Glossary
Broker Brokers make connections across communities of practice, enable
coordination, and open new possibilities for meaning. Brokers facilitate the
transition of mathematical concepts from one community to the other.
Community of Inquiry Group of individuals involved in a process of empirical or
conceptual inquiry into problematic situations.
Curriculum Script An event-structured organisation of knowledge, forming a
loosely ordered model of goals, resources and actions for teaching the topic,
incorporating potential emergent issues and alternative courses of action. It interweaves mathematical ideas to be developed, appropriate topic-related tasks to be
undertaken, suitable activity formats to be used, and potential student difficulties
to be anticipated, guiding the teacher in formulating a suitable lesson agenda,
and in enacting it in a flexible and responsive way.
Didactic Incidents An event of the didactic system that modifies the dynamics of
the situation.
Didactical Performance A didactical performance involves the ad hoc decisions taken
while teaching on how to actually perform in the chosen didactic configuration and
exploitation mode: what question to pose now, how to do justice to (or to set aside)
any particular student input, how to deal with an unexpected aspect of the mathematical task or the technological tool, or other emerging goals.
Documentational Genesis The transformation of a resource in a document.
Double Approach The didactic and ergonomic approach, which analyses teachers’
practices by the mean of five components: cognitive; mediative; institutional;
social; and personal.
Double Dialectic The first dialectic between the personal students’ meanings of
a didactic situation and its scientific meaning and the second dialectic between
the teachers’ personal interpretation of the first dialectic and the researchers’
interpretation.
Double Instrumental Genesis From the same artefact, two instrumental geneses
lead to two different instruments, one as a result of teacher’s professional genesis,
the other as a result of personal genesis.
A. Clark-Wilson et al. (eds.), The Mathematics Teacher in the Digital Era,
Mathematics Education in the Digital Era 2, DOI 10.1007/978-94-007-4638-1,
© Springer Science+Business Media Dordrecht 2014
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Glossary
Hiccup The incidents within lessons where teachers experience perturbations,
triggered by the use of the technology, which seemed to illuminate discontinuities in their knowledge.
Instrumental Distance The set of changes (cultural, epistemological or institutional) introduced by the use of a specific tool in mathematics ‘praxis’.
Instrumental Genesis The process through which humans transform artefacts into
instruments.
Instrumental Orchestration The intentional and systematic organisation and
use of the various artefacts available in a learning environment by the teacher
in a given mathematical task situation, in order to guide students’ instrumental
genesis.
Instrumentalisation The process through which humans transform tools into
instruments.
Instrumentation The process through which humans learn to use technological
tools.
Meta-didactic Transposition The model that describes the dynamic process that
occurs, during a teacher education programme, in the dialectical interactions
between the community of teachers and that of researchers and their evolution
over time, in the context of the institutions involved.
Mutualisation The construction of shared knowledge in the classroom that results
from individual or group work and often involves joint action between teacher
and students.
Pedagogical Technology Knowledge The construct of pedagogical technology
knowledge (PTK) is used as a lens for examing crucial variables related to teachers’ use (and non-use) of technology in mathematics. It includes the need to be a
proficient user of the technology, but more importantly, to understand the principles and techniques required to build didactical situations incorporating it, and
to enable mathematical learning through the technology.
Praxeologies The tasks, techniques, and justifying discourses that develop during
the process of teacher education.
PTK See Pedagogical Technology Knowledge.
Structuring Features Framework A framework design to support the identification and analysis of teaching expertise. It contains the following elements:
working environment; resource system; activity structure; curriculum script; and
time economy.
Teachers’ Pedagogical Identities The embodiment of a teacher’s knowledge,
beliefs, values, life history, and experiences of participating in diverse professional communities that influence how that person has learned ‘how to think’,
‘how to act’, and ‘how to be’ as a teacher.
Technical, Pedagogical and Content Knowledge (TPACK) Originally
Technological Pedagogical Content Knowledge [TPCK], now Technology,
Pedagogy and Content Knowledge [TPACK] represents an extension of the now
classic conceptualisation of teacher knowledge PCK to include Technology.
Glossary
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Theory of Didactic Situations A model that describes the dynamics of the
interactions between teacher and students in the classroom as a ‘game’ where
teachers and students win when students learn.
Zone of Free Action The zone of free action (ZFA) refers to the set of activities,
objects, or areas in the environment that promote an individual’s actions.
Zone of Free Movement The zone of free movement (ZFM) describes the
constraints that structure the ways in which an individual accesses and interacts
with elements of the environment.
Zone of Proximal Development The zone of proximal development (ZPD) refers
to the current extent to which an individual can develop new knowledge, beliefs,
goals and practices.