A Guest Post Series by Dr. Joseph Torres, Ph.D.
Dr. Joseph Torres, Ph.D. is a a mathematician; a teacher of math, science, and music at a classical Catholic high school; a philosophy student at Holy Apostles College and Seminary, a former literature student at Signum University; an amateur theologian; a lover of Catholic liturgy; a major Tolkien nerd; and so much more. You can read more of his work at A Melodious Mathematician’s Metaphysical Musings, linked above. Joe, thank you for your incredible contribution to Teaching With Magic!
Authors as Teachers
Since we have explored the pedagogical projects of Merlyn and Morgan, we will now consider their authors as educators. As La Jeunesse demonstrates, Merlyn is an in-universe avatar for White himself. As such, White’s project and pedagogy is the same as Merlyn’s. Through the literary experiment which White presents in his novel, he teaches his reader about the problem of
war and encourages his reader to develop new hypotheses and potential solutions to that problem.
On the other hand, Morgan is not an avatar for his author. Instead, Twain is himself a character in his novel’s prologue and epilogue. He is the recipient of Morgan’s journal and transmits that journal to his reader. Therefore, we should not read Morgan’s viewpoints and strategies as a reflection of Twain’s, and we should distinguish carefully between their two projects.
Since Morgan and Twain’s projects are distinct, we will explore the ways in which Twain uses Morgan’s alternative timeline structure to teach his readers. The results of Hank Morgan’s propagation of industrial capitalism and democracy are catastrophic. The image of Morgan at the end of his life pining for his lost family and the world he has left behind gives to Twain’s readers
an image of the psychological consequences of Morgan’s actions (419-421). Twain’s observations are relevant to his reader because Morgan was from Twain’s present and operates under the prevailing assumptions and worldview of that age. Therefore, anachronistic characters such as Merlyn and Morgan act as literary devices through which the author can insert modern assumptions
and beliefs into the Arthurian conversation, and through which the author communicates to the reader ideals and cautions.
Practical Lessons for Non-Fictional Educators
Since we have explored the pedagogical content of White and Twain’s novels, it only remains for us to consider the implications of this content for contemporary educators who lack Merlyn and Morgan’s memories of the future. Note carefully that knowledge of the future does not entail pedagogical success. As we have seen, both Merlyn and Morgan have significant failures as
they carry out their respective pedagogical projects. Thus, the first lesson we may take from these educators is an understanding of our own limitedness: if even teachers who know the future can fail, then we should not expect perfection from our own efforts, even as we always strive for improvement in our practice.
Besides a consciousness of our own limitedness in effecting the results we desire in our students, the novels offer practical advice on pedagogical methodology. Many mathematics educators focus their attention on the communication of algorithms for solving an array of standardized problems. However, this approach does not prompt a deeper understanding of the
mathematical landscape in most students. This algorithmic approach is characteristic of Harootunian and Quinn’s Pragmatist who focuses on factual issues and the problem of the here and now instead of on broader considerations. Students who successfully complete an algorithmic
education may find it difficult to solve problems that are not on the standardized list to which algorithmic educators are working. Like Morgan’s students, the students of the algorithmic approach are left open to significant failures in new situations that occur outside the relative safety of the classroom.
If the algorithmic approach imitates Morgan’s ultimately unsuccessful approach to education, then we must ask ourselves whether there are ways of imitating Merlyn’s generally successful approach. As we have seen, Merlyn focuses on crafting experiences based on Arthur’s input so that Arthur may arrive at a deep understanding of a general problem from which Arthur
himself organically develops and tests a solution. To imitate this, mathematics educators need to identify large problems around which they will structure educational experiences. Where Merlyn desires to communicate a deep understanding of the problem of war, calculus teachers may desire
to communicate a deep understanding of the tangent line problem or the area problem. Whatever problem the course centers around should be deep enough that it admits multiple angles of consideration.
Once the teacher has established the problem around which his/her course will center, he/she must next plan experiences for the students. Merlyn chose to turn the Wart into different animals so that he could experience the problem of war from the perspective of the victim, the warrior, the aggressor, and others. The Calculus teacher may instead construct experiences of different representations of the same function and ultimately of a diversity of functions. In order to imitate Merlyn, these experiences should allow students to explore and make their own observations rather than relying on their instructor to force-feed them the observations the instructor wants them to make. While non-fictional instructors may not have magical abilities, they can still construct instructive experiences in which their students can make their own observations and arrive at a deep understanding of a general problem.
One might object to this experiential method of teaching that students might not learn as many algorithms as in the algorithmic approach, and therefore that it is less effective. The validity of this objection depends ultimately on our purpose as educators. If our primary intent is for students to pass a standardized test, then I agree that the algorithmic approach is more effective in the short term. However, if our goal is for students to take away a deep understanding of the mathematical landscape from which the student can develop their own solutions to new problems, then the Merlyn approach offers promise where the algorithmic approach offers us the same despairing students that we currently have. However, the implementation of this approach will
require a restructuring of our curricula and our expectations of our students and potentially even the restructuring of our educational institutions.
Finally, while I have used the example of a Calculus class in this section due to my own experience as a mathematics professor, these insights apply across disciplines. For a further example outside of mathematics education, consider the case of a professor who is developing a course on adaptations of the King Arthur legend. First, the professor must choose the problem around which they will organize the course. For instance, he/she may want the students to wrestle
with and ultimately develop an answer to Tennyson’s question of “why should any man / Remodel models” (ll. 37-8). The professor should then plan experiences centered around texts that will confront the student with different approaches to the issue. Therefore, although the problems and experiences will inevitably vary from one discipline to another, the technique in question is
applicable across disciplines.
Thus, Merlyn’s emphasis on organically developing solutions to well-understood problems generates both temporary and long-term success, while Morgan’s emphasis on factual questions and the production of immediate results produces only temporary success. Furthermore, due to both characters’ anachronism, their authors are able to use the legend of Arthur as a place to test out contemporary ideas: Twain shows us the dangers of unbridled industrial capitalism, while White is able to test out different approaches to peace and war.
The long-term efficacy of Merlyn’s approach and the lack of it from Morgan’s approach should lead educators to consider the manner in which they resolve the difficulties that students undergo. In particular, this should prompt research on ways that teachers can create meaningful educational experiences for their students that promote deep understanding of problems and issues. Furthermore, it should encourage educators to consider ways to allow students to develop their own solutions to well-understood problems organically. Finally, it should motivate teachers to ponder the structures on which modern education is founded and whether these structures promote a merely pragmatic approach to problem-solving or whether they in fact enable mankind to think for himself.
Adderley, C. M. “The Best Thing for Being Sad: Education and Educators in T. H. White’s ‘The Once and Future King.’” Quondam et Futurus, vol. 2, no. 1, 1992, pp. 55–68.
Harootunian, Jeff A., and Robert J. Quinn. “Identifying and Describing Tutor Archetypes: The Pragmatist, the Architect, and the Surveyor.” The Clearing House, vol. 82, no. 1, 2008, pp. 15–19.
La Jeunesse, Jake. “T. H. White, ‘The Once and Future King’, and the Scientific Method.” Arthuriana, vol. 22, no. 2, 2012, pp. 21–36.
Tennyson, Alfred. “The Epic.” Selected Poems, edited by Christopher Ricks, Penguin Books, 2007, pp. 29–31.
Twain, Mark. A Connecticut Yankee in King Arthur’s Court. SeaWolf Press, 2019.
White, T. H. The Once and Future King. The Berkley Publishing Group, 1987.