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1 What impact does the teacher’s nonverbal communication have on children’s learning and confidence in Maths? Introduction There are many accepted methods by which a teacher can maximise children’s learning and confidence in the classroom including consideration and implementation of effective communication skills, both verbal and nonverbal. Verbal skills such as the use of praise, effective questioning and dialogic teaching are focused on widely in PGCE courses, staff training sessions and general educational literature. However, there is less emphasis on the value of effective nonverbal communication and consideration of how this might affect children’s progress (White & Gardner. 2012: p6). Throughout my time in the classroom I have considered how the teacher’s persona and communication skills can affect the learning environment. As a trainee primary educator, I am developing my own style of teaching and reflecting on the effect that I have, directly and indirectly, on the children’s confidence and progression. The context for my research is a mixed year 5 and 6 class in a small rural school. As I have a personal enjoyment of Mathematics and an interest in children’s mathematical learning, which is also a subject of national debate, my goal in undertaking this research is to maximise my personal effectiveness as a teacher in Mathematics. In addition, I hope that the discussion of the impact of nonverbal communication may be of some interest to colleagues in the teaching profession. Literature Review Human communication is “the process of creating meaning through symbolic interaction” (Adler & Rodman. 2009: p2).”Like words, some nonverbal behaviour can have symbolic meaning” (Adler & Roadman. 2009: p4). Indeed, nonverbal communication is recognised as an important factor in daily human communication (White &Gardner. 2012: p10) as well as an established area of study across a number of disciplines (Adler &Rodman. 2009: p3). This being the case, it seems that research regarding aspects of nonverbal communication in the classroom is underrepresented (White & Gardner. 2012: p10, Woolfolk & Galloway. 2001: p78).

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Page 1: learning and confidence in Maths? - · PDF filelearning and confidence in Maths? ... are adept at reading nonverbal communication and such reading does have an impact on educational

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What impact does the teacher’s nonverbal communication have on children’s

learning and confidence in Maths?

Introduction

There are many accepted methods by which a teacher can maximise children’s

learning and confidence in the classroom including consideration and

implementation of effective communication skills, both verbal and nonverbal. Verbal

skills such as the use of praise, effective questioning and dialogic teaching are

focused on widely in PGCE courses, staff training sessions and general educational

literature. However, there is less emphasis on the value of effective nonverbal

communication and consideration of how this might affect children’s progress (White

& Gardner. 2012: p6).

Throughout my time in the classroom I have considered how the teacher’s persona

and communication skills can affect the learning environment. As a trainee primary

educator, I am developing my own style of teaching and reflecting on the effect that I

have, directly and indirectly, on the children’s confidence and progression. The

context for my research is a mixed year 5 and 6 class in a small rural school. As I

have a personal enjoyment of Mathematics and an interest in children’s

mathematical learning, which is also a subject of national debate, my goal in

undertaking this research is to maximise my personal effectiveness as a teacher in

Mathematics. In addition, I hope that the discussion of the impact of nonverbal

communication may be of some interest to colleagues in the teaching profession.

Literature Review

Human communication is “the process of creating meaning through symbolic

interaction” (Adler & Rodman. 2009: p2).”Like words, some nonverbal behaviour can

have symbolic meaning” (Adler & Roadman. 2009: p4). Indeed, nonverbal

communication is recognised as an important factor in daily human communication

(White &Gardner. 2012: p10) as well as an established area of study across a

number of disciplines (Adler &Rodman. 2009: p3). This being the case, it seems that

research regarding aspects of nonverbal communication in the classroom is

underrepresented (White & Gardner. 2012: p10, Woolfolk & Galloway. 2001: p78).

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This study can be placed in a tradition of research that is concerned with observing

the individual (in this case the teacher) and the nonverbal manifestations of

personality trait or emotional stress that is communicated in a nonverbal manner

(Woolfolk & Galloway. 2001: p78). Adler and Rodman recognise the communicative

value of nonverbal behaviour and its ability to convey emotion, thereby defining

relationships (2009: p135). In the classroom, the nonverbal communication of the

teacher plays a part in defining the relationship between the teacher and the

students. Although Adler and Rodman (2009: p137) state that nonverbal

communication is ambiguous, White and Gardner are of the opinion that “Students

are adept at reading nonverbal communication and such reading does have an

impact on educational achievement” (White & Gardner. 2012: p37).

Previous research in this field has acknowledged the importance of nonverbal

communication in the classroom and it’s potential. However, early ideas regarding

nonverbal communication in this context have focused on the role of nonverbal

communication as a strategy for behaviour management. Researchers such as

Woolfolk and Galloway, writing in 2001, perceived an awareness of nonverbal

communication as “a window through which to view teachers’ and students’

perceptions of classroom events, their attempts to cooperate with or co-opt activities,

their effective reactions to situations and individuals, and the effects of these

reactions on ongoing reactions” (Woolfolk & Galloway. 2001: p83). In summary, to

continue to manage but also understand interactions and relationships within the

classroom (Woolfolk & Galloway. 2001: p83). This research registers the importance

of nonverbal communication in the formation and sustaining of positive relationships

as an end in itself, but does not fully appreciate the potential of nonverbal

communication to facilitate learning at a more fundamental level.

Indeed, it is the link between nonverbal behaviour and confidence and achievement

in the classroom that is pivotal. Gresalfi (2009) argues that the social factors in the

classroom are central to learning, and in particular interactions with others. Although

she sees student dispositions as being regulated and encouraged by classroom

practices, these are unavoidably based on the nature of interactions between

students and teachers, in which nonverbal communication is a factor. As Battey

(2013) states, discourse around best practice teaching in Mathematics is often

focused on teacher knowledge and instructional practices. In response to research

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on the negative treatment of Afro-American students, Battey (2013) claims that

Mathematics instruction alone will not lead to raised attainment in all children, so

defines a “relational interaction as a communicative action between two people that

conveys meaning. Therefore, it could incorporate nonverbal communication, an

extended verbal exchange, or a quick comment to a student. These relational

interactions enable or restrict access to quality Mathematics regardless of the form of

instruction provided.”

Whereas Battey (2013) sees nonverbal communication as part of relational

interactions that mediate access to Mathematics teaching and learning, Seeger

(2009) explores meaning making in Mathematics. Seeger proposes that the teaching

and learning of Mathematics should have an empathic basis where the social and

emotional aspects of learning are fully considered. “As Mathematics educators we

have to acknowledge that everything that is done in the classroom is producing

meaning..(and).. arouses feelings and emotions and that these feelings and

emotions are (an) integral part of the process of meaning and sense-making. They

are not some kind of accessory, sometimes blocking the way of exact logical

reasoning. They are essential and necessary for self-controlled and independent

reasoning and living. Emotional attachment is crucially important for a development

of an explorative habit” (Seeger 2009: p222). As noted, Adler and Rodman (2009:

p135) identified aspects of nonverbal communication as conveying emotion and

defining relationships, but Seeger (2009) has stated that the emotional and relational

element within a classroom are at the very foundation of mathematical learning.

Methodology

All research must be rooted in a value system that makes due consideration of the

ethical issues involved. Therefore, ethical considerations underpin my research

methodology in line with University of Worcester guidelines. Informed consent of

both parents/carers and children was a key consideration. I sent a letter to

parents/carers in which I explained the parameters of the research project and asked

their permission for their child to partake. I made a distinction between the collection

of data and the use of data in the research project, and made it clear that consent

could be withdrawn at any point, although children would still have to partake in the

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lesson. I received 17 positive replies. I also considered the appropriate method and

timescale of data storage, undertook a risk assessment of the process of data

collection, the emotional difficulties that some children may encounter as a response

to negative nonverbal communication, as well as issues of confidentiality and

anonymity.

This research is an experimental study (Bell & Opie 2002: p81) where the purpose is

to test whether pupil’s confidence and progress in learning is affected by the

nonverbal communication of the teacher. Pupil’s learning was assessed through a

mathematical activity, observations of learning behaviours and a questionnaire on

mathematical confidence. Would the teacher’s nonverbal communication affect the

children’s ability to solve mathematical calculations? Would the teacher’s nonverbal

communication observably change the learning behaviours of the children, and

reflect in their levels of mathematical confidence?

For the purposes of this study, the teacher’s nonverbal communication is the

independent variable and the pupil’s learning is the dependent variable (Bell & Opie

2002: p92). It was crucial to limit the number of variables overall in this research, so I

purposely kept the same conditions for each lesson - children, classroom, observer,

lesson structure, very similar lesson content, pitch, pace, expectation etc. In the first

lesson, I taught using positive nonverbal communication, and in the second,

negative. My class mentor observed my nonverbal communication in both lessons

against a checklist of indicators (Appendix 1) so as to be comparing particular, rather

than random, areas of nonverbal communication. She also observed the class as a

whole and made a case-study of two children with reference to their learning

behaviours such as persistence, engagement, ability to work independently and so

on. The indicators of the children’s learning behaviours were purposely left open so

as not to limit the observations taken. Children were asked after each lesson to

complete a questionnaire on their confidence in learning in Mathematics in general

and during this class in particular.

To limit variability and bias, I chose a selection of core nonverbal behaviours across

the accepted range of indicators that could be distinctly manifested in a negative as

well as positive manner (see the Positive and Negative Nonverbal Communication

Observation Sheets in Appendix 1). The indicators had to be clearly observable for

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the purposes of this research, both for the benefit of the adult observer as well as to

establish two distinct learning environments for the children. The negative nonverbal

communication indicators chosen were meant to convey, for example, my boredom,

impatience, dissatisfaction, strictness and dominance. Conversely, the lesson

displaying positive nonverbal communication was intended to demonstrate my

interest, friendliness, helpfulness, enthusiasm, cheerfulness and approachability to

the children. Observation of my nonverbal communication was an important factor in

this research because it establishes the validity of the test, i.e. the learning

environments were indeed significantly different when considering the teacher’s

nonverbal communication.

A second field of study that I drew on for this research was the designing of the

questionnaire. I attempted to ensure that the questions were clustered and there was

progression through the questionnaire in order to focus each question and prevent

“dotting around” (Gillham 2007: p25). Questions moved from fact to opinion in a

logical manner. I opted to use a scaled response format for ease of analysis, and I

included some follow-on questions (if yes/no,...) (Gillham 2007: pp31-34). The

children were asked to complete these independently and in silence in order to stop

‘cross-contamination’ of answers.

Findings and Analysis

I had both quantitative and qualitative data to draw on in this study. In the first lesson

where I displayed negative nonverbal communication, 13 out of 17 children achieved

the correct answer using the grid method of multiplication. In the second lesson

where positive nonverbal communication was stressed, 15 out of 17 children

answered the question correctly. Clearly, more children achieved the correct answer

when the teacher displayed positive nonverbal communication. However, the

positive nonverbal communication lesson was second, so the children had had more

practice in this type of calculation by this stage.

Identical questionnaires were completed by the children after each lesson. I have

attached the questionnaire as Appendix 2 and the results table extrapolated from the

completed questionnaires as Appendix 3. Many of the questions elicited very similar

answers from the children. However, when asked the question ‘Did you enjoy the

Maths lesson that you’ve just had?’, 10 children replied ‘yes’ after the negative

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nonverbal communication lesson but 15 replied yes after the positive. When asked

‘Did you stay focused on the lesson?’ 12 children stated that they had in the negative

lesson, and 16 in the positive. When asked ‘Did your teacher explain the method in a

way that you understood?’ 6 children replied ‘yes’ and 7 ‘no’ in the negative lesson,

whilst 14 replied ‘yes’ and 3 replied no’ in the positive. More children were unsure as

to whether their teacher liked the grid method of multiplication in the negative

nonverbal communication lesson. Lastly, when asked ‘Was Mrs. Small friendly and

helpful to the class in this lesson?’, in the negative nonverbal communication lesson,

7 children replied ‘yes, 6 ‘no’, and 4 ‘not sure’. In the second, more positive lesson,

16 thought that I had been helpful and friendly, no children thought that I hadn’t

whilst 1 child was unsure.

Both sets of the above data were limited in the information that they produced. The

children’s mathematical attainment was only marginally better in the positive

nonverbal communication lesson, whilst many of the questionnaire answers from

both lessons were very similar. However, the children clearly picked up on the

nonverbal communication messages in my behaviour in terms of my friendliness and

helpfulness, as well as the effectiveness of my explanation of the Mathematics

involved in the lesson. They self-assessed their enjoyment and focus as being higher

across the group when the teacher was more positive nonverbally. As an initial

finding, the attainment levels of the class were only marginally affected, but the

relationship between teacher and students was more markedly affected. As children

thought I did not explain the Mathematics so clearly, perhaps we could propose that

access to the curriculum was limited by negative nonverbal communication on the

part of the teacher.

Qualitative data was collected by the class teacher observing learning behaviours

across the whole class and making case studies of Child A and Child B. This data is

more illuminating and backs up the tentative findings from the questionnaire

answers. Child 2 tried to engage with the teacher in the first lesson but responded to

the nonverbal negatives by giving up and not trying to ask a question or seek

reassurance again. Instead, she looked to her partner for reassurance, although she

remained engaged in the task. A poor teacher-student communicative relationship

potentially slowed her progression. Child 1, however, showed a marked difference in

levels of engagement. In the negative lesson, he was leaning back in his chair, arms

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folded, avoiding eye contact and whispering to his neighbour. He was not engaged,

and the observer thought that this was because he was worried. In the second, more

positive lesson, he was engaged and conversational, sat up and watching the board.

He put his hand up to check the answer with the teacher and did not turn to his

neighbour for support. He worked consistently, being more motivated.

Across the class, the observer noted that in the positive nonverbal communication

lesson, all children were engaged. They displayed confidence in their learning and

collected resources to be ready for the lesson. In the negative lesson, however,

many children looked anxious and turned to each other for reassurance rather than

the teacher. Only two children put their hand up regularly, and another gave up

trying. Some children were keen to show me their maths strategies, and the observer

thought that some children were trying to win me over! Many displayed closed body

language, and there was lots of muttering. They appeared disconcerted by my

behaviour. One child got up. However, the observer observed that there was a

length of uninterrupted effort with all children focused.

It is not as simple as to say that engagement was higher and the disruption lower

when the teacher was more positive. In the negative lesson, children appeared to be

more independent learners, and were given an uninterrupted opportunity to have a

go. The observer thought that overall the focus was good in this lesson, even though

there was muttering between some children. This behaviour is an example of low

level disruption, and one child got out of their seat. However, in the positive lesson

where more children were putting their hand up and were conversational with me,

perhaps they did not show enough learning resilience. Although when we consider

the two children who were case studied, Child 2 showed motivation to continue with

the task, although she gave up trying to talk to the teacher. This means that an

opportunity to scaffold or extend her learning was missed. Child 1 did not stay on

task, and so the teacher-student relationship for him is crucial to his levels of

engagement, and therefore his access of the curriculum.

Discussion

On reflection, there are areas of my methodology that could have been improved for

this research. In particular, the questionnaire was limited. I realised this immediately

after the two lessons when the class, class teacher and I were discussing the

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morning’s experience. The class teacher was asking children questions such as

“What was Mrs. Small doing?”, “How did this make you feel?” and we had an

engaging and interesting discussion around the research. I should have framed the

questions on the questionnaire in this child orientated language, and included more

open questions. Although this would have been harder to analyse comparatively,

overall I think that I may have had more variety in the answers. As Sudman and

Bradburn (1983: p17) state, “One of the criteria for the quality of a question is the

degree to which it elicits the information that the researcher desires. This criterion is

called validity.” My questionnaire did not have enough validity.

This has led me to consider how I might have collected data in an entirely different

manner. For example, visually recording and then analysing the nonverbal

communication in the classroom. This would have been an opportunity to focus more

closely on the “exchange of behaviours” (Woolfolk and Galloway. 2001:p77) rather

than the nonverbal variables of an individual. “Studies of individuals tend to see

influence as flowing in one direction, usually from teacher to student, while studies of

interactions often recognise that pedagogical influence is reciprocal” (Woolfolk &

Galloway. 2001: p78).

The children responded in an observable manner to my nonverbal communication,

thereby showing that nonverbal communication has meaning and is part of regular

human communication (White and Gardner page 10). The teacher-student

relationship was affected. This could be seen across different pedagogical areas. For

example, behaviour in the classroom was affected, as was engagement and focus

on the task. Some children became disengaged immediately that the teacher-student

relationship was negatively compromised, whilst others showed resilience to keep on

trying. For these children, I think that progression might be the issue if they were

exposed to a more ’distant’ teaching style because the opportunity to extend their

learning might be lost. Certainly, we have seen that nonverbal communication does

indeed play a part in defining the relationship between the student and teacher.

This research was too limited in scope to fully answer the question of whether the

teacher’s nonverbal communication affects children’s confidence and achievement in

Mathematics. This research has shown that communication does affect the

classroom learning environment, and we could propose that deep changes could be

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made in the children’s learning if the communication skills of the teacher were

compromised. In line with Battey’s argument (2013), nonverbal communication

conveys meaning in communicative interactions and therefore can mediate access

to quality Mathematics teaching and learning. This limited experimental research did

show that both Child 1 and Child 2 were compromised in their access to

Mathematics teaching, albeit in different ways, due to the ‘relational interaction’

between me as the teacher and them as the students. I agree with Seeger (2011)

that everything in the classroom produces meaning, and I believe that emotional

security allows a safe learning environment in which to take intellectual risk and

embark on a meaningful and personalised learning journey. This emotional security

in a classroom is created largely through the teacher’s teaching persona which

includes nonverbal communication along with other factors.

Conclusion

Although being a limited and somewhat inconclusive research project, this study has

extremely formative for me as a teacher. It has forced me to consider the emotional

basis of learning, and the interaction between social relationships and effective

teaching and learning. Perhaps effective learning cannot take place without

meaningful and positive communication at the heart of the classroom.

When I was teaching using negative nonverbal communication, I could see the

children’s confusion and anxiety on their faces, and I did not feel satisfied that I was

reaching my potential as a teacher. I realise that my development as a teacher is

also dependent on the relationship I can form with the students. In that sense,

positive communication, including nonverbal aspects of communication, affects the

confidence and progression of both students and teachers.

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Reference list

Adler, R.B. & Rodman, G. (2009) Understanding human communication.10th edition.

New York, Oxford University Press.

Battey, D. (2013) “Good” Mathematics Teaching for Students of Colour and Those in

Poverty: The Importance of Relational Interactions within Instruction. Educational

Studies in Mathematics. [Online] 82(1), 125-144. Available from:

http://mt6qm6wx6p.search.serialssolutions.com/?ctx_ver=Z39.88-

2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-

8&rfr_id=info:sid/summon.serialssolutions.com&rft_val_fmt=info:ofi/fmt:kev:mtx:journ

al&rft.genre=article&rft.atitle=%E2%80%9CGood%E2%80%9D+mathematics+teachi

ng+for+students+of+color+and+those+in+poverty%3A+the+importance+of+relational

+interactions+within+instruction&rft.jtitle=Educational+Studies+in+Mathematics&rft.a

u=Battey%2C+Dan&rft.date=2013-01-01&rft.issn=0013-1954&rft.eissn=1573-

0816&rft.volume=82&rft.issue=1&rft.spage=125&rft.epage=144&rft_id=info:doi/10.10

07%2Fs10649-012-9412-

z&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10649_012_9412_z&para

mdict=en-US [Accessed 16th April 2015].

Bell, J. & Opie, C. (2002) Learning from research. Buckingham: Open University

Press.

Gresalfi, M. (2009) Taking up Opprtunities to Learn: Constructing Dispositions in

Mathematics Classrooms. Journal of the Learning Sciences. [Online] 18(3), 327-369.

Available from:

http://www.tandfonline.com.proxy.worc.ac.uk/doi/abs/10.1080/10508400903013470#

.VTBDS-l_nIU [Accessed 16th April 2015].

Please note that there are no page numbers on the online article by Melissa Gresalfi,

so her work is cited in my text but without page numbers.

Gillham, B. (2007) Developing a questionnaire. 2nd edition. London, Continuum.

Seeger, F. (2011) On meaning making in Mathematics Education: Social, Emotional,

Semiotic. Educational Studies in Mathematics. [Online] 77(2/3), . Available from:

[Accessed 17th April].

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Sudman, S. & Bradburn, N.M. (1983) Asking questions: a practical guide to

questionnaire design. San Francisco, Jossey-Bass.

White, J. & Gardner, J. (2012) The classroom x-factor: the power of body language

and nonverbal communication in teaching. London, Routledge.

Woolfolk, A.E. & Galloway, C.M. (2001) Nonverbal communication and the study of

teaching. Theory into Practice. [Online] 24 (1), 77-84. Available from:

http://worc.summon.serialssolutions.com/search?utf8=%E2%9C%93&s.q=Woolfolk+

and+Galloway#!/search?q=Woolfolk%20and%20Galloway [Accessed 16th April

2015].

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Appendix 1

Primary Subject Specialism Research Katrina Small 05.02.2015

Positive Nonverbal Communication Observation Sheet

Nonverbal behaviour Examples (please highlight)

Additional observations

Posture

Forward body lean (accompanied by smile) Direct orientation to the class Erect posture, confident walk

Gesture

Plenty of gestures Approving head nods Open palms Emblems (eg. thumbs up) to accompany positive verbal message.

Facial expression

Smiling Raised eyebrows to show interest.

Eyes

Eye contact with most/all of chn. Direct eye contact for support.

Voice: Intonation

Conveys cheerfulness, friendliness, openness Consistent with verbal message. Reasonably loud and clear. Few hesitations.

Use of space: Distance from student. Teacher’s use of classroom space.

Close proximity to student, in ‘bubble’. Down at their level, possibly at right angles. Teacher travelling freely around class. Nearer at some point to all students, not some.

Accenting: emphasising verbal message with nonverbal communication.

Say “yes” and nod. Stressing a particular word.

Congruity/incongruity: consistency of verbal and nonverbal communication.

Say that you are interested to hear a child, step forward, lean in, make eye contact.

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Appendix 2

Did the nonverbal communication in this lesson convey some or all of the following? friendliness, helpfulness, interest, enthusiasm, cheerfulness, approachability, etc

Primary Subject Specialism Research Katrina Small 05.02.2015

Negative Nonverbal Communication Observation Sheet

Nonverbal behaviour Examples (please highlight)

Additional observations

Posture

Forward body lean (accompanied by frown) Indirect orientation to the class Hands on hips Slouching, shuffling

Gesture

Few gestures Closed palms Lack of emblems (eg. thumbs up) to accompany positive verbal message.

Facial expression

Frowning Raised eyebrows to show disbelief, annoyance. Jutting chin, curled lip

Eyes

Brief and limited use of eye contact Eye contact made with only a few chn Direct eye contact to exert authority

Voice: Intonation

Conveys boredom, frustration, impatience Inconsistent with verbal message. Unclear, hesitating

Use of space: Distance from student. Teacher’s use of classroom space.

Lesson taught from the front. Teacher fairly static Only approach some students on occasion Quite some distance from chn maintained.

Accenting or not: emphasising verbal message with nonverbal communication.

Bland delivery, lack of stress on words.

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05.02.2015

Pupil Questionnaire

Please circle your answer from the options available. There is no right or

wrong answer.

1. Do you usually enjoy school?

Yes No Sometimes

2. Do you usually enjoy Maths lessons?

Yes No Sometimes

3. Are you good at Maths?

Yes No Sometimes

4. Did you enjoy the Maths lesson that you’ve just had?

Yes No Not sure

5. Did you stay focused on the lesson?

Yes No Not sure

6. Did the rest of the class stay focused on the lesson?

Yes No Not sure

Congruity/incongruity: consistency of verbal and nonverbal communication.

Say yes but shake head oor use a dismissive hand gesture

Did the nonverbal communication in this lesson convey some or all of the following? Boredom, impatience, frustration, dissatisfaction, indifference, strictness, dominance.

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7. Did you get the last question right?

Yes No Not sure

8. If not, do you know where you went wrong?

Yes No Not sure

9. Did you understand the grid method of multiplication before this lesson?

Yes No Partly

10. If not, did this lesson help you to understand the grid method a bit better?

Yes No Partly

11. Did you feel confident using grid method multiplication today?

Yes No Not sure

12. Did your teacher explain the method in a way that you understood?

Yes No Not sure

13. Does your teacher like grid method multiplication?

Yes No Not sure

14. Was Mrs. Small friendly and helpful to the class in this lesson?

Yes No Not sure

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Thank you for completing this questionnaire.

Appendix 3

Questionnaire Results

Question

number

Negative nonverbal

communication

Positive nonverbal

communication

Yes No Sometimes Yes No Sometimes

1 8 0 9 8 0 9

2 11 1 5 10 1 6

3 7 2 8 8 1 7

4 10 3 4 15 1 1

5 12 0 5 16 0 1

6 7 0 10 8 0 9

7 13 4 0 16 1 0

8 2 3 3 1 0 2

9 15 1 1 14 2 1

10 0 1 1 5 3 2

11 13 2 2 15 1 1

12 6 7 4 14 3 0

13 2 0 15 6 0 11

14 7 6 4 16 0 1