This document analyzes classroom interactions in a year 8 mathematics classroom using critical discourse analysis. It summarizes the key points of the classroom discussion, where students took turns explaining graphs they drew to explore the concept of gradient. The analysis uses Fairclough's three-dimensional framework to examine the discourse as text, discursive practice, and social practice. It finds that in this classroom, students were empowered and agency was shared, in contrast to more traditional classrooms where the teacher maintains most of the control. The discourse encouraged generative understanding over simple reproduction of knowledge.
International Journal of Humanities and Social Science Invention (IJHSSI) is an international journal intended for professionals and researchers in all fields of Humanities and Social Science. IJHSSI publishes research articles and reviews within the whole field Humanities and Social Science, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Telefun. a pragmatic approach to functional learning materials developmentslidemajal
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This paper describes and traces the development of a function-based module, TELEFUN, which the writer produced to teach telephone English to Francophone Public Servants learning English in the language training program of the Canadian Government.
Lexical and syntactic ambiguity is a natural phenomenon in languages of the world. Generally, languages
are having lexical and syntactic ambiguity based on their prose and verses. Beside human beings, lexical
Ambiguity and polysemy is a big problem for the machine and online translation. For answering this problem and
finding the exact meaning of the word and sentence. the translation should through the context in which the word
is used. This paper deliberates upon types of ambiguity in Pashto and later discusses the kinds of lexical and
grammatical ambiguity in the Pashto data. Pashto lexemes were taken from the phrases, sentences and verses of
the Pashto poetry. 300 ambiguous words and lexemes were analyzed and described through Pashto examples. The
research shows that there were lexical, syntactical, semantic and grammatical ambiguities in Pashto language, and
grammatical ambiguity was described in hierarchal way with in Pashto examples in prose and verses.
A brief review of theoretical underpinning, definitions and typical configura...James Cook University
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Yazdi Amirkhiz, S. Y., Kamariah, A. B., Roselan, B., Arshad, A. S., & Hajhashemi, K. (2012). A brief review of theoretical underpinning, definitions and typical configurations of collaborative writing. International Journal of Applied Linguistics & English Literature, 1(4), 197-204.
Abstract: The aim of this paper is to review the underlying concepts, theoretical background, the existing definitions, various forms of collaborative writing normally used in educational settings as well as some sample studies carried out in different contexts. The article begins by providing an epistemological dichotomy of the existing educational paradigms and discusses the positioning of collaborative learning in relation to the dichotomy (transmissional vs. transformative). It then considers how collaborative writing is theoretically backed up by the ideas of Bakhtin (1981), Halliday (1978), and Vygotsky (1978). The review also compares the salient definitions of collaborative writing and critically contrasts various configurations of collaborative writing with regard to the findings of research studies. The article concludes by recommending a few directions for the future research.
Relationship between Creativity and Tolerance of Ambiguity to Understand Metaphorical Polysemy: A Pilot Study
Maha Ounis,
University of Sfax, Tunisia
The Sixth International Conference on Languages, Linguistics, Translation and Literature
9-10 October 2021 , Ahwaz
For more information, please visit the conference website:
WWW.LLLD.IR
International Journal of Humanities and Social Science Invention (IJHSSI) is an international journal intended for professionals and researchers in all fields of Humanities and Social Science. IJHSSI publishes research articles and reviews within the whole field Humanities and Social Science, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Telefun. a pragmatic approach to functional learning materials developmentslidemajal
Â
This paper describes and traces the development of a function-based module, TELEFUN, which the writer produced to teach telephone English to Francophone Public Servants learning English in the language training program of the Canadian Government.
Lexical and syntactic ambiguity is a natural phenomenon in languages of the world. Generally, languages
are having lexical and syntactic ambiguity based on their prose and verses. Beside human beings, lexical
Ambiguity and polysemy is a big problem for the machine and online translation. For answering this problem and
finding the exact meaning of the word and sentence. the translation should through the context in which the word
is used. This paper deliberates upon types of ambiguity in Pashto and later discusses the kinds of lexical and
grammatical ambiguity in the Pashto data. Pashto lexemes were taken from the phrases, sentences and verses of
the Pashto poetry. 300 ambiguous words and lexemes were analyzed and described through Pashto examples. The
research shows that there were lexical, syntactical, semantic and grammatical ambiguities in Pashto language, and
grammatical ambiguity was described in hierarchal way with in Pashto examples in prose and verses.
A brief review of theoretical underpinning, definitions and typical configura...James Cook University
Â
Yazdi Amirkhiz, S. Y., Kamariah, A. B., Roselan, B., Arshad, A. S., & Hajhashemi, K. (2012). A brief review of theoretical underpinning, definitions and typical configurations of collaborative writing. International Journal of Applied Linguistics & English Literature, 1(4), 197-204.
Abstract: The aim of this paper is to review the underlying concepts, theoretical background, the existing definitions, various forms of collaborative writing normally used in educational settings as well as some sample studies carried out in different contexts. The article begins by providing an epistemological dichotomy of the existing educational paradigms and discusses the positioning of collaborative learning in relation to the dichotomy (transmissional vs. transformative). It then considers how collaborative writing is theoretically backed up by the ideas of Bakhtin (1981), Halliday (1978), and Vygotsky (1978). The review also compares the salient definitions of collaborative writing and critically contrasts various configurations of collaborative writing with regard to the findings of research studies. The article concludes by recommending a few directions for the future research.
Relationship between Creativity and Tolerance of Ambiguity to Understand Metaphorical Polysemy: A Pilot Study
Maha Ounis,
University of Sfax, Tunisia
The Sixth International Conference on Languages, Linguistics, Translation and Literature
9-10 October 2021 , Ahwaz
For more information, please visit the conference website:
WWW.LLLD.IR
Critical Discourse Analysis (CDA) is an interdisciplinary approach to the study of discourse that views language as a form of social practice. Scholars working in the tradition of CDA generally assume that (non-linguistic) social practice and linguistic practice constitute one another and focus on investigating how societal power relations are established and reinforced through language use
International Journal of Humanities and Social Science Invention (IJHSSI) is an international journal intended for professionals and researchers in all fields of Humanities and Social Science. IJHSSI publishes research articles and reviews within the whole field Humanities and Social Science, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
GRADUATE SCHOOL.METHODOLOGY OF COLLEGE TEACHING
Source: Learning and Teaching in Higher Education: The Reflective Professional: Greg Light, Susanna Calkins, Roy Cox
Since the term of discourse analysis is very âambiguousâ, there are many scholars from different schools of Discourse Analysis who suggested their definitions, methods. Consequently, there are many schools of discourse analysis which encompass diverse methodological approaches.
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Introduction: Family Talk
SHARI KENDALL
Families are the cradle of language, the original site of everyday dis-course, and a touchstone for talk in other contexts.1 Families are created
in part through talk: the daily management of a household, the intimate
conversations that forge and maintain relationships, the site for the ne-
gotiation of values and beliefs. Yet there has been a greater focus on lan-
guage in workplaces and other formal institutions than on discourse in
this first institution. The chapters in this volume fill this gap in socio-
linguistic research by bringing together a variety of linguistic studies based
on a single set of data: the naturally occurring, face-to-face interactions of
four American families. The studies emerged from a three-year socio-
linguistic project carried out at Georgetown University to examine how
parents in dual-income families use language to constitute their identi-
ties as parents and professionals at home and at work, as well as the in-
teractional and social consequences of these ways of speaking. Since the
workplace has received relatively more attention in studies of discourse,
this volume focuses on the language the four women and four men use as
1. I appreciate Deborah Tannenâs and Cynthia Gordonâs helpful comments on this
chapter.
McPherson, James M., et al. Family Talk : Discourse and Identity in Four American Families, Oxford
University Press USA - OSO, 2007. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/apus/detail.action?docID=415302.
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they interact with one or more family members, with the addition of one
fatherâs social talk about family at work.
The volume contributes to the discourse analysis of naturally occur-
ring interaction in general, and of family interaction in particular, while
also making significant contributions to theories of framing in interac-
tion and the linguistic creation of identity. Together, the chapters extend
our knowledge of family discourse and identify new ways in which family
members construct, negotiate, and enact the individual and collective iden-
tities that constitute a family. Furthermore, whereas the vast majority of
work on family discourse focuses on mothers, several chapters consider
the relatively understudied language of fathers. Likewise, a substantial
amount of research on family discourse has been based on mealtime in-
teractions recorded in the presence of researchers (Blum-Kulka 1997;
Erickson 1982; Ochs & Taylor 1995; Ochs et al. 1992; Pontecorvo & Fasulo
1999; Paugh 2005). In contrast, the studies in this volume are based on
interactions that occur in a wide range of settings, which more fully rep-
resent these familiesâ experiences. As such, the chapters contribute to the
socioli.
This guide for students and practitioners is introduced by Christopher J. Hall, Patrick H. Smith, and Rachel Wicaksono. This presentation talks about discourse analysis and its several definitions including the pervasive relevance of discourse (analysis), linguistic approaches to discourse analysis, social approaches to discourse analysis, and themes in contemporary discourse analysis. This will discuss the nature of discourse analysis in context significant to all PhD Language Studies students around the globe.
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IV Convegno CKBG, Pavia 29-31 gennaio 2014
Feldia F. Loperfido
UniversitĂ degli Studi di Bari
UN CORSO DI APPRENDIMENTO BLENDED COME CONTESTO A SUPPORTO DELLâESPRESSIONE DEMOCRATICA DI SĂŠ
Simposio: Apprendimento sostenibile e tecnologie: come supportare lo sviluppo nei contesti educativi ed organizzativi
Discussant: Vittore Perrucci (UniversitĂ della Valle dâAosta)
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
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Francesca Gottschalk from the OECDâs Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
A Strategic Approach: GenAI in EducationPeter Windle
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Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
How to Make a Field invisible in Odoo 17Celine George
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It is possible to hide or invisible some fields in odoo. Commonly using âinvisibleâ attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
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Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
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In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
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Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Hanâs Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insiderâs LMA Course, this piece examines the courseâs effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Palestine last event orientationfvgnh .pptxRaedMohamed3
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An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Analysing classroom interactions using critical discourse analysis
1. ANALYSING CLASSROOM INTERACTIONS USING CRITICAL
DISCOURSE ANALYSIS
Steve Thornton Noemi Reynolds
University of Canberra John Curtin College of the Arts
There is a long history of studies of language and mathematics. Much of this has
focused on the language of mathematics, and the role of language in developing
mathematical understanding. A more recent emphasis has been on how language in
the mathematics classroom illustrates power relationships. In this study we use the
tools of critical discourse analysis, including systemic functional linguistics, to
examine the extent to which student agency is promoted and evident in a year 8
mathematics classroom in Australia.
There is a long history of studies of language and mathematics. Pimm (1987)
suggests that there are three levels of relationship: mathematics and language, the
mathematics of language or conversely the language of mathematics, and
mathematics as a language. Zevenbergen (2000) discusses mathematics as a register
with its own specialised vocabulary, semantic structure and lexical density. She
maintains that language is a form of cultural capital, and suggests that students must
learn to âcrack the codeâ of the mathematics classroom, a task which is less accessible
to students from working class backgrounds than to students from middle class
backgrounds.
A second emphasis, particularly in the constructivist literature, has been the role of
language in learning mathematics. Brown (2001) points to the role of language in
developing understanding, noting that mathematics can only be shared in discourse,
mediated through social events. Alrø and Skovsmose (2002) stress that the quality of
communication in the classroom is inextricably linked to the quality of learning, and
discuss the role of dialogue in the learning of mathematics. In contrast to lessons
containing genuine dialogue, many traditional mathematics lessons amount to little
more than a game of âguess what the teacher thinksâ (Alrø & Skovsmose, 2002).
A more recent area of focus on language in mathematics has been on how language
in the mathematics classroom illustrates power relationships (Walkerdine, 1988;
Zevenbergen, 2000). In a set of papers edited by Barwell (2005), bringing together
the fields of mathematics education and applied linguistics, several writers
considered issues such as the nature of academic mathematical discourse, and the
relationship between the teaching and learning of mathematics and studentsâ
induction into mathematical discourses. They claim that a view of language as a
social practice is inseparable from a view of mathematics as social practice.
In this study we use the tools of critical discourse analysis to examine the extent to
which student agency is promoted and evident in a year 8 mathematics classroom.
2006. In NovotnĂĄ, J., MoraovĂĄ, H., KrĂĄtkĂĄ, M. & StehlĂkovĂĄ, N. (Eds.). Proceedings 30th Conference of the
International Group for the Psychology of Mathematics Education, Vol. 5, pp. 273-280. Prague: PME. 5 - 273
2. Thornton & Reynolds
CRITICAL DISCOURSE ANALYSIS (CDA)
Critical discourse analysis emerged in the 1980s as an attempt to synthesise language
studies and social theory (Fairclough, 1992). It looks critically at the nexus of
language/discourse/speech and social structure, attempting to uncover ways in which
social structure impinges on discourse patterns and power relations (Blommaert &
Bulcaen, 2000). It thus has the potential to look beyond superficial aspects of
classroom language, and to illuminate aspects of agency (Boaler, 2003) and power in
the classroom.
Fairclough (1992) considers discourse as a mode of action in which people act on the
world and each other, in addition to being a mode of representation. He stresses that
there is a dialectic relationship between discourse and social structure, with discourse
on the one hand being constrained by social structure, and on the other as being
socially constitutive. He sketches a three-dimensional framework for conceiving of
and analyzing discourse, considering âevery discursive event as being simultaneously
a piece of text, an instance of discursive practice and an instance of social practiceâ
(p4).
The first dimension is discourse-as-text, i.e. the linguistic features and organization of
concrete instances of discourse. Building on the work of, for example, Halliday
(1978), Fairclough maintains that text analysis must include a consideration of
vocabulary, grammar, cohesion and text structure.
Faircloughâs second dimension is discourse-as-discursive-practice, i.e. discourse as
something that is produced, distributed and consumed in society. He introduces the
concepts of âforceâ to describe what the text is being used to do socially, âcoherenceâ
to describe the extent to which an interpreting subject is able to infer meaningful
relationships and to make sense of the text as a whole, and âintertextualityâ to
describe how texts are related historically to other texts (p 83).
Faircloughâs third dimension is discourse-as-social-practice, drawing on the Marxist
concepts of ideology and hegemony. He claims that ideology is located both in the
structure of discourse and in the discourse events themselves. For example, he
suggests that the turn-taking practice of a typical classroom implies particular
ideological assumptions about the social identities of and relationships between
teacher and pupils (p 90). Hegemony concerns power that is achieved through
constructing alliances and integrating groups. For example, in the classroom the
dominant groups exercise power through integrating rather than dominating
subordinate groups, winning their consent and establishing a âprecarious
equilibriumâ.
Fairclough claims that this framework âallows one to combine social relevance and
textual specificity in doing discourse analysis, and to come to grips with changeâ (p
100)
5 - 274 PME30 â 2006
3. Thornton & Reynolds
THE CLASSROOM
A transcript from a year 8 lesson (âNoemiâs classroomâ) is provided in Appendix 1.
This transcript is representative of the pattern of discourse observed throughout the
lesson. The classroom atmosphere is relaxed and friendly, with a productive working
relationship between students, and between the teacher and the students.
In Noemiâs classroom the students are exploring the mathematical concept of
gradient, and attempting to discover for themselves the effect of changing a in the
equation y = ax + b. They have drawn graphs using two or three numerical values,
and are reporting to other students in the class on their findings. Students take it in
turns to walk to the front of the class and sketch graphs on the whiteboard, explaining
to other students what they have discovered, and responding to what other students
have said.
ANALYSIS OF THE DISCOURSE
Faircloughâs (1992) three-dimensional framework is used to analyse and compare the
discourse in the two classrooms.
Discourse as text
We discuss the field, tenor and mode of the text (Halliday, 1978), thus looking at the
ideational, interpersonal and textual functions of the discourse (Morgan, 2005).
The field of discourse is overtly mathematics, with few, if any, diversions. In contrast
to the patterns of interaction observed, for example, in the TIMSS 1999 video study
(Hollingsworth et al., 2003), the teacher intervened only to regulate the conversation
(âOne at a time, pleaseâ â Teacher), and to suggest things for the students to think
about. In Noemiâs classroom the discourse is concerned with mental processes, the
conversation being dominated by statements such as âI thinkâ. On the other hand in
many traditional classrooms the emphasis is on material processes or the creation of a
product such as a solution to a problem. In Noemiâs classroom the discussions are
public rather than private discussions, with students laying open their reasoning for
public debate and potential criticism. There is a predominance of self and other
questioning (âI was wonderingâŚâ â Sarah).
Noemiâs classroom thus features a discourse that is generative (Brown, 2001) rather
than reproductive, with the goal (ideational function) of developing consensus around
understanding a mathematical concept (âWell, it was about what Catherine saidâŚâ â
Sam). On the other hand many of the TIMSS 1999 video classrooms featured
reproductive discourse, with the apparent goal of students being to guess what was in
the teacherâs mind.
The tenor of the discourse suggests the interpersonal function of language. In
Noemiâs classroom Carly uses the personal pronoun âyouâ in an inclusive sense (âitâs
what you think will best showâŚâ), rather than the exclusive sense commonly found
in mathematics texts, thus giving agency to other students. She also uses the phrase
âwhat I found wasâŚâ, indicating a high degree of personal ownership of the
PME30 â 2006 5 - 275
4. Thornton & Reynolds
mathematics she was investigating. Noemiâs classroom is marked by a high level of
mutual support (âGo, Carlyâ, and frequent applause). Students frequently self-correct
(âI think what I was explainingâŚâ â Catherine), in contrast to more traditional
classrooms in which correction is carried out by the teacher. Noemiâs classroom thus
features a discourse in which students are empowered and emancipated
mathematically, with relatively equal power relationships and knowledge being co-
constructed.
The mode of the discourse refers to the certainty of the conclusions and the way in
which cohesion is achieved (the textual function of language). In Noemiâs classroom
there is a clear flow in the discourse, with students building on what others have said.
It has a predominance of given/new structures, a feature of mathematical argument
(âI think that what Catherine said makes sense, but I thinkâŚâ). Students talk at
length, rather than giving short answers as reported in the analysis of the TIMSS
videos, in which the average student response length was fewer than five words
(Hollingsworth et al., 2003). Student discourse in Noemiâs classroom is punctuated
by âumâ and ill-constructed sentences. Mathematical language is often vague or ill-
defined, and symbols are used imprecisely (âif it was at 1 it would be at threeâ, rather
than âif y = 3x, then when x =1, y will be 3â â Campbelle). However in watching the
video it is clear that the other students understand what is being said as it is
accompanied by diagrams on the whiteboard. In contrast to many classrooms, the
teacher does not intervene to correct language, nor to clarify what students say. The
tentative nature of the language and concepts is valued (âOn with my crazy
schemeâŚâ â Sarah), rather than mathematics being seen as something that is clearly
defined and absolute.
Thus Noemiâs classroom allows students to see mathematical knowledge as both
personal and social, rather than mathematics as something impersonal waiting to be
uncovered. Cohesion in Noemiâs classroom is achieved through private and public
reflection (âI was just thinkingâŚâ â Sarah) rather than through the apparently
objective structure of mathematics as revealed by the teacher or text. In Noemiâs
classroom the âdance of agencyâ (Boaler, 2003), in which agency moves between
students and the agency of the discipline, is evident.
Discourse as discursive practice
In Noemiâs classroom the texts (conversations) are initiated by the students, re-
expressed and reformulated by other students, and distributed publicly as students
come to the whiteboard. The texts are then consumed by the class, and the cycle of
production, transformation, distribution and consumption is repeated. In contrast the
conversations in many traditional classrooms, such as in the TIMSS 1999 video
study, are controlled by the teacher, the students responding in ways which they hope
will be acceptable to the teacher, with each interchange being self-contained, initiated
and concluded by the teacher. The âforceâ of the discourse in Noemiâs classroom is
thus the social goal of including the entire class in the development of a shared
understanding of the mathematical concept of gradient.
5 - 276 PME30 â 2006
5. Thornton & Reynolds
Although a preliminary reading of the transcript of Noemiâs classroom, in the
absence of the video with the accompanying whiteboard diagrams, may appear to
lack coherence, in reality students in the class are able to construct a coherent and
meaningful interpretation of what others were saying. Students are able to make
sense of and build on what others say (âa lot of what Campbelle said was actually
correctâŚâ â Catherine), and the producer of each discourse event expects other
students to understand (âitâs really up to you and what you think will best show the
lines on the graphâŚâ â Carly). In more traditional classrooms coherence is
produced by the teacher, by asking leading and prompting questions of students.
Noemiâs class has manifest internal intertextuality in that each piece of discourse is
related to a previous one. There is some evidence of students using conventional
structures of mathematical argument, particularly as they strive to produce a
generalisation of how changing the value of a affects the slope of the line. While
they start by looking at specific examples, they attempt to generalise (âlike can we
represent the numbers on the y and x axis with something else?â â Sarah). At the
conclusion of the transcript, Sarah shows a graph on the whiteboard in which the x
axis increases in intervals of 1, while the y axis increases in intervals of a. She
concludes that in this case every line will make a 45° angle with the axes. The text
in Noemiâs classroom illustrates a social practice which requires students to make
their thoughts publicly available and to use the ideas of others to jointly build an
understanding of a mathematical concept.
Discourse as social practice
There is a marked contrast in the turn-taking practices and ratio of teacher to
student talk between Noemiâs classroom and the more typical pattern of Teacher â
Student â Teacher observed in many of the TIMSS 1999 video lessons, in which
the ratio of teacher to student talk was of the order of 8:1 (Hollingsworth et al.,
2003). Noemiâs classroom is characterised by a high level of equality between
students and between the teacher and students. Power is located with students, and
willingly given by the class to each student who is speaking (âGo Carlyâ). To a
lesser extent students ascribe power to the argument produced by each student as
they attempt to understand and build on each utterance. This is in contrast to more
traditional classrooms in which students almost universally agree with what the
teacher says.
In Noemiâs classroom students see themselves as active participants in learning,
who have power over both the mathematics and the discursive practices of the
classroom. Students in many other classrooms willingly accept a more passive role,
in which the mathematics being learnt has power over them, and in which the
teacher maintains control of the discursive practice of the classroom. The hegemony
of such classrooms is maintained through an unspoken alliance between teacher and
students, in which the students become passive partners in maintaining a classroom
where agency resides with the teacher.
PME30 â 2006 5 - 277
6. Thornton & Reynolds
CONCLUSIONS
Critical discourse analysis has been used to analyse the conversation patterns and
content in a year 8 mathematics classroom. In Noemiâs words:
âMy aim in my Mathematics classroom is for students to regard Mathematics as an art
which belongs to them, a means of regarding and interpreting the world, a tool for
manipulating their understandings, and a language with which they can share their
understandings. My studentsâ aim is to have fun and to feel in control.
âAt the start of each year group responsibilities are established by class discussion and
generally include rules such as every member is responsible for the actions of the other
members of their group (this includes all being rewarded when one makes a significant
contribution to the class and all sharing the same sanction when one misbehaves),
members are responsible for ensuring everyone in their group understands what is going
on at all times and students have some say in the make up of their groups .
âMy role is primarily that of observer, recorder, instigator of activities, occasional
prompter and resource for students to access. Most importantly, I provide the stimulus for
learning what students need, while most of the direct teaching is done by the students
themselves, generally through open discussion. Less obvious to the casual observer is my
role of ensuring that students have the opportunities to learn all that they need to achieve
required outcomes. It is crucial that I, as their teacher, let go of control of the class and
allow students to make mistakes and then correct them themselves. An essential criteria
for defining one of my lessons as successful is that I do less than 10% of the talking in
the whole lesson.â
Noemiâs classroom exemplifies many of the conditions for learning through dialogue
described, for example by Alrø and Skovsmose (2002). The discourse is exploratory,
tentative and invitational, contains emergent and unanticipated sequences, is
immediate, recognises alternative ideas even those that are strange (using shapes
instead of numbers in an equation), and has a collaborative orientation in which
students are vulnerable yet maintain high levels of mutual obligation.
In this way her classroom can be considered to be both empowering and
emancipatory for students (Freire, 1972).
References
Alrø, H., & Skovsmose, O. (2002). Dialogue and learning in mathematics education:
Intention, reflection, critique. Dordrecht: Kluwer.
Barwell, R. (2005). Language in the mathematics classroom. Language and Education,
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Appendix 1: Transcript of Noemi's classroom
Class Go Carly
Carly Um, I think that what Catherine said makes sense but I think that when it
comes to the values that you go up by on the graph itâs really up to you
and itâs what you think will best show the lines on the graph. But what I
found with âaâ is that the higher the value of âaâ the more acute the angle
will be compared to the y-axis. So say, um, it was 4x then it will be closer
to the y-axis than 2x. âCause 2x will be here the 4x will be here. I found
that the lower the value the closer it was to the x-axis. But the higher the
value the closer it was to the y-axis. (Applause and a âwhooâ)
Sarah Just a question. I was wondering do you even need the, um ⌠the
numbers. âCause where it says 5a donât, canât you just go like 7a + 2 or
something. Like can we represent the numbers on the y and x axis with
something else? Laughs
Class Laughter, murmurs.
Cameron Like shapes? (Laughter) So you could like do like squares, circles,
trianglesâŚ
Sarah Yeah but this is just more easy. (Inaudible)
Teacher One at a time please. Could we just have one at a time? Kate, what did
you just say?
Kate I was saying that if you replace the numbers with like shapes and letters
and stuff itâs just a complicating thing âcause we all know the number
system and itâs simpler for us than all these other symbols.
Sarah Yeah, but what Iâm saying is, like, if, why weâre using the number system
weâre really, um, pinpointing the graph âcause then weâre saying ⌠one,
PME30 â 2006 5 - 279
8. Thornton & Reynolds
one and y one, sorry, and weâre just you know weâre really pinpointing, I
mean using numbers and if we like if we can find a way to represent it
with letters then weâd be able to make it whole infinity, infinity instead of
just drawing on the graph. Does that make sense?
Class Muttering, faint âNoâ
Teacher That might be something for people to have a think about. Sam, you had a
comment before Sarah ⌠talked about this stuff.
Sam* Well, it was about what Catherine said about having the ⌠axis and the
lines, the scale was being affected by âaâ. What I you know thought was
that âaâ doesnât just affect the y-axis but it affects the x-axis as well. I
mean that if youâre making a graph you want to put the, make the line
cover the largest amount of distance possible. For example, that would
look a lot better than having a graph that looked like that. âCause itâs a lot
easier to read. See? If, if, if - a good way to be able to get a graph, a graph
looking like this (points to one graph) or like this (points to another
graph) depending on whether a is negative or positive would be good. So
thatâs where the scale comes in. (Edited) (Applause)
Campbelle Um, I found that with those ones that itâs kind of saying that for every one
x thereâs going to be 3 y. So, with ⌠if itâs one, two three - if it was at 1 it
would be at three, if it was that because that for every 1 x there is 3 y. If it
was at 2 it would be at 6 and so on. So itâs, yeah, like that and with that
one for every 1 x thereâs 4 y. (Applause)
Teacher Catherine?
Catherine I think what I was explaining what I was doing before as 3x, I think I was
mixing up the scale, um, a lot Campbelle was saying is also actually
correct. If it was 1 it would be 3, so if y = 415x, then, well x = 1 then up
here and 415. If youâre going⌠I donât know what youâd go up by but it
would be like, um, that so it would go up there and that here it would go
there so like right straight like that. (Edited) (Applause)
Oakley (edited)
Teacher Any other comments? (Waits) I was going to give you something else to
think about.
Sarah On with my crazy scheme to play, to change the numbers⌠Crazy scheme
is cool. Um, I just thought of this âcause I was just thinking you know
how I could do itâŚand you know how it says up here 3 plus you know
how she said up by 3 so then the y-axis would go up by 3...back to the y =
ax that meansâŚ.(camera cuts out).
*This child has a stutter.
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