1.Introduction
Over the past 25 years or so, theories of genre and situated
learning have allowed researchers to develop some understanding of how novices
become experts through immersion in professional and disciplinary contexts (e.g., Artemeva and Fox 2014; Lave and Wenger 1991; Rogoff 1990). The majority of such genre studies have
predominantly focused on rhetorical and linguistic instantiations of the underlying
regularities in genres (e.g., Artemeva and Freedman 2006; Freedman and Medway 1994; Swales 1990). More recently,
however, scholars from different fields have acknowledged that humans draw on a
variety of meaning-making means that “almost always appear together: image
with writing, speech with gesture, math symbolism with writing and so forth” (Jewitt, Bezemer, and O’Halloran 2016, 2; emphasis in the
original). In other words, genre needs to be understood as a multimodal phenomenon
and studied as such. This understanding, coupled with the view of “genre as social
practice” (Tardy 2012, 167), has allowed genre researchers not only to see
their objects of study as multimodal (e.g., Crawford Camiciottoli and
Fortanet-Gómez 2015; Engberg and Maier 2015; Mondada and Svinhufvud 2016) but also to draw on “multimodality
as a tool for…research” (Maiorani and Christie 2014, 2).
Further, as the title of this volume suggests, a study of
genre is a study of engagement. While our overall program of research aims to
develop a better understanding of how experts use and how novices acquire genres of
disciplines and professions (e.g., Artemeva 2008; Artemeva and Fox 2010, 2011; Fogarty-Bourget
2013), we are particularly interested in the unpacking of multimodal
strategies used by experts to engage novices, including students, in genres (e.g.,
Artemeva 2008; Fox and Artemeva 2012). In
this chapter, we report on one such investigation of engagement strategies, a
combination of gestures, writing, and speech, used by university mathematics
instructors while performing a professional genre.
2.Chalk talk: A multimodal professional genre of mathematics
In our large-scale study of mathematics teaching in
university (e.g., Artemeva and Fox 2011; Fox and Artemeva
2012), we have observed that a significant number of those who have advanced
degrees in mathematics choose academic careers and are employed by colleges and
universities (cf. American Mathematical Society 2016, para. 7).
When interviewed about their profession, these mathematicians say that their
professional work includes both research and teaching (cf. Mann and Good 2012).
The authors of several recent publications have noted that
some research (e.g., Barany 2010) and teaching (e.g., Fox and Artemeva 2012; Viirman 2013) practices in
the field of mathematics are much more similar to each other than such practices in
many other fields (e.g., architecture, economics, social work; cf. Dias et al. 1999). For example, Barany and
MacKenzie (2014) have demonstrated that writing on the chalkboard,
accompanied by the articulation of what is being written with subsequent
metacommentary about what has been written, is characteristic of
mathematicians’ research practice, while Artemeva and Fox
(2011) identified this practice as typical of teaching university
mathematics across geographical, national, and linguistic contexts. This typified
and recurrent professional practice, or genre (Miller 1984, 2015; Tardy 2012), used in both mathematics
research and tertiary teaching, has been referred to as chalk talk
1 (e.g., Fox and Artemeva
2012; Viirman 2013). As several
studies indicate (e.g., Artemeva and Fox 2011; Greiffenhagen
2008), chalk talk is used with a purpose to involve novices and/or peers in
the process of “doing mathematics” (Greiffenhagen 2008, para. 35)
in real time.
We have identified chalk talk as a multimodal (cf. Jewitt, Bezemer, and O’Halloran 2016) genre that unites the
writing on the board, articulating what is being written, moving, gesturing, and so
on (for details, see Fox and Artemeva 2012). Such genres are best
characterized by Kendon (2004, 1), who observes that “humans,
when in co-presence, continuously inform one another about their intentions,
interests, feelings, and ideas by means of visible bodily action” and
“configurations” of actions that “are used in conjunction with [other] expressions”
such as “complements, supplements, substitutes or as alternatives” (emphasis added).
Following Kendon, we treat chalk talk as an embodied genre (cf. Haas and Witte 2001).
2.1Engagement in the multimodal genre of chalk talk
Our chapter draws on Hyland’s (2001; 2005) view of engagement in written genres and extends
it to a study of engagement in the multimodal embodied genre of chalk talk.
Hyland (2001, 555) argues that successful academic writers use
a variety of discipline-specific linguistic “devices” to engage their readers, and
notes that “meanings are ultimately produced in the interaction…in specific social
circumstances” (Hyland 2005, 175). This understanding
underlies our study of the meanings produced by university mathematics instructors
in order to engage students in the genre of the chalk talk lecture.
We echo Geertz (1980, 103) by
combining an investigation of “particular symbolic forms” (that is, writing,
movement, gaze, gestures, speech, etc.) and their contextualization within the genre
of chalk talk “in such a way as to bring parts and the whole simultaneously into
view”. Our previous research has indicated that chalk talk is “interactive,
meaningful, and engaging as a way into disciplinary doing and being” (Fox and Artemeva 2012, 87; emphasis added). Some researchers
(e.g., Barany and MacKenzie 2014; Fox and Artemeva
2012; Viirman 2013) have already discussed a few
integral parts of chalk talk, used in mathematics research and classroom contexts,
such as mathematicians’ writing on the board, their posture, movement, and so on.
However, as Crawford Camiciottoli and Fortanet-Gómez (2015, 4) note, in
lectures, “all modes may be indispensable in order to understand
communication” (emphasis added). Indeed, research provides evidence that “much of
mathematics learning…cannot be other than sensuous and embodied” and “that any
dichotomisation of the ‘mental’ and the ‘embodied’ is generally and in principle
false” (Williams 2009, 202). Such embodied creation and “interpretation
of meaning” (Salvato 2015, 1) are often conveyed through gestures in
the performance of the multimodal genre of chalk talk, and yet, as Weinberg, Fukawa-Connelly, and Weisner (2015)
have noted, research focusing on the meanings that mathematics instructors create
through gestures has been limited. Our study responds to Weinberg, Fukawa-Connelly,
and Weisner’s call for more research of such nature by focusing specifically on
gestures used by university mathematics instructors with the intention to engage
students in doing mathematics in real time.
2.2Gestural silence as an engagement device
In our study of university mathematics instructors teaching
in the lecture classroom, we have noticed that at some prominent points in the
performance of the chalk talk genre, the instructors would stop gesturing. The
chapter zeros in on this phenomenon. By drawing on Huckin’s observation that “often
what is not said or written can be as important, if not more so, than what
is” (2002, 348; emphasis added), we have concluded that the
communicative functions and, hence, the meanings created by the absence of
gestures, or instances of non-gesturing (also known as gestural rest
positions), and the speech, writing, and other communicative modes
corresponding to them, call for a focused investigation.
The use of silence, or not saying, in interaction has
been acknowledged as meaningful in a variety of discursive contexts (e.g., Huckin 2002; Rowe 1986). For example, Jaworski and Sachdev (1998, 286) noted that secondary school
students perceived teachers’ silence “as a facilitative device enabling students to
gain access, organise and absorb new material”, while Rowe (1986)
reported that teachers’ longer pauses (increased wait-time) after asking questions
and after student responses had led to dramatic increases in the length and
frequency of students’ contributions. Acheson (2008, 542) took a
step further toward the multimodal understanding of silence and accompanying
stillness as “more than background for discursive language and behavior,”
concluding instead that they were rhetorical, communicative events. Yet only a
handful of researchers (e.g., Cibulka 2015; Dosso and Whishaw
2012; Sacks and Schegloff 2002; Svinhufvud 2018) have investigated gestural stillness, or rest
positions, when the hands do not move.
In this chapter, we focus on gestural stillness and the
meanings it creates when used by university mathematics instructors in the genre of
the chalk talk lecture. The research question that we pose is, how do university
mathematics instructors, performing the genre of the chalk talk lecture, use
gestural rest positions to engage students in doing mathematics?
3.Conceptual framework
We have drawn on Rhetorical Genre Studies (RGS) in our
investigation of the multimodal typification (Schutz and
Luckmann 1973) in the chalk talk genre (e.g., Artemeva and Fox
2011; Fox and Artemeva 2012). RGS has developed out
of Miller’s (1984) view of genre as a typified response to a
recurrent social situation and as social action, motivated by a need and related to
a context. Moving away from a more traditional definition of genre as a stable
combination of textual patterns, RGS sees genre as “a broad rhetorical strategy
enacted” within a community (Smart 1993, 124). In other words, RGS
interprets recurrent, somewhat stable utterances (Bakhtin 1986),
or genres, as reflections of deep underlying social regularities and the choices
that rhetors make when they use, take up (Bawarshi 2015; Freadman 1994), or “challenge and change these genres” (Freedman 1999, 765). The term rhetoric in the name of
this approach refers to “the use of language to accomplish something” (Swales 1990, 6). We have expanded the notion of rhetoric to
include “conceptual actions as well as physical actions” (Cobb
2000, 30), and combined RGS with the elements of speech act and gesture theories
to unpack the communicative functions of the multimodal engagement strategies used
by university mathematics instructors in chalk talk lectures (e.g., Fogarty-Bourget 2013).
In his discussion of speech act theory, Austin (1975) differentiates between locutionary and
illocutionary acts. In locutionary acts, the locutionary force of an utterance
represents its literal meaning, and in illocutionary acts, the illocutionary force
represents the communicative meaning of the utterance (i.e., the effect the
utterance is intended to have on the listener/s). Among others, examples of speech
acts include directives such as commands, requests, and invitations, and
expressives, such as apologies, greetings, and thanks. In his study of
the deliberate omission of information relevant to a particular topic in a
particular context, or textual silence, Huckin identified speech-act
silences, or “active, communicative silences” (2002, 348),
which are used to fulfill communicative purposes through illocutionary force, as
follows: (1) the speaker or writer intends the silence to be perceived as having
communicative import, (2) the listener or reader can arrive at this understanding
only via shared expectations, that is, only by invoking the same frame of reference
as the speaker/writer, and (3) the illocutionary force of the silence can be worked
out by the reader or listener using principles of linguistic pragmatics (Huckin 2002, 349).
Speech act theory is vast and complex. In this chapter, we
draw only on its selected elements that allow us to account for the spoken content
of the instructors’ utterances as well as the pragmatic and contextual elements of
utterances such as, for example, gestural and prosodic cues. Integrating RGS with
selected elements of speech act theory allows for a broad analysis of verbalized
features while providing an accurate understanding of the actions performed by the
speaker.
In addition to selected elements of speech act theory, our
study draws on the work of Bavelas, Coates, and Johnson (2002) who
describe how listeners insert their responses into speakers’ narratives by using
speech, gesture, and gaze. For example, non-specific listener responses, such as
“yeah” and “mhm”, often accompanied by nodding, are used to convey attentiveness and
understanding without being designed to address what the listener is saying at the
moment (Bavelas et al. 2002, 568). Specific listener responses,
however, are tightly connected to the precise moment in the speaker’s narrative by
supplying relevant utterances and facial expressions. A listener who provides such a
response goes beyond conveying understanding and contributes to the narrative by
“briefly but frequently becom[ing] a co-narrator” (Bavelas et al.
2002, 569). Further, bodily resources such as gesture, gaze, and movement
add to the speaker’s illocutionary force as well as to the listener’s contributions
to a dialogue which is produced through collaborative action.
To further investigate and understand the role of gestures
in the multimodal genre of chalk talk we have complemented our theoretical framework
with gesture studies. We use Kendon’s definition of utterance as “any unit of
activity that is treated by those co-present as a communicative ‘move’, ‘turn’ or
‘contribution’. … Such unit of activity may be constructed from speech or from
visible bodily action or from combinations of these two modalities” (Kendon 2004, 7). Kendon’s view of a speaker’s utterance, which
is always produced “to achieve something” (Kendon
2004, 225; emphasis in the original), is strikingly similar to the view of
stabilized utterance (Bakhtin 1986) as social action (Miller 1984; 2015), which is foundational
to RGS. Therefore, Kendon’s gesture theory can be seen as compatible with and
complementary to RGS. Further, his research has demonstrated how gestures can be
integrated into utterances in the process of meaning making to add to their (a)
propositional meaning and (b) function to do things (Kendon
2004, 225). When speakers employ the modes of gesture and speech together, they
achieve an “ensemble of meaning” through the attainment of “semantic coherence”
between the modes of gesture and speech (Kendon 2004, 108). As gesture
and speech interact, a more complex coherent unit of meaning is created.
3.1Research on gestures
As noted by Kendon (2004, 15),
gesture is used to describe “actions that have the features of manifest
deliberate expressiveness”. The production of a gesture involves a body part (in our
case, a hand or two hands) moving through a series of phases which, from the
beginning to end, constitute a gesture unit, or movement excursion (Kendon 2004, 11–12) (see also McNeill 1992). Kendon (2004) further
observes that the gesture unit begins when the hand departs from the rest
position, also known as the “home position” (Sacks and
Schegloff 2002, 137), into a stroke. The stroke is the movement of
the gesture that “peak[s]” (McNeill 1992, 83) or is “accented” (Kendon 1975, 357), where it is sometimes held for a moment (a
post-stroke hold), before returning to the rest position
(recovery/retraction). The rest position is not included in the gesture
unit, nor is it described as carrying meaning; rather, the meaning of a gesture is
thought to be expressed by the stroke phase and any accompanying post-stroke hold
(Kendon 2004, 112).
Until recently, rest positions have been largely excluded
from gesture studies. Only in the past few years have gesture researchers (e.g., Andrén 2012; Bressem and Ladewig 2011; Cibulka 2015; Ladewig and Bressem 2013)
begun to shift their attention from the stroke itself to other phases of
gesticulation, namely, holds and retractions, in an effort to learn more about their
communicative properties and roles in face-to-face interaction. Despite the growing
number of studies focusing on the individual gesture phases, relatively little
attention has been paid to those phases which are not accompanied by movement. For
example, in a study of a natural conversation in Japanese, Cibulka
(2015, 5) has investigated the “intermediate positions of non-gesturing” that
occur following the stroke but before full retraction (Cibulka uses the term “home”
to refer to a rest position). He defines the spatial location where the hands
produce gestures as the gesture “stage” which “denotes the actual location where the
stroke is performed” (Cibulka 2015, 5) and describes two phases of
non-movement that occur in midair – provisional home positions and prolonged hold
phases that stretch over speaker turns. Speakers appear to use the provisional home
position to create a “momentary suspension of their pursued line of action and
produce a ‘just-for-now’ stance” (Cibulka 2015, 20). Further,
Cibulka (2015, 19) states that “speakers of an initiating
action can deploy prolonged hold phases in order to keep the action open and to urge
for a responsive action from the recipient” and suggests that these intermediate
positions exist along a continuum ranging from “stage” to “home” (rest), thus
allowing speakers to weaken or strengthen their claim of speakership: the closer the
suspension occurs to the stage area, the stronger the claim over speakership; the
closer the suspension occurs to home, the weaker the claim over speakership. This
observation implies that hands occupying a rest position convey a surrendering or
yielding of speakership. Cibulka, however, does not focus on rest positions per
se.
In one of the few studies that do focus on rest positions,
Sacks and Schegloff (2002, 138) observe that generally,
gesturing hands return to the same rest position from which they depart. The
researchers refer to a “moving home position”, which occurs when the hand (or hands)
performs small, often repetitive movements (or moves digits), either
with or without an object, further referred to as fidget, and returns to
fidgeting after each gestural excursion. In these cases, although the hand is in
motion, it is nonetheless occupying a rest position (i.e., it is not involved in
gesturing). Some researchers characterize rest positions as lacking in movement and
hand tenseness (Bressem and Ladewig 2011; Ladewig and Bressem 2013), while others describe certain rest
positions in which hand tenseness is present (e.g., Dosso and Whishaw
2012; Sacks and Schegloff 2002).
Few studies mention that rest positions have a capacity to
convey communicative meaning. Those studies that do, tend to highlight rest
positions as the indicators of the property of non-speakership (not being in the
role of speaker) or speech conclusion. For example, Dosso and Whishaw
(2012) suggest that rest positions can be indicative of what a speaker may
do next, such as intent to continue or discontinue speakership. Andrén’s (2012, 160) research also indicates that body movement
combined with the semantics and timing of speech often makes action completion
“intersubjectively manifest”. Although Andrén focuses on bodily actions that involve
the handling of physical objects and not on rest positions, his study suggests that
rest positions can be used in an expressive and meaningful way, a phenomenon that
requires further research. Just as a speaking subject can exercise
speech-act silence while continuing to gesture, a gesturing
subject can exercise gestural silence (Fogarty-Bourget 2016; 2017) through stillness or non-gesturing, while continuing to
produce speech, facial expressions, and other movements.
4.Methods
This multiple methods qualitative study (cf. Tashakkori and Teddlie 2010) focuses on gestural silences used
by university mathematics instructors to engage students in doing mathematics. The
study was approved by a university ethics review board and informed consent was
obtained from all the participants. The corpus of video recordings that served as a
source for this study had been originally developed as part of a large-scale study
of teaching mathematics to university students in international contexts and
included video recordings of chalk talk lectures taught in eight different languages
in 11 countries (e.g., Artemeva and Fox 2011). In order to control
for the language of instruction, we selected a sub-corpus of video recordings of
chalk talk performances by mathematics instructors teaching in English in North
American universities. The sub-corpus included seven lectures taught by six
different instructors, amounting to a total of 392 minutes of video footage.
The data were analyzed using fine-grained qualitative
multimodal thematic analysis (QMTA) (Fogarty-Bourget 2013) which
has its roots in qualitative thematic analysis (Saldaña 2009), constructivist
grounded theory (Charmaz 2006), and multimodal interaction
analysis (Norris 2004). Similarly to constructivist grounded theory, QMTA
involves phases of continual coding and categorization that can be carried out
concurrently until saturation (Glaser and Strauss 1967) is
achieved, where saturation is the point at which “gathering fresh data no longer
sparks new theoretical insights” (Charmaz 2006, 113). Unlike
constructivist grounded theory, QMTA can be used deductively under existing
theoretical frameworks as well as inductively to generate theory.
The analysis was carried out as follows: (1) Data were
uploaded into NVivo 10 (QSR International 2012), a computer research
application that organizes and facilitates the analysis of multimodal data (cf. Fogarty-Bourget 2013; Gasiewski et al. 2012). The
parts of the video recordings with the instructors holding their hands still (not
gesturing) were demarcated and transcribed. (2) Descriptive coding was applied to
lower-level actions, defined as the smallest complete actions that carry meaning (Norris 2004, 11) such as a laugh, pause, or eye-movement, and
then higher-level actions, defined as communicative actions made up of a multitude
of lower-level actions such as whole speech-acts. (3) Descriptive codes were grouped
together (when appropriate) into categories, and (4) categories were then grouped
together into overarching themes (cf. Charmaz 2006). The coding
process was continued until saturation was achieved. The application and grouping of
descriptive codes formed the basis of a coding tree. The developed coding tree was
applied by two researchers independently to selected video excerpts. Outcomes were
reached by consensus.
5.Findings: Communicative functions of gestural silences
The analysis revealed typified and recurrent patterns of the
instructors’ use of gestural silences and co-occurring speech acts (cf. Austin 1975; Bavelas et al. 2002),
speech-act silences (Huckin 2002), and body configurations, which
may work together with other verbal and nonverbal behaviours to construct meaning
(e.g., Andrén 2012; Cibulka 2015). The
identification and description of these patterns of activity allowed us to develop a
better understanding of the roles gestural silences play as an engagement strategy
in the genre of chalk talk.
Our findings suggest that mathematics instructors use some
ensembles (Kendon 2004) of gestural silence as “devices” (Hyland 2001) to engage students in doing mathematics; for
example, some devices are used to demonstrate instructors’ attentive listening as an
invitation to students to provide a response to a question (cf. Jaworski and Sachdev 1998; Rowe
1986).
Figure 1.Participants using gestural silence in the wrist-grip
position to make evident the action of attentive listening 1A. Instructor posing
a question to the students 1B. Instructor issuing a question followed by a
command. Both instructors maintain the position while waiting for, and listening
to, student responses. Text enclosed in square brackets identifies speech acts
or silences; text enclosed in short dashes following square brackets identifies
speech-act silences; text enclosed in asterisks indicates an embodied action;
italicized text in quotation marks indicates direct speech; italicized text
enclosed in round brackets indicates that the speaker is gesturing during the
articulation
| 1A | 1B |
|
|
|
[interrogative] “What’s the first
step when I have an actual value?”
[silence] -waiting for student
response-
[silence] -listening to student
response-
[non-specific listener response]
*nodding* “Yeah”
|
[interrogative] (“So, how are you
gonna prove this?”)
[silence] -waiting for student
response-
[imperative] “Tell me in one
sentence why it’s true”
[silence] -pause- [hint] “You can
use two, if you need to, but if you can (do it in
one)”
[silence] –waiting for student
response-
[explanation] (“I keep telling
you folks, don’t try to find a proof. Understand why
it’s true and then write down that
understanding”)
[non-specific listener response]
(“Yeah”)
[silence] -listening to student
response-
|
An example of how instructors use gestural silence to make
evident their action of attentive listening is provided in Figure 1. Figure 1A depicts a mathematics instructor who, after having written a line
of text on the board, has turned to the students and, gripping her right wrist with
the left hand, has brought both hands to rest in front of her in a wrist-grip
position as she poses a question to the students. She holds her hands this way as
she scans the classroom, awaiting responses. After a few moments, a student
responds, and the instructor maintains her position as she listens to the response.
When it becomes evident that the response is correct, the instructor begins to
nod her head in agreement with the student but does not move her hands until the
student has fully articulated the response.
Our analysis of the video data suggests that the mathematics
instructors considered in this study take up the wrist-grip position when attempting
to engage students in a discussion of what has been written on the chalkboard. The
position is often paired with a question or command, or used when pausing the
commentary to ensure that the students have understood the content
(checking). The instructors typically maintain the wrist-grip position while
waiting for students to respond and listening to the students’ responses, and use
the position, in coordination with such speech acts as directives and interrogatives
and/or speech-act silences, to create gestural silences whose function is to
indicate the change of their role from instructors doing mathematics and
providing explanations to instructors as listeners. This change appears to
signal to students that the instructor expects a response and invites them to
participate by demonstrating that the instructor is prepared to listen. For example,
the instructor in Figure 1A uses the wrist-grip position to communicate to the students her
role as attentive listener by coordinating the position with an interrogative,
maintaining the position silently while both waiting for and listening to the
response, and pairing the position with head nodding. As mentioned above,
non-specific listener responses, including head nodding, are used to convey
attentiveness (cf. Bavelas et al. 2002). Figure 1B provides another example of an instructor using the wrist-grip
position in much the same way as the instructor in Figure 1A: the instructor asks a question, assumes the wrist-grip position,
and silently waits for students to respond. When no students come forward, he issues
a command to the students (“tell me in one sentence why it’s true”) while
maintaining the wrist-grip position. When there is no response from the students, he
provides some further explanation (a “hint”) and then resumes the position. Once a
student does respond, the instructor maintains the position while listening to the
response.
Figure 2.Participants using gestural silence in the fist held
high position to engage students in what has been written on the
chalkboard 2A. Instructor prompting students to complete the statement he
has written on the chalkboard 2B and 2C. Instructor has finished
writing on the chalkboard and retracted the hand used for writing into the rest
position while turning to face the students. Text enclosed in square brackets
identifies speech acts or silences; text enclosed in short dashes following
square brackets identifies speech-act silences; text enclosed in asterisks
indicates an embodied action; italicized text in quotation marks indicates
direct speech; italicized text enclosed in round brackets indicates that the
speaker is gesturing during the articulation
| 2A | 2B | 2C |
|
|
|
|
(*points at student with open
hand*) *returns to rest position*
[silence] -listening to student
response-
[clarification]
“Sorry?”
[silence] -listening to student
response-
|
*turns from chalkboard to face
students* *scans classroom*
[silence] -waiting for student
response/checking-
|
[clarification]
(“So this is what
you”)
*turns from chalkboard to students*
“should memorize”
*scans classroom*
[silence] -listening to student
question-
|
Figure 2 presents a position that appears to be shaped by the actions
involved in the embodied performance of chalk talk as a disciplinary genre (cf. Hyland 2005, 177) of doing mathematics; for example, the
instructor’s action of writing on the chalkboard or pointing at students to prompt a
response. The position appears to be used to engage students in doing mathematics by
allowing them to participate in what the instructor has written on the chalkboard,
articulated, and discussed.
Figure 2A presents an instructor prompting students to complete the
statement he has written on the chalkboard. He points at a student with an open
hand, then retracts it, adopting the rest position of a fist held high. His
hand remains resting while he listens to the students’ responses. When it becomes
clear to him that no student has the correct answer, the instructor moves his hand
from the rest position in order to explain the problem further. Figures 2B and 2C depict two other instructors who have finished writing on the
chalkboard and retracted the hand used for writing into the rest position while
turning to face the students. Figure 2B shows the instructor after he has explained mathematical content,
gesturing with an open hand at the chalkboard; when finished explaining, he retracts
his hand into a fist and turns to face the students with his hand still held up. He
maintains the position as he scans the room for questions or comments (checking).
Observing none, he continues with the explanation. In much the same way, the
instructor presented in Figure 2C finishes writing on the board, retracts his hand, and turns to
the students while maintaining the rest position. He provides brief metacommentary
about what he has written on the board, while fidgeting with the chalk in his
fingers (a “moving home position” [Sacks and Schegloff
2002, 139]). He then scans the class (checking) for questions or comments. A
student interjects and the instructor maintains the rest position while listening.
Once the student has concluded, the instructor moves his hand from the rest position
to articulate a response.
Although the type of position illustrated in Figure 2 is very much representative of a home position in the Sacks and Schegloff (2002) sense, it does not seem like
a typical rest position used in everyday situations (cf. McNeill
1992, 376) because of the degree of muscle tension required for the hand
to remain raised upright. The position was observed in all video-recordings
of university instructors in the sub-corpus used in the study, consistently used as
a device to engage students in doing mathematics. This finding speaks to the
typified and recurrent nature of gestures and gestural silences as a feature of the
chalk talk genre.
In other words, our observations suggest that by employing
gestural silences, speakers can make their rest positions highly expressive and use
them to construct specific meanings, including, but not limited to, action
completion and non-speakership (cf. Andrén 2012; Cibulka 2015; Dosso and Whishaw 2012). In
particular, university mathematics instructors seem to use some gestural silences,
such as those discussed in this chapter (see Figures 1 and 2), in chalk talk as recurrent engagement devices that “acknowledge and
connect to” the students, “recognizing… [their] presence…, pulling them along with
their argument, focusing their attention, acknowledging their uncertainties,
including them as discourse participants, and guiding them to
interpretations” (Hyland 2005, 176; emphasis added). In other
words, the instructors appear to combine the described positions with other
multimodal resources such as writing, speech, gaze, and body configurations to
create meaningful ensembles of gestural silence used to engage with the
students who are present in the classroom, acknowledge their feedback, and include
them as participants in the process of doing mathematics.
In terms of meaning construction, these positions closely
resemble the provisional home positions (Cibulka
2015, 19) that span across speaker turns “to keep the action open and to urge
for a responsive action from the recipient”. The instructors use gestural silence to
involve the students in a discussion about what has been written on the chalkboard.
The stillness of instructors’ hands creates a temporal opening, or “window,” for
students to take up turns at talk by raising their hands or interjecting. These
windows close when the instructors break the gestural silence. Figures 2B and 2C suggest that the communicative function of a combination of hand
stillness and body orientation (turning from chalkboard to the students) is used to
acknowledge the students as participants in the discussion of what has been written
on the board by signalling to them that they are free to comment. In other words,
the listeners can work out the illocutionary force of the silence based on the
situational context (cf. Huckin’s [2002] discussion of speech-act
silences).
In terms of execution, these positions also resemble the
provisional home and prolonged hold positions (Cibulka 2015) depending on
the continuing action taken up by the instructors once the gestural silence is
broken, whether they drop the hand, launch into the next gesture, or resume writing.
These observations lend support to Cibulka’s (2015, 7) claim
that phases of non-movement that take place in midair are “difficult at times to
tell apart”. For the purpose of this chapter, however, differentiating between these
positions is not essential; what is important is that these “intermediate
positions of non-gesturing” (Cibulka 2015, 5; emphasis
added), like rest positions, can also be used to create episodes of gestural
silence.
Our analysis suggests that, within the context of chalk
talk, typified and recurrent gestural silences employed by instructors
have a particular situational importance. The performance of chalk talk
requires near continuous movement of instructors’ hands as they write on the board
and provide metacommentary on what they have written. The gestural rest positions
with the hands remaining relatively close to the gesturing stage (cf. Cibulka 2015) or to the chalkboard allow the instructors to
create gestural silences during which they can briefly switch from doing
mathematics to attending to students, while keeping the hands
available for gesturing and writing. Furthermore, because the performance of the
chalk talk genre requires mathematics instructors to be highly active, alternating
between writing on the board and concurrently articulating what is being written,
turning to the students, providing metacommentary about what has been written on the
board, moving, pacing, gesturing, and so on (Artemeva and Fox 2011), the
points in the lecture when the instructor’s hands are held still stand out as
deliberate and expressive communicative actions (cf. Kendon 2004). In other words, the study indicates that through
the stillness of their hands, mathematicians create what Acheson
(2008, 542) calls communicative “events” in which the shift from doing
mathematics to engaging the students in doing mathematics becomes
palpable.
6.Conclusions and implications
As noted above, the overall purpose of our research program
is to develop an understanding of the typified and recurrent multimodal strategies
used by experts to engage novices, including students, in disciplinary and
professional genres. In this chapter, we take up Weinberg,
Fukawa-Connelly, and Weisner’s (2015) call for more studies of the meanings
that university mathematics instructors create through gestures by focusing on how
such instructors use gestural silences (Fogarty-Bourget 2016; 2017) to engage students in doing mathematics.
In order to unpack the meanings constructed by mathematics
instructors when using gestural rest positions, we have developed a combined
conceptual framework that draws on Rhetorical Genre Studies and borrows from speech
act and gesture theories. The conceptual framework has been complemented with Huckin’s (2002) theory of textual silence, which has
been expanded to include gestural silence. In our analysis of the
communicative functions performed by gestural silences, we have drawn on a corpus
of video recordings of university chalk talk lectures delivered in English in North
America. We have observed that the mathematics instructors in the lecture classrooms
considered in this chapter create complex meaningful ensembles of gestural silences
and use them as engagement “devices” (Hyland 2005, 188) in order
to involve students in doing mathematics. These gestural silences have allowed us to
identify two roles played by mathematics instructors during chalk talk: those of (a)
attentive listeners and (b) initiators of a dialogue.
More importantly, we have identified typified and recurrent
ensembles of gestural silence that appear to be shaped by the embodied nature of the
chalk talk genre, for example, writing on the board, turning, gesturing, and
interacting with students. This finding supports Hyland’s
(2005, 177) observation that “devices” used for the purpose of engagement
are shaped by the “disciplinary cultures” in which they come to be used. Indeed, in
this study we have identified typified and recurring rest positions – or gestural
silences – which indicate a change in the mathematics instructor’s role from
performer-doer to listener-verifier-supporter. In this context, gestural silences
appear to act as deliberate and expressive (cf. Kendon 2004)
devices that encourage student engagement when instructors use them to signal that
they are fully attending to and focusing on students as partners (albeit novice
ones) in doing mathematics. Further research could compare genres across disciplines
and identify such devices shaped by other disciplinary cultures.
Our research has important implications for future studies
of professional genre and engagement: if we understand genres as essentially
multimodal, we need to further develop multimodal methodologies that would allow us
to investigate all meaning-making means used in such genres in a variety of
contexts. Specifically, to better understand how novices learn the genres of their
professions, we need to develop research questions that, instead of privileging
linguistic means of meaning making, would “attend to all semiotic resources being
used to make a complete whole” (Jewitt, Bezemer, and O’Halloran
2016, 3).
Notes
1.Originally, the term ‘chalk-and-talk’ appears in Mason (1994). We use the term chalk talk in a
different, disciplinary-specific sense that pertains to the genre of the
university mathematics lecture (Artemeva and Fox
2011; Fox and Artemeva 2012).