The Mathmagics of Media Princesses: Informal STEM Learning, STEM Rhetorics, and Animated Children’s Movies

The movie Moana (2016) took a stance on an academic mathematical debate. Set on a fictional Polynesian Island, the movie follows the title character as she prepares to become her people’s leader. Told that she must not travel too far beyond the geographical boundaries of her island, Moana still decides to investigate the ecological devastation of her home through making a long ocean journey, finding a demigod, facing demons, and learning to navigate along the way. In her navigational education, she finds she needs to recognize that her ancestors were “voyagers,” a term that has been debated in academic scholarship. Used by mathematicians and anthropologists, “voyaging” can refer to the long-distance navigation of not just the Polynesian peoples but also the peoples of the nearby Marshall Islands, as Sara Hottinger has recently reviewed (125-158). The ethnomathematical research about the practice has been variously praised for demonstrating complex mathematical practices of non-Western peoples and criticized for being a non-mathematical ritual at best. Through using a modified version of “voyaging,” instead of navigating or calculating, and through framing the practice as cultural and remembered, the movie Moana mirrors broader rhetorics of mathematical success, which tend to limit female characters’ performances of math.

Moana follows a history of similarly missed opportunities. From the 1950s until now, many children’s movies have focused on heroines who, though often excited about learning, are nevertheless not presented as interested in mathematics. An adherence to such omissions leads to surprising outcomes. For example, the 1951 movie Alice in Wonderland jettisons mathematical material in favor of the linguistic jokes of the original Victorian stories. The following 1959 movie Donald in Mathmagic Land returns to the mathematical content of the Alice stories, except Donald does so through a male narrative and a male character who acts in ways that reinforce his gender presentation. The portrayals matter, as Jack Halberstam has argued about related movies, because they reflect and reinforce ways of being in the world. Children’s movies, for Halberstam, reflect narratives of success and failure, and the heterogeneous, cooperative acts of Pixar misfits present a “queer” alternative to the heteronormative, capitalist fairy tales of Disney (21-22). According to feminist scholar Sara Hottinger, building on the work of British sociologists Valerie Walkerdine, Heather Mendick, Melissa Rodd, and Hannah Bartholomew, such narratives especially matter in math (5). Walkerdine and Mendick separately came to the conclusion that British girls of the late-1990s and early-2000s could not reconcile mathematical success with normative femininities. Rodd and Bartholomew, writing slightly later, found that female math students were more likely to say that their achievement was the result of hard work, while their male counterparts often claimed their successes came from natural ability. Arguing that “our culture” considers “femininity and mathematical talent…discursively incompatible” (5), Hottinger focuses on the textbooks and articles that either reinforce or begin to subvert such associations. The following paper focuses on the media portrayals of mathematical success, especially the absence of stories of math achievement for female characters and even their creators. In doing so, I follow Halberstam in arguing for the importance of studying media portrayals of success along with discursive and ethnographic examples. Children’s movies importantly have participated in the broader rhetorics of mathematical success, twisting narratives in order to preserve the absence of female mathematical knowers.

Drawing attention to the participation of children’s movies in academic debates, this paper additionally seeks to add to our understandings of STEM rhetorics. STEM, after all, stands for “science, technology, engineering, and mathematics,” though the mathematical M often receives poor coverage. The recent technical communication articles about “quantitative literacy” show the trickiness of defining math skills from rhetorical perspectives (Colombini & Hum 380; Grawe and Rutz 3-5). Furthermore, G. Mitchell Reyes’s review essay “Stranger Relations” indicates some theoretical frameworks that could explain the perceived disconnect between (modern) rhetoric and mathematics and that could provide some opportunities going forward. As Reyes has noted, rhetoric scholarship already exists that explores the relationship between the seemingly distinct fields. The work of Giovana Cifoletti, Jessica Mudry, Jordynn Jack, and James Wynn, in particular, all show that rhetoric and math can be considered together because of their historical interconnections. This article shifts focus, investigating the implications of math rhetorics for the recent past. Specifically, I use explicitly feminist scholarship to uncover how female characters (and by extension, women) have been rendered silent in the context of mathematical conversations.

The patterns of silence and omission become especially pressing when considered with respect to the recent Peitho articles about STEM rhetorics. Though American science education developed gendered tracks slowly, as historian Kim Tolley has shown (1-12), we do face their enduring legacy today. Many messages—subtle and profound—now reinforce the presentation of STEM disciplines as “male, technical, and insular” (Brewer 251-252). Drawing attention to the history of STEM’s gendered expectations in America, Jordynn Jack has analyzed collections of children’s toys. Though the emergent marketing of girls’ scientific toys might lead some to claim gender parity in STEM, Jack notes that “scientific and technical elements” of the toys are “feminized” in order to “limit the disruptive potential of these toys, confining them safely within the pink world girls are used to” (“Objects in Play” n.p.). STEM messages matter, according to Brewer and Jack, because they concern who will be the nation’s future scientists and engineers, and they thus affect many Americans even beyond the children who are encouraged to see themselves as future STEM professionals (or not). As I will argue, children’s movies similarly participate in making possible certain visions of future STEM workers. They limit the pool of role models for mathematically-inclined young people, which limits their entrance into math professions or broadly STEM professions. STEM exclusion is not just the concern of girls and women, too, as extensive research has confirmed that limited visions of STEM promote exclusivity far beyond gender expression (Hacker 10). Moreover, as I will explain in the final section, such messages affect our views of the present as well as the future, leading to the omission of female mathematicians who are working today.

In focusing on animated children’s movies, this article indicates how rhetorical scholarship can provide perspectives on “informal STEM learning.” Defining informal STEM learning, the National Science Foundation recognizes how “learning occurs across the lifespan and in places and spaces beyond schools or the school day.” Examples of the major “sectors” of the field include “mass media, museums/zoos/aquaria, after school, science outreach, citizen science, cyber-enhanced learning, science communication, among others,” which all “have particular potential for supporting learners from underrepresented groups” (NSF “AISL” n.p.). Movies, in particular, provide a means of addressing large numbers of children, implicitly teaching them social expectations even beyond the classroom. As part of the larger project, the Center for Advancing Informal STEM Learning (CAISE) has compiled and collated a lot of evidence to show how film, among many environments, contributes to STEM understanding at some level. Mirroring how rhetoric scholars have argued that visual representations influence gender expectations (David, 2001; Gigante, 2015; Gigante, 2018), CAISE indicates how films shape expectations surrounding science and math. Still, further scholarship is needed in the broader project of informal STEM learning because of how common such situations are: they might occur in various places with varying expectations, audiences, personnel, and oversight. This article brings informal STEM learning to the attention of scholars in feminist rhetorics, who have much to add to the project of compiling “research findings that articulate what works, for whom, why, and in what contexts” (NSF “AISL” n.p.). In fact, this article shows how explicitly feminist perspectives can allow us to draw attention to what has and has not worked in informal STEM learning.

In order to indicate considerations of informal as well as formal learning environments, this paper has three parts. The first indicates how the 2016 movie Moana intervened in an academic mathematical debate through subtly taking a stance on the subfield of “ethnomathematics,” defined as the study of the mathematical practices of diverse (usually non-Western) cultures. The second section argues that the history of omissions relates to the presentation of female characters as well as non-Western ones, through analyzing the 1950s movies Alice in Wonderland and Donald in Mathmagic Land. The paper ends through considering the presentation of the mathematicians behind Moana’s computer animation, pointing out the consistent omission of female mathematicians from media coverage, confirming broader cultural messages. Following Halberstam, I also mention one potential alternative, an animated children’s movie that focused on a female math student and political activist, Flatland (2007), though the movie had a limited release and limited viewership, compared to the other examples. Throughout, this article argues that children’s movies have mirrored broader American rhetorics of mathematical success, which tend to omit female mathematical knowers. In doing so, the article adds to research on STEM rhetorics through showing how a grounding in informal STEM learning is possible but also how the project should involve questions about what counts as both STEM and learning.

Moana, the Mathematician

At face value, Moana seems to have little to do with math, beginning with a heavily modified story of the creation of the Polynesian islands, explaining how the demigod Maui stole the heart of the creator goddess Te Fiti. The narrator is revealed to be Moana’s grandmother, teaching the children of the island the stories of their people. After the class ends, the toddler Moana wanders the shore, and the ocean reveals a stone with the same pattern as Te Fiti’s missing heart. Before she can touch it, Moana’s father (revealed to be the chief of their people) takes her away, and her parents raise her away from (but within sight of) the ocean. As a young woman, Moana begins to recognize the ecological devastation of her island and suggests going beyond their geographical barrier (a reef) for more fish. Though her father forbids it, she still tries with her boat, and the tides overpower it. Back on shore, her grandmother shows her a secret cave with ancient ships, large enough to show that her people once did not stay close to their island. Handing over the ocean’s stone, her grandmother explains that Moana must leave and convince Maui to restore Te Fiti’s heart in order to save her people. Moana spends the rest of the movie learning navigation from Maui and her ghostly ancestors, gradually gaining the skill to use the stars, her hand, and the tides to sail, steer, and plot the course to Te Fiti. All ends happily: Moana’s island is restored, and the movie ends with her teaching navigational skills to her people on what appears to be a long-distance voyage. A story of cultural heritage and ecological salvation, Moana is also therefore about learning navigation, an important task but not an explicitly mathematical one here. The movie subtly argues against the ethnomathematical scholarship about the heavily mathematical content of Pacific Islander navigation, making Moana seem to be successful though not through mathematics.

Ethnomathematics, as a field, has been constructed to resist many Euro-American assumptions about mathematical success, though with limited results. Math rhetorics in Euro-American contexts usually assume Western mathematics to be universal, value-free, and singular, i.e. the only mathematics. There is only one route to success in those mathematical contexts (and broadly STEM contexts): finding the singular, right answer within the singular, right mathematics. Yet ethnomathematics reveals the variety of maths within the variety of cultural groups and communities in the world, and does so using the techniques of anthropology, history, psychology, education, and (Western) mathematics. According to ethnomathematics, there must be many paths to success, even within Western mathematics, because the world contains so many ways to, in the terms of Crystal Broch Colombini and Sue Hum, “explore, translate, visualize, and express” (383). Despite the global potential of the field, ethnomathematics has not been an entire success. Even when administrators and colleagues approve of the field (which happens rarely), ethnomathematics scholarship often debates the field’s status, definition, knowledge, disciplinary basis, purpose, and interdisciplinarity. It should be noted that ethnomathematics’s status has some parallels to rhetoric and composition.

Even beyond intradisciplinary debates, there are some who question the entire construct. Sara Hottinger’s interpretation of ethnomathematics echos Jordynn Jack’s arguments about the “pink world” of girls’ science toys. In analyzing gender expectations in textbooks from elementary school to college, Hottinger devotes special chapters to two classes often required of college-level math majors: history of mathematics and ethnomathematics. Drawing on a combination of discourse analysis and education, her chapters argue that textbooks in the history of mathematics construct a normative (Western, male) sense of mathematical success. Ethno-mathematics, for Hottinger, “despite its liberatory purpose, actually reinforces the dominance of Western mathematics and its construction as both universal and value-free” (125). Because math classes and textbooks consider “non-Western” or “cultural” mathematics as separate from Western mathematics, ethnomathematics reinforces students’ sense of the boundaries of the presumed one and only mathematics. In particular, its separation from history of mathematics (and other math classes) makes ethnomathematics seem like something else, present though marginal. Extending Hottinger’s analyses from textbooks to children’s movies, this section follows the ways that Moana took a stance on an ethnomathematical debate through presenting Moana as a navigator though not explicitly a mathematician.

Marshallese navigation, a counterpart of the Polynesian navigation depicted in Moana, has been a contentious area of research in ethnomathematics. Foundationally, American mathematician Marcia Ascher included an overview of the navigation of the Marshall Islands within her ethnomathematics textbook Mathematics Elsewhere: An Exploration of Ideas Across Cultures (2002). Called “Models and Maps,” Ascher’s chapter aimed to expand Western ideas of mathematical modeling through considerations of the Marshallese “stick charts” needed for long-distance voyaging (95). The Marshall Islands, made of twenty-nine atolls and five coral islands in two chains, have proven a unique navigational challenge because of the northwest-southeast orientation of the island chains, which breaks the swell of the northeast trade wind across the Pacific. So, in order to navigate the unique wave patterns and land masses, Marshallese peoples have developed navigational charts, which Ascher calls “stick charts” because of their weaving from palm “sticks” (95-97). Because of the oppressive colonial rule of the islands, by European entities, Japan, and then the United States, Marshallese navigators were reluctant to share their maps with Ascher and other Westerners, which leads her to present them as historical. A recovery of the maps/models is also not exactly her focus. Rather, the chapter locates Marshallese mathematical practices within the map traditions of the West, emphasizing the ways that the “non-Western” mapping practices diverge from Western traditions and giving reasons why (89-126). By doing so, Ascher does expand notions of global mathematical practices, though only through rough, comparative interpretations, i.e. establishing a “mathematical Other” (Hottinger 126).

Though Ascher presents such navigational practices as historical, (pseudo) mathematical, and “improperly” saved by the Pacific Islanders themselves—because of their “lack” of “writing systems,” museums, and archival collections (122)—more recent scholars frame Marshallese navigation as cultural practice. American anthropologist Joseph Genz, in his 2009 dissertation and a subsequent 2011 article, frames Marshallese navigation as a practice in need of collaborative, (post)colonial recovery. Working with Marshallese navigator Captain Korent Joel, Genz explains how colonial rule prohibited what he calls “voyaging” because the German and Japanese administrations assumed the local navigational practices were dangerous and costly (10). The subsequent U.S. rule only made problems worse, as the nuclear tests on the atolls caused massive relocation, disease, and ecological devastation, including the sudden destruction of a navigation school. Captain Korent, according to Genz, started the recovery efforts in response to the revitalization of indigenous canoe building—incidentally, a movement that directly “inspired” the animators of Moana (Garcia et al. n.p.). Still, Genz found the research on Marshallese navigation equally challenging because the knowledge was prized for its specific techniques, which one elder said he would rather “take…to the grave” than share with outsiders (19). Viewing such interactions as “cultural…reluctance” (19), Genz nevertheless argues for the value of the “revival of voyaging in the Marshall Islands” (1). In a 2016 re-interpretation of Genz’s work, Sara Hottinger follows the work of Gayatri Chakrovarty Spivak and Roi Wagner, and notes that the silence in Genz’s work reinforces the sense of Marshallese navigation as ethnomathematically Other, specifically a matter of cultural anthropology, not mathematics.

In fact, Moana does follow anthropological literature in presenting Pacific Islander navigation as cultural practice. Throughout the movie, Moana repeats that her ancestors were “voyagers,” using a modification of the term “voyaging” from Genz, his mentors, and his collaborators’ descriptions. Through song and musical montage, Moana has visions of her ancestors navigating, which frames the practice as about the identity of her people and her self.  Following a generous reading of ethnomathematics, Moana here appreciates herself as a mathematician—and her people as mathematicians. After all, as the chorus of ancestors sing, they could plot courses, develop systems of astronomical terminology, and perform meteorological readings, in order to learn about their place and identity. Still, the depicted practices have little specificity, not only in lyrics but also in montages where Moana ties knots, repairs sails, and holds her hand to the night sky. (There is nothing approaching the characteristic maps and charts.) Overall, Moana presents Pacific Islander navigation as vaguely cultural, a matter of heritage and ancestry, remembered in song and native language. Given the frequent presentation of Western mathematics as universal, beyond culture, beyond peoples and language, Moana’s navigation therefore makes little sense within Western STEM knowledge systems.

Likewise, the statements of Moana’s creative team do not demonstrate ethnomathematical scruples. In news interviews, directors Ron Clements and John Musker claim to be inspired by stories of Polynesian mythology and later research trips to Fiji, Samoa, and Tahiti (Sarto n.p.). As Westerners, they were particularly fascinated by the idea of the “lost” knowledge of “voyaging,” though they did not acknowledge the importance of colonialism for causing the loss. Putting together an Ocean Story Trust, they worried more about potentials for their “story” to cause offense instead (Giardina n.p.; Robinson n.p.; Ito n.p.).

Polynesian navigation became a bigger part of the story as Moana’s gendered experiences were less emphasized through script drafts. Though Taika Waititi initially wrote Moana’s journey about her finding a place among a family of brothers, later versions emphasized her recovery of her cultural heritage. Consistently conceptualized as a heroic tale of “the ocean,” it was less important that the drafts keep the same character as the advocate of navigation, which meant that role passed among the chief/father, grandmother, and eventually Moana (Giardina n.p.; Topel n.p.). In final stages of production, Aaron Kandell and Jordan Kandell joined the writing team, suggesting the ancestors’ chorus and what the Kandells, following the relevant anthropological literature, called “the Cave of Wayfinders” (V. n.p.). The terminology of “wayfinders” and “wayfinding,” though important academic concepts for describing systems of geographical knowledge, ultimately did not appear in the movie, and the entire navigation system was systematically simplified with the borrowing of techniques from throughout many and varied peoples of the Pacific Islands. As news outlets have attested, the studio’s portrayal of navigation follows the broader pattern of Moana’s appropriation, simplification, and commodification of Polynesian cultures (Constante n.p.; Grandinetti n.p.). As in the case of the boats depicted in the movie, which animators claimed as “their” re-discovery (Garcia et al. n.p.), Moana’s creators ultimately did not respect elders’ intellectual rights or the status of navigation as prized for its specific techniques (Madigibuli n.p.).

Such a treatment of Polynesian navigation follows a history of Disney’s commodification of non-white peoples. The 1946 Song of the South famously included offensive stereotypes of African-American English and African American people (Watts 276-277), leading one journalist to call the movie “propaganda for white supremacy” (qtd. in Gevinson 956). Understandably, given Song of the South, some critics of Moana have worried about the encouragement of “brownface” among audiences (BBC News n.p.). Interestingly, the 2009 movie The Princess and the Frog, an earlier project of Moana’s creative team, has not been so heavily criticized, though a Black Louisianan is the core Princess. Given the mixed responses, it would be helpful to have more research about Moana’s participation in depictions of non-white peoples in animated children’s movies. Without losing sight of ethnocentric dynamics, this article continues through outlining a history of the omission of female characters from explicitly mathematical stories.

Along the lines of informal STEM learning, what is being taught in Moana? Pacific Islander navigation does relate to academic research in a subfield of mathematics, though it’s difficult to tell from the movie. Moana’s presentation makes the navigational techniques seem general, ancestral, and remembered. Emphasizing anthropological terminology and assumptions, Moana is unlikely to be recognized as a repository of math learning at all. Though Moana holds the promise of “supporting learners from underrepresented groups” through presenting non-Western mathematicians and mathematical practices (NSF “Mathematics and Statistics” n.p.), the movie instead follows Disney’s broader history of separating female characters from explicitly mathematical stories.

Moana begins to indicate what research on STEM rhetorics can learn from texts of informal learning, as well as vice versa. As opposed to texts generated from laboratories, field work sites, military installations, and hospitals, Moana allows us to see some of the limits in considering a text to be scientific/mathematical or not. It has been made clear, for instance in Jack’s work (Science on the Home Front 127-137), that such considerations of marginality and periphery face projects of feminist science, which infuse STEM practices with greater attention to gender, reflexivity, genre, and contextual knowledge. Moana and children’s animated movies generally urge us to see beyond texts incorporated into traditional STEM classrooms, to the possibilities that could exist in the recognition of informal STEM learning and its bounds. Overall, Moana and similar texts point out how STEM rhetorics should be careful to note the limitations of understanding STEM content within Western contexts.

Alice’s Mathmagics?

The earlier history of animated children’s movies also allows for the investigation of the demarcation of explicitly classroom texts from informally educational ones, questioning the status of education even beyond Western STEM. Particularly in the case of Donald in Mathmagic Land (1959), animated children’s movies have gone to great lengths to prevent the depiction of mathematical women. As film scholar Martin F. Norden has argued, Donald in Mathmagic Land depended heavily on the earlier Alice in Wonderland (1951) and more broadly on Lewis Carroll’s original Alice stories (119-121). Carroll, after all, was the pseudonym of the Oxford mathematician Charles Lutwidge Dodgson, and many mathematical references and jokes famously appeared in Alice’s Adventures in Wonderland, Through the Looking-Glass, and The Hunting of the Snark. As mathematician Robin Wilson recovers in the 2008 book Lewis Carroll in Numberland, not all of the jokes were at Alice’s expense and in fact Alice consistently attempts to talk about arithmetic with the Mock Turtle, the Gryphon, Humpty Dumpty, the Red Queen, the White Queen, and the Cheshire Cat (1-8). In fact, rather than making fun of Alice, it seems the math jokes prove more in line with the metatextual references to recitation, spelling, and the medium of the book itself (Fiss 258-260). That said, the mathematical references did not appear in the animated movie Alice in Wonderland, despite its reliance on the original stories, making Donald in Mathmagic Land possible. Alice and Donald ultimately reinforced American math rhetorics of the time (and since), in which women are rarely portrayed as mathematically successful, especially in explicitly educational films.

The production of the movie Alice in Wonderland waffled between attempts to create a story more like the studio’s triumphs and one more like the original Alice books. Initially conceptualized as a live-action movie in the 1930s, the plot and vision grew through the creative teams’ worries about literary reputation and studio expectations. According to the documentary Through the Keyhole (2011), the early versions appeared too serious and too indebted to the literary originals, while the later versions centered on fictional persecution of Alice and Carroll/Dodgson with new art and new stories. The colorful artwork stayed, though the plot proved variously vexing. As Walt Disney’s biographer Bob Thomas implied, it seemed there was a sense that Alice needed to have a hero/rescuer like the princes in Snow White and Cinderella. Though Disney considered casting the White Knight as Alice’s “prince,” he ultimately dropped the idea because “he was intimidated by the threats of Lewis Carroll purists” (Thomas 220). In the end, the movie was accused of “Americanizing” a British classic (Thomas 221), but Alice in Wonderland did not satisfy American “cartoon” fans either, since it seemed to be too much about a girl who learned for herself. The story of Alice’s learning did come from the books, though American audiences of the time generally did not find the plot satisfactory. Alice in Wonderland seemed less about a female character’s need for saving and more about her education.

Despite the educational focus, Alice’s creative team also left out the math. The movie Alice in Wonderland follows the picaresque style of the original stories, though in an even more episodic fashion. Framed with depictions of Alice daydreaming on the banks of an Oxford river, Alice in Wonderland follows a series of short conversations between Alice and other beloved Carroll characters: the Doorknob, the Dodo, Tweedle Dee and Tweedle Dum, the White Rabbit, the Flowers, the Caterpillar, the Cheshire Cat, the Mad Hatter (and other Tea Party guests), and the Queen of Hearts. Though the original stories featured nonsensical calculations and discussions of arithmetic with a few characters, none of those reappeared, in favor of conversations about language, stories, poetry, singing, manners, education, and the law. The closest approximation of a mathematical discussion appeared in the Mad Hatter’s Tea Party, in the explanation of “unbirthdays.” In dialogue wholly made up by the Disney creative team, the Mad Hatter begins through stammering an explanation of the number of unbirthdays: 365 minus 1. Alice then realizes the Tea Party marks her unbirthday, too. Presenting subtraction, as well as knowledge of the number of days in a typical year, the Unbirthday scene does not feature Alice; the other Tea Party guests explain the concept. Though Alice does catch on to the categorization of birthdays and unbirthdays, which relates to a “key developmental indicator” of “data analysis” in preschool mathematics (HighScope 1), the scene is one in which she is fundamentally taught—and taught far below the level of her expressed age. Moreover, the conversation is far from the sophisticated mathematical jokes of Carroll/Dodgson about modular arithmetic, non-Euclidean geometries, and alike. The movie Alice distinctly omits mathematics, by comparison.

Soon after Alice’s box-office flop, Donald in Mathmagic Land allowed the creative team to return to the omitted conversations. As Martin Norden observes, Donald in Mathmagic Land brought back senior animators from Alice, Wolfgang Reitherman, Les Clark, and Joshua Meador, who served as sequence directors for Donald. Furthermore, Hamilton Luske, one of Alice’s three listed directors (of many more unlisted directors), served as supervising director for Donald. And Milt Banta, one of the eventual scriptwriters for Alice, became a story contributor in the development of Mathmagic Land. Donald’s creative team included so many overlapping employees that its production served as a rough reunion for most of the Alice contributors. Inspired by Mary Blair’s artwork from Alice, Donald in Mathmagic Land was constructed in a way that “practically guaranteed a visual and thematic bond between the two films” (Norden 119). Still, unlike Alice, the characters visit the “Wonderland of mathematics,” exploring Pythagorean music, the golden section, Western architecture, human proportions, chess, mental games, and the concept of infinity.

Ultimately, Donald in Mathmagic Land follows a very abbreviated history of Western mathematics, confirming the presentation of the Western mathematical system as creative though still universal, i.e. the only “correct” mathematics in the world. Donald begins through a game of tic-tac-toe between Donald and the Pencil Bird from Alice, continuing through visual jokes about division (where a stream of numerals breaks into smaller numbers when they hit rocks) and square roots (where the branches/roots of trees bend at ninety-degree angles). Once the Spirit of Adventure explains to Donald where he is, he expresses frustration, saying “Mathematics? That’s for eggheads” (n.p.). The Spirit corrects him, explaining the mathematical origins of music with stories about Pythagoras and the Pythagoreans of Ancient Greece. After a jam session, the Spirit returns to the use of proportion in Greek, then Roman, and Renaissance architecture. Explaining that mathematics is universal, extending in centuries of architecture and many specimens from nature, the Spirit nevertheless argues “the rules are always the same” (n.p.). Lest the lesson remain unclear, the Spirit introduces a variety of games from chess, baseball, football, basketball, and billiards, and he concludes with a host of inventions, showing how the mathematical mind leads to scientific innovation. Through visual and verbal references, the Spirit implies that Western math built the inventions since the Renaissance: the wheelbarrow, car, train, and airplane; the spring, the clock, and the telephone; and the record player. He concludes that only math will open the possibilities of such inventions for “the curious and inquiring minds of future generations” (n.p.). Donald in Mathmagic Land waffles between the presentation of mathematics as a creative product of Western cultures and as a universal, singular system: the only truly “clean” mental system for any past, present, and future innovation.

In explicit comparisons with Alice, Donald in Mathmagic Land reinforces not only expectations surrounding Western math but also Donald’s gender presentation. Famously a character with a very short temper, he does not have a tantrum when forced to enter Alice’s world. The Spirit, in explaining chess, first talks about Lewis Carroll’s use of the board as a setting for Through the Looking Glass. Then, faced with the chess pieces annoyed at Alice, Donald is accused of being a pawn, a situation he detests. The Red King and Red Queen listen to his protestations that he’s really Donald Duck, but they talk about how that name is really just arbitrary. Mentioning that Donald could just as easily be “an Alice” (n.p.), he finds himself diving off the board and ultimately eating baked goods that make him grow to gigantic size. The Spirit continues talking about chess until Donald’s clear boredom causes the Spirit to change topics to baseball. As explored earlier, Donald’s Alice scene reinforces the mathematical content generally missing from the earlier Alice movie. More surprisingly, throughout the scene, Donald wears a wig and Alice’s outfit (a light-blue dress, a white apron, and a headband). Initially in his usual sailor suit and cap, Donald is transformed when the Spirit first says the word “Alice,” and he remains in the dress until the narrator changes topics, saying the word “baseball,” which gives Donald a (male) baseball uniform. Because of the frame, it’s clear that the Donald/Alice character of the scene is not an attempt at a female character but instead a decidedly male character cross-dressing. As in other elements of mid-century American popular culture, including a “university cross-dressing phenomenon” in California and elsewhere, Donald’s Alice scene seemed “to promote the same notion” from 1950s writing and culture “that only a truly masculine man can be trusted to embody and represent womanhood” (Wilkie 234). In other words, appearing in a dress just reinforces Donald’s masculinity.

Because of the educational legacy of Donald in Mathmagic Land, it is important to acknowledge what precisely is being taught. Its theatrical release placed Donald with Darby O’Gill and the Little People, but Donald in Mathmagic Land was more educational from the outset. From a post-war studio that had spent “the war years…making instruction and technological films in which abstract and obscure things had to be made plain and quickly and exactly applicable” (qtd. in Norden 122), Donald in Mathmagic Land was an attempt to explore how instructional cartoons could be entertainment. Speaking to reporters after the premiere, Walt Disney noted how “the cartoon” was “a good medium to stimulate interest,” saying “we have recently explained mathematics in a film and in that way excited public interest in this very important subject” (qtd. in Smith 198). In various re-releases (on TV, VHS, and DVD) and in attempts at tie-in materials (including at least one comic book), Donald in Mathmagic Land became the studio’s most popular educational film for the STEM classroom and one of the best-known educational movies of any distributor.

In educating audiences, however, the movie did little to resist the math rhetorics of its time. Donald framed mathematics as a product of Western culture, though singular and universal: invented by people stretching back to the Ancient Greeks and yet the only, one, true mathematics, fundamentally applicable to all things (and people) everywhere. Though more recent research in ethnomathematics would question the assumptions, Donald did repeat normative (Western) understandings of mathematics through its depiction. Furthermore, the absence of female characters allowed the studio to resist portraying girls’ achievements of mathematical success, making it seem merely a matter of male students and male knowers. Overall, the movie Donald in Mathmagic Land supports the construction of what Sara Hottinger calls “a normative mathematical subjectivity” common in the United States “that limits the way marginalized groups are able to see themselves as practitioners of mathematics” (11). From then until now, Donald has seemed to present mathematics as the realm of Western men. In doing so, Donald in Mathmagic Land has not lived up to the promise of informal STEM learning.

With respect to informal STEM learning, the movies Donald in Mathmagic Land and Alice in Wonderland encourage us to pay attention to omissions, particularly about success. Previous analyses of feminist rhetorics have established the importance of silence for our work. Organizing our work around Peitho, as an allegorical figure, already brings new possibilities, as Michele Kennerly and Carly S. Woods have argued, because Peitho (as opposed to Rhetorica) already brings together “the delectation aroused by beautiful speech” and “coming together deliberately”: “private and public…verbal and corporeal” (23). A string of Peitho articles, especially about digital rhetorics, similarly have analyzed “silence” and being “silenced” (Gutenson and Robinson; Beemer). This article follows theirs in asserting how STEM rhetorics need to consider moments of omission as well as moments of speech. After all, the feminist implications of Donald in Mathmagic Land and Alice in Wonderland cannot be fully explained without attention to what is not said and not portrayed. As Jack Halberstam has observed, such moments matter for constructions of success and failure. Halberstam analyzes similar omissions, ones having to do with political action, noting that there are alternatives in CGI animation (especially Pixar movies): diverse characters coming together in “political allegory” and “queerness,” locating success in “anarchy and anti-familial bands” (21-22). Particularly when placed in an animated educational film centering on a character meant to embody children’s immaturity, the omission of female characters can lead Donald’s “future generations” to not see themselves in the story, against the optimism of informal STEM learning, reinforcing limited notions of mathematical success and promoting the exclusivity of math and STEM broadly.

Furthermore, the examples of Alice in Wonderland and Donald in Mathmagic Land present another consideration for grounding STEM rhetorics with instances of informal STEM learning: their differences not only emphasize expectations surrounding (Western) STEM but also assumptions about the limits of explicitly educational texts. Though Donald in Mathmagic Land had a box-office release, the movie was designed to “explain[]” and “excite[] public interest” from the start (qtd. in Smith 198), and its subsequent marketing strongly encouraged classroom uses. Alice in Wonderland, though about education, was neither used in STEM classrooms nor discussed as instructional. In the case of Donald vs. Alice, the explicitly educational text—first informally, then formally—was the one that reinforced expectations surrounding Western STEM content and assumptions about Western learning, including the absence of female characters learning math. In other words, instances of informal STEM learning can encourage our consideration of what counts as Western education as well as what counts as Western STEM.

STEM Rhetorics and Informal STEM Learning From the Future to the Present

Through the cases of Moana, Donald in Mathmagic Land, and Alice in Wonderland, this article shows how animated children’s movies can add to the project of researching informal STEM learning, what has and has not worked, and what considerations emerge from grounding visions of feminist STEM rhetorics in informally educational texts. For STEM rhetorics, the example of the 2016 movie Moana shows the limitations of judging STEM content within Western contexts. Likewise, the comparison of the 1950s movies Alice in Wonderland and Donald in Mathmagic Land demonstrates the importance of considering expectations surrounding learning in both formally and informally educational texts. In terms of informal STEM learning, all movies demonstrate the viciously pervasive omission of female characters performing mathematics. Though the three examples come from one movie studio, this article is not about individual failures, the specific lack of female characters doing math from one institution. Rather, Moana, Alice in Wonderland, and Donald in Mathmagic Land lead us to consider the broader narratives of mathematical success that appear and reappear in Euro-American cultures, especially the historical absence of broader frameworks for acknowledging and promoting female mathematicians and math students.

Though Halberstam notes the importance of computer-generated animation for making possible queer and collective stories, the media portrayals of CGI also reinforce the lack of female mathematicians, as in the case of Moana again. As a heroic story of “the ocean,” Moana’s development funded mathematical research into computational fluid dynamics. Building on previous academic publications, some of which were made possible by previous, studio-funded research, teams of mathematicians at the University of California at Los Angeles (UCLA) created new models in order to make the Ocean appear as a more expressive, interactive character. Though some news articles peripherally mentioned the involvement of a senior female mathematician in the research program, most focused on the ways that a team of young men (a young professor and his graduate students) made possible the mathematical bases of the character. Following a UCLA News story, dozens of media outlets picked up on the idea that “[male] mathematicians brought the ocean to life” (Wolpert n.p.). Such media responses have been explained through the under-representation of women in academic mathematics; as of 2014, according to the National Science Foundation, only 28.9% of all Ph.D. degrees in math went to women. However, under-representation is not a good excuse for complete omission. Rather, the media responses seem to be a way of confirming broader views of mathematical success, ones that restrict the possible roles that women can occupy. We need to keep analyzing exclusionary views for the sake of our present, as well as our future.

This article urges that we at least notice exclusions in American math rhetorics, and that we work toward greater inclusivity at least as part of our projects to build better STEM rhetorics. Sara Hottinger speculates that exclusionary dynamics might have kept her out of mathematics (1-5), and her book has started to inspire similar stories. I too did not pursue graduate work in mathematics; though I don’t regret that choice, I do find I often have to explain why those campus visits made me uncomfortable. Because of these reasons and more, I am especially interested in alternatives to the usual narratives of white, male mathematical success. Flatland: The Movie (2007) makes one such attempt, casting a small, orange hexagon with a female voice as the most talented math student and most powerful political activist of her world. (Hers is a nonsensical, intensely satirical, world, existing in a geometrical plane, where everyone is a shape, which determines their role in society.) Despite intriguing choices, the movie Flatland was limited in its reach, in part because the movie was self-distributed and in part because another adaptation with the same name came out that year. In arguing for greater inclusion of female characters who do math, far greater than blockbuster movies can provide, I am hoping that mathmagics (the magical worlds of math ideas) can be more accessible to more people. Since informal STEM learning exists beyond individual institutions, beyond schools and even beyond movie studios, we all can participate in the critical reshaping of STEM rhetorics.

Acknowledgements

The author wishes to thank colleagues, family, Peitho’s editors, and anonymous reviewers for helpful feedback throughout. The child development center Little Huskies provided resources, perspective, and, as always, their extraordinary expertise in childcare and education.

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