Lived mathematical experience

1. Lived mathematical experience Bal Chandra Luitel Assistant Professor, Kathmandu University & Member, WISDOM^e Research Group

2. Presentation Outline • Lived experience • Mathematical experience • Lived mathematical experience • Why to research on lived mathematical experience • A possible research framework

3. Lived Experience: What is in the East? • In Sanskrit जीवानुभव(Jiivaanubhava ) is likely to represent the meaning of lived experience. • Jiva – Human and other creatures; anu – following, along, by the side of; bhava – beings-in-themselves (cf. things-in-themselves) Being Becoming

4. Lived Experience: Etymology • Erfahrung– Life experience (in the sense of accumulation –Erfahrungen) • Erlebnisse– Lived experience (experience of a particular moment) (phenomenologyonline.com) • Ex+peritus= out of + tested, that can be passed over (http://www.etymonline.com)

5. Definitions • Immediate and pre- reflective consciousness of life (Dilthey in Van Manen, 1990) • Lived experience as immediate sensibility, a very source of perception (Morleau-Ponty, in Van Manen, 1990) • Lived experience is the realm of Geist – mind, thoughts, consciousness.... phenomenologyonline.com

6. Mathematical experience • Experience of/about mathematical objects! • What types of objects are they? • Are they real, actual, physical objects? • Where do they exist – in our mind, in the natural/physical world or...? Where is mind, by the way? • Can mathematics be always abstract? Can other things not be abstract? How to differentiate between mathematical and non-mathematical experiences?

7. Mathematical experience • For a learning experience to be a mathematical experience, this interaction must enable the induction of critical features that are mathematical; that is, those elements in the interaction that are most potent to bringing about discernment of invariant structures that concern numbers and/or shapes, and ways to re-produce or re-present the structures. (http://www.cimt.plymouth.ac.uk/journal/leung.pdf)

8. But the question is • What is mathematics really? (Hersh, 1997, 2006)

9. Lived mathematical experience Four key features • immediacy, • intentionality, • self-constitutive, • Hermeneutical (Luitel, in press/2011)

10. Immediacy • refers to the shortest possible proximity of life-world and conscious experiences. • a more immediate engagement with mathematical phenomena (and objects) is the precondition for generating lived mathematical experiences

11. Intentionality • Modified version of intentionality (Husserl’s concept of pure experience) • The notion of intentionality refers to the directedness of conscious experience towards things or objects in the world. • Not always a priori objects but emergent mathematical objects... • Conscious experience (but how to differentiate?)

12. Self-constitutive • Pascal's triangle, Roll’s Theorem, ... • The dimension of self... • What is the role of the person who experiences mathematics? • The subjective-objective dimension of mathematics? • East (s) and West(s) in relation to the concept of self

13. Hermeneutical • One and Many in mathematics (Ernest,1998) • Multiple or singular? • Interpretive nature of mathematics? • Excluded or included middle? • Continuum or dichotomy? • Contextuality of mathematics? • Mathematics for complexity science

14. Researching lived mathematical experience • Why?: To capture a range of lived mathematical experiences and foster them in teaching and learning of mathematics • How?: Write your own experience; interview students, teachers and mathematicians • Who?: Mathematics teachers, teacher educators, mathematicians can undertake and particiapte

15. How to document?? • Descriptive – but this is insufficient! • Reflective and narrative approach • Poetic approach – ineffable experiences • Uses of metaphors • Non-textual genres

16. Quality Standards • Incisive? • Illuminating? • Pedagogically Thoughtful? • ...