance through modelling lessons. These relationships developed from a researcher-participant to more of an instructional coaching relationship. Modelling and individualised support seemed to influence teachers utilising the curriculum resource and fully understanding how and why to incorporate questioning into lessons. This research points to the potential invaluable and essential component of individualised support for teachers using these resources with their students. It seems that a traditional CPD workshop, according to teachers in this research, was not as beneficial as one-on-one support. Schools may consider how they can integrate support for teachers in their classrooms when learning to use new resources or implement reformed curriculums, as this research indicates it can increase teachers’ motivation to use the provided resources and slowly integrate new pedagogical skills. More research is needed on how much modelling and individualised support are necessary to aid in the success of a curriculum resource as a form of CPD.

In conducting this research, we recognise that education is a complex system ultimately experienced differently by each teacher and student. As this research was conducted in an Irish setting at the primary level with a small group of participants, we acknowledge that simply changing the research setting may have resulted in alternate outcomes. Each teacher has individual preferences for professional learning, beliefs about teaching, and past experiences influencing how they teach mathematics. Further research should be done with broader populations to determine if curriculum resources are valuable forms of CPD. It is also necessary to investigate whether this approach to CPD can help teachers learn other pedagogical skills. Additional studies should also examine how such curriculum resources impact student achievement in mathematics. Finally, it is necessary to understand better how individualised support for teachers impacts curriculum implementation and how it relates to the barriers to CPD during curriculum reform.

Despite these limitations, the findings of this study indicate the need to provide effective CPD that considers the context in which curriculum reform occurs. This study further indicates that including teachers in decisions about CPD and their learning preferences may be essential to designing and implementing CPD that supports curriculum reform. Reimagining CPD during curriculum reform may be an invaluable step towards helping teachers develop the pedagogical skills necessary to deliver curriculums as written effectively.

Disclosure statement

No potential conflict of interest was reported by the authors.