Learning mathematics and its relevance through a digital storytelling assessment task at university

Abstract

Storytelling is a valuable form of human expression that allows audience members to connect their own experiences with the narrative. As a pedagogical tool, storytelling has been explored mainly in primary school education but rarely in higher education. However, its potential for assisting students in learning mathematics and the societal benefits that its application can bring has been largely overlooked. Using Cultural-Historical Activity Theory (CHAT) to analyse university students’ experiences of a digital storytelling assessment task, we explore students’ perception of their learning and the relevance they ascribed to mathematics. We conclude that it is vital that students can reconcile why mathematics is important for society and how that affects them in their personal lives. We should also make sure that we equip students with valuable skills, such as how to work effectively in a group, which can give them more agency in shaping their learning experience.

KEYWORDS:

• Digital storytelling
• undergraduate mathematics
• mathematics assessment
• relevance of mathematics
• video creation

MSCs:

• 97-11
• 97A99
• 97D40
• 97U80

1. Introduction

Throughout history, mathematics has played a fundamental role in human development and has been, and continues to be, unquestionably vital to the economic progress of industrialised nations. However, many negative myths about mathematics exist that permeate our modern cultures and because of these inaccurate beliefs, many students throughout all levels of education are held back in their mathematical learning (Boaler, 2018). The attitudes and values that students develop due to these misconceptions include, amongst others, the beliefs that mathematics is intrinsically different and inaccessible to all but a few; that success in mathematics is due to a fixed inherited talent rather than to effort; or that mathematics is value and culture free (Ernest, 2015). Of these myths, one has been particularly harmful: that mathematics is an abstract subject disconnected from society and day-to-day life. The effects of this can be seen in numerous students at all levels of education – including university level students studying mathematically-demanding subjects such as science, engineering and technology – for whom mathematics is ‘something strange and useless’ (Petocz & Reid, 2005, p. 789), and persistently asking: Why do I have to learn this? Many of them echo the words of one of the students in Harris et al.’s (2015, p. 329) research on the value of mathematics for engineering students: ‘I don’t see the relevance. I mean I actually do enjoy maths sometimes as well but I just do not see the relevance of it’. It is, therefore, important to bring relevance to the learning of mathematics, so that more students can make sense of the subject, why it is important to learn it and the societal benefits that its application can bring.

This paper is part of a larger study that aims to research how storytelling can help university students make sense of mathematical concepts and their relevance to the real world. Here we explore what students learned, from their perspective, by engaging in a digital storytelling assessment task and how this task influenced their perception of the usefulness of mathematics. The assessment task was introduced as part of a foundation (bridge) undergraduate mathematics unit (class or course, in the US; module, in the UK) at an Australian university. The task consisted of creating a three-minute video where groups of three students created a narrative about a mathematics concept seen in the unit and explained how this concept is relevant to society. By engaging students in this assessment task, the aim was to find out if they perceived that they learned something of value. This included the process of creating videos as a group, the development of important skills, and if they saw these mathematical concepts as relevant to themselves and others.

2. Storytelling and education

2.1. Storytelling and its use in education in general

Storytelling is a valuable form of human expression and the transference of knowledge and culture passed from one generation to the next preserves and shares heritage. Sharing experiences and relating them to others through storytelling can be very impactful. Understanding the past assists with comprehending the present and this underpins the essence of learning. For example, teachers preserve mathematical knowledge and culture by telling their students the story of al-Khwarizmi, the father of algebra, or the story of Archimedes, who used mathematics to save his city from invasion. With these inspirational stories, teachers communicate how real people struggled and came up with solutions to societal problems, and how mathematics was developed in those sociocultural contexts. Concrete stories can make a subject interesting and enjoyable (Inan, 2015; Smeda et al., 2014) because they create a scaffold which allow students to connect their own experiences with the narrative. Zazkis and Liljedahl (2009, p. ix) assert that ‘we tell stories in the mathematics classroom to achieve an environment of imagination, emotion and thinking. We tell stories in the mathematics classroom to make mathematics more enjoyable and more memorable’. Hence, communicating the relevance of mathematics through, for example, the story of al-Khwarizmi, Archimedes and others has the potential to be more impactful to students than only teaching, for instance, the rules of algebra. Having this human connection with what is learned might counteract the myth of mathematics being purely abstract and detached from its human origins.

Building on storytelling, digital storytelling is told through the creation of relatively short movie clips, blended with digital media such as text, pictures, voice-over narration, music and video through the use of computer software (Robin, 2016). Creating a story is not just a simple matter of sequencing events. It is a form of meaning-making (Bruner, 1991) where the storyteller needs to transmit ideas with the intention of convincing others of their importance. Stories need to be well-structured so they can be effective and recalled (Turgut & Kışla, 2015). Hence, the process of creating a digital story also requires the storyteller to develop important skills in preparing scenarios and using audio-visual elements effectively to make the story stronger (Banaszewski, 2005; Demirer, 2013). Researchers have reported that many students find storytelling activities engaging (Karakoyun, 2014; Wang & Zhan, 2010).

Research findings about digital storytelling and young children showed promising results that it improved their motivation, problem-solving competence and learning achievements (Hung et al., 2012). However, as Marsico (2017) points out, the potential of narrative thinking in the educational setting has been largely overlooked. In a systemic literature review undertaken by De Jager et al. (2017, p. 2572), their findings of digital storytelling in education concluded that the potential was there to ‘encourage a deeper level of reflection and engagement on a specified topic, while at the same time improving participants’ digital literacy and storytelling skills’. In a more recent review of research on digital storytelling in language learning, Lim et al. (2022) found that not all claims in the articles they reviewed were supported with evidence. Hence, there is a need for more empirical research on the potential of storytelling in education.

2.2. Storytelling in mathematics education

The significance of storytelling as an educational tool has been on the rise in both the humanities and social science subjects however in the teaching of mathematics, there are limited studies on the topic, and these predominantly focus on students in preschool and primary school education. For example, Cemil (2015) worked with pre-school pre-service teachers in creating digital mathematics stories. The pre-service teachers reported that they liked the method used to create stories and mostly felt positive emotions during the storytelling activities. They also reported that their pre-school students found the stories entertaining. Marsico et al. (2019) in their study of high school students using digital storytelling in mathematics concluded that learners developed logical and narrative thinking skills when working within authentic contexts. More recently, Sherwood and Makar (2022) explored the use of storytelling in statistics. Using Bruner’s (1986) theoretical ideas on narrative, they found that students’ contextualised stories help them make sense of their statistical learning. Bruner himself suggested that the learner needs to first make sense themselves to be able to explain and provide meaning to others through a narrative (1986). In this paper, we do not want to give the impression that incorporating storytelling in mathematics education is an easy task. We acknowledge the nature of mathematical knowledge – a highly hierarchical system – and the challenges that a storytelling pedagogy in science, technology, engineering and mathematics (STEM) present (Tan et al., 2014). However, the potential of storytelling for the learning of mathematics and for students’ development of important skills warrants further research.

Moreover, the fact that most studies in storytelling focus on young children, or adults writing stories for children, does not provide a reason why digital storytelling cannot be applied to learning mathematics at tertiary level. Özpinar et al. (2017) researched mathematics students in higher education and concluded that a vast majority of them enjoyed the units that incorporated digital storytelling and they wanted this technique to continue in their future units. Additionally, a study by Walters et al. (2018) on pre-service teachers found that digital stories produced by students provided an authentic learning experience which also gave them a strong sense of ownership – with students being in the ‘director’s seat’ (Kearney & Schuck, 2005) – and like previous findings, it enabled them to engage more deeply in the mathematics than what they would have in their normal course of study.

Storytelling activities are sometimes done as collaborative student endeavours. Mercer and Littleton (2007) found that groupwork and dialogue can improve the quality of students’ thinking and educational attainment, by helping them to develop strategies for tackling challenging problems, and the ability to reason and argue constructively by accepting feedback from others to refine the work. In their study of storytelling in statistics education, Sherwood and Makar (2022, p. 26) concluded that findings from the literature on contextualised stories ‘suggest that sensemaking is enhanced by facilitating the co-construction of knowledge with input from peers or teachers, correcting errors in students’ stories or filling in gaps in understanding’. In this paper, we further believe that by creating a story as a collaborative group, students would need to collectively imagine new contexts in which they can use what they have learned in their mathematics lessons. It is not sufficient for them to know how to solve an equation for example, but we assume that they will need to be able to see beyond this knowledge to imagine how it can be used to solve real-life problems that are critical to our society’s progress. Given that the storytelling task that is the focus of this paper was part of the students’ assessment, this would further intrinsically engage students because we know that assessment drives attitudes and behaviours towards learning in a significant way. There is also an urgent need to develop innovative assessment methods in mathematics, that assess more than a narrow and specific set of competences, in order not to rely on closed-book examinations which continue to be the most common summative assessment method in tertiary education in many industrialised nations, including Australia (Iannone & Simpson, 2022; Varsavsky et al., 2013).

The previous review of some of the most salient literature on the use of storytelling – digital or otherwise – both in education and mathematics education in particular, reveals that there is much that we do not yet know about the full potential of this pedagogical technique.

3. Theoretical framework

We took a socio-cultural view of learning and, in particular, a second-generation Cultural-Historical Activity Theory (CHAT) perspective was adopted to analyse students’ data. In CHAT, individuals make sense of the world while participating in object-oriented, tool-mediated social activities, with community rules and division of labour, such as that of creating a digital story as part of a group assessment task. These components form an activity system, which according to CHAT forms the basic unit of analysis (Engeström, 1999; Figure 1).

Figure 1. Activity system based on Engeström (1999).

Every human activity has an object, the ultimate reason behind the various behaviours of individuals, groups or organisations. Kaptelinin (2005) defines the object of activity as the sensemaker, which gives meaning to and determines values of various entities and phenomena. For example, if the object (or motive) of a student in engaging in an assessment task was to learn more about how mathematics is relevant to society, this will define the kind of meanings and values that this student would ascribe to the activity. These meanings and values would be different if the object of this student’s activity was to only satisfy the assessment requisite and get a pass mark. It is important to notice that there is no objectless human activity; there is always a motive or motives of engagement. In order to achieve the object of activity, individuals use tools (e.g. camera, editing software, the internet), and are bounded by rules of the community (e.g. how to communicate with groupmates, antiplagiarism rules) and a division of labour (i.e. who does what in an activity such as a groupwork task).

As previously stated, many students are unable to perceive the relevance of Mathematics and, therefore question the relevance of learning such concepts. In this study, we wanted to know if students were able to see the relevance of mathematics by participating in an assessment task that required them to develop a story within a short video about the relationship between a mathematical concept they had covered in classes when applied to a real-world setting.

Hernandez-Martinez and Vos (2018) used CHAT to define relevance as a connection between the subject of the activity (e.g. a student) and other elements of the activity system. They provided four points for analysing relevance: Relevance according to whom? Relevance of what? Relevance to whom? Relevance to what end?

For example, a student (relevance to whom?) can find Pythagoras’ theorem (relevance of what?) useful to calculate the height of a building (relevance to what end?) because their lecturer (relevance according to whom? – someone in the community) gave this example in class, or the student found this example on a website (in which case the relevance was introduced by the use of a tool: the internet). However, this theorem might not be relevant to another student who is not interested at all in calculating building heights (interest relates to a personal or internal motivation). But it might become relevant for them in the future if they are required to lead a construction or surveyance team (Relevance according to whom? introduced by a division of labour where the subject takes a leadership role in the activity). It is important to notice that the question of Relevance to whom? looks for subjective reasons, or why do ‘I’ have to learn this?, while the question of Relevance according to whom? looks for objective reasons, or why do ‘we’ (as a society) have to learn this? One of the aims of mathematics education is to help most students reconcile these two sources of relevance; that is, to solve the relevance paradox identified by Niss (2002), so that mathematics is personally (subjectively) relevant as well as socially (objectively) relevant.

Using this framework, the research questions for this study were:

RQ1. What did students learn by participating in the assessment task of creating a digital mathematics story?

RQ2. How did students perceive the relevance of a mathematical concept to the real world by communicating a story through a video?

4. Methodology

4.1. Background to the assessment task

The study was carried out in a foundation mathematics unit (course or module) at an Australian university. The unit acts as a bridge for students who come to university without a high school advanced mathematics qualification or for mature students who are returning to study after several years of having left school. Most of the students in the unit are enrolled in the Bachelor of Science undergraduate degree, but not necessarily wanting to pursue a major that is heavily mathematics oriented (e.g. Chemistry, Biotechnology, Environmental Science). There are also some students undertaking other courses that require mathematics as a prerequisite (e.g. Computer Science, Engineering). Historically, most students that enrol in this unit does not come with positive experiences in their school mathematics and see the subject as ‘something strange and useless’ (Petocz & Reid, 2005, p. 789), unable to see the relevance of it to their studies.

The assessment task used in this study aimed to bring relevance to mathematics and engage these students in the subject. Students were asked to form groups of three students and to develop over a period of eight weeks, a three-minute video with a story about a mathematical concept of their choice that was covered in their classes, that conveyed its importance and relevance to the real world. Since the potential mathematics concepts for the videos were already taught in class, it was assumed that students already had a fundamental understanding. However, it was expected that they would undertake further research in their chosen mathematical concept and demonstrate how it could be applied to the real world, particularly in a context that was of their interest.

Students were also provided support in the form of resources about effective communication techniques and storytelling methods; the creation of storyboards; how-to guides to the use of video editing software; some good examples of digital storytelling (e.g. www.mathstory.org/resources/); and, written advice on how to collaborate effectively in a group and how to solve potential problems. Students were encouraged to approach the lecturer informally by email or after small group tutorials (which were face-to-face at the time when COVID-19 restrictions were being partially lifted) to discuss initial ideas or questions about the mathematics concept they had chosen. Along with the video, students submitted a one-page group project report describing their activities during the production of the video, including minutes of meetings, division of tasks and active contribution of each member to the project. The five learning outcomes of the task were described in the assessment criteria (Table 1). Each criterion, marked on a scale of 10, was accompanied with a description of what the assessor would look for to give full marks. This task was worth 15% of the total marks in the unit. The other assessment pieces in the unit consisted of weekly online quizzes, a mid-semester test and a final examination.

Table 1. Criteria used to assess the task.

Number	Criteria
1	Demonstrates understanding of the mathematics concept presented: a project should show understanding throughout by giving complete, appropriate, and insightful explanations of the mathematics concepts; there should be no misconceptions.
2	Demonstrates understanding of the relation between the mathematics and the real world: the explanations given for the links between the mathematics concepts and the real world are well justified, argued, appropriate and insightful; these links should be realistic and have an appropriate level of complexity; the explanations for the relevance of mathematics are completely convincing.
3	Demonstrates originality and communication skills: the ideas are communicated appropriately and effectively, having in mind a diverse audience; the ideas presented are highly innovative, unusual or novel, displaying certain levels of surprise; personality is highly reflected.
4	Demonstrates time management skills: the group shows a well-designed, realistic time plan for the completion of the project, with clear goals and priorities, to-do lists, due dates, meetings, and delegation of tasks.
5	Demonstrates group work skills: there is evidence of a joint, active effort to commit and contribute evenly to the task by all members of the group; the outcome of the project is highly coherent.

4.2. Data analysis

For this paper, we analysed qualitative data from interviews with six volunteer students from the unit. All students in the unit (n = 126) were invited to participate in the study but these six were the only ones that volunteered to be interviewed. Each interview lasted on average 30 min. Students were asked to describe how they chose the topic for the video, what was the story of the video, how effectively they worked as a group, what they thought they learned from engaging in this task and if they could see the relevance of that mathematics concept after doing this assessment activity. Given the relatively short duration of the interviews, it was not possible to focus on the details of the process of how students produced the story but rather on the outcomes of that process (i.e. their perceptions of the learning that took place from engaging in the task).

We took an interpretivist approach to data analysis (Schwartz-Shea & Yanow, 2013). We sought explanations and answers to our research questions in the subjective interpretations of these students through their accounts of their activity; how they perceived their learning in terms of the mathematics or otherwise and the relevance they ascribed to the mathematics through engaging in this assessment. The focus was on the students’ accounts rather than on more ‘objective’ forms of measure such as a summative judgement (e.g. a grade), the lecturer’s expert feedback or an analysis of the videos. We were interested in the students’ experience of the task, how the task helped them (or not) learn mathematics and if it brought relevance for them. The value of our results resides in the fact that research has shown that perceptions strongly affect student motivation and engagement, and subsequently, their learning and achievement in mathematics (Christenson et al., 2012; Middleton et al., 2017). Indeed, Iannone and Thoma (2023, p. 7) explain that ‘the way in which a student perceives the task […] is a big influence on their engagement with learning’.

Each interviewee was a volunteer, representative student from the group that undertook the assessment task; we used the pseudonyms S1 to S6 to describe the students, each representing their views on how the group interacted and worked together to produce the video. Ethics clearance from the university’s Ethics Committee was obtained (Ref. 20214303-6608). The interviews were transcribed, and using N-Vivo (analysis software), we coded using reflexive thematic analysis (Braun & Clarke, 2019, p. 594) which is about ‘the researcher’s reflective and thoughtful engagement with their data and their reflexive and thoughtful engagement with the analytical process’. In particular, we used theoretical thematic analysis, or ‘theory-driven’ approach, with codes from CHAT and the CHAT-based definition of relevance. That is, we first identified in the transcripts the sensemaker (i.e. the motive of activity), any tools used in producing the digital story (e.g. resources, software, etc.), the social rules by which the students abode in their communities (i.e. their group), and if there was an overt division of labour. We also identified any source of relevance mentioned by the students (e.g. a personal interest, someone mentioning an application of a concept that made it relevant to them, etc.). Then, we searched for connections between these codes in the form of interrelations between the different components of the activity system, looking for patterns that ultimately could answer our research questions. For example, once we identified a particular sensemaker of a student, we looked for any connections to other components of the activity system in order to understand how these components seemed to shape the student’s motive of activity (i.e. why the student was engaging in certain ways with the assessment task). Similarly, we looked for sources of relevance mentioned by the students to understand why they ascribed (or not) any relevance to the mathematics they chose for their digital story. We note that not all nodes in the CHAT triangle (see Figure 1) were identifiable in the students’ transcripts, leading us to conclude that those aspects of the activity were less influential for those students.

5. Results

5.1. The sensemaker and mathematical learning

Each group decided on the topic of their story (Table 2). The idea was that this would enable them to have ownership of the topic – in the sense that it was not imposed on them by the lecturer – and the flexibility to produce a video that was of interest to them. We hypothesised that the more interested they were in the topic, the more engaged they would be in the task and the better quality of the story.

Table 2. Stories and topics chosen by groups and motive for the choice.

Group#	Brief description of story and mathematics topic	Motive for choosing topic according to S#
1	The story was about an imaginary student who pondered about the relation between mathematics and music after a piano lesson. Geometric sequences were used to explain the frequencies of the 12 music notes.	They saw the topic in a website and found it interesting. S1 also had a personal connection with music.
2	The video was the story of a baker who needed to order a collection of ingredients in two different bundles. Inequalities were used to describe and analyse the problem to determine the most cost-effective option to purchase.	All members of the group were comfortable with the topic and the level of mathematics that it entailed.
3	The story told the origin and history of percentages and how this concept developed from ancient Rome to the Dark Ages. A second scene described present uses of the concept in Finance and Business.	The topic was easy to understand, and they believed it could get them higher marks.
4	The story revolved around a ‘mystery murder’ scenario which was solved by using logarithms (using Carbon14 methods). A final scene explored how logarithms could be used to represent large quantities, such as the number of sweets (Skittles) in a bag.	The group felt they could grasp the topic and were comfortable with it. They thought they could still learn a little bit more about it.
5	The story was about a family that enjoyed playing video games and found out that quadratic equations are behind many of their activities. For example, in World of Warcraft, players buy and sell armour and weapons and a quadratic equation could be used to determine the best price to sell. Also, when firing projectiles, a quadratic equation could describe the best trajectory to follow in order to hit a target.	The other members of the group enjoyed playing video games and thought it was an extremely popular topic. Even though S5 felt it was not a ‘real-world’ topic, she decided to go along with the group and ‘into new waters’.
6	The story was about the planning of a party and how fractions could be useful. For example, fractions were used to calculate ratios in recipes (e.g. baking a cake) and to split things equally (e.g. lemons for drinks) by using division of fractions.	Another member of the group really wanted this particular topic. Even though S6 thought the topic was very basic, he agreed to choose the topic because the group dynamics were not good and, in those circumstances, he did not want to choose a more complex topic.

Using Kaptelinin’s (2005) definition as a basis, the sensemaker – the motive of the activity – was very different in each case as can be seen in Table 2, and hence this would have a different effect in these students’ engagement and how they perceived the learning that took place. Other elements of the activity system such as the division of labour or the social rules also influenced these students’ sense making and perceptions of their learning in important ways.

S1 [Geometric sequences] and S4 [Logarithms] thought that the task helped them understand the mathematical concepts covered. S1 said:

Yes, I would say yes, because before making this video, my understanding about geometric sequences was purely about perhaps just about money […]. But after doing this video, I understand that geometric sequences have a deep connection with music […]. So, I think my understanding about geometric sequences has deepened, really deepened through this video-making process.

Further, S1 explained that working in a group made an actual difference to her understanding:

It really helped my understanding of this concept, because I think through group project you work with different people, which means I have to communicate with others. […] So, one of our group members said: ‘Oh, I’m just, I’m not going to lie but I don’t understand what’s going on behind this concept. So, if anybody could explain to me … ’. […] I started to think ‘how am I going to explain the things, how am I going to maybe use some basic simple language to get my meaning across’.

S4 expressed similar thoughts to S1:

Yeah, most definitely. We wanted to learn about the subject because a few of us just hadn’t grasped the concept as well. So, by doing the thing [the video] we would also be able to learn a little bit more about it. […] I think the points that [the lecturer] wanted, like a real-world application, the actual mathematics behind it and, yeah, just the collaboration of doing it within a group. Once you start talking about something you have to learn it a bit better, and in so doing you’re filling in the gaps on what you already do and don’t know. […] In my little talk I alluded to that, that I exhumed a body and utilizing the Carbon14 model of decomposition I was able to demonstrate that the body had decayed x amount of kilos. And from that, you can do some mathematics and figure out how old that body actually was using the logarithmic scale that I was using. […] Our group was great because everybody did collaborate quite well.

On the contrary, S2 [Inequalities], S3 [Percentages], S5 [Quadratic Equations] and S6 [Fractions], did not believe they further developed their understanding of mathematics whilst undertaking this task. S2 explained:

It felt like we were doing it for no reason, really, because [the lecturer]’s lectures are so comprehensive. He’d already covered it and … We understood how it could be applied. It was just a matter of showing that we understood how it could be applied, which you could just equally do through a test or anything.

However, despite these comments S2 did not perceive the experience as completely negative but instead appreciated the ability to be creative in mathematics:

We did appreciate, as I said, that … there was a maths assignment where you could have a creative outlet. So that was nice. In the end, the video that we produced, we were pretty happy with it. […] So, we weren’t able to just all get together and do the same thing [because of the pandemic]; we had to do it segmentally and we did get points deducted for that, but that’s understandable.

Similarly, S3 thought they did not learn any more mathematics from this task but realised some benefits of presenting mathematics in this way:

I will say not really, since we basically learned percentages during primary and high school […]. I did an example question, which was a business question that people use about calculating their interest rate from revenue and expense. And I heavily put that in there. And I talked about why people would use percentages in everyday life. […] I think a video is somehow professional[ly] lighter, somehow [it] convinces someone to learn or watch it rather than reading. So, I think that videos are really good.

S5 and S6 experiences could be summarised by the following quote: ‘I didn’t learn anything that I didn’t already know’ [S6]. Moreover, their topic choice was not deliberate as was the case of S2 and S3. Their group dynamics were determinant in their experiences. S5 was a mature student whilst the other members of the group were younger students that recently completed high school and enjoyed playing video games. The group worked well, and she described her group as ‘very approachable’. However, it was clear that the group had difficulty in choosing a topic that was of interest to everyone, so they settled on the video games topic that was of interest to the younger members of the group. Being a mature student, the topic was not what she would have preferred to do, and she was concerned of the group dynamics and the perception that she was much older and would not share the same interests. Instead, she overcompensated for her perceived limitations and ended up doing the entire editing work, ‘being very picky about the audio and the video, making it look good’.

In the case of S6, his group experience was ‘really awful’, feeling ‘not listened to and excluded’. The groupwork dynamics were not successful and the division of tasks left the project looking like three independent assignments that were thrown together to form one video. S6 stated that:

[The other] group members were really focused on how many marks it was worth and how they could divide it up. And so, you do your section, you do your section, and I’ll do mine. […] And then we’ll just stitch it all together at the end.

In his reflection, S6 thought that maybe if he had been in a different group ‘with somebody who had similar interests or similar levels of enthusiasm’, the experience would have been completely different because ‘at the beginning I was really excited about the idea … I really like maths, from merely [being] interested in it, and I thought it could be fun’.

5.2. The relevance of mathematics

The sensemaker (i.e. in this case, Relevance to what end?) did not only affect these students’ perceptions of their mathematical learning through this task but also how they saw the relevance of the mathematical concepts that they worked with in the video (Relevance of what?).

S1 related personally to the topic (Relevance to whom?), making it relevant to her. She said:

When I was little, I played the piano […] I enjoyed music very, very much. […] I think I lost my interest in the music after many years practicing, after my mother pushing me, getting some awards, and going to some competitions. But now I think my interest, my passion about the music came back again, because I did this project. I understand the maths behind it. And I’d say there’s a lot to learn.

Even though S1 expressed her interest in music as a child as partly her enjoyment of music and partly her mother’s demands, she clearly voiced that now she could see the relevance of the mathematics to her passion for music. She also expressed a belief that this topic could be relevant to others because both mathematics and music, ‘are very relevant to everyone’s life. […] Lots of people had never thought that there might be this connection between these two. But it is actually very, very, very relevant’ (Relevance according to whom?).

S3 mentioned a variety of examples where percentages could be relevant, and included herself when talking about relevance to whom? She mentioned it would be relevant to people in business, calculating shares and interest rates, or ‘just looking at a sugary soft drink and seeing how much sugar is in there’. She also mentioned other professions that would benefit such as ‘gamblers, nutritionists, scientists, a lot of people in engineering’. The variety of examples given by S3 points to a personal reflection on the relevance of this concept (Relevance to whom?) beyond the teacher or someone else attributing relevance to the concept (Relevance according to whom?).

S4 thought that the mathematical concept, and the task were ‘very relevant’. He explained:

I think something similar should be done with each subject. Maybe not a fully elaborated movie but maybe just a short clip on real-world applications […]. Because a lot of times I was doing the maths this year and I was struggling to figure out a real-world application. So, this was actually quite good in the aspect that it tied a little bit in.

By participating in the task, S4 thought that mathematical concepts could be given relevance even though he said he did ‘find [them] quite ridiculous actually [the exponential equations they used] but it’s a concept that you could see anybody can grasp’. When asked according to whom these concepts are relevant, he replied: ‘Well, according to us as students who chose the topic’.

S2 was able to relate the concept to an aspect of his personal life but did not ascribe real relevance to it: ‘As a Scout, yes, because there’s a lot of camps that we have to manage for. But, would I use inequalities to make those decisions? No’. This is an example of the relevance paradox (Niss, 2002) where the person seems to attribute some societal relevance to the mathematics (i.e. it could be used to manage Scout camps) but at the same time they consider it to be irrelevant to their personal circumstances (i.e. he would not use it).

S5 mentioned that she ‘raised concern because it was gaming and gaming is not the real world’. Similar to S2, S5 could see the mathematics in gaming but failed to ascribe relevance to it:

We did supply and demand and showed the formula with the graph, and with the projectiles we did the same thing as far as we actually wrote out the formula in the video. […] But it’s not like you go and do these things and then, ‘Oh, there’s a mathematical formula behind that’.

This is a further example of the relevance paradox where S5 acknowledge that certain aspects related to games can be modelled with quadratics (someone else assigning this relevance – Relevance according to whom?) but that gamers like herself would never use quadratics while gaming. Hence, they could not see a personal relevance.

For S6, the fact that the concept chosen was so basic meant that the personal and societal relevance of it was very limited. He said:

I think if you were prepared to get academic maybe [the concept could be relevant] and really … you could invent something, but really it was grade 2 maths. I don’t think it was very relevant, it was absolutely basic.

6. Discussion and conclusions

Making sense and bringing relevance to the learning of mathematics should be important aims given that many students often ask: Why do I need to learn this? The assessment task described in this paper aimed at engaging students that regularly have problems making sense of mathematics and hence do not see the relevance of it.

Our RQ1 was: What did students learn by participating in the assessment task of creating a mathematics digital story?

According to the data, the task ‘most definitely’ helped two of the students (S1 and S4) make sense and learn something of their chosen mathematical concept. Having to first make sense of the concept themselves to be able to explain it to others, and subsequently explain it using a story, showed that digital storytelling can help some students learn mathematics. Storytelling done in collaboration with others, especially when students experience a good working relationship with their peers, further helped them ‘fill gaps’ and ‘grasp’ the concepts, by pushing them to make their own meanings before conveying those meanings to others in a narrative. Creating a story is not just a simple matter of sequencing events but it is a form of meaning-making (Bruner, 1991). Stories need to be well-structured so they can be effective and recalled (Turgut & Kışla, 2015), something that we can see in these two students’ accounts. The reader should note that we are not claiming that these students acquired a profound understanding of, for example, the complex relationship between mathematics and music. But they learned something as they got a sense of how this relationship works, and as S1 said: ‘And I’d say there’s a lot to learn’, which indicated an important metacognitive awareness. In our view as highly experienced educators, this is something that is rarely achieved in most traditional lectures or through closed-book examinations. Furthermore, the reader should remember that this was a foundation unit, and these students were only starting their university mathematics education, most of them coming from a background of disaffection or even alienation from the subject.

Students S2 and S3 were motivated by the assessment marks rather than the learning itself, and believed their understanding did not develop further because ‘I didn’t learn anything that I already know’. They could not see the task as helping them set higher expectations for learning, hoping instead for the ‘higher marks’ only. They did however concede that they were able to appreciate the value of the task as a ‘creative outlet’ or to ‘convince someone [else] to learn’. These perceptions point to the potential of digital storytelling in developing students’ creativity (Özpinar et al., 2017; Walters et al., 2018) and other useful skills (Banaszewski, 2005; Demirer, 2013).

Students S5 and S6 were influenced negatively by their group experiences: rules and division of labour in the activity shaped in important ways their engagement and learning in this task. While S5 was happy to work with her group, the fact that her peers were substantially younger than her meant that the mathematics learning took a second place and instead her efforts concentrated on the aesthetics of the video: ‘the audio and the video, making it look good’ and ensuring that she did not let the group down. In the case of S6, the poor working relations within his group meant that the chosen topic was so basic that he considered nothing useful could be learnt.

These results provided us with the opportunity to understand the motive for engaging in this task (i.e. the sensemaker) and how it is crucial in shaping students’ perceptions of learning. As lecturers we could influence this aspect in a better way by suggesting topics that can potentially stretch students’ knowledge instead of being ‘very basic’ or ones that they ‘already know’. Students then can choose from a list of topics the one that interests them the most. This is in line with what Tan et al. (2014, p. 632) found in their ‘edu-tainment’ approach in science education, where they realised ‘that it is important to closely consider the type of knowledge that we desire students to acquire through the instructional design – not all knowledge forms are equal’.

Our RQ2 was: How do students perceive the relevance of a mathematical concept to the real world by communicating a story through a video?

Our data showed that the task helped S1, S3 and S4 to see the relevance of their chosen concept. Whether they related mathematics to a passion, to a variety of applications or to a personal realisation of where a concept can be applied, these students were able to reconcile their personal motive (Relevance to whom?) with a societal motive (Relevance according to whom?) for studying the subject, and hence appreciated that mathematics can be ‘actually very, very, very relevant’. In essence, we can say that storytelling helped these students to reconcile personal and societal relevance by providing an opportunity to make sense and to communicate to others why a piece of mathematics should be important.

On the contrary, S2 and S5 saw that mathematics could relate to certain aspects of the real world (e.g. a Scouts’ camp or video games) but were unable to attribute personal relevance. They suffered a case of the relevance paradox. This outcome points to the fact that it is not a trivial task to develop pedagogical or assessment practices that ensure the paradox will be solved by all students. More needs to be done to ensure students can craft stories that involves them personally acting in the world, and this might mean designing lessons that encourage more imagination and creativity.

The case of S6 is somewhat disappointing. This was an enthusiastic student that ‘really like maths’ and thought that the task ‘could be fun’. Even though his sensemaker was geared towards learning more mathematics, the community and division of labour to which he was subjected meant that his original motive to engage in the activity was derailed, and he had to change his object of activity to one where he thought the mathematics was not very relevant.

From these results, we learned that it is vital that students are able to reconcile the subjective and objective character of relevance, that is, why mathematics is important for society and how that affects them in their personal lives. We also learned that it is important to have better control of other aspects of the activity system such as how to work effectively in a group. This could be done by offering better training in how to collaborate and work effectively as a group, which is often overlooked as a soft skill, but one that has been identified as a sought after twenty-first century skill. This could help some students have greater agency of their learning experiences, shaping these into more inventive, fun or valuable ones. Speaking of the whole cohort of students, we did not encounter students saying they had technological problems in filming or editing their videos. We know that many of today’s students are familiar with or even create content in social media platforms, something that require some digital skills and even certain level of storytelling competence. However, not all of them were able to create compelling stories which makes us conclude that storytelling is also a skill that requires learning and development of expertise.

We note that our results should be seen in the context of qualitative research, contributing to ‘analytic generalisations’ (Schwandt, 2007) that, along with other studies, complement our understanding of how storytelling affects mathematical learning and engagement. However, the different perceptions that we encounter in our data make our results interesting and useful in making sense of how students might perceive storytelling as part of their university studies.

The use and research of storytelling as a pedagogical tool in undergraduate mathematics is in its infancy. There is much that we do not know about it, but this paper is an attempt at raising awareness of its potential and we hope to grow interest and engage others in using narratives in their teaching, especially in STEM disciplines. Researching learning and/or assessment innovations that have the potential to bring learning and relevance to students’ mathematical understandings is important if we want to challenge cultural myths and change negative perceptions and attitudes about mathematics that plague our classrooms and societies. Our data showed that digital storytelling can help some students reconcile the personal and societal characteristics of mathematics relevance, however further reflection and research are needed to help other students effectively communicate the importance of mathematics and to develop critical skills to be better prepared in a rapidly changing society.

Disclosure statement

No potential conflict of interest was reported by the authors.