Mathematics Educational
Research potentials for
Mathematics-curriculumteacher-researchers
On conventions and demands supporting professional
Mathematics-Teachers’ critical position within the
Educational framework
Athanasios Strantzalos
Dr.Math. & M.Sci.Did.Math.
- currently affiliated with the Institute of Educational Policy, Greece
- member of CARN:
https://www.carn.org.uk/
What is this presentation dealing with?
• The Critical Education (CE) movement – with its contradictions and innerconflicts (Ross, 2016) – has provided us with a framework where the
“political” and the “pedagogical” are consciously, openly and
reasonably/dialectically intervened in a lively whole
• Given the central role of the “political” (with its social and sociocultural
side-variations), much is provided for willing teacher-researchers in terms
of “social/gender/race studies”, “language (and discourse) studies”,
“history” etc., since “Dialectics” was meant to deal with such issues from
the beginning on (including Hegel’s dialectics and Freire’s mixture of
literacy-critical consciousness-development-revolution)
What is this presentation dealing with?
• Considering Mathematics Education (ME) as an indispensable feature of CE:
• reasonability systematized,
• frame of concrete reasoning and generalization, that overcomes the danger of overevaluating personal experience and putting aside systematical theory; antithesis
pointed out as a potential educational failure also by Giroux (1988: p. 256)
• frame in which the theoretical is put alongside the practical/empirical in a functional
pairing
• data-elaboration aiming at planning and/or affirming plausible outcomes to timely
known procedures
• we turn to Critical Mathematics Education (CME) and deal with certain
features of it, mainly as concerns the role of Mathematics-TeacherResearchers and the corresponding Critical Curriculum Research:
On CME/Curriculum Research and its Critical
features
• Teaching- and Research-Methods of CME have to deal with the dichotomy of the
social and the individualist aspect of otherwise collaborative learning (Ross,
2017(this conference); Nunes and Bryant, 1996; Lerman, 2001; Valero, 2002)
• Collaboration refers mostly to the formulation and elaboration of a “dialogical
learning framework” (discourse) (Civil & Planas, 2004) within which learning
happens as the adoption of certain norms, values and notions of importance
• As McLaren (2015: p. 130) puts it “…[there is] a distinction between being
schooled and experiencing an education. Education requires the cultivation of
critique, or critical consciousness,…”
• Even the post-modernist adaptation of “Curriculum” refers to «teachers, pupils
and content (be it text or task) coexisting and co-acting at an instance that is
concretely definable in space and time, to which instance teachers and pupils are
creating themselves as such along with civilization (in the sense of experienced
knowledge)» (Carlson, in Tsafos, 2014: 288)
On CME/Curriculum Research and its Critical features
• The above give rise to elaborations of “social interactions” as tools to
interpret the “classroom dialectics”:
To that, let us consider tutors and learners as “active social individuals” whose
engagement in social interactions abides to principles of “autonomies” and
“heteronomies” (Castoriades in: Straume, 2016) defined against an established
collection of normative regulations (the instituted society); these consist also
of “established epistemologies” or, in our frame, “established pedagogical
contexts and methods”, but also of established social interactions (according to
authority/class/gender etc.) that constitute what is to be taught and learned
• Diminishing the “autonomous potential” in these dialectical scheme is one of
the main reasons of criticism towards Critical Pedagogies, as e.g. in (Giroux,
1983) or (Ross, 2016), and supports tendencies towards “social
(establishment) reproduction”
On the role of Mathematics-Teachers
• Classical Mathematical Pedagogies tend to adopt Socio-Cultural aspects that
support norms and questions of diverse educational-political establishments, be
it the cognitive-skills-approach (Freudenthal, 1981; Stinson et al., 20012; Bishop,
2008; Schoenfeld, 2013; Mason, 1998; Kinard & Kozulin, 2008), or CME (Winter,
1996; Elliott, 1994; Skovsmose, 1994; Stinson et al., 2012; Bishop, 2008; Valero,
2002); even if mathematics teachers usually have no means of describing the
corresponding demands and principles (Bishop, 2008)
• In “Realistic Mathematics Education” (RME), pupils are considered as active
agents of their own knowledge-construct while dealing with “real-life” problems
elaborating their (subjective) tools and paving their own paths of learning
(Panhuizen & Drijvers, 2014: 522-523)
• while a Mathematics Teacher is supposed to be apt to evaluate, elaborate, assess
and reflect upon a vast variety of didactical methods...
• BUT, evaluation, elaboration, assessment and reflection are not conceived by the
Mathematics Teacher as timely, locally and socio-culturally existent, but rather
as “objectively definable notions and content”
On the role of Mathematics-Teachers
• Referring back to Castoriades, the frame within which the social interaction
of the Mathematics Classroom happens is a dual one:
• On the one side, one should consider the epistemological trends of Mathematics as
such  Mathematics Teachers in Greece are primarily (educated) Mathematicians
and secondly (artisan) Teachers
• On the other hand, one should keep in mind that pupils’ engagement with ME is
defined socially/subjectively, rather than objectively and Mathematics Teachers are
acknowledged accordingly as such
• In this sense, evaluation, elaboration, assessment and reflection are termed
and elaborated by the individual practitioner-teachers in terms of their
“Professional Identification” (rather as “constituted” than as “constructed
identity”), moreover since
• “…Advocacy of scientific models of teaching has come mainly from outside
the classroom rather than from teachers themselves…” (Coldron & Smith,
1999)
On the role of Mathematics-Teachers
• Referring to an “educated Mathematician’s” conceptual universe, it is of no
surprise that the trend is “teaching consists of a procedure of presenting,
transferring and transplanting objective and valuable knowledge”…
• Given the “post-scientific” character that tends to be appointed to Mathematics,
and the value placed upon (an abstract and fuzzy idea of) “critical thinking” in a
purely mathematical context…
• Also given the trend for Mathematics that “they serve the needs of the Marketsociety” (calculations rather than qualitative (but rational) conclusions), to which
Mathematicians are well adaptable as “skillful problem-solvers”…
• Given, furthermore, the “spectacle-image” of a Mathematician (think of
Hollywood productions, such as “Proof”, “The man who knew infinity”, “The
imitation game”, “A beautiful mind”) as a single-minded, anti-social, but “genius”
person…
• And given last, but not least, examinations and assessment that rule and
determine the (social and professional) future of the pupils…
On the role of Mathematics-Teachers
• It is not surprising that Mathematicians and Mathematics Teachers tend to
create and support a Personal Identity of the “few chosen” (see, e.g.
“Mathematics is not meant for everyone”) that were (successfully)
educated in a Scientific Discipline that is “autonomous and valuable
independently of its applications” (the latter ones being numerous enough
to support also the “value per applicational multiplicity”); a “Platonic world
of concretely organized ideas and knowledge that need – in the long run –
no society to interact with”…
• It is of no surprise that they (we?) tend to also consider, e.g. Non-Euclidean
Geometries solely as implications of the theoretical and elaborative power
of Mathematics to “know (and do calculations upon) the unreachable in full
detail”, rather than a historical point (of a certain time-length) of an
epistemic and conceptual revolution, where the notions “space” and
“spatial transformation” themselves were re-conceived and re-defined
On the role of Mathematics-Teachers
• A “heteronomous” didactical/scientific tradition:
• University-curricula serving primarily (as they are expected to) the “Mathematical
Disciplines”, but
• Conceiving of the “Didactics of Mathematics” as a mere “optimal elaboration of the
given curriculum”, in a curious abomination against (Critical) Curriculum Research
• Pedagogies of Mathematics as a “training in standardized methods” and a “race” for
the most technical, artificial and “clever” task (mostly valued accordingly as the
amount of pupils that fail to “solve”, rather than according to its “learning impact”,
whatever this could mean…): Math-Teachers as skillful artisans …
• Referring back to Castoriades and his “Athenian Democracy”-analysis:
• it is all ineffective (take into account any criteria you wish: PISA?, University-entry-exams?,
stance of pupils towards Mathematics?),
• But we fail to see the “marching Spartans” and stick to our self-satisfying “Athenian
Democracy” of the few…
A role for Mathematics-Teacher-Researchers
• Within the same contextual trading of the educational frame as above, we claim
that Emancipatory/Transformational Collaborative Action Research (CAR) is a
preferable method for the self-re-identification of the Mathematics Teacher
towards an Education that facilitates tendencies like the “(self-) institutionalising
society” of Learning
• The latter conceptualizes and contains the collective potentials (that are greater
than the sum) of its autonomous members, preferably “breaking the didactical
contracts along the way” (Brousseau, 1997; Brousseau et al., 2014), to refer back
to certain instances of classical ME…
• It is unquestionable that CAR promotes and facilitates forms and norms of
interaction and “community” for class- and crisis-sensible teaching-practitioners,
thus breaking the solitude sought for if the status-quo is to remain unchanged,
but furthermore
• As John Elliott (McKernan, 1996: p. x) puts it: “… To be ‘educational’, action
research needs to address concerns about the educational quality of students’
curricular experiences, and the pedagogical conditions under which they are
accessed […] In education, action research is ‘curriculum action research’ ”
A role for CME & CAR & Curriculum Action
Research
• Basic “Mathematical Experiences” (Mathematische Grunderfahrungen),
that were expressed as early as 1996, but…:
• …any material and content that is sought for General Public Education should, in a
publicly -open and -evaluated manner, imply and postulate its indispensable
characteristic for General Educational purposes. This may be conceived of as an
every-day task of teaching.
• The word “experience” itself should enforce the demand that the Teaching of
Mathematics should be more than the synthesis and quotation of information and
algorithms: Mathematics should be experienced (remember McLaren?) or even a
pupil should be put (subordinated) to them, only to reflect upon them in the
sequel!!!
Heinrich Winter (1996): Mathematikunterricht und Allgemeinbildung
A role for CME & CAR & Curriculum Action
Research
• Elements of CME have been around in the Literature of ME for years. A mere
inspection of their elaboration and interpretation in the late 20th and early 21st
centuries would reveal the facts that:
• Their critical features were willingly ignored, and they were adopted as mere
technicalities (as, e.g., is the case with H. Winter and references to his work in the
Greek National Curriculum…)
• As we pointed out earlier, also as posed in the 2nd Panhellenic Symposium on Action Research earlier
this year, this is a problem with which both Critical Educational Researchers and Action-Researchers
should be faced
• These same critical features would facilitate CME in the footsteps of U. d’Ambrosio
or/and O. Skovsmose, if it is taken into account that simple transplant of methods or
features, independently of practitioner research is counter-critical, in the sense we
explained before, moreover since it wouldn’t support the correspondingly needed reprofessionalization and self-identification of Professional-Mathematics-Teachers!
A role for CME & CAR & Curriculum Action
Research
• Issues of CE and of Critical Citizenship Education are indispensable in CME and
a preferable field of research for teacher-researchers, as we have been able to
experience (Vasileiadis & Strantzalos: ISCAR 2016), and, moreover, such issues
prove themselves to be worthy of ME, in the sense that pupils gain deep
insights into the tasks and corresponding methods and notions
• In referring to “Educational Dialectics” and the Historical Features (as, e.g., by
Non-Euclidean Geometries) that emerge as needed in these Dialectics, a
preferable and innovative role is expected to be played by corresponding,
educationally-sensitive, Research on the compound discipline of History-andDidactics of Mathematics (Strantzalos, 2011)
A role for CME & CAR & Curriculum Action
Research
• Action-Research, also CAR, is a preferable framework also for the fruitful
interaction of Secondary and Tertiary Education, under certain presuppositions (Katsarou, Strantzalos et al., 2015), providing a broad array of
possible experimentation:
• Referring to our implications above on University curricula and their impact
upon the stances of Professional Mathematics Teacher towards features of
CME, it is possible that – as far as this interaction is concerned – there should
be a tendency towards deschooling educated Mathematicians (in this case
also as concerns validity of epistemic results in Mathematics VS in Educational
Science) and reschooling them back as Mathematics-Teacher-Researchers via
practitioner CAR-&-Critical-Curriculum-research!
A role for CME & CAR & Curriculum Action Research
• As should be expected by someone reciting “Action Research”, all
theoretical aspects mentioned here should be “data-driven”, or, at least,
“supported by reflections-upon-action”
• Corresponding research outcomes and settings will be presented tomorrow
in this Conference, as part of a “small-Symposium on Action-Research”! See
You there!
Thank You all!
Any questions?