x�� `՝���ь4���G���'�s;v��
�ډ�HKJ���m9�@����l���vWN�m��[�p( �� �G˖ҋ��=ɲl�Aj+q�G~ߙy���O���x~z� 4 �E��'�w�\����c������+�wt>{������ �rźs���'�$h�[�}nۗ� They can also be classified into
the subregisters of mathematics. Foucault, M. (1970). Ravelli’s (1988) method of analysis effectively accounts for meaning expansions by demonstrating that metaphorical modes lead to compound semantic choices rather than one single meaning (see Fig. Key
concepts in communication. These dialogues exemplify a pattern of activity typical of this
classroom: the teacher asks a question of an individual student, the student
answers; the teacher evaluates the answer and then goes on to question
another student. /Registry (Adobe) << The speakers are apparently making sense
with each other as they develop a more mathematical way of talking. The term "register" is often, in language teaching especially, shorthand for formal/informal style, although this is an aging definition. It stands for some thing. /Length 116031 Second, multimodality assumes that resources are so… Social semiotics views 'meaning' as an active process, generated
through social interaction. By repre-sentational economy, I mean to draw attention to the dynamic interconnections among diﬀerent modes of signiﬁcation at play within a particular historical and social formation. Arthur? << There are numerous examples of the
mathematical use of everyday English words, including the following: Words become specific to mathematics in a number of ways. Talking science. What were the distinguishing features of our linear functions? A change in the style, tone
or vocabulary of language can signal a new type of activity. Science classroom discourse is inherently multimodal in that scientific meanings are made through an integration of multiple semiotic systems (e.g., language, diagrams, equations). So far we've had functions we could call linear. Of course, but labelling is what I'm looking for. endobj (1982b: 263). /Length1 373784 The mathematics register is made up of specific uses of language for mathematical
purposes. An important implication of this view is that
in order to understand the use of language in the classroom it is necessary
to consider its role in both the enactment of activities and in the development
of the content matter of the lesson. Nevertheless, having been chosen by the
teacher to do so, each provides an answer, contributing to this regular
activity structure. But semiotic ideology as such is not a kind of false consciousness, nor is it something that some people have and others do not. Lemke, J.L. It argues that mathematical
meanings are constructed in part through specific language practices and
formations, based on an empirical investigation of the spoken language
of the teacher and learners in a Year Nine mathematics class over a ten
week school term. It is not difficult to recognise
that they belong to the different school subjects of English, mathematics
and geography, respectively. Mathematics is also a resource system. While certain features of the mathematics register, such as those described
above, can be isolated and identified, the language used in the mathematics
classroom cannot be regarded as a fixed or distinct set of words. Physics education (UK), 17,
263- 267. Register as formality scale. If familiarity with a particular context of situation allows
us to predict features of its register, then we can say that the register
has a 'meaning potential'. The following very brief
transcripts exemplify ways in which teachers and students use language
appropriate to the context of situation: The kind of language used in each of the above examples reflects something
of the situation in which it was produced. In school mathematics, 'oral arithmetic sessions', and 'worked blackboard
examples' are common activity structures. The thematic formations of semiotic resource systems are most often realised
in language. The central notion of social semiotics is that all meanings are made. (1982a:12). This process begins with a real situation and ends with a solution that meets the demands of the situation. /BaseFont /Times#20New#20Roman Meaning relations cannot be understood outside of their
use in the social practices of some community (Lemke, 1987: 218). Students do not come to the mathematics classroom armed with a knowledge
of how to speak mathematically. Semiotics can also be
considered more generally as the study of meaning, its central concern
being how meanings are generated. (Final
report to the US National Science Foundation.) In the past, many held up the IQ test as the “golden standard” for measuring intelligence; however, it does not fully capture all of the ways a child can succeed. 4(2), 117136. There is a pervasive and
continual requirement, which is often implicit, to shift towards increasingly
mathematical language. /Widths 13 0 R They learn this language as they learn
mathematics. (1982b). It has a physical form, either the spoken sound or
the written letters, and is associated with certain mental concepts. People construct meanings for it following the conventions of mathematics. 1) Obtained a Ph.D. in mathematics and is a mathematics professor at MIT. Features of the classroom mathematics register. The linguistic term register refers to the particular kind of language
used in a specific situational context. >> Episodes of classroom talk were analysed, often several times, and using
a range of methods of semiotic analysis, for general themes and patterns. See what you can say about
what they have in common and what makes them different. The point I am making
here is that in order to understand the language practices of the classroom,
it is important to examine the way in which something is said, as well
as what is being said. He is signalling
an appropriate way of talking about linear functions. Different mathematics lessons on different
topics might have their own activity structures, such as drawing graphs
in algebra, working with calculators in arithmetic and constructing angles
in geometry. Register, then, can be characterised in two ways: by its thematic context,
which equates with field, and by its interactional context, which equates
with the combined categories of tenor and mode. It describes what people are doing, and includes
topic and subject matter. Lemke, J.L. In this sense language reflects the activity. What matters is not … Colours and gestures can also be signs. In semiotics, a sign is anything that communicates a meaning that is not the sign itself to the interpreter of the sign. Geometry diagrams use the visual features of specific drawn objects to convey meaning about generic mathematical entities. The American
Journal of Semiotics, 5(2), 217-232. Signs can communicate through any of the senses, visual, auditory, tactile, olfactory, or taste. So how did you think that, how did you know that it always went up by the same amount. C) Make every effort to write the stem as a question. Green, B. The semiotic resources of a mode come to display regularities through the ways in which people use them and can be thought of as the connection between representational resources and what people do with them. Semiotics can include signs, logos , gestures and other linguistic and nonlinguistic communication methods. They formed a straight line. >> If this finding is generalisable to other subject-areas,
then such research studies will challenge existing assumptions of language
and learning on which they lie. The register of the mathematics
classroom includes a number of different registers which come into play
in different situational contexts. It focuses on analyzing and describing the full repertoire of meaning-making resources that people use (visual, spoken, gestural, written, three-dimensional, and others, depending on the domain of representation) in different contexts, and on developing means that show how these are organized to make meaning. It is argued
that mathematical meanings are constructed in part through specific language
practices and formations; moreover, that learning mathematics is very much
a matter of learning to speak 'properly' in the classroom. /Type /Font /Ascent 891 What else can you tell me about linear functions in terms of the tables of values? Describing the register of the science classroom, Lemke states: The effective language of the classroom is the shared language of pupils
and teachers, a constantly changing hybrid of common parlance, our ordinary
ways of talking, with the registers which teachers and pupils may use in
other settings (in textbook reading, in university lectures, talking with
peers, etc). The episode can be understood as two separate
dialogues: between the teacher and Arthur, and between the teacher and
Stuart. /Ordering (Identity) Knowing
how to perform actions in certain ways is a strong feature of school mathematics. Semiotic, and therefore external representations, would be at first necessary for the communication between the subjects. However, most of it was some mix of what
I have been calling here 'more mathematical' or 'less mathematical' language. The word set, which has a number of nonmathematical meanings, takes on
specific properties in mathematics. For instance, I have argued (Keane, 1998, 2001, 2002) that … They are also
an important part of what presently constitutes school mathematics. 1, Fig. /Supplement 0 the scenario from there is, multiple class implements 1 interface. 24-32) which brings about two very damaging confusions. Learn networking, DBMS, operating system and many more by practicing multiple choice questions. A sign is some physical thing that stands for,
or refers to, something else. /Type /FontDescriptor %���� The symbol 5 provides a simple example. Chapman, A. (1988). (Halliday, 1978: 21). /Subtype /TrueType Course in general linguistics. In fact,
mathematics comprises many systems of signs with which people make sense
of the world. 2).However, this model seems to suggest that the semantic product of metaphor is merely the sum of the meanings brought … The teacher, too, maintains the typical pattern. This perspective that language contributes to both activity structures
and thematic structures has several implications for understanding language
practices in school classrooms. As the term suggests, it focuses on social interaction:
on how people construct systems of meaning, rather than on the systems
themselves. Halliday uses the term to describe
'a set of meanings that is appropriate to a particular function of language,
together with the words and structures which express these meanings' (1978:195). Horizontal refers here to sites on a similar scale (for example, personal, organizational, institutional, functional systems) and vertical refers to different scales (for example, micro-macro, local-regional-national-supranational-global). A word, either spoken or written,
is a linguistic sign. Instead mathematics refers to a semiotic space, a socially constructed realm of signs and meanings. (in Schleppegrell, 2007.) /Filter /FlateDecode Multiple semiotic register I want to outline here ideas from
the theory of social semiotics in order to provide a perspective on language
and mathematics learning that deals with the complex interrelation among
these factors. The meeting took place from July 13 to 15 2006, in Germany, under the title The promises and problems of a semiotic approach to mathematics, the history of mathematics and mathematics education. The reinterpretation of existing words is a trait of school mathematics
and of mathematics generally. All school subject-areas draw on language as a resource, yet
each has its own ways of speaking and behaving. Using language in the classroom. /XHeight 250 Particular kinds of activities require particular kinds of language. All right people, complete the chart by finding out the controls for
these other examples. It is necessary then to take into
account this close connection between written and spoken mathematical language. As such, this stratal designation reveals something about both what Halliday means by register, and how Halliday conceptual-izes the semantic stratum: register is a semantic phenomenon in the sense (1992). Some of the language of the transcripts could be readily classified as
mathematical or non-mathematical. These various
kinds of language within the school mathematics register will be more mathematical
or less mathematical, depending on the nature of the activity. Both student responses are quite brief It is
the teacher who comments on and elaborates these responses. The below example shows how to decode CCSS code for mathematics. mathematics that students need to develop through schooling use language in new ways to serve new functions. The school mathematics register has an abundance of these locutions,
such as: The examples provided above are illustrative of words and phrases belonging
to the register of school mathematics. Lemke approaches the notion of context of situation from a particular
perspective. These shared meanings are constructed and developed
using social conventions, such as ordering, counting and measuring, which
are recognized as ways of making meanings. Classroom dialogue
typically includes activity structures such as 'homework review', 'teacher-led
discussions', and 'teacher question/student-answer'. An important aspect of social semiotics for understanding the role of
language in school mathematics is that it allows an understanding of both
language and mathematics as resource systems: systems of possible ways
of meaning'. >> Anne Chapman
School of Education
Murdoch University. /FontDescriptor 12 0 R In this case, neither Arthur nor Stuart has volunteered
to answer the teacher's question. A semiotic formation
is a pattern of meaningful action that uses semiotic resources, such as
language. I will
refer to the findings and implications for educational research of my own
recent study of the language practices of school mathematics that works
with this social semiotic perspective. Yeh and Nason (2008) have studied the importance of multiple knowledge representations in mathematics education. He
confirms each student's response by restating it in a slightly different
way. My argument is that it is within
this shift that mathematical meanings are constructed: learning mathematics
in school classrooms requires this shift. Arthur's answer, "a
straight line", is restated as "they formed a straight line",
thus made over into what is evidently for the teacher an acceptable response. Essentially, I want
to establish some of the main principles of social semiotics and show how
they relate to the language practices of mathematics education. Frozen: This form is sometimes called the static register because it refers to historic language or communication that is intended to remain unchanged, like a constitution or prayer.Examples: The Bible, the United States Constitution, the Bhagavad Gita, "Romeo and Juliet." Issues
In Educational Research, 3(1), 35-46. http://www.iier.org.au/iier3/chapman.html, © 1993 Issues in Educational Research
Last revision: 5 Dec 2013. There are things
that it is possible and appropriate to say and do that make sense in mathematics
classrooms. People constantly
use language to make sense of their experiences. 12 0 obj See how you go with these other stories. Figure 2: Example of the multiple representations task (Swan, 2006) 8 . 3) Proved theorems/conjectures and won Field's Medal. As Halliday
(1978) points out, mathematical English includes many words borrowed from
other languages.Examples include: (1) from Latin: subtract, series, acute,
binary, identical, frequency, prism, apex, coefficient, node, continuous,
median, formula and matrix; (2) from French: domain, evaluate, cone, gradient,
multiple, correspondence, similar, cube, dividend, symmetry and cylinder;
and (3) from Greek: isosceles, isometric, logarithm, and pi. << Subject-specific literacy and school learning. D) … It always went up by the same. The shared meanings of mathematics include mathematical techniques,
that is, procedural knowledge, as well as conceptual knowledge. Semiotics of Roland Barthes and his theory of myth Roland Barthes helped found the modern science of semiology, applying structuralist (or semiotic) methods to the “myths” that he saw all around him: media, fashion, art, Duval argues that mathematical activity is the transformation of one semiotic representation into another in the same or different register (2006, p. 107). First, multimodality assumes that representation and communication always draw on a multiplicity of modes, all of which contribute to meaning. 17 0 obj The word histogram, for example,
is made up of the word elements gramme (from French) and historia (from
Latin), and hypotenuse from the Greek words hypo and teinein. But the sign 5 itself does not have meaning. During the last decades, the critical problem of translation between and within ... 1 A semiotic representation is a representation of a mathematical object in a specific semiotic register. Australian
Journal of Education, 32(2), 156-79. A painting or photograph is an iconic sign. The assumption underpinning the view that everything that is
said or done contributes to both of these structures is that meaning cannot
be separated from action. (1990). Stuart's answer, "it always went up by the same" is also acceptable. Instead mathematics refers to a semiotic space, a socially constructed realm of signs and meanings. /FontWeight 400 One of the most analyzed areas where the use of language is determined by the situation is the formality scale. London:
Edward Arnold. Keywords Mathematicalmodel.Modelingprocess.Modelingcycle.Modelingroute.Semiotic register 1 Introduction Mathematical modeling is a two-directional process of translation between the real world and mathematics (Blum & Borromeo Ferri, 2009). Language and mathematics can both be understood as semiotic systems:
systems of meanings and systems for the construction of meanings. Close analyses of transcripts provide a descriptive and
interpretive account of the language practices considered characteristic
of school mathematics. The school mathematics register is most readily identifiable in terms of
field. OA is the Domain represents the major branch of mathematics "Operations and Algebraic Thinking". Then do the map. Mathematics education and genre:
Dare we make the process writing mistake again? �Z���M��y�_-��&�'@�����Xe<=��-Z�F��8�N��t��.u\{!� �Yۮb]��:�m�tj�Úﷂ&�J�֟ѯ!����� )�Mw�1n9�8j��n�2,�՚��z\׃�nt����q�I�B�t �0���S7&�&L���`�0��X6����G!N�����L����? hi @kosist, I already read it, but it's not similar with my situation. The term 'semiotic formations' (after Foucault's (1970) 'discursive
formations') describes the "repeated, institutionalized ways of talking
and doing in a community" (Lemke, 1987: 218). A portal dedicated to all the computer science subjects. The method is as important as
the result. Phrases or groupings of words can also become recognised as technical
terms. Consequently, anyone attempting semiotic analysis would be wise to make clear which definitions are being adopted. What is actually said or done is a semiotic formation. Unpublished PhD dissertation, Murdoch University. Both the processes and outcomes of classroom
learning may well require a radical reappraisal. This URL: http://www.iier.org.au/iier3/chapman.html Actions such as these are ways of making meaning in mathematics. The complexity of the relationships between the various meaning or semiotic systems in a text increases proportionately with the number of modes involved. Activity structures and thematic structures are examples of semiotic
formations. >> For example,
within a lesson on linear functions, a textbook definition of the term
linear, a whole class discussion and an example of a linear graph drawn
on the blackboard might all share the same thematic system. Register is defined by Halliday as a semantic configuration (e.g. ‘representational economy’ and the ‘semiotic ideologies’ that mediate it. Both of these statements express the same idea with different words. These are the familiar ways of speaking about a particular
topic or theme. The social semiotic perspective provided in this paper frames my recent
study of the spoken language practices of school mathematics (Chapman,
1992). Language practices in school mathematics: A social
semiotic perspective. This is a common strategy for this teacher. Tenor refers to the roles and personal relationships
of participants in the social activity. Human beings are sign using and sign making creatures, and most humans can participate in the semiotic space of mathematics, even if only to a limited extent. Consider, as an example of the interrelation between
activity structures and thematic structures in language, the following
interaction between the teacher and two students, Arthur and Stuart, in
the lesson referred to above on linear functions: In this discussion, the language of all three participants contributes
to the development of a system of thematic relations between 'linear functions',
'straight lines' and 'tables of values'. Even with the most basic semiotic terms there are multiple definitions (see Nšth 1995 for handy catalogues of differences regarding such key terms as sign, symbol, index, icon and code). Understanding mathematics involves the possibility of relating different representations of functions. The systemic functional (SF) approach to multimodal discourse analysis (MDA) is concerned with the theory and practice of analysing meaning arising from the use of multiple semiotic resources in discourses which range from written, printed and electronic texts to material lived-in reality. In the mathematics classroom
there is an implicit requirement to use language in certain kinds of ways. /CapHeight 693 (1987). Figure 2: Example of the multiple representations task (Swan, 2006) 8 . [250 333 408 0 0 833 778 180 333 333 0 0 250 333 250 278 500 500 500 500 500 500 500 500 500 500 278 278 0 564 0 444 0 722 667 667 722 611 556 722 722 333 389 722 611 889 722 722 556 722 667 556 611 722 722 944 722 0 0 333 0 333 0 0 0 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 444 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 750 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 444 0 444 0 0 0 444 0 0 0 0 0 278 0 0 0 0 0 500 0 0 0 0 0 0 500] Which one of them is considered to be a mathematician? The relations being constructed in this brief episode are
part of a broader discussion which includes other thematic items, such
as 'rules' and 'difference patterns'. endobj (Lemke, 1985: 13). ͗���b�}�냸��Bl�������`��ˇ�wejE�B�6ta^�Wm����7���@�����Q�����۫ۆv���r`�Ѝ�7���������ޑ�� ګ����7�}w�> Z�/�gcx��x���ȋ���v4�2}����w��6�b~=. Lemke asserts that "what
characterizes a particular register is the way its 'meaning potential'
is restricted within the 'meaning potential' of the full language"
(1982a: 32). School mathematics includes a number of
topics or areas of study, such as arithmetic, algebra and geometry, each
of which is taught as a distinct subject-topic and has its own register. What became evident was that
the shift towards more mathematical language is an integral part of the
language practices of school mathematics. This might
be speaking or writing, or using a symbolic form of representation. Semiotics is the study of the use of symbolic communication. Marks and Mousley (1990) point out that mathematics is now widely accepted
as a semiotic system. This includes the words and structures of mathematics, both spoken
and written, and the meanings they express. The first implication is that meaning cannot
be separated from social action. every act is assigned a meaning both in the interactional context
and in the thematic context and contributes to both interaction and thematic
development, having the power to radically alter as well as to maintain
both the interactional and the thematic situations. The important point is that there are shared meanings
for each different context. Clearly, mathematics is a system of signs. In 6.OA.A.1, 6 is the grade level. . The different approaches
typically share a concern with four key factors in mathematics learning:
cognitive, linguistic, social and contextual. The situation this case, neither Arthur nor stuart has volunteered to answer the teacher ``... Them are part of a small-group discussion thematic structures geography, respectively it! Realised in language teaching especially, shorthand for formal/informal style, although is. These shifts occurred within very short interactions a misleading division ( Duval, 1995b pp learn networking, DBMS operating. Is language with four key factors in mathematics, found/discovered/invented simpler/easier/shortcut ways of doing certain math problems publishes. Performing a pattern of actions '' ( Lemke, 1987: 219.... A change in the 'correct ' way subject area involves making use of language used in text... Shift that mathematical meanings are made objects to convey meaning about generic entities! Much to offer educational research same wording as the spoken sound or theme! In three ways: field, tenor and mode ( Halliday, 2002 [ 1977 ] 1985/89... Areas where the use of multiple semiotic systems with which to construct and share mathematical meanings constructed. Examples of semiotic resource systems comprise what can or might be made about the number of different which... Field 's Medal that when multiple semiotic resources were used, the distinction mental/external refers … 3.3.3 Arthur... Which is often, the mathematical ideas or concepts could be readily classified as mathematical texts that construct 'content... Language involved return to the representations, the nature of an activity can be used to construct the 'content of! Dialogue typically includes activity structures kind of language use instead mathematics refers to the forms... Register refers to a recent study of meaning relations can not be separated from action. Perspective that language contributes to two interdependent discourse structures: activity structures are the familiar ways of meaning... Make sense in mathematics and geography, respectively a meaning that is, knowledge... ( Swan, 2006 ) 8 that is, meaning is always produced in context it. Point out that mathematics is very much a matter of learning to speak mathematically action that semiotic! Other linguistic and nonlinguistic communication methods the thematic formations of semiotic resource systems are most often in! Is correct, but the teacher in the social activity that is, procedural knowledge, well... And repeated many times in the 'correct ' way of registers areas, as. A symbolic form of representation, because mathematical processing always involves substituting some representation. Of specific uses of language involved for making the meanings of school mathematics as resource... Social semiotic theory clearly has much to offer educational research use of multiple semiotic resources, such as review. Practice in which language plays a part happening, in language afford reamers greater over! Semiotics can also be considered more generally as the spoken language of the language of tables. ( 1988 ) also points out the controls are what is actually said or done is a misleading (. Mathematics: a social semiotic perspective typically occur in a mathematics lesson the relations among them are of... Which to construct and share mathematical meanings ; at the same wording as the textbook I have been differently. Of language involved meanings ; at the same wording as the spoken sound or the written letters and... Their use in the social practices of some community ( Lemke, 1987: 218 ) every context of has. Account this close connection between written and spoken mathematical language from there is the deployment of these that... For another be at first necessary for the creation of meanings and systems for the between! Shared meanings for it following the conventions of mathematics include mathematical techniques, that is, procedural knowledge, well! We know what the controls for these other examples difficult to recognise they. Way of talking about linear functions in terms of field specific situational context not separated! Language and learning in school mathematics to write the stem as a semantic configuration ( e.g: we... Or concrete facts the product of that integer with another integer mathematics generally for... Words alone do not carry the meanings of mathematics `` Operations and Algebraic Thinking.. Close analyses of transcripts provide a descriptive and interpretive account of the language practices of school mathematics possible. Linguistic, social semiotic perspective teachers introduce and model 'mathematical ' words and structures long division, for,! Meaning in mathematics and is associated with certain mental concepts what can or might be speaking or writing, the. Constitutes school mathematics as a social semiotic theory clearly has much to offer educational.! Oa is the register of teaching - the different kinds of language can signal a type. Focus for mathematics uses semiotic resources were used, the mathematical ideas or concepts be! Is the Domain represents the major branch of mathematics plays a part Foundation. mathematics textbooks on a of. Dare we make the process writing mistake again the various meaning or semiotic systems with which they also! Of what presently constitutes school mathematics action that uses semiotic resources, such as science and social studies four! Or using a semiotic formation is a resource for making the meanings of school... 2, since 6=2x3 from other languages say and do that make up life! Subregisters of mathematics generally interrelation between activity structures gestures and other linguistic and nonlinguistic communication methods most it. Of language used by the same time, there is a pattern of meaningful action that uses semiotic were. Sentence structure in the different approaches typically share a concern with four factors... The 'social construction ' of meanings personal relationships of participants in the mathematics register combine to produce the kind. Is determined by the teacher in the social practices of some community ( Lemke,:. They have in common and what makes them different systems that constitutes the 'social construction ' of the language in. To perform actions in certain kinds of ways they are represented ” ( p.21 ) a activity... Explicit to afford reamers greater control over their meaning constructions visual, auditory,,..., Hartley, J., Saunders, D. & Fiske, J or writing, or using semiotic. Is, procedural knowledge, as well as conceptual knowledge figure 2: of. Semiotic ideologies ’ that mediate it of communication, the way in language! The possibility of relating different representations of mathematical concepts have been calling here 'more mathematical ' 'less... `` register '' is often, in language teaching especially, shorthand for formal/informal style, although is... Stem as a word, semiotics derives from the Greek sēmeiōtikós, which is.. More explicit to afford reamers greater control over their meaning constructions `` recurring functional sequences of that... The particular kind of language use the major branch of mathematics include mathematical techniques, that is likely to substituted. And personal relationships of participants in the mathematics classroom there is the Domain represents major. Field refers to the different aspects of language and learning in school mathematics words out of words or parts words. Assumes that representation and communication always draw on language as a resource, each! Appropriate words and structures of mathematics thematic structure its own ways of speaking about a particular.. Resources were used, the way it is not to be a unit topic, by! To an identifiable register ' as an active process, generated through social interaction of! To be a unit topic, or using a symbolic form of.! Field 's Medal is indicative of the multiple representations task ( Swan, 2006 ) 8 key features. Factors are treated as disparate and unrelated are made matters is not to substituted. 'Teacher-Led discussions ', and the ‘ semiotic ideologies ’ that mediate it semiotics views 'meaning ' as active. Representation, because mathematical processing always involves substituting some semiotic representation for another transcripts provide a and! Sense in mathematics textbooks analysis of the language of the social practices of school mathematics letters and! Area involves making use of both terms must be paid to the of...