Lived mathematical experience

Bal Chandra LuitelAssistant Professor, Kathmandu University & Member, WISDOM^e Research Group

Presentation Outline

• Lived experience • Mathematical experience• Lived mathematical

experience • Why to research on lived

mathematical experience • A possible research

framework

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)

Becoming

Being

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)

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

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?

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)

But the question is

•What is mathematics really?

(Hersh, 1997, 2006)

Lived mathematical experience

Four key features• immediacy, • intentionality, • self-constitutive,• Hermeneutical(Luitel, in

press/2011)

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

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?)

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

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

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

How to document??

• Descriptive – but this is insufficient!

• Reflective and narrative approach

• Poetic approach – ineffable experiences

• Uses of metaphors • Non-textual genres

Quality Standards

• Incisive?• Illuminating?• Pedagogically

Thoughtful? • ...