Theoretical research
frameworks on history of mathematics in
mathematics education:
current needs and
emergent perspectives
David Guillemette
Université du Québec à Montréal
Considering recent works on the field of research
Clark & al. 2016, in their concluding remarks (p. 175)
(1) to put emphasis on pre- and in-service teachers’ education
(2) to design, make available and disseminate a variety of didactical source material
(3) to perform systematically, carefully and applied empirical research in order to examine in detail and evaluate convincingly the effectiveness of HPM perspective
(4) to acquire a deeper understanding of theoretical ideas put forward in the HPM domain to carefully develop them into
coherent theoretical frameworks and methodological schemes.
Considering recent works on the field of research
Barbin, Guillemette, & Tzanakis (2019), in the section Current concerns and emergent questions in the field:
(1) the need for common ground between history of mathematics and mathematics education,
(2) the need for effective theoretical and conceptual frameworks,
(3) the need for more in-depth empirical studies and
(4) the need a more refined reflection around the interdisciplinary role of history.
The need for proper theoretical
and/or conceptual frameworks in
the field of research
The need for theoretical and/or conceptual frameworks in the field of research
Barbin (2015) pointed out important epistemological differences between frameworks coming from :
mathematics,
history of mathematics
mathematics education
Attention to the epistemological stance deployed in
research
The need for theoretical and/or conceptual frameworks in the field of research
For Fried, Guillemette & Jahnke (2016), a proper theoretical and conceptual framework in the field should at least address the
question of:
Why we ought to learn history or historical elements related to mathematics?
What part of pupils and students intellectual lives is touched by history?
Moreover, our own view of mathematics, of the past, should be problematized, by asking: What it means to stand facing the past?
Some emergent perspectives
The humanist perspective
The hermeneutic perspective
The discursive and pragmatic perspective
The sociocultural perspective
The dialogical and ethical perspective
The humanist perspective
Holistic perspective (Fried, 2001)
as opposed to professional mathematical training, ought to contribute to students’ growing into “whole human beings”
(Fried, 2007, p. 219)
Knowledge and self-knowledge
“a movement towards self-knowledge, a knowledge of ourselves as a kind of creature who does mathematics, a kind of
mathematical being” (id., p. 218)
A Saussurian perspective (Fried, 2008)
The hermeneutic perspective
Merging horizon of the author-mathematician and the learner (Jahnke, 1994, 2014)
Concepts borrowed to Gadamer
Experience of dissonance or alienation. Students learn
something about their own mathematics by experiencing and reflecting on the contrast between modern concepts and their historical counterparts
requires ‘decentering capabilities’. “...we take it to mean, the capacity to adopt the other’s perspective, to ‘wear her
conceptual spectacles’ (by keeping away as much as possible our own perspectives) (Arcavi & Isoda, 2007, p. 114)
The discursive and pragmatic perspective
Reading a text amounts to enter a dialogue
Thinking as communicating, the thinking of an individual is considered as a special case of “interpersonal communication“ or as a “combination of communication and cognition” (Sfard, 2008)
Learning meta-discursive rules in mathematics
Inquiry-reflexive learning environment (Kjeldsen & Blomhøj, 2012, 2016;
Kjeldjsen & Petersen, 2014)
Historical texts as cognitive artefacts (Kjeldjsen & Petersen, 2014)
References to pragmatism (cf. Peirce)
The sociocultural perspective
Changes in language as learning in mathematics (Ball &
Bass, 2003)
Developing competencies of prospective teachers
(Pedagogical content knowledge, mathematical content knowledge) (Jankvist 2010; Mosvold, Jakobsen &
Jankvist 2014; Smestad, Jankvist & Clark 2014)
The dialogical and ethical perspective
History as a place to meet other ways-of-being and ways-of-doing in mathematics
Historico-cultural perspective in mathematics education (Radford, 2012, 2013, 2018)
Experience of Otherness (Guillemette, 2018)
Developing empathy through the experience of otherness in mathematics, toward a nonviolent mathematics education (Guillemette, 2017, 2018)
Dialogical perspective (cf. Bakhtine)
Toward rigorous, coherent and instructive studies in the field
Situate ourselves as researchers on an epistemological and methodological level
Taking into account the point of view of the participants that are experiencing history in an educational context, but also the point of view of the researcher, in relation to historical artefacts and history
To give access to this share meaning
To clarify the role and the potential of history in a consistent and coherent way
Support empirical research