Elsevier

Journal of Pragmatics

Volume 107, January 2017, Pages 46-59
Journal of Pragmatics

Self-directed okay in mathematics lectures

https://doi.org/10.1016/j.pragma.2016.11.007Get rights and content

Highlights

  • Self-directed okay serves intra- and inter-personal functions in Math lectures.

  • Self-directed okay helps emphasize key content and procedures in Math lectures.

  • Self-directed talk and discourse markers must be addressed in teacher preparation.

Abstract

This article investigates the inter-personal and intra-personal functions of the discourse marker (DM) okay in sequences of self-directed talk during university Mathematics lectures. This article takes a conversation analytic approach to the use of okay in the self-directed talk of three graduate students giving Mathematics lectures at a U.S university. While research focuses on okay almost exclusively as a transition, our microanalysis reveals that self-directed okay appears in three general locations and functions intra-personally to direct the teachers’ attention and inter-personally to mark transitions, to open self-repair sequences, and to verbalize thought processes in sections of discourse in which the lecturer is using non-verbal resources to emphasize information or demonstrating how to do math, which we call pedagogically-directed talk. By using self-directed okay, the three instructors focus their own attention while giving their students insight to their cognitive processes, emphasizing key information, and maintaining joint attention to the interactive practice of the university lecture at a point when student attention could become diverted from the task at hand. Findings suggest that self-directed okay is not merely a transition but concurrently serves critical intra- and inter-personal functions and that resources like self-directed okay should be taught as instructional practices for novice teachers in teacher preparation programs.

Introduction

This study addresses the use of okay in sequences of self-directed talk in university Mathematics lectures. Both the use of discourse markers (DMs) and self-directed talk, or self-talk, have been demonstrated to affect listening comprehension, be affected by online planning, and facilitate classroom interaction (Hall and Smotrova, 2013, Steinbach Kohler and Thorne, 2011, Tyler, 1992, Williams, 1992). In large part though, the two (DMs and self-directed talk) have been studied as distinct characteristics of classroom discourse and have been attributed discrete inter-personal and intra-personal functions. This study seeks to overcome this binary categorization of DMs and self-directed talk by conceptualizing language as a dynamic semiotic resource that serves concurrent intra-personal and inter-personal functions.

Our study contributes to the growing bodies of literature on naturally occurring classroom interaction, DMs, and self-directed talk. We discovered the occurrence of okay within sequences of self-directed talk while viewing video recordings of university-level Mathematics lectures as part of a research project involving the use of DMs in STEM (Science, Technology, Engineering, and Mathematics) classrooms. During our investigation of DMs, we noticed that there were times when okay was uttered at a clearly lower volume than surrounding talk and with the speaker's eyes averted from the students and typically toward a non-verbal resource, such as the chalkboard or notes. While these moments often occurred at times when speakers were making transitions between parts of a lecture, we observed that they also occur within sections of discourse when teachers display attention to recipient design (Sacks et al., 1974) and write on the board. In such sequences, we argue okay in self-directed talk is a minute yet mighty resource for self-regulation and teaching.

Our analysis reveals that DMs are critical not only to the discourse structuring of lectures for the other (students), as okay has generally been characterized in the literature, but also for the self (teacher). In addition, we show that self-directed talk is both a resource for self-regulation and a dynamic resource for maintaining student attention and doing teaching by doing being a Mathematician. Such findings are significant for those interested in talk-in-interaction in addition to those involved in teacher preparation at the university level.

Generally speaking, okay is viewed as a transition and marker of common ground. This reflects findings from talk-in-interaction studies of okay in both informal and institutional contexts (Bangerter and Clark, 2003, Condon and Čech, 2007, Gaines, 2011, Müller, 2005, Schiffrin, 1987). For a concise synopsis of research on okay, see Gaines (2011). The following subsections review the findings of corpus, variation, and conversation analysis (CA) studies focusing on okay in university classroom settings with a specific focus on sequential location, prosody, and non-verbal resources as well functions. We argue that while studies have mentioned the relevance of non-verbal resources their analyses have lacked attention to gesture and the use of video data to support and present their analyses. We also suggest that okay has been considered only as a signal to listeners about the speakers’ next discursive move and that the intrapersonal and interpersonal power of okay has largely been ignored.

According to studies of okay as a DM (Rendle-Short, 2000) and as a structural marker (Schleef, 2008), it typically occurs around transitional spaces and is most often found at the beginning of sections of discourse and less frequently at the end and in the middle of stretches of discourse (Levin and Gray, 1983, Rendle-Short, 2000, Swales and Malczewski, 2001, Schleef, 2008). In beginnings, okay is spoken with the same (or increased) volume and pitch as surrounding speech, falling intonation, and potentially in breaths or dental clicks (Rendle-Short, 2000, Schleef, 2008). Pauses and non-verbal actions regularly precede okay when it opens sequences and it is followed immediately by another DM such as so (Rendle-Short, 2000, Swales and Malczewski, 2001, Schleef, 2008). While okay is overwhelmingly found at the beginning of stretches of discourse in our data, this sequential position is not the focus of our analysis.

The instances of okay we analyze are at the end and within sequences of talk. At the end of sequences, Rendle-Short (2000) reports that okay is produced at a lower volume and pitch but still with falling intonation. In her data, okay in this position is followed by a pause in which a computer science lecturer changes the slide for his presentation. Other studies also note pauses either before or after instances of okay, and that okay might be produce in an attenuated manner with gaze averted from the students and possibly toward notes (Levin and Gray, 1983, Schleef, 2008). While we are concerned with the sequential locations and prosodic features of okay, participants’ gaze, gesture, and orientation to non-verbal resources such as chalkboards or lecture notes are of particular interest to us.

Schleef (2008) states that lecturers in the Natural Sciences employ non-verbal resources such as the chalkboard to explain content and that movement from developing information in writing to speech requires structural markers as “a way to lexically highlight and structure important and often visual material” (Schleef, 2008: 76). While mentioning non-verbal resources, Schleef (2008) does not provide any detailed analysis or discussion of them. Rendle-Short (2000) accounts for non-verbal resources and to some extent gaze and gesture, but she describes participants using slides prepared in advance while our participants, mathematics lecturers, are developing information in situ on the chalkboard.

We also argue that the detailed analysis of gaze, gesture, and the use of non-verbal resources in coordination with the prosody is essential for a deeper understanding of okay in the middle of sections of discourse. Only Rendle-Short (2000) analyzes okay in the middle of stretches of discourse. The prosodic structure of okay varies within sequences based on the function it serves: a comprehension check, to bracket a definition, or to mark a change in footing. As a comprehension check, okay is produced quietly with rising intonation and may be preceded by a pause. When pairs of okay bracket a definition, the first is spoken prominently but the second is spoken quietly and both with falling intonation. In Rendle-Short's (2000) data, the first bracketing okay is preceded by a pause but not the second. The bracketing okay resembles okay at the beginning and end of stretches of talk but only encase a single definition. To mark a change in footing, Rendle-Short's (2000) participant produces okay at the same volume and pitch as the surrounding speech and with no pauses on either side. While Rendle-Short's (2000) transcription accounts for gaze and gesture, she does not take them into account in her analysis.

In sum, okay occurs primarily between sections of discourse in lectures. At times, e.g., the end of sequences (Rendle-Short, 2000) and during embedded hesitations (Schleef, 2008), okay is produced at a lower volume and perhaps with the speaker's gaze averted from the audience and toward non-verbal resources. These quieter examples of okay are focus of our analysis. While studies mention the significance of non-verbal resources in sequences, none give thorough analysis or theoretical discussion of okay as an embodied, multimodal, and mediating resource (Douglas Fir Group, 2016). Our paper provides a fine-grained sequential, prosodic, and multimodal analysis of okay that highlights the role of gesture, gaze, and the development of information on the chalkboard in understanding the multiple functions of okay in university mathematics lectures.

Okay functions primarily as a marker of transitions in both institutional and non-institutional interaction. Beach (1993, p. 338) emphasizes that the power of okay emerges from its “dual character” that is both backward and forward-looking. This dual character is particularly suited for university lectures. Levin and Gray (1983) and Schleef (2008) distinguish five functions of the lecturer's okay: textual markers, attention getters, pre-closings, elaborations, and embedded hesitations.

Okay as a textual marker transitions between large sections of discourse without making explicit connections between the two sections. Textual markers are what Swales and Malczewski (2001) call “new episode flags” and Rendle-Short (2000) broadly categorizes as okay at the beginning of sequences. Swales and Malczewski (2001: 154) show that 35% of the instances of okay are “new-episode flags.” Attention getters (Schleef, 2008) are used immediately before the opening of the lecture, and pre-closings precede the closings of sections of discourse. Elaborations mark shifts not between sections of discourse but within sections of discourse. As discussed in the last section, Schleef's (2008) lecturer's okay happens at discourse boundaries following but not typically followed by a pause. Such tokens of okay are not the focus of this paper. For an overview of the functions of okay in lectures, see Table 1. Functions of okay that we analyze are marked with an asterisk.

From Schleef's (2008) taxonomy, only embedded hesitations are significant to our analysis. Embedded hesitations occur during “sections of hesitation […] often accompanied by paper shuffling, with the instructor apparently talking more to him- or herself than to the audience [which are] spoken with less intensity” (Schleef, 2008: 71). Within embedded hesitations, okay transitions between using semiotic resources to orient one's self to the task of lecturing and delivering the content of the lecture. Schleef (2008) only briefly discusses the form of the embedded hesitations and only acknowledges its function as a mediator of lecturers’ psychological functions, i.e., confirming to the self that one is ready to make the next discursive move. While not commenting on the speaker's mental processes, Rendle-Short (2000) shows that okay often follows sequences in which a lecturer closes a stretch of discourse and changes the slides on the overhead projector. She proposes that okay functions to close the non-verbal sequence of changing slides before resuming the lecture.

Two of the aforementioned three functions of okay in the middle of sections of discourse Rendle-Short (2000) outlines are significant to our analysis: to bracket a definition, and as a change in footing. In our data, we will see instances of okay that vary slightly in form but none the less bracket information and mark changes in footing. We extend Rendle-Short's (2000) analysis beyond the discussion of okay functioning as a DM and suggest that okay serves powerful but nearly imperceptible intrapersonal and pedagogical purposes in addition to structuring the lecture.

In summary, research shows that okay transitions between key points in academic lectures and that frequencies of okay in the speech of lecturers vary based on academic discipline and L1 (Levin and Gray, 1983, Rendle-Short, 2000, Schleef, 2008, Liao, 2009). Okay in academic interactions has overwhelmingly been characterized as a small but powerful indicator of a teacher's intended next turn, a cue from the teacher to the students. An understudied aspect of okay is its presence in self-directed talk. To the best of our knowledge, only two studies (Levin and Gray, 1983, Schleef, 2008) mention okay in this light and those do so briefly, only acknowledging its intra-personal dimension. The simultaneous intra-personal and inter-personal functions of okay as part of self-directed talk are the focus of this paper's analysis. The following section will outline key findings in research on self-directed talk, self-talk, and private speech in academic contexts.

Steinbach Kohler and Thorne (2011) use the term self-directed talk to describe the phenomenon that psychologists call private speech and sociologists call self-talk. The concept of self-directed talk does not supplant the previous two but bridges them by recognizing that language may serve concurrent intra- and inter-personal functions. The bifurcation of private speech and self-talk is based on the approach, that is developmental psychology or sociology respectively, taken to the object of study and not on the object of study itself, i.e. talk produced in the presence of others yet apparently directed toward the self. In a lengthy footnote in fact, Goffman (1981: 95) writes that his concept of self-talk is what Vygotsky calls private speech and goes so far as to suggest that the later may be a better term for the phenomenon. While these two constructs have been treated as mutually exclusive, recent studies recognize that language for intrapersonal purposes can simultaneously serve interpersonal functions and vice versa.

Smith (2007) recognizes the co-occurring inter- and intra-personal functions of private speech in her study of bilingual school children but focuses almost exclusively on the intra-personal so we will not discuss her study in depth. In their study, Steinbach Kohler and Thorne (2011: 87) show that self-directed talk “acts as a resource for [intersubjectivity's] maintenance, opening up slots for group problem solving and interactional achievement.” In addition, self-directed talk emerges as a result of sequence and participatory organization, specifically as a function of sequential misalignment linked to co-participants’ interactional non-availability at a particular moment in time. The authors demonstrate that participants transitioned into extended displays of self-directed talk as a face-saving strategy in response to non-recipiency. These findings illuminate the intra- and interpersonal functions of self-directed talk by learners in the language classroom. Self-directed talk feeds directly back into the architecture of the unfolding interaction.

Hall and Smotrova (2013) look at how self-talk acts as an interactional resource to maintain shared focus on the institutional task during moments in which a teacher is struggling with non-verbal pedagogical resources like computers and transparencies. The analysis also unpacks how, in moments when students could “check out,” teachers’ self-directed talk not only maintains students’ attention but also engages students in the process of solving the problems they encounter. Hall and Smotrova (2013) propose that by explicitly stating their trouble in the form of self-talk teachers invite students to participate in the resolution of the trouble and that the students’ collaborative responses empathetically aid in moving the action of the classroom forward.

In the final excerpt Hall and Smotrova (2013: 88) present, there is an okay in a stretch of self-talk, and like research on okay Hall and Smotrova (2013) show that gaze and non-verbal resources are integral features of self-directed talk. Similarly to Rendle-Short's (2000) computer science lecturers, Hall and Smotrova's (2013) participants are working with prepared non-verbal resources. We argue that all contexts have affordances and constraints that affect the unfolding of talk. While self-talk in some instances may manage moments of struggle, other instances of self-talk arise during sequences in which teachers use multiple non-verbal resources such as lecture notes, clocks, and the chalkboard to monitor and produce the emergent lecture.

From a sociocultural perspective, private speech is a vehicle through which language is internalized and its self-regulatory powers are harnessed (Azmitia, 1992, Feigenbaum, 1992, Lantolf and Yanáñez, 2003, Ohta, 2001). John-Steiner (1992: 288) reflects upon the self-regulatory powers of language during public lectures given by seasoned academics in various fields. “[E]mbedded private speech, occur[s] […] at times when the speaker needs to reorganize his/her approach, either because of a time limit or shift in lecture focus” and can consist of multiple utterances and involves the speaker breaking eye contact with the audience, speaking at a low volume, and perhaps referring to notes. John-Steiner (1992) argues that private speech allows speakers to adjust their course of action and to cue the audience that they are doing so.

In addition, private speech in lectures can serve explicitly stated self-regulatory utterances such as “I better write that down.” John-Steiner (1992: 288) states, “uses of private speech play a central role in thinking” and that sequences of private speech occur in her data 2 to 3 times per hour. Private speech research acknowledges that speech uttered in the presence of others must have social implications (Azmitia, 1992, Ramirez, 1992). Nonetheless, it appears that little attention has been paid to the social context of interactions involving self-directed talk. It is the method employed that causes the neglect of the socio-historically situated context of interaction.

Broadly speaking, two veins investigating what this article calls self-directed talk emerge in the research. One focuses on the intra-personal functions of private speech, primarily self-regulation and language acquisition, in the processes of L1 and L2 development. The other has unpacked inter-personal dimensions and sequential contingencies of self-talk amongst language learners and university instructors. Recent research drawing on both CA and sociocultural theory has complemented the developmental and sociological approach to private speech and self-talk by demonstrating how self-directed talk is a key component in the co-construction of classroom interaction.

We contribute to the research on self-directed talk in three ways. First, we further the understanding of self-directed talk not as an intra-personal or inter-personal resource but as a concurrently intra- and inter-personal resource that teachers use in a self-regulatory and pedagogical manners. In addition, we link the practice of self-directed talk directly to linguistic, i.e., okay, and non-linguistic, i.e., gaze, gesture, and the chalkboard, resources. Finally, we show how self-directed talk can act as a pedagogical resource in the context of the university Mathematics lecture. Our methodology is informed by recent scholarship that draws on socio-historical approaches to development and language and employ CA analytic methods to better understand second language learning and teaching (Kasper, 2001, Waring, 2016).

Section snippets

Data

This study focuses on the use of okay by three graduate students teaching a 200-level calculus course on vector analysis at a large U.S. research university. The context of the math lecture was chosen for investigation for three reasons:

  • 1.

    The recent focus on teaching and learning in STEM by private and public agencies as well as universities;

  • 2.

    The unique context of the math lecture in contrast to other instructional environments at the university in which okay has been studied;

  • 3.

    Incidental noticing

Conclusion and implications

DMs and self-directed talk are phonetically minimal yet inter-personally and intra-personally robust resources for Mathematics TAs. As Hall and Smotrova (2013: 88) point out, teaching is intricate, involved, and “institutional” (Goffman, 1981: 155), and teachers must possess “the capacity of a dexterous speaker to jump back and forth” (Goffman, 1981: 156) so that they can “routinely sustain more than one state of talk simultaneously” (Goffman, 1981: 155). Delivering a Mathematics lecture

Acknowledgements

An earlier version of this paper was presented at AAAL 2015 in Toronto. We would like to thank our esteemed colleagues Joan Kelly Hall, Lucy Pickering, and the attendees of the Penn State CA Research Group and the Applied Linguistics Roundtable for the insightful comments and discussions on self-talk, private speech, and discourse markers during data sessions and presentations held from 2014-2015. We are also endebted to three anonymous reviewers and the journal editor for their time and

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