Mereological (Part-Whole) Intuitions in Teaching

• In Event: 67.041 - New Perspectives on Intuition in Teaching

Abstract

Purpose. To identify and investigate a neglected but important type of intuition - part-whole intuition - in lesson planning and teaching.

Theoretical Framework. Mereology, (from the Greek μερος, 'part') the theory of the relations of part to whole (Varzi, 2016).

Method. The paper uses philosophical analysis - breaking concepts into parts to gain a better understanding of issues.

Analysis. In an undocumented letter, Mozart states he can survey a contemplated musical composition whole, like a fine picture at a glance... I do not hear in my imagination the parts successively, but I hear them, as it were, all at once’” (See also, Spranza, 2017). Closer to home, a typical conference paper is organized as a sequence of parts (purpose, framework, results, etc.). Through rereadings and rehearsals, authors can form powerful intuitions of the whole to guide them through a secure and excited presentation, even - like a Ted Talk - without notes.

Typical school lessons are also organized as structured wholes that can be intuited. As the presentation example suggests, part-whole (mereological) intuitions have an important role in teaching. In geometry teaching, the invitation to invent a proof “is not solely to motivate an answer; rather, it is much deeper and educationally wider… to motivate the understanding and the beauty of the resolved uncertainty brought by the certainty of a proof.” Grasping the proof as a whole, he says “should be as much an emotional experience as a rational achievement” (Kobal, 2017). While proof validity is confirmed by deliberate checking of each line, the proof as a whole is experienced in an immediate unitary intuition akin to a perception. The student “sees” or “gets”the proof.

Results. Part-whole intuitions may be found in many school subjects. A literature lesson, for example, may pose the critical question how various parts of the story - details of plot, characterization and setting etc., are brought together to achieve a satisfying whole. Through discursive investigation teachers work with students toward a collective intuition of the whole. Komisar (1968) defines “teaching” as acting collaboratively with students to generate such upshots. But to collaborate in generating such intuitions, teachers must have them. They are advised to preview lesson content and (re)charge such intuitions to serve as internal reference points in teaching.

Firm intuitions of knowledge content, however, are insufficient guides to teaching. Teachers also draw on pedagogical knowledge and experience in planning activities to achieve pedagogical aims. Lesson plans are also wholes composed of parts, and like other designs, can fise to the level of art. Teachers can seek mereological intuitions of lesson designs, which, like geometric proofs, can resolve uncertainties and generate feelings of security, excitement and beauty to inspire and guide teaching.

Significance. Mereological (part-whole) intuitions in teaching remain largely unstudied. GIven their potential roles in lesson planning and teaching future research on intuition in teaching can advance by attending to them.

Author

• Leonard J. Waks, Temple University