1 Introduction

At the time of our writing, the world continues to contend with COVID-19. Mathematics is used to picture this and other crises (Skovsmose, 2021), in part through the use of data visualizations and other data representations (DVs).Footnote 1 New digital platforms and tools enable multimodal representational features in DVs, including audio, video, or animation, as well as interactive features. These representational forms extend beyond conventional graphs (e.g., static bar or line graphs; Sheiber, 2017). New representational forms allow for enhanced data storytelling as well as the integration of art and activism (e.g., Chalabi, 2020; Lupi & Posavec, 2016). On one hand, the prevalence of DVs and data-driven arguments about COVID-19 in news journalism (Kwon et al., 2021) provides artifacts ripe for mathematics curricula through their connections to mathematics topics such as percent and number, rates of change, probability, and modeling. On the other hand, since data and DVs are a key resource for understanding, framing, and solving problems, as well as communicating their solutions (Boyd & Crawford, 2012; Stenliden et al., 2019), data literacies are crucial for education about the pandemic and for its resolution (Aguilar & Castaneda, 2021; da Silva et al., 2021). Moreover, the very prevalence of DVs signals a need that they become more central to mathematics education. In this commentary, we argue that innovative DV forms can broaden opportunities for mathematics learning. Multimodal, interactive, and narrative elements, among others, enable new forms of DVs to tell stories about crises in more explicitly visceral and emotionally engaging ways than conventional graphs. Our purpose is not to argue that conventional graphs should be replaced but rather to consider new visualization forms as equally valuable resources for mathematics learning, particularly during times of crisis.

Innovative DV forms offer pedagogical affordances with respect to the goal of using mathematics to help students make sense of their own and others’ lives during times of crises. Such a goal includes the use of mathematics to understand crises such as the COVID-19 pandemic on an aggregate level but also to make sense of crises on an individual level with an emphasis on emotion as well as intrapersonal and interpersonal experiences. These different approaches to using mathematics to make sense of crises are not opposites, but rather complementary and interrelated. Konold et al. (2015) argue that while statistics is “fundamentally about the behavior of aggregates” (p. 322), students should be able to move flexibly between seeing data through an individual, point-wise perspective and through an aggregate, global perspective, based on the purposes and questions at hand. Individual-based perspectives can ground truth and instantiate, challenge, interrogate, or build towards aggregate trends, while aggregate views are necessary for seeking patterns or conducting statistical analyses (Ben-Zvi & Arcavi, 2001).

In this commentary, we convey that innovative DV forms offer alternative and potentially complementary ways to make sense of the world through data, particularly during times of crisis. We highlight opportunities for mathematics educators to recognize the plurality of representations in DVs, to understand the affordances that particular DVs can contribute to instructional goals, and to curate sets of representations that most effectively work together towards those instructional goals. In the first part of this commentary, we provide a brief overview of related literature about DVs in mathematics education and about newer forms of DVs. Then, we present the idea of pedagogical affordances as a lens through which to analyze the particular opportunities presented by different forms of DVs. Next, we introduce three examples of DVs from news journalism that are viscerally and emotionally engaging in different ways, discuss their pedagogical affordances for mathematics teaching and learning, and suggest possibilities for pairing innovative DVs with conventional graphs in generative ways. Finally, we discuss how these three examples suggest new possibilities for using DVs in mathematics education during times of crises.

2 Data visualization and mathematics education

2.1 DVs in mathematics education

DVs appear in K-12 mathematics education in terms of graph reading and writing, with graphs as tools for data analysis, data representation, and communication. At the elementary level, students are typically introduced to bar graphs, circle graphs, dotplots, and scatter plots; at the middle and high school levels, this expands to include graphs of functions and, sometimes, other plots (e.g., box-and-whiskers plots; Bargagliotti et al., 2020). The latest PISA Mathematics Framework (OECD, 2018), for example, emphasizes graphing as a tool for analysis, problem-solving, and for communicating one’s thinking efficiently and abstractly. There is also a growing emphasis on mathematical representations more generally, especially with respect to mathematical modeling, a domain that includes data analysis and statistical modeling (Ben-Zvi et al., 2018; Biehler et al., 2018; Burkhardt, 2018; Maass et al., 2019; Schukajlow et al., 2018). The U.S. PreK-12 Guidelines for Assessment and Instruction in Statistics Education II, for example, note that evolutions in technology have produced “amazing data visualization tools” and “unconventional representations” (Bargagliotti et al., 2020, pp. 11, 95). In that document, however, the focus is on extracting conventional statistical information from newer representational forms, rather than on highlighting how these representations could add opportunities for learning. In short, there is potential to tap into the expanded range of DVs and benefit from their affordances.

2.2 DVs in news journalism

DVs are social texts that tell stories from specific points of view (Rubel et al., 2021). Data journalists have become increasingly intentional about attending to audiences’ bodies and emotions to more fully capture the experiences of people with respect to real-world phenomena and better engage audiences through data (see e.g., Cairo, 2016; Chalabi, 2020; McCandless, 2000). These trends can be seen as a revival of DV practices prevalent in the nineteenth century, when appeals to emotion were embraced (see Brasseur, 2005 for examples from Florence Nightingale; Battle-Baptiste & Russet, 2018 for examples from W.E.B. Du Bois). Kostelnick (2016) refers to that period as a golden age of statistical graphics, in how designers broke traditional design conventions by making abundant use of color and narrative elements. Such practices were subsequently rejected in the twentieth century through modernist movements that insisted on minimalism and Enlightenment-era appeals to rationality over feeling (Kennedy & Hill, 2018; Kostelnick, 2016).

Today, there is widespread acknowledgement that DVs are storytelling devices that can evoke emotions and engage the body (Kennedy & Hill, 2018; Kostelnick, 2016; Matuk et al., 2022). In particular, interactivity allows readers to interact with data in more ways and can readily evoke emotional and visceral responses (Cairo, 2016; Kennedy & Engebretsen, 2020). Interactivity includes the layering of multimedia (i.e., audio, images, text, video; Hill & Bradshaw, 2018), incorporating dynamic features (e.g., hovering that shows tooltips, zooming in and out, time sliders, adding filters and search functionality; Segel & Heer, 2010), and shifting the perspective or the dimensions of the data display (e.g., manipulating a data dashboard or expanding or shrinking a data table). These features are thought to provoke emotional responses by engaging readers’ senses (e.g., fear; Oh & Hwang, 2021), drawing readers in closer proximity to the data by allowing them to customize the data display or explore it using their bodies (e.g., Roberts & Lyons, 2020), or allowing readers to receive real-time flows of information (see Kostelnick, 2016).

We subsequently consider how innovative DVs, as storytelling devices designed to capture people’s engagement in new ways, can be leveraged for mathematics education. Through three examples and the lens of pedagogical affordances, we illustrate how multimodal, interactive, and narratively compelling DVs create opportunities for sensemaking about crises and for learning mathematics.

3 Pedagogical affordances

Mathematics teachers can excerpt DVs from news journalism to support students to use mathematics to understand real world events and crises. In the process of curating these resources, teachers take numerous considerations into account, including their beliefs and convictions about education, their instructional goals, their understandings of their students, the availability of materials, and their school context (see Pepin et al., 2017; Remillard & Heck, 2014). While excerpting DVs for classroom use, mathematics teachers must consider what instructional possibilities they offer. These possibilities can be understood in terms of affordances.

Gibson’s (1986) concept of affordances describes the relationship that exists between an acting agent and its surrounding environment. The affordance of an object is what it allows an acting agent to do (Norman, 2013), such as the case of a coffee mug handle that allows a person to pick up a hot mug without burning their hand. This concept depends not only on the object's properties but also on the acting agent and the context. Certain acting agents may not be able to use a mug handle—for example, a mug handle may be unusable by some animals or a person with a broken finger—the handle may not be perceptible, or the acting agent may not understand how to use or wish to use the handle. Thus, affordances are relational phenomena, not standalone properties of objects removed from their conditions of use (Norman, 2013). Affordances do not guarantee action (Dindyal et al., 2021), and the likelihood that an affordance becomes actualized may depend on issues of discoverability, accessibility, and feedback (Norman, 2013).

Nagashima et al. (2020) discusses the notion of pedagogical affordances as the "properties of an instructional tool that could help achieve instructional goals, or that would put a limit on achieving the goals" (p. 1). The affordance of an instructional tool depends on the teachers’ instructional goals, which shape what constitutes an affordance and how such affordance is perceived and activated (Nagashima et al., 2020). For instance, if a mathematics teachers’ instructional goal is to support students in understanding the importance of equally scaled axes on a graph, then a DV that includes a scaled axis serves as an affordance toward that goal. However, if the teacher does not make that goal explicit, the affordance offered by the DV may not be perceived by students or activated in the course of instruction. Pedagogical affordances therefore can describe the instructional possibilities created by text, diagrams, or graphs that conceptualize real-world phenomena in various modes (Wu & Puntambekar, 2012). Studying the affordances of a representation includes considering how it prompts individuals to relate displayed information to their own lives, identify and name their feelings about a social issue or natural phenomena, examine familiar concepts in new forms, and form connections between topics.

We seek to convey the potential of innovative DVs for mathematics education by highlighting the instructional possibilities that such DVs afford. In the following section, we examine three examples of DVs from news journalism focused on the COVID-19 pandemic and highlight complementary pedagogical affordances offered by conventional representations of the same data. These examples are not comprehensive and are but an initial sampling of innovative DVs that have emerged in news journalism and other forms of public media.

4 Three examples of DVs

4.1 Example 1: Bui and Badger (2020)

Bui and Badger’s (2020) DV, published in the New York Times, models levels of audible noise in New York City (NYC) using data gathered by street-level microphones (see Fig. 1). The DV is a line graph that depicts sound levels between February 2019 and May 2020 to contrast sound levels from before the pandemic with the lockdown in March 2020. Audio clips from two points are layered on top of the graph, which are activated when a user clicks on images of sound waves corresponding with the clips. These audio clips illustrate, in a particular way, the impact of the pandemic’s first vicious wave in NYC.

Fig. 1
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Screenshot from Bui and Badger’s (2020) DV depicting sound levels in New York City before and during the pandemic

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Because the audio clips are layered as attached to two points on the graph, the representation does not detract from the pedagogical affordances of a traditional line graph. Figure 1 still utilizes a coordinate system to denote data values and trends. The audio clips provide audible embellishment that highlights the intended contrast. Furthermore, the audio clips bridge a gap between the line graph as a model of changes in sound levels and the meaning of individual points on the graph (what a street sounds like at a particular sound level). In other words, the audio clips can serve as a scaffold for readers to connect the line graph to the phenomenon that it is modeling––the varying levels of street sound in NYC from before the pandemic to its first lockdown. The audio clips thus add dimension to the line graph by offering a means of experiencing the quantified measures with auditory senses.

The choice to represent and include audio in Bui and Badger’s (2020) DV is not arbitrary—it provides an opportunity for meaningful connection to people’s experiences during lockdown. The quiet in the streets demonstrated in this DV, produced by the constrained mobility in response to public health recommendations, marks the deep human estrangement and loneliness that was experienced in that period. The integration of audio alongside the visual representations invites the reader to not just see but to hear and feel how that loneliness sounded. Different from framing human mobility as dangerous with humans as disease vectors, this DV highlights the social meaning of mobility and, as was the case, the social meaning of limited mobility. Bui and Badger’s (2020) DV opens space for mutual acknowledgement and engagement with feelings like loneliness and isolation that have accompanied the pandemic (Dutta, 2021).

By integrating sound into their DV, Bui and Badger (2020) establish a sensory and emotional connection between the reader, the mathematics, and the phenomenon. In so doing, they call into question conventions in mathematics education that focus only on visual representations of data. The inclusion of audio in the DV challenges the notion that all types of raw data (in this case, audio) should ultimately be formatted according to a quantitative scale that can be plotted and shows how other forms of data can be integrated in meaningful ways. One could imagine a DV embedding continuous audio corresponding with a graph to enable readers to experience a dataset’s variability, or even using audio alone as a model for a data set, even data that is not about sound (see data sonification, Beans, 2017). We note that audio is only one example of an alternative medium that can enhance or serve as a mathematical representation. One can also imagine a DV that invites the reader to feel the data through other senses, for example through fluctuations in temperature or different types and intensities of smells.

4.2 Example 2: Hart (2021)

Hart's (2021) 500,000 Lives Lost DV (see Fig. 2), published in Reuters, conveys the number of people in the United States who died from COVID-19 as of February 2021. The interactive DV uses points to represent each individual life, points which amass along a vertical timeline. The points fluctuate in their density over time in correspondence with waves of the pandemic. Hart engages the reader interactively through touch: readers must scroll down to view the entire vertical timeline. Each flowing point represents a person’s death, and the quantification of aggregated deaths is visualized through the amassing of these individual points; the spacing of the dots has the effect of generating a visual sense of accumulation rather than on conveying exact magnitudes.

Fig. 2
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Screen shot from Hart’s (2021) 500,000 Lives Lost DV. Permission pending

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Hart's (2021) DV is not amenable for precisely measuring values or rates; however, the graduated density of the dots, which fluctuate between narrow and wide clusters over time, produces a visual and tactile experience that can likely support the learning of concepts like rate of change. Points representing individual deaths are not evenly spaced out and there is no marked axis for the reader to determine aggregates by date. Yet extreme values become evident through the scrolling, as the intermittent dots turn into a line of dots and then quickly to a thick, dense, and wavy band of dots. At the same time, Hart reminds the reader of the individual lives lost that are at the core of the aggregated data, and how these lives relate to the collective. On the left side, the DV includes mini-obituaries of some individuals that provide names, ages, and some details about their lives. On the right side, the DV anchors the magnitude of 500,000 relative to numbers of lives lost during select historical milestone events. These techniques further remind readers of the human and social significance of the data on an individual and societal level. Layering aggregate data and meaningful individual qualitative data, setting up comparisons with memorable historical events, and framing the magnitude of lives lost through individual dots, are techniques that anthropomorphize data (i.e., anthropographics, Sorapure, 2022).

Fig. 3
figure 3

Reproduction of Fig. 2 using a conventional graphical display (U.S. CDC COVID-19 Data Tracker). The data and data representation in Fig. 3 comes from the U.S. Center for Disease Control’s (CDC) COVID-19 Data Tracker, which allows users to create customizable bar graphs that display COVID-19 related data based on a chosen date range. Figure 3 shows the daily number of such deaths reported to the CDC between February 6, 2020 and February 22, 2021, which is the same statistic and date range as in Hart’s (2021) DV

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Figure 3 represents a similar dataset but uses a conventional bar and line graph representation. Deaths are organized by date and aggregated into thin vertical bars scaled according to magnitude. The entire time interval is compactly expressed in a single frame, displaying the entire distribution all at once and making it easier to observe overall patterns. This representation is conducive for identifying extreme values, intervals on which the graph is increasing, and other kinds of rates of change.

Pairing conventional graphs like Fig. 3 with innovative ones like Hart’s (2021) DV can provide opportunities for learning in terms of making important mathematical connections. For example, connections can be drawn toward the different ways that time is represented, the variety in how axes are used, different levels of or need for precision, and the relationship between representations of individual values (in this case, lives lost) and aggregate measures. Other connections can be drawn between increasing/decreasing intervals and slope values that are more conveniently calculated using Fig. 3––but often elusive in meaning to beginner graph readers––with the cascading density of points in Hart’s DV. Similar connections can be drawn regarding extreme values and how they are represented in each DV. These mathematical connections can create opportunities for a deeper understanding of not just the mathematical concepts but what they represent––in this case, the widespread pain and loss related to COVID-19.

4.3 Example 3: Chalabi (2020)

Chalabi's (2020) Companies that have profited from the pandemic, published in The Guardian, stays within the parameters of visual modality; however, it challenges conventions by mixing conventional mathematical representations (i.e., a bar graph) with political illustrations for the purpose of activism through storytelling (see Fig. 4). Chalabi represents several U.S. retail companies’ additional profits in 2020 compared to the previous year using a nontraditional bar graph whereby the bars are composed of illustrated images of workers stacked on top of each other on their hands and knees. Illustrations of the executives wearing suits representing each company stand on the backs atop each stack of kneeling workers. Chalabi’s DV is an example of how a DV can be used to tell complex, compelling stories that render the DV emotionally engaging. The spatial positions of the people shown in the DV (workers on hands-and-knees as compared to company owners standing on top) draw attention to the inequality, social hierarchy, and inhumanity connected with the excess profits that corporations experienced during the COVID-19 pandemic. Chalabi’s DV instantiates that visualizing data can enable mathematics to be used to challenge injustices.

Fig. 4
figure 4

Company profits during the pandemic (Chalabi, 2020)

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Chalabi’s (2020) DV makes clear how traditional DVs tend to obscure human dimensions related to who benefits and who are exploited by current arrangements. In the case of capitalism, it relies on invisible labor and the invisibility of that labor is reinforced by how typical DVs essentially hide it from view. Chalabi’s DV, however, shows corporate profits while highlighting the labor that makes these profits possible. The DV, together with the accompanying text, is intentional in narrating that companies’ huge profits were only made possible by the workers taking risks on the front lines during the pandemic. The DV subtly allows reference to other aspects of the context, like the owners’ genders and race—nearly all of the leaders of these companies seem to be White men (though it misses the opportunity to highlight the genders and races of workers).

By making human bodies and their identities visible, Chalabi’s (2020) DV affords the instructional possibility of highlighting the connection between income inequality, particularly in the context of crises, with gender and race. These instructional possibilities may open up conversations in which students can reflect on their own identities and lived experiences during crises, such as may be the case for students who were required to work, or whose family members were required to work, during the COVID-19 pandemic. In this sense, the mathematics classroom may become more than a space for students to understand the technical dimensions of crises, but also a space where students can use mathematical representations to make sense of their lived experiences and view them in social context.

Figure 5 shows the same data but in a traditional bar graph and is ripe for conventional statistical analyses such as finding various measures of central tendency. The simplicity and reproducibility of this graph enables its ease of production or modification. A teacher might consider remaking Fig. 5 so that the y-axis is unevenly scaled to demonstrate one way that graphs can be misleading. Chalabi’s (2020) DV is a bespoke design, and does not possess this same flexibility in terms of modification or reproducibility. The juxtaposition of Chalabi’s DV with Fig. 5, however, invites learning opportunities through their contrast. For instance, the narrative of Chalabi’s DV is foregrounded, exemplifying how DVs are always social texts with a particular perspective, whereas the narrative that is communicated through Fig. 5 is more ambiguous. The hand-drawn nature of the illustrations in Chalabi’s DV further accentuates that a person created the DV (Alamalhodaei et al., 2020). The reminder that people, not data, make the choices that determine how a DV is made can inspire additional voicing of stances on societal issues and can create opportunities for healing around these social issues, increase potential for mathematical power and agency, and improve relationships with mathematics (Kokka, 2018, 2022).

Fig. 5
figure 5

Reproduction of Fig. 4 using a conventional graphical display (R). The authors created Fig. 5 using the ggplot2 library in the open-source statistical computing software package R. The authors used the same data source behind Chalabi’s (2020) DV (Brookings, 2020)

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The conventional bar graph of Fig. 5 relies on a minimalist design style with simple bars, a grayscale color palette and precisely marked x- and y-axes. These design choices foreground the numerical qualities of the data—as opposed to its social, cultural, political, and ethical dimensions or context. The minimalist style of Fig. 5 is aligned with widespread practices in the DV community that minimize the use of color and other stylistic choices in order to present the “raw facts” of the dataset without any emotional appeal. The belief that data visualization should be minimalistic can be attributed to Tufte (2001), who believed that DVs should remove superfluous information to appeal to reason alone without the interference of emotional—and thus subjective—factors (D’Ignazio & Klein, 2020). It can be argued that Tufte’s design philosophy is the dominant paradigm for data visualization in mathematics curricula. Presenting both Chalabi’s (2020) DV alongside Fig. 5 as valid alternatives for making sense of crises through a mathematical representation offers the opportunity to thoughtfully accept, reject, or add nuance to this dominant paradigm or to consider in which situations one might be preferable. Finally, debates about the use of mathematical representations prompted by the contrast between these figures invite broader philosophical discussions about the nature of mathematics itself.

5 Discussion

The prominence of DVs in news journalism, which increasingly showcases innovations in DVs, creates new opportunities and calls for expanding the set of DVs that are incorporated into mathematics curricula. The preceding examples highlight the potential impact that such DVs might have on mediating mathematical engagement with social crises like the COVID-19 pandemic. All three examples combine aesthetic elements with mathematical qualities of space, variation, and quantity and generate pedagogical affordances that open up possibilities for shifting students’ relationships with and understandings of mathematics. This is especially true when such affordances are paired with those offered by conventional graphs.

All visualizations or other representations of complex phenomena are imperfect models of reality. As models, they make some elements of phenomena visible and render others invisible. Traditional graphs afford certain pedagogical opportunities but have not kept pace with the development of newer forms of DVs that seek to render phenomena visible in different ways. The examples of DVs in this commentary showcase multimodal, interactive, and narrative features, among others, that could create opportunities for students to construct their understanding of quantities and patterns in data from an alternative vantage point or sensory perspective. In addition to contributing to sensemaking, DVs with innovative features may provide opportunities to shift students’ relationships with mathematics by centering their identities, experiences, and agency in the mathematics classroom. Multimodal features, such as those found in Bui and Badger’s (2020) DV (Fig. 1), can enable teachers to direct students’ attention toward sensory dimensions of crises beyond the visual and, through multimedia technologies, invite students to experience these dimensions on a visceral level. Interactivity, such as that found in Hart’s (2021) DV (Fig. 2), can be used to position students as active participants in engaging with DVs. Illustrations, such as Chalabi’s (2020) DV (Fig. 4), can help students see the humans behind a data-driven story and thereby see themselves within the story. In these ways, the mathematics classroom can become a space for students not just to connect to but also grapple with the realities of their lived experiences during times of crisis, turning the mathematics classroom into a potential place for empowerment and healing (Kokka, 2018).

To emphasize, we do not argue for the elimination of conventional graphs from the mathematics curriculum. Instead, innovative DVs raise issues for researchers and practitioners to consider when selecting, adapting, and using DVs from popular media. Using innovative DVs in the classroom involves trade-offs, such as a loss of precision that might occur, for instance, by eliminating a visible axis in favor of enabling students to experience data through scrolling and touch. Just like conventional graphs, innovative DVs are only partial representations of reality. Nonetheless, solely presenting students with minimalist graphs in the name of precision or apparent neutrality can exact a price, such as removing the people most affected from the forefront of the representation. Including graphs that make the human creators and human impact (often an unequal impact) of crises visible can invite awareness and motivate critical questions.

Lastly, we do not claim that traditional graphical representations cannot be used to evoke emotion in learning settings, nor that using innovative DVs ensure emotional engagement. As Kennedy and Hill (2018) suggest, all DVs have emotional qualities, but some DVs are more explicit about these emotional qualities than others. Because pedagogical affordances do not guarantee action, we emphasize that exactly how a DV engages students depends not only on the features of the DV but also on the teacher’s decision making, the classroom culture, and the other aspects of the learning environment.

6 Conclusion

Emerging guidelines and research in statistics, data literacy, and data science education acknowledge the rise of innovative DVs (Bargagliotti et al., 2020) and encourage students to explore and create new means of visual expression that more fully capture lived experiences (Lee et al., 2022). Our commentary adds to this work by considering particular affordances of innovative DVs while situating how they might elicit emotion and experience as potentially generative aspects of making sense of crises through a mathematical lens. We argue for increased attention in mathematics education to innovative DVs. This is an opportunity for mathematics education to keep pace with contemporary trends in data representation. Moreover, this is an opportunity to expand what it means to use mathematics as a way to understand ourselves, one another, and broader aspects of society.