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The role of intuition in the process of objectification of mathematical phenomena from a Husserlian perspective: a case study

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Abstract

The research is a study of the Husserlian approach to intuition, informed by Merleau-Ponty’s theory of perception, in the case of a prospective teacher of mathematics. It explores the two major stages-categories of intuition, the essential relations between them, and their vital role in the emergence of empirical and abstract mathematical objects, as they are used by the student in order to conceptualise mathematical phenomena. The student’s activity is analysed to its intuitive origins, and an intuition of essences manifests its significance for generalisations and insights for mathematical proofs. Through an in depth phenomenological data analysis, intuition is delineated as an essential mediator between the learner’s world-as-lived and her objectification process. Finally, some implications for teaching and learning are suggested.

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Notes

  1. Husserl, 1991 and 1989a respectively, in the references.

  2. This issue also amounts to the difference between Kant’s representation and Husserl’s re-presentation, which exceeds the space limitations of this paper.

  3. The body as (intentional) subject, not as an object (cf. Reuter, 1999, pp. 71–72).

  4. The extract is from Merleau-Ponty’s notes on Husserl’s Origin of Geometry.

  5. Examples of a categorial intuition and an intuition of essences are given in sections 5.3.2, 5.3.4 respectively.

  6. It doesn’t mean that we suppose intuitive processes to be limited to individual processes: we acknowledge that for the fullest understanding of intuitive processes in the learning practice attention needs also to be paid to the social-cultural dimensions, as it is attempted in Andrà & Santi, 2013, Andrà & Liljedahl, 2014.

  7. A different perspective of this session appears at a paper that was published recently (Brown, Heywood, Solomon, & Zagorianakos, 2013).

  8. The picture is included with the permission of the student.

  9. The application of her new object in her technique is also perceived as a better apprehension of the newly-constituted object (cf. section 2.4).

  10. She ‘saw’ that the sought curve is not a straight line from her bird’s-eye view (section 5.2) and she removed her previously intuited x-axis barrier by applying her just objectified ‘technique’ (section 5.3.3).

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Authors and Affiliations

  1. Manchester Metropolitan University, Myrtidiotissis 7, 17456, Alimos, Athens, Greece

    Andonis Zagorianakos

  2. Lomonosov Moscow State University, Moscow, Russia

    Anna Shvarts

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  1. Andonis Zagorianakos
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  2. Anna Shvarts
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Correspondence to Andonis Zagorianakos.

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Zagorianakos, A., Shvarts, A. The role of intuition in the process of objectification of mathematical phenomena from a Husserlian perspective: a case study. Educ Stud Math 88, 137–157 (2015). https://doi.org/10.1007/s10649-014-9576-9

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