Roland O'Daniel's List: Discourse in Mathematics Classroom Research

pg 258 "In collaborative discussions, the teacher's comments direct students not only to understand what others are saying, but also to respond to, extend, or connect to those ideas. For example, the teacher can ask, "Does anyone want to build on what sally just said?"...However, the teacher can encourage students to  work directly with one another's ideas and can take steps to foster such interactions."

pg 258-9 "To get students to listen to, comprehend, and extend other's ideas, teachers must ask them to do this consistently and not only in a whole-class format. For example, during a group work, the teacher can actively support collaborative discussions by engagin all students at the table in the conversation...the teacher responded only to "group questions"  or called on specific students to ask the question to make sure that everyone was in agreement with the necessity for a question and what the topic should be.

pg 258 "We capture differences in these kinds of discussions by talking about three key aspects of pedagogy: positing students for discussion, managing wrong answers, and connecting and linking across ideas."

Annecdotal evidence from observation and analysis of lesson film.

pg 257 "We focus on two kinds of classroom discussions: sharing discussions and collaborative discussions. In sharing discussions, students share their answers and teachers value their contributions... In collaborative discussions, students also share their ideas, but in addition, the build on the thinking of their classmates' responses, take up classmates' ideas, and work with these ideas explicitly to extend the line of thinking that emanates. "

pg 88 "Questions such as the following might orient this work.
* What is the communicative history of a particular activity structure (e.g.,
science talk) in a given classroom?
* How is disciplinary knowledge interactionally accomplished through
discourse within this activity structure?
* What do individual children discursively contribute to this collective
activity, and how do their contributions change over time?
* How do the voices of individual children, reflective in part of community
membership, intermingle over the course of the construction of classroom
discourse?"

pg 76 "When Michaels asked her why she didn't explain her solution processes in the first place, Elizabeth responded", I didn't understand your question" (Michaels & O'Connor, 1990, p. 16)."

Teachers must scaffold/support metacognitive questions so that students become aware of their thinking patterns. Students do not automatically understand how to express their thinking verbally or in written form so teachers must, "Embed Communities of Discourse"in their instruction.

jjpg 72 "Classroom Discourses and Educational Reform
Educators working across disciplinary domains have begun to recognize that educational reform requires addressing traditiona classroom discursive practices. Inquiry learning, for instance, cannot occur as long as teachers and students communicate largely in ways reflective of direct instruction, where the teacher and the classroom texts hold the key to knowledge in the form of the "right" answer. Many educational reform efforts that have made discourse a  centerpiece of reform have done so from a sociocognitive or sociocultural theoretical framework. Examples of such efforts from three academic discipline areas-reading and language arts, science, and mathematics illustrate how research on discourse has played a key role in attempts at improving classroom teaching and learning."

Discourse must change if instruction is to change.

Key component of sociocognitive framework is that students communicate with each other around the construction of understanding/content.

"In my own work on narrative discourse and classrooml earning( see Hicks, 1993), I have argued that narrative discourses should be examined in light of the speech activities in which participants are engaged. In this sense, narrative can be explored as a family of discourse genres in which children and teachers construct extended oral
or written texts that order, describe, explain, or emplot events, both real and fictional."
pg 70 "Studies of children's language use and classroom learning have suggested a
relationship between such extended talk about events and children's successful
participation in school tasks(Snow, in press). In large part, such studies have
connected children's narrative performances with their literacy learning. Since
oral narrative genres represent extended discourse in which the speaker constructs
a text as opposed to a single utterance, studies of children's oral
narratives have been viewed as a possible "window" onto their classroom
literacy learning. Such work has often been focused on sociolinguistic differences
in the narratives constructed by children from differing communities.
Recall that Heath's ethnographic study of communities' ways with words
revealed important differences in narrative socialization. In subsequent studies
of children's classroom narratives, Michaels (1981) found cultural differences
that supported Heath's work. The Sharing Time narratives of Black children
were rooted more in an "oral" discourse style, where events were connected
through linguistic devices like repetition, such as one might find in poetry.
The SharingT ime narratives of White children tended to be more essayist
or "literate"in nature, in that a single topic was chosen and events connected
to the topic were related in a sequential manner. Researchers like Sarah
Michaels have concludedt hat differing forms of narrative discourse may
provide children with differential access to literacy. As Scollon and Scollon
(1981) note in a chapter titled "The L iterate T wo Year Old," preschool children
in many middle-class families may be literate long before they are able to
read and write."

Implications for dealing with different student populations and needs to address different cultural learning styles.

Classroom Genres of Discourse:
Triadic
pg 69 Monologic form of talk. A child in a mathematics classroom may be asked to elaborate on how she arrived at her answer to a problem... The speaker is given the floor for a much longer period of time. The "rules of the game"-the participant frameworks that define social roles and obligations-have shifted somewhat so that the speaker no longer expects an immediate response.
pg 70 Narrative discourses, oral and written texts representative of a series of connected events, may be another overarching discourse genre in the classroom, one with many variations in both form and function...Two examples that come to mind are (a) Morning Circle (or First Circle) and Sharing Time, where children construct narratives of personal experience (Dorr-Bremme1, 992;Kantor, Green, Bradley, & Lin, 1992; Michaels, 1981), and (b) Journal Writing, where children
typically write journal entries grounded in fictional or personally experienced events (Dyson, 1989, 1993; Hicks & Kanevsky, 1992)."

pg 70 "In my own work on narrative discourse and classrooml earning( see Hicks, 1993), I have argued that narrative discourses should be examined in light of the speech activities in which participants are engaged. In this sense, narrative can be explored as a family of discourse genres in which children and teachers construct extended oral or written texts that order, describe, explain, or employ events, both real and fictional."

Different forms of discourse in the classroom. Focus on discourse (especially in younger students) that is not fully content related. A major difference is that the context of the learning for younger students is more closely tied to the general understandings at the secondary level discourse can move to more content 'heavy'/specific, but it should be noted that discourse/learning is still a social construct and context is still critical. A scaffolded approach must be made, processes identified, routines developed, long-term focus on helping students understand content related/specific discourse that is less connected to personal/fiction constructs.

pg 67

"In his article "Reevaluating the IRF Sequence," Gordon Wells (1993)
describes how one classroom teacher moved between direct modes of instruction
involving a triadic form of discourse with explicit evaluation and discourse
that resembled more what Tharpe and Gallimore (1988) refer to as
an instructional conversation."

Reference for Wells: Wells, G. (1993). Reevaluating the IRF sequence: A proposal for the articulation of theories of activity and discourse for the analysis of teaching and learning in the
classroom. Linguistics and Education, 5, 1-37.

Need definition of triadic discourse (between teacher-student-student?)

Reference for Tharpe and Gallamore: Tharpe, R. G., & Gallimore, R. (1988). Rousing minds to life: Teaching, learning, and schooling in social context. New York: Cambridge University Press.

Definition of instructional conversation:

According to Cazden (1988, p. 54), instructional conversation is "talk in which ideas are explored rather than answers to teachers' test questions provided and evaluated." Goldenberg provides five critical features of this type of teacher-student interaction:

• It is interesting and engaging.
• It is about an idea or a concept that has meaning and relevance for students.
• It has a focus that, while it may shift as the discussion evolves, remains discernible throughout.
• There is a high level of participation, without undue domination by any one individual, particularly the teacher.
• Student engage in extended discussions -- conversations -- with the teacher and among themselves.

pg 67

"the IRE/IRF sequence has come to be associated with broader teaching practices or philosophies, such as the direct instruction of skills or the elicitation of so-called known-information questions, questions where the teacher is seeking the "right answer." The IRE sequence has, for some educational researchers, come to be associated with a "skill and drill" mode of instruction, and reform efforts have therefore made such modes of communication one of their primary targets of change."

Further evidence of lower-level discourse expectations.

pg 66
"IRE/IRFT: he Unmarked Case?
Across the literature on classroom discourse, certainly the most robust
form of talk documented has been that of the Initiation-Response-Evaluation
(Cazden, 1988; Mehan,1 979) or Initiation-Response-Follow-up (Sinclair &
Coulthard, 1975; Wells, 1993) sequence. This genre has come to be viewed
as what linguists call the unmarked case; it constitutes somewhat of a norm.
Perhaps the robustness of the IRE/IRF sequence across classroom settings
can be related back to the example of mother-child interaction shown in
Example 4 (lower-level, fill in the blank/rote memory kind of response) . There, as the more capable adult in that example assumed an instructional role, she provided conversational slots so that the child could successfully participate in joint book reading. The provision of such slots or  openings for learners may be a means through which caretakers, and teachers, provide access to discourses and forms of knowledge beyond the child's independent means.

The IRE/IRF organization of classroom lessons has been documented
largely for group discussion activities in which the teacher asks a question,
a child (or a group of children) responds, and the teacher follows through
with a comment, often evaluative in nature. The following example from
Courtney Cazden's own teaching illustrates the typical triadic structure of
classroom lessons. In this example, the teacher has been eliciting children's
birthplaces as a means of helping them learn about geography, distance, and
family origins. One student, Prenda, has been called on to identify her birthplace
and then to find it on a map."

Confirms my experiences in the classroom that teachers rely on very low level, one word responses from students as the majority of interactions.

pg 62

"This concludes my discussion of theoretical perspectives on discourse and
learning. I might summarize this section by stressing that discourse is an
inherently social construct that mediates, indeed partly constitutes, the teaching
and learning that take place in classrooms. Through meaningful classroom
activity, children appropriate the discourses that situationally define "what
counts" as knowing within disciplines. In the following section, I turn to
current research on classroom discourse. I explore prominent classroom
genres, such as the Initiation-Response-Evaluation/Initiation-Response-Follow-
up instructional sequence; efforts at educational reform tied to discourse;
the "embeddedness" of classroom discourses in community-based discourses;
and the heterogeneous discourses that are woven into one text or turn of talk.
Each of these topics is elaborated through reference to work of current
researchers in the field. Because of the breadth of this field, I cannot hope
to cover all of the research that would fall under a given topic. Rather, I
provide exemplars that will, I hope, enrich readers' understanding of the
research topics currently being addressed within the field of classroom
discourse."

Nice synopsis of the discourse conversation so far.

pg 59

"How do teachers teach and children learn these more formal academic
discourses?  There have been some efforts to incorporate the explicit teaching
of academic genres into literacy instruction (see Reid, 1987, for a discussion of
the controversy surrounding "genre instruction"). However, a sociocognitive
perspective on discourse would suggest that children learn academic discourses
through their repeated participation in meaningful social activity (Rogoff, 1990). Classroom teachers set the stage for this learning process by providing the discursive" slots"t hat enablen ovice learnerst o participatein disciplinaryp ractices.T his can occur withing roupd iscussionsi n which the teachero rchestratesc lassroom discourse (NCTM, 1991, p. 35), or it can occur in small group or one-on-one conferences."

Difficult to teach the content literacies in generic form as the learning is social and must be connected to the learning before it is internalized. Further evidence/necessity that discouse must be established/developed/supported in the content area.

pg 58

"Literacy is generally thought of as the ability to read and write. However,
some theorists have extended the meaning of literacy to encompass more
than just the ability to read and write. Full literacy, according to some, entails
mastery of secondary or formal institutional, often academic discourses (Gee,
1989). These secondary discourses typically involve ways of describing,
explaining, and questioning that are dissimilar to "ordinary" conversation."

Great rationale for the inclusion of dialog in our conversations of literacy and nice description that content literacy is more that conversation and contains skills/concepts/components that need to be taught/supported/developed.

Implications for teachers: scaffolding/gradual release/experiences that include multimodal forms of communication ...

pg 58

"Similarly, some theorists would suggest that "learning science" is a process that is framed by discourse genres, forms of activity, and ways of establishing semantic
links among events, objects, and persons (see Lemke, 1988, 1990; Rosebery,
Warren,& Conant, 1992). Other researchers have explored similar issues
with respect to mathematics instruction (Ball, 1991, 1993; Bill, Leer, Reams,
1992; Hiebert & Wearne, 1993; Lampert, 1990; Spanos, Rhodes, Corasaniti
Dale, & Crandall, 1988)."

Connections between interactions in math and science classes are closely related.

Also, several references to consider:

Ball, D. (1991, November). What's all this talk about "discourse"? Arithmetic Teacher; pp. 44-48.
Ball, D. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal, 93, 373-397.

Lampert, M. (1990). When the problem is not the question and the solution is not
the answer: Mathematical knowing and teaching. American Educational Research
Journal, 27, 29-63

pg 55

"and teacher and student interactions in classroom settings have drawn upon sociocognitive theory to explain how children learn in what Vygotsky termed the
"zone of proximal development" (Vygotsky, 1978; see also Rogoff & Wertsch,
1984). A central metaphor that has emerged from this work is that of scaffolding
(Wood, Bruner, & Ross, 1976)."

Important for classroom practice to recognize the necessity of scaffolding and creating experiences that push students development but don't move too quickly for students to garner experience/cognitive benefit.

pg 53

"Discourses, some of which may be conflicting
identities for them. For instance, my own working-class roots can be in
conflict with the Discourses that I must assume for the purpose of being
an academic; similarily, academic Discourses may be in conflict with the
Discourses that are associated with my being a woman (Ellsworth, 1989;
Hollingsworth1, 994).
It is important to add that academic discourses also embody such ideologies;
they are also Discourses. Thus, learning to "talk science" or "talk math"
involves more than just learning a set of linguistic forms; it also involves
learning beliefs and values (Lampert, 1990; Lemke, 1990; Yackel et al.,
1990). Gee (1989, 1990) and Lemke (1990) both point out that the ideologies
embodied in such academic discourses maybe in conflict with some children's
home and community discourses. Minimally, these academic discourses may
be unfamiliar to children who have not experienced at home what Scollon
and Scollon (1981) term essayist literacy."

Important to understand that discourse is not separated from environment, culture, experience.

Toward an operational definition of discourse from the cognitive perspective: "For reasons that will become more clear as this review progresses, the term discourse implies communication that is socially situated and that sustains social "positionings": relations between participants in face-to-face interaction or between author and reader in written texts."

"The term discourse implies a dialectic of both linguistic form and social
communicative practices. One can talk of discourse in terms of oral and
writtent exts that can be examined after the fact and socially situated practices
that are constructed in moment-to-moment interaction ( Fairclough, 1992;
Gee, Michaels, & O'Connor, 1992). Thus, use of the term discourse implies
a decision about how classroom communicationis to be theoretically positioned
in research on teaching and learning"

pg 2

"...core recommendations of the reform movement are carried out: students use visual models and manipulatives; they work together in groups; they are expected to focus on the process of doing mathematics rather than on just obtaining an answer; they are expected to discuss their understadnings and to communicate their findings; they work on open-ended problems that often require more than 1 class period to solve; and they are asked to make conjectures, to justify their thinking, to assess their knowledge, and to take a degree of responsibility for their learning. In short, many of the visible elements of reform are present in this classroom and provide a comparatively rich environment for learning mathematics."

 Nice description of components of a reform oriented classroom, but more specifically the processes that are critical to developing a focus on dialog in the classroom. In a middle school setting, but nothing prohibits this approach in the secondary setting.

Finally, not strong research, much self-report and qualitative in nature, but can still access the processes/strategies/focus/routines

References for further research:

Manouchehri, A., & Enderson, M. C. (1999). Promoting mathematical discourse: Learning from classroom examples.

Mathematics Teaching in the Middle School, 4 , 216–222.

Langer, J. A. (2001). Beating the odds: Teaching middle and high school students to read and write well.

American Educational Research Journal, 38 , 837–880.

Pugalee, D. K. (1999). Constructing a model of mathematical literacy.

The Clearing House, 73 (1), 19–22.