Using student personas when developing digital mathematics learning resources to improve teacher training

Abstract In this study, we discuss how the use of student personas can support pre-service teachers developing digital mathematics learning resources and improve mathematics teacher training programs. The use of modern technologies in schools requires that pre-service teachers prepare for new challenges, including the development of digital learning resources. To be able to develop such resources during teacher training, pre-service mathematics teachers without direct contact with students need insights into particular characteristics of mathematics students. We argue that personas, a tool and approach adopted from user experience research, can provide such insights. For this purpose, we interviewed four pre-service mathematics teachers who were developing digital learning resources in the span of a semester. We analyzed the data using grounded qualitative content analysis approaches and identified the following key aspects of personas usage for mathematics teacher training: (A) personas can act as an information tool, (B) personas can act as a planning and feedback tool, (C) the use of personas can trigger reflection processes for pre-service teachers, and (D) sustained work with personas may increase its impact. Our results indicate that personas can offer pre-service teachers support when developing digital learning resources and contribute to their professional development.


Introduction
Training pre-service mathematics teachers to use technologies fruitfully is important as new technologies are increasingly (Lavicza et al., 2022) and frequently (Weinhandl et al., 2021) used for learning mathematics as well as other subjects.For pre-service mathematics teachers to be able to develop practice-ready digital learning resources during their teacher training, it is necessary that they are supported as they learn to take into account students' needs and goals.As there are usually limited opportunities in training pre-service mathematics teachers for direct contact with students, other tools should be integrated into mathematics teacher training for this purpose.One way to help pre-service mathematics teachers learn to consider student needs and goals is to use personas.Personas are simplified representatives of a homogeneous group of users (Minichiello et al., 2018;Sundt & Davis, 2017) and have their origins in user experience (UX) research.In our research group we have carried out numerous studies on student persona development and successfully utilized them in teacher training (Weinhandl et al., 2022(Weinhandl et al., , 2023)).In this study, we asked pre-service mathematics teachers to use mathematics student personas that we had previously developed (Weinhandl et al., 2022) while they were developing digital mathematics learning resources.Our research question was: How can the use of personas when developing digital mathematics learning resources be utilized and implemented in teacher training?
Since our study aimed to explore something entirely new, we used a constructivist grounded theory approach (Charmaz, 2006) with data collected during interviews and think-aloud activities.

Theoretical background
In this section, we present the origins and goals of persona research, discuss Technological, Pedagogical And Content Knowledge (TPACK) as a framework for conceptualizing and studying mathematics teacher training, and review mathematics teacher training practices for learning about the use of digital technologies in classrooms.

Mathematics student personas
Personas are a tool of UX research and are simplified representatives of a homogeneous user group (Minichiello et al., 2018;Sundt & Davis, 2017).Personas are intended to make it easier for developers of digital systems to put themselves in the shoes of potential users of a system-a task that can be particularly challenging when users of a system are young people or children (Antle, 2008).When developing personas, researchers need to give special consideration to the needs, desires, fears and technical experiences or access requirements of these fictitious users (Lilley et al., 2012;van Rooij, 2012).In our work, as in prior studies (e.g., Lilley et al., 2012;Minichiello et al., 2018;Sundt & Davis, 2017), a typical persona consists of the user groups' needs and goals, background information concerning the user group, as well as a picture of the representative of this group.Even though personas have been used in the tertiary STEM field (Guy, 2017;Vorvoreanu et al., 2016), there is little research on personas of secondary mathematics students.
Following, an iterative design process that included input from a total of 96 in-and pre-service teachers, 83 upper secondary students, and 3 mathematics education researchers, we developed a total of five student personas that represented a variety of secondary mathematics students' needs, goals, and dispositions toward mathematics (Weinhandl et al., 2022).We provide one example of such a student persona in Figure 1.
One of our goals for the development of secondary student personas was for the personas to become a useful tool for mathematics educators when they design, develop and assess digital learning materials.In this paper, building on prior work, we explored how the use of mathematics student personas may assist pre-service mathematics teachers in particular, as they learn to develop and assess digital learning materials for a variety of students.We hypothesized that the use of personas in this context could make it easier for pre-service mathematics teachers, who had not yet had an opportunity to teach in a classroom, to take into account the needs, goals and motivations of young learners.And in doing so would then further contribute to their training and professional development as mathematics teachers.Because our work intersects (i) mathematics teaching and learning, (ii) technology use, and (iii) teacher training, our study was informed by the Technological Pedagogical Content Knowledge (Mishra & Koehler, 2006) framework, a framework that has previously been shown to support the exploration and understanding of pre-service teachers' use of technologies (Pamuk, 2012;Wang et al., 2018).

Technological, pedagogical, and content knowledge (TPACK) in mathematics teacher education
In order to integrate technologies fruitfully into their teaching, mathematics teachers need technological, pedagogical, and content knowledge (TPACK, Mishra & Koehler, 2006) as well as contextual knowledge about those technologies (Mishra, 2019).Of particular importance for our study are pedagogical content knowledge (PCK), technological pedagogical knowledge (TPK) and technological pedagogical content knowledge (TPACK).PCK means finding teaching approaches to fit the content, or how elements of the content can be designed for better teaching.TPK includes the understanding that there is a range of digital tools for a particular task, the ability  (Weinhandl et al., 2022).
to select a digital tool based on its suitability, knowledge of pedagogical strategies, and the ability to utilize these strategies when using technologies.TPACK summarizes each of these areas of knowledge, and can be the basis when teaching with technologies.TPACK requires (i) an understanding of how to represent concepts using technologies; (ii) pedagogical techniques that involve using technologies in constructive ways to teach content; (iii) knowledge of mathematical concepts that students might typically struggle with and how technologies can help support student learning of these concepts; (iv) knowledge of students' prior knowledge and epistemologies; and (v) knowledge of how technologies can be used to build on existing knowledge and develop new epistemologies or strengthen old ones (Mishra & Koehler, 2006).In addition to these areas of knowledge, contextual knowledge is also important for teachers (Mishra, 2019).Contextual knowledge includes, among other things, knowledge about available technologies or policies that a teacher might operate with.The updated TPACK Model developed by Mishra (2019) is shown in Figure 2.
In order for pre-service teachers to develop their technological pedagogical content knowledge, there need to be opportunities for them to plan, implement and evaluate technology-enhanced learning activities (Açikgül, 2020).Cooperative work and discussions with other teachers about the use of technologies can also promote the development of TPACK (Yeh et al., 2021).Jang and Tsai (2012) suggested that classroom experience helps to increase TPACK, whereas Patahuddin et al. (2016) emphasized that it is authentic classroom experience that can help to improve the TPACK of mathematics teachers.Authentic classroom experience creates the conditions, and opportunities, for teachers to design and plan learning activities while having their actual students in mind, attending to their needs and goals.However, access to the classroom on a regular basis is often not possible, or even available for pre-service teachers.In order to support pre-service mathematics teachers as they develop their TPACK and learn to attend to students' needs and goals, we developed some mathematics student personas to assist pre-service teachers with the design of digital learning materials.

Mathematics teacher training for using technologies
Mathematics teacher training is one of the key factors in determining whether teachers acquire TPACK and how, or how well, pre-service teachers integrate digital technologies into their lessons once they enter the classrooms.Doğan (2012) emphasized more than a decade ago that pre-service mathematics teachers should be prepared to incorporate different computer-based activities into their lessons.This means that mathematics teacher training programs need to be structured in a way that offer pre-service teachers opportunities to experience, work with, and design with digital tools and software (Clark-Wilson & Hoyles, 2019;Doğan, 2012).These experiences with digital technologies should also make it easier for pre-service teachers to see some of the potential benefits of using technologies (Gurevich et al., 2017;Weinhandl & Lavicza, 2019).
However, given that the use of technology can sometimes lead to a decline in mathematics students' performance (Odell et al., 2020), it is important for teachers to be able not only to recognize the potential benefits of using technologies in their classrooms, but also to know how to do so in service of their students' needs and goals.It is therefore necessary for teacher training programs to appropriately and sufficiently support pre-service teachers as they learn to utilize technologies in their lessons.
In our study, we provided this support by offering pre-service mathematics teachers opportunities to develop digital literacy through the design and testing of digital mathematics learning resources while receiving feedback and guidance from more experienced teachers and mathematics education researchers.Beyond collaborating with more experienced educators, we also invited the pre-service mathematics teachers to collaborate with each other when developing the digital resources.Our goal was that through these collaborations, we could help establish a local community of practice with shared concerns and passions (Voskoglou, 2019;Wenger et al., 2002) that would further support the learning and professional development of participating pre-service teachers.

Methods and methodological background
In this section, we first provide some details regarding the initial development of student personas.We then describe the methods of data collection and analysis we employed in the current study.

Developing student personas
We employed tools and methods of (i) qualitative educational research and (ii) personas techniques to develop representatives of student groups, i.e., student personas (see Figure 1).There is of course no such thing as the one describing all mathematics students, and to ensure we had enough variation in our data for the development of student personas we invited both preand in-service teachers to respond to a web questionnaire.We asked them to describe what they consider typical mathematics students, focusing on students' interests, fears, goals, needs, challenges with, and dispositions toward mathematics.
In the case of in-service teachers, we asked teachers to describe a typical mathematics student from their school environment.In the case of pre-service mathematics teachers, we asked them to describe (i) themselves as a secondary mathematics learner, and (ii) a less interested or gifted classmate.A total of 74 pre-and in-service teachers responded to our questionnaire and we used the collected data to develop the preliminary versions of the mathematics student personas.These versions were validated and improved by obtaining additional input from 83 upper secondary students, 4 pre-and 18 in-service teachers, and 3 mathematics education researchers, resulting in the final version of 5 student personas.For more details on the development of mathematics student personas we refer the readers to Weinhandl et al. (2022).
In our current study, we employed the previously developed personas to identify what aspects of student personas, and of the use of personas for the design of digital learning materials, are important in mathematics teacher training.To our knowledge, this is the first usage of secondary mathematics student personas in this context, so our work can be considered as a case study guided by constructive grounded theory: our findings are grounded in the data of our study, and it is possible that other researchers might come to different conclusions in a different context (Charmaz, 2006).
In line with Cohen et al. (2007), it is characteristic of case studies that real people in real-world settings are investigated while these people are experiencing a targeted intervention.The people we investigated in our study were pre-service mathematics teachers enrolled in a teacher training program.The FLINK project (https://www.jku.at/flink-in-mathe/)served as the real-world setting, where these pre-service mathematics teachers were employed at the time.The targeted intervention was that the pre-service mathematics teachers should use the previously developed student personas when designing digital mathematics learning resources, mainly in the form of GeoGebra-Applets.For example, the pre-service teachers were asked to develop digital learning resources in alignment with, and in response to, secondary mathematics students' motivations and interests, as these were captured in the mathematics student personas.

Participants and context of our study
For the selection of the study participants, we followed a purposeful recruitment process targeting academically motivated pre-service teachers with prior experience in the design of digital learning resources.Given the novelty of our study and our grounded theory approach, we decided that the use of "extreme cases" of pre-service teachers would help us collect crucial information that would expand the current body of knowledge (Eisenhardt, 1989).
We first asked the instructors of the mathematics teacher training program at the University of Linz, School of Education (8 in total) to name student teachers who they thought stood out during their training due to their mathematical, didactical and social teamwork skills.At least three different instructors had to make a recommendation for the respective student teacher to be considered eligible to participate in our study.A total of nine pre-service mathematics teachers fit this criterion.
We were also interested in student teachers who had some familiarity with the design of digital learning resources, so we examined who of the recommended student teachers had been involved in the design of digital learning materials for at least three months at the time of recruitment, through their participation in the FLINK project.This reduced the total number to six possible participants, with four agreeing to participate in our study.
The four pre-service teachers were at the end of their bachelor's or the beginning of their master's degrees.They were all female students in their 20s, reflecting the distribution of demographic characteristics of pre-service teachers in Austria (Statistik Austria, 2023).

Data collection and time frame of our study
We collaborated with the pre-service mathematics teachers for more than one semester while they developed digital mathematics learning resources using personas.We organized the development of the resources with the use of personas in three distinct phases.We present the main goal and task for each of these phases in Table 1.
We also provide examples of two learning resources designed for student personas interested in leisure time activities such as sports and baking (Figure 3).The idea was that this could encourage learners to engage with the mathematical content behind their personal interests, highlighting that mathematics can occur in everyday situations.https://www.geogebra.org/m/dg2puee7(Ski racing) and https://www.geogebra.org/m/vmtkcztn(How much cake would you like).
At the end of each phase, we conducted qualitative interviews with the pre-service mathematics teachers and used think-aloud approaches when they presented the digital learning resources they had either developed or selected to work with during each phase of the project.This resulted in 12 interviews: 4 interviews at the end of each of the 3 phases.We conducted all interviews online, asking participants to share their screens as they were discussing the learning resources they had designed, modified, or selected.Each interview lasted about 15 min and we used audio recording and screen capture technology to collect our data.

Data analysis and development of the results
At the end of each data collection cycle (following the three project phases described above), we transcribed the recordings of the interviews conducted during that cycle and skimmed through the transcripts to familiarize ourselves with the newly collected data.Next, we analyzed the data in line with grounded theory approaches (Charmaz, 2006;Strauss & Corbin, 1997) and qualitative content analysis approaches (Kuckartz, 2019;Mayring, 2015).
The coding team consisted of one mathematics education researcher and three research assistants.All coders coded each interview in its entirety first, before meeting to discuss codes.During the first coding phase, the coders used open coding techniques (Charmaz, 2006;Strauss & Corbin, 1997) to open up the data and develop initial units of meaning.The codes of the open coding analytic phase consisted of a keyword, a definition of the code, and a prototypical example of the code.A subset of our codes is shared in Table 2, and the full list can be found in the codebook at the following link (Supplementary material 1).
Then, the four coders met, compared the individually developed open codes, and merged similar codes.The coders merged codes if both conditions were met: (i) the codes had a similar description and (ii) they had been assigned to similar text passages in the transcripts.Then, as a team, we used qualitative content analysis techniques (Kuckartz, 2019;Mayring, 2015), and mainly summary techniques, to thematically organize the revised codes in categories.
We conducted a total of three analytic cycles of two coding phases each, following the collection of interview data at the end of each phase of the project.We used the agreed upon codes and categories from the previous analytic cycle at the beginning of our next analytic cycle.The final set of merged and thematically organized codes informed the findings we discuss in this paper.read through the student personas.Pay particular attention to the characteristics and needs of each student persona. 2 connecting learning materials to student personas.
have a look at already existing digital learning resources (within the project); match the learning resources to student personas attending to their characteristics and needs.3 Working with multiple student personas in mind.
Develop (or assign) digital learning resources specifically to two personas, while attending to their characteristics and needs.(the research team assigned two specific student personas to each study participant.)

Validation processes in our study
To ensure the quality of the results developed in our study, we followed the recommendations of Jonsen and Jehn (2009) for qualitative and exploratory studies, and used mixed methods, different sources and different coders.We combined grounded theory and qualitative content analysis approaches, with four coders per interview cycle and think-aloud techniques in addition to interviews.At the end of each coding cycle we calculated intercoder reliability ratios using both Cohen's Kappa (1960) and Miles and Huberman's (1994) formulas (Table 3).
The key figures of the respective interview rounds indicate very high intercoder reliability.This high level of agreement between coding by independent coders indicates that the categories are comprehensively formulated and different from each other.

Results
Our analysis showed that there were 4 key aspects of student personas that can be particularly relevant for teacher training of pre-service mathematics teachers.These were: (A) personas as an information tool, (B) personas as a planning and feedback tool, (C) triggering reflection processes through working with personas, and (D) continuity in working with personas.We discuss each one of these findings in the following sections and share some participant quotes from the interviews we conducted.Participant names are pseudonyms, and for each quote we note the interview round it originated from as an indication of how much experience the interviewees already had in working with personas at the time of their statement.

Personas as an information tool (regarding characteristics of mathematics students)
Pre-service teachers in our study identified student personas as a useful information tool when they created digital mathematics learning resources.For example, student personas can provide insights into the interests and motivations of different mathematics students.This can be Table 2. example codes from our study.

Keyword
Definition Prototypical example ease of use a compact representation of the personas is important for their practicability.
"the presentation should be compact, not too long and easy to grasp at a glance."insight into characteristics of different mathematics students Personas serve as an information tool for mathematical (needs and goals) and extra-mathematical (interests) information about students.the information can be used to create materials for different personas.
"for me it is important to know the needs of the students.the students' goals are also important because as a teacher i have the responsibility to help the students achieve their goals."trigger reflection processes (related to the user) Working with personas triggers a reflection on the heterogeneity of the student body, the diversity of students (differences and similarities) and the relevance of differentiation.it also leads to a broadened perception of student facets by expanding one's own knowledge and assumptions about students.
"With the personas, i think it comes out well that even average students have different goals and needs.i also often find myself not responding well to very motivated pupils because i limit myself to the minimum.however, it is important not to forget such students and to give them sufficient support."particularly relevant if there is no contact with schools or real mathematics students when creating those resources.
Olivia, round 1: I would actually be interested in what motivates the 10-or 11-year-olds.Maybe a lot of them are really motivated more by the content or that they want to know why something applies.
In addition to foregrounding students' interests and motivations that can guide the design of learning resources, sometimes student personas were also used as a reminder of students' goals and dispositions toward mathematics, as the quote from Nora below suggests: Nora, round 1: For most personas it is listed how much they like mathematics or even how much effort they want to put into mathematics.That was important or good because then we just developed some learning resources that are for more interested students who want to put more time and effort into it and for students who want to get to the goal faster and then put little effort into it.
We found that information that was particularly relevant for the pre-service mathematics teachers when creating the learning resources were the goals, needs, enjoyment, and challenges of mathematics students: Flora, round 3: Basically, the goals and needs, because I want to meet the students where they are at.And somehow, I need to know what their goals are, so that we can walk a common path.And beyond that, a little bit of enjoyment, because it should be fun for them and they should learn that math is cool.
Importantly, the usability of such an information tool played a decisive role.For the pre-service mathematics teachers in our study, the compact presentation of the information was important and well-received: Flora, round 3: So these points are really presented very briefly, I think that's quite good.
In summary, we found that for the training of mathematics teachers, an information tool that presents the characteristics of different mathematics students in a compact way can be useful.Student personas can be such an information tool, especially when they provide positive user experiences.

Personas as a planning and feedback tool (for differentiated learning resources)
We also found that personas can support pre-service mathematics teachers in creating differentiated learning resources.Pre-service mathematics teachers in our study cared about differentiation and considered students' diversity and the student body's heterogeneity when they developed and assessed digital learning materials.They indicated that in this context, student personas facilitate the development of different learning resources for different students: Flora, round 2: That was actually the main thing, eh, as I think I said at the very beginning, somehow, that there is simply such a diversity of interests in any case and that there are just a lot of different students and you always have to be a bit careful that you don't just … well, we are all very similar in our team and have very similar interests and that we also have to be a bit careful that we include a bit different things.
The pre-service mathematics teachers in our study achieved a differentiation of digital mathematics learning resources taking into account personas' interests and preferences.For example, pre-service teachers attended to the visual design of activities by incorporating graphic elements that connected mathematical content to student personas' interests.
Another way in which pre-service teachers in our study differentiated the materials they developed was through the difficulty and structure of tasks they developed, by attending to student personas' academic performance and willingness to perform: Nora, round 1: […] we have narrowed down a bit whether the personas are weaker students or stronger students and we have adapted it accordingly.
Flora, round 2: But what I have noticed most recently is that I have noticed that I have to cater to different interests a little bit, also in terms of design and so on.So not only do all the students have the same interests as me, for example, or as in our team.But that you also have to incorporate different things.
The goal of the pre-service mathematics teachers of our study when using such differentiation strategies was, among other things, to promote the students' enjoyment of working with the learning resources created and that students focus less on fears and problems.Furthermore, as Olivia's quote below suggests, the pre-service mathematics teachers wanted to consider the students' abilities and subject-specific requirements when creating learning resources: Olivia, round 3: And somehow, if you look more at it, OK what does the student like?What can you somehow give them?Or how can I make it more fun?I think we might have gained a lot if we were more involved in this somehow.
Personas can be explicitly used as a planning or feedback tool when creating differentiated learning resources.In this way, personas can be included at the beginning of the learning resources development, i.e., in the planning and conceptualization of the resources.The use of personas at this stage of the development of digital learning resources was in fact seen as very valuable by the pre-service mathematics teachers in our study: Antonia, round 3: Well, I think that you have to think about the applet at the very beginning, before you even think about it: I want to make the applet for the person, for the type of student.And then think about how to build it up and so on […].
However, personas can also be used as a feedback tool at the end of the development of digital learning resources.As a feedback tool, personas can give feedback, on the one hand, about the fit of specifically created learning resources for different students and, on the other hand, about a whole collection of learning resources.
Olivia, round 3: And yes, also that we take it as we have done it now.And say, OK, pick out two types now and think about: Does this fit in with your teaching?Or to the resources that you have planned?I think that has a lot of added value.
In summary, personas can be used as a planning tool and feedback tool when creating differentiated learning resources for students.Here, the focus can be on mathematics-specific aspects, such as the difficulty level of a task, or general aspects, such as the graphic design of the learning resource.

Triggering reflection processes through working with personas
We also found that working with personas stimulated different types of reflection processes in pre-service mathematics teachers in our study.On the one hand, an intrapersonal reflection took place, where questions about the pre-service mathematics teachers' own student selves were involved.Through the work with the personas, the pre-service mathematics teachers reflected on how they were as students and what they would have needed in the mathematics classroom they attended or concerning mathematics learning resources they had worked with.
Antonia, round 1: […] and I think it's good to be reminded that maybe some people aren't that into it or that math just isn't that important to them.Well, I quite like math and I think it's quite good to be reminded that there are also some who don't see math as so important.
[…] That one also takes into account that there are many different types.
On the other hand, while dealing with one's own student-self, the view can also be directed away from the "self " to the other students.This change of perspectives leads to a transition to interpersonal reflection processes.
Olivia, round 2: And, for example, it often says that the person wants to get through with the minimum of effort.That's something I don't know about myself and where I also have a hard time understanding.And I think the personas have made it a bit clearer to me that I have to take a broader view than my own.
The interview data showed that working with personas could also stimulate interpersonal reflection on the heterogeneity and diversity of the student body.Pre-service mathematics teachers in our study recognized that students are different and that, in addition to their differences, they can also have commonalities, including what these commonalities might be based on.
Flora, round 3: Well, yes, the personas have definitely helped me to remember more and more that there are many different types of students and that you have to take this into account when designing learning resources and planning lessons.That you make sure that there is always something for many different types.
Furthermore, the pre-service mathematics teachers of our study reflected on the relevance of differentiation, although recognizing limits concerning differentiation in this context: Antonia, round 1: But I do think that it is important, for example, that you have different levels, that you perhaps also really do difficult ones where you really have to sit down and think about how I could solve this now, because it is not so easy, and I think that is important.Or when I was reviewing, I also looked to see if there was something for such really good students, and sometimes we have such resources, but that doesn't always work.
In addition, we found that working and dealing with personas expanded pre-service teachers' knowledge and, in particular, their assumptions about individual students.This expanded perception of the different facets of individual students enabled pre-service mathematics teachers in our study to perceive individual students more holistically: Olivia, round 1: I liked the fact that the goals and what these people need were always listed in great detail, and that you could see that there is always more to it than what you might think at first glance.[…] Exactly, and also that you can see that their, that is, these problems that go along with it, that they are quite different for everyone […].
Finally, we found that the use of student personas supported a reflection on students' living environment.In the course of this reflection, the pre-service mathematics teachers in our study realized that there were also important issues in the lives of the students beyond mathematics lessons, notably the students' living environment, interests and problems: Antonia, round 1: What might also be interesting […] is how they are in the other subjects.I think that is often really interesting because there are so many other subjects and maybe if someone is interested in drawing or somehow artistic, then you can also get them on board in such a way that you give such examples.
According to our analysis, working with personas might trigger different reflection processes that are particularly relevant for the mathematics teacher training: There can be intrapersonal reflection on one's student self as well as interpersonal reflection on the heterogeneity of the student body, broadening one's perception of the facets of individual students.

Continuity in working with personas
We also found that when working with personas -especially in teacher training -it is important for pre-service teachers to engage with this tool over a more extended period of time.Specifically, personas should be recalled repeatedly so that they can be explicitly or implicitly incorporated into the development of learning resources that take into account the needs of the students, or into the planning of differentiated lessons.One of our study participants suggested that one way to achieve such longer-term engagement with the personas was in the form of frequent read-throughs or in conjunction with specific work assignments asking them to use the personas.
Olivia, round 3: And then I've been thinking about this… yes, it's been almost half a year somehow… again and again and also, above all, this incentive that the interview then comes, was good for us to deal with it again and again.Because otherwise you get so lost in what you're doing.And I don't know, they're also hanging in the office now and now we were all at home.I don't know if we would have dealt with it again and again otherwise.So, I think that was important, yes.
In addition, our participants suggested that the longer-term engagement with the development of learning resources with personas can lead to a detailed engagement with content-related mathematical topics and their didactics, thus enabling a deeper understanding of them: Antonia, round 3: Yes, well, with FLINK project it is sometimes the case that you, I think, simply go through the curriculum content much more precisely than you… That is not possible at all in the studies, that you break down every topic so finely and discuss it so precisely […].
Hence, continuity in the use of personas is required to meet the needs of the students, to differentiate effective lessons and to achieve a deeper understanding of mathematics and its didactics.
In sum, the four aspects described above are particularly relevant to pre-service mathematics teachers when developing digital learning resources with personas.We further discuss these aspects in the following section.

Discussion
Our research aimed to explore aspects of personas and the use of personas in developing digital mathematics learning resources by pre-service mathematics teachers and make them relevant for their teacher training.We found that when it comes to teacher training of pre-service teachers, (A) personas can act as an information tool, (B) personas can act as a planning and feedback tool, (C) the use of personas may trigger reflection processes, and (D) sustained work with personas is important.
Our results showed that personas can be an information tool that gives pre-service mathematics teachers an insight into the characteristics of mathematics students when creating digital learning resources.Personas as an information tool can therefore be seen as an extension of Antle's (2008) statement that personas should be a facilitator for the developers of digital systems to better put themselves in the shoes of potential users of such systems.This insight into how personas can improve teacher training is particularly relevant when there is little or no contact between pre-service mathematics teachers and actual mathematics students.
According to Patahuddin et al. (2016), authentic classroom experiences contribute to the development of TPACK in particular.Since there is often not enough contact with students during teacher training, it is often challenging to realize authentic classroom experiences that take students' needs into account when developing digital learning resources, and our study showed that personas can support this.The information about potential students through the utilization of personas can enable pre-service mathematics teachers to more authentically plan differentiated teaching resources, underpinning the function of personas as a planning and feedback tool, and therefore promoting the development of TPACK.
As for the development of the personas and the information they contain, the needs of fictional users should be considered along with other vital aspects such as desires, fears and technical experiences of these fictitious users (Lilley et al., 2012;van Rooij, 2012).Our study showed that the pre-service mathematics teachers assigned different relevance to different aspects of personas.They indicated that student personas' needs were particularly useful to them when creating digital learning resources, a finding that highlights Lilley et al. (2012) and van Rooij (2012) arguments that needs, wishes, fears and technical experiences are essential aspects of personas.
Additionally, "Triggering reflection processes through working with personas" shows that working with personas can trigger reflection processes, such as interpersonal reflection and intrapersonal reflection.Reflecting on how teaching approaches and content can be best combined in the classroom to meet students' needs contributes to the development of pedagogical content knowledge (PCK) and, thus, TPACK, according to Mishra and Koehler (2006).According to Açikgül (2020), pre-service mathematics teachers should plan technology-enhanced lessons for the development of TPACK already in their teacher training, Our study participants did that through cooperative work and discussion with others, facilitating the development of resources.According to the characterization of such a community of practice by Voskoglou (2019) and Wenger et al. (2002), such interaction on a common concern can, in turn, contribute to professionalization of pre-service teachers.
Regarding the "Continuity in working with personas" theme in our study, besides the fact that TPACK is continuously built up (Jang & Tsai, 2012), teaching experience, in particular, also contributes to an increase in TPACK; our study showed that continuity is also an important aspect when dealing with personas.Longer-term engagement of pre-service teachers with mathematics student personas in developing digital learning resources can thus go hand in hand with further development of TPACK.
Overall, results of the study, we believe, contribute to the research and further development of secondary mathematics student personas, extending STEM-and teacher education-related research (Guy, 2017;Vorvoreanu et al., 2016), where the use of secondary mathematics student personas had limited research.

Conclusions and further research
Our study indicated that in mathematics teacher training, there is often insufficient contact between pre-service mathematics teachers and real mathematics students.Such contact is needed to gather information about students necessary for developing learning resources and lessons.Based on the results of our study, personas can be an information tool by giving pre-service mathematics teachers an insight into the characteristics and needs of mathematics students.Concluding, the integrating personas into mathematics teacher training can bring learning gains for pre-service mathematics teachers.By aligning the produced learning resources with the personas, more authentic teaching experiences can take place, contributing to the development of TPACK and, subsequently, increasing professionalization of pre-service mathematics teachers.
Pre-service mathematics teachers in our study had already completed several internships at schools and related courses as part of their teacher training.Although this has already brought them into contact with real mathematics students, it can be challenging to integrate these rather limited experiences from the internships into their courses.In order to ensure that courses take into account characteristics and needs of different students when dealing with content and creating assignments and teaching resources, personas could be integrated into courses from the beginning and worked with on an ongoing basis.As the study showed, personas can be used effectively for planning and obtaining feedback on lesson planning and learning resources.Therefore, assignments for the creation of lesson plans or learning resources in individual courses should encourage students to engage with personas.Another possible use of personas in mathematics teacher training is the school internship.For example, students in teacher training can make connections between real mathematics students and the personas during observations.Due to the lack of experience with real mathematics students, pre-service mathematics teachers often have little understanding of the heterogeneity of their future students.However, dealing with heterogeneity and differentiation plays a significant role in teacher training and their future work.The theoretical preoccupation with these topics in teacher training can be supplemented by a practical examination of students' different needs and characteristics through personas, as personas can offer realistic insights into the differences and similarities of students.This interplay of theory and practice can lead to an authentic engagement with heterogeneity and differentiation in teacher training and have the potential for in-service professional development.

Table 1 .
overview of project phases.

Table 3 .
intercoder reliability in our study.