A Philosophy for the Powerful Learning of Mathematics

Author: Calvin Wilkinson

  • Thesis download: available for open access on 6 Oct 2018.

Wilkinson, Calvin, 2015 A Philosophy for the Powerful Learning of Mathematics, Flinders University, School of Education

This electronic version is made publicly available by Flinders University in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material and/or you believe that any material has been made available without permission of the copyright owner please contact copyright@flinders.edu.au with the details.


Human philosophy is fundamentally about Being-human. In contrast to the process−relational philosophy of Whitehead however, research into mathematics education has been almost exclusively analytical or meta-analytical. As a result the holistic and complex notion of Being-mathematical is largely ignored. Consequently the interaction between the philosophical and the practical in mathematics education remains limited, misdirected, and sometimes inappropriate. Therefore mathematical processes continue to be conceptually inaccessible for many individuals; understanding instrumental, and the difficulties encountered only partially overcome by rote or procedural learning. The current study proposes a way forward through a dialogic complementarity of symbol processing and situated action that is ethical, informed by Dialogical Self Theory, and which promotes creativity and problem solving. In these terms the learning of mathematics is referred to as powerful mathematical learning, which is expounded as a phenomenological argument of eidetic intuitions that includes the development, the uses, and the meaningfulness of mathematics. Necessarily as a creative work, the first three stages of Wallas’ process of creativity, namely, Preparation, Incubation, and Illumination are executed. The fourth stage of the creative process is a combination of Verification and Validation. As a precursor to a possible future research study, the essential ideas of powerful mathematical learning are conveyed as a systemic basis together with how the system can be examined logically and empirically, through the use of measurement principles and the employment of multi-level modelling strategies and causal structures.

Keywords: Mathematics Education, Dialogical Self Theory, Powerful Mathematical Learning, Process of Creativity, Phenomenology, Being-ethical, Globalisation, Popper's Three Worlds
Subject: Education thesis

Thesis type: Doctor of Philosophy
Completed: 2015
School: School of Education
Supervisor: Carol Ruth Aldous