Vol 15 No 8 - July 2016

International Journal
of
Learning, Teaching
And
Educational Research
p-ISSN:1694-2493
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Vol.15 No.8

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International Journal of Learning, Teaching and
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VOLUME 15 NUMBER 8 July 2016
Table of Contents
A Primer about Mixed Methods Research in an Educational Context ...........................................................................1
Elizabeth G. Creamer
The Pursuit of „Balance‟ by a Greenhorn Supervisor...................................................................................................... 14
Mark Prendergast
Language Barriers in Statistics Education: Some Findings From Fiji............................................................................. 23
Sashi Sharma
The Conundrum of Handling Multiple Grouped Statistics Class at a Tertiary Education and the Impact on
Student Performance ........................................................................................................................................................... 35
Victor Katoma, Innocent Maposa and Errol Tyobeka
Exploring Estonian Students‟ Ability to Handle Chemistry-Related Everyday Problem Solving ........................... 49
Klaara Kask
The Importance of Educational Technology to Pedagogy: The Relevance of Dewey ................................................. 58
Jamie Costley
Bridging Research and Practice: Investigating the Impact of Universally Designed STEM Curriculum on the
Concept Acquisition of At-Risk Preschoolers .................................................................................................................. 65
Michelle R. Gonzalez, PhD
An Education Leadership Program‘s Continuous Improvement Journey Toward a StandardsBased System ...... 79
Peters, R., Grundmeyer, T. and Buckmiller, T.
A Survey on Assessment of the Prevailing School Fees for Private Secondary Schools in Tanzania ....................... 97
Veronica R. Nyahende & Benedicto C. Cosmas

© 2016 The author and IJLTER.ORG. All rights reserved.
1
International Journal of Learning, Teaching, and Educational Research
Vol. 15, No. 8, pp. 1-13, July 2016
A Primer about Mixed Methods Research in an
Educational Context
Elizabeth G. Creamer
Virginia Polytechnic Institute and State University
Blacksburg, Virginia, USA
Abstract. Changes in the academic enterprise, including the growth of
large-scale team-based research, likely account for the growing presence
of projects that are framed to involve mixed methods. This
methodological essay provides a non-technical introduction to mixed
method approaches. It is directed toward an audience motivated
primarily by content area, rather than methodological, interests.
Different methodological constructs are illustrated by using a single
mixed methods study about promoting active play in school
playground. A distinction is made between mixed and multi-method
research, with the recommendation that the mixed method label is most
appropriate when there is the intent to communicate that the interface
between qualitative and quantitative strands is key to understanding the
way the research was executed and the conclusions that are drawn.
Keywords: mixed method; visual methods
Changes in the academic enterprise likely account for the growing
presence of projects that are framed in a way that involve mixed methods.
Part of this may be related to the gradual reconfiguration of long-standing
disciplinary boundaries and to an increase in interdisciplinary research
that incorporates expertise from multiple content areas. It is also related
to the ever-expanding role of external funding sources in shaping the
agendas of research scientists. The growth in team-based research and the
use of large data sets also can be linked to increasing interest in mixed
methods research, as can be the higher expectation for repeated
experiments and ever greater competition to secure access to publication
space in the most the highly ranked journals. Technological innovations,
such software that allows for the analysis of data generated from social
media or that pinpoints geographical location, has also opened the door
for the investigation of more multi-layered and innovative research
questions about social phenomenon.
The purpose of this methodological essay is to provide a non-
technical introduction to mixed methods approaches to research that is
directed toward a broad cross-disciplinary audience motivated by content

2
area interests rather than methodological ones. My intent is to address an
audience unfamiliar with mixed methods. I will provide a broad
overview that distinguishes mixed method from multi-method research
without itemizing the traditional set of mixed method data collection and
sampling procedures and incorporating a lot of specialized jargon. The
kind of overview provided by the article will make it useful as a reading
assignment in a survey course designed to introduce a variety of methods
or as background reading for a general audience interested in learning
some of the basic methodological assumptions of mixed methods
research.
After first considering evidence about the prevalence of mixed
methods research across a variety of academic fields, the paper identifies
different ways that mixed methods research has been defined and how it
is distinguished from multi-method research. We then move to consider
different ways that both qualitative and quantitative approaches can be
used to create a more nuanced and comprehensive picture of a
phenomenon. Next, I offer the architectural arch and keystone as a
metaphor for mixed methods research and the types of inferences that are
drawn from the integration of the qualitative and quantitative strands.
Different ways that integration across phases can be accomplished are
explored next. Throughout, different methodological constructs are
illustrated by using a single mixed methods study about promoting active
play in school playgrounds in Australia (Willenberg et al., 2010). These
authors used multiple methods that integrated data from observational
methods and a photo ordering technique to identify characteristics of
school environments that promote physical activity.
Prevalence of Mixed Methods Research Across Disciplines
Available evidence does not entirely confirm the alarm that is
occasionally voiced that mixed methods has become the "gold standard"
or "best practice" in social and applied research. Content analyses of the
characteristics of the mixed methods literature conducted in a variety of
disciplinary contexts do not support the idea that there has been an
explosive growth in articles reporting research in ways that are indicative
of a mixed methods approach. What these analyses support, however, is
that it is an approach more likely to be utilized in applied disciplines, like
education and the health fields, that value the perceptions of patients or
clients, than in "pure" fields that are more theoretically driven (Alise &
Teddlie, 2010).
Accumulated knowledge from an ever-growing number of reviews
of the literature provides conclusive evidence that while the label is used
in many different ways, research bearing the mixed methods label
appears in an astonishingly diverse array of academic fields. Multiple
content analyses about the prevalence of the approach provide evidence

3
that is being used in academic fields as diverse as library science,
business, marketing, education, health sciences, family science, school
psychology, library science, counseling, construction engineering, and
sports management.
A seminal piece by Alise and Teddlie (2010) convincingly
documents that the dominant approach remains quantitative. Based on
Alise's ambitious content analysis of 600 publications from 20 prestigious
journals in applied (i.e. education and nursing) and non-applied
disciplines (i.e. psychology and sociology), their analyses demonstrate
that quantitative approaches retain the hold as the research approach
used in the majority of publications (69.5%). Qualitative research is used
second most frequently (19.5%), followed by mixed methods approaches
(11%). Figure 1 uses a pie chart to summarize the prevalence of
qualitative, quantitative, and mixed methods approaches reported by
Alise and Teddlie.
Figure 1: Research methods used by pure and applied disciplines as reported by Alise
and Teddlie (2014)
Definitional Issues
Experts define mixed methods research in many different ways
(Johnson, Onwuegbuzie, & Turner, 2007). The label was originally
conceived to apply almost entirely to studies undertaken to enhance
validity by triangulating results from more than one source of data for
purposes of confirmation. In variations that might be used to study
children's activities on school playgrounds, triangulating data collected
69%
11%
20%
Research Methods Pie Chart
Quantitative
Mixed Methods
Qualitative

4
through self-reports of preferred activities and observational methods to
confirm the types of equipment used would reflect the long-standing use
of multiple sources of data to enhance validity.
A second common way to define mixed methods research is in
terms of analytical procedures. This definition envisions mixed methods
research as a combination of a qualitative or inductive approach to
analysis with a quantitative, hypothesis testing or deductive approach.
Yet others simplify the definition by focusing on the types of data
collected. From this perspective, qualitative research is delimited to the
collection of textual data or symbols, such as might be found in
transcripts from individual or group interviews or by accessing entries in
social media. A quantitative approach is simplified to the collection of
data in the form of numbers.
In terms of definition, one can be sure that the term mixed methods
is used to mean many different things. Where there is agreement,
however, is that it involves a combination of qualitative and quantitative
approaches to data collection and/or analysis.
Distinguishing Qualitative and Quantitative Approaches
There are both qualitative and quantitative approaches to making
sense of most phenomena that involve people. In research about
playground equipment, for example, a qualitative approach to data
collection and analysis is more likely than a quantitative one to yield
information about contextual factors that mediate how and when children
use equipment. Variations in weather, type of surface, presence or
absence of other children, and supervision or participation of adults
might all emerge as unexpected results with this type of approach. A
quantitative approach, on the other hand, might pinpoint that the most
active children are using loose equipment, like soccer balls, and that they
almost always are using them in concert with other children.
Different strategies for coding photographs of children on
playgrounds can be used to illustrate qualitative and quantitative
approaches with visual methods. Figure 2 is a photograph that can be
coded using both a qualitative and quantitative approach.

5
Figure 2: Photograph to illustrate qualitative and quantitative ways to code (Used with
permission from Cherie Edwards, Doctoral Student)
Using the quantitative schema applied by Willengberg et al. (2010) to
capture behavior at carefully timed intervals, the two boys in the
photograph would be coded as active. In their schema, behaviors like
sitting, lying, and standing but not moving, were coded as sedentary;
walking or climbing were coded as moderately active; and children that
were running, jumping, skipping, or hopping were coded as active.
A qualitative approach to coding the photograph showing the two
boys with a soccer ball could consider both what is present and what is

6
missing, but might be expected, in the photograph. For example, codes
might be developed to single out elements of the environment that might
influence activity levels. For example, the presence of another child as
well as the soft surface might encourage active play. Fitting with a
qualitative mindset, our imaginary researcher coding this photograph
might also take note of what is not present, but might be expected. This
could include consideration of the absence of near-by adults in the
photograph.
Our imaginary researcher now has both qualitatively and
quantitatively derived data that are linked because one answers a
descriptive "what" question and the other addresses the conceptual or
"why" question. Linking of conclusions from the different strands of a
study to create an explanatory framework is one way to integrate the
qualitative and quantitative strands of a study. The same example can
illustrate other ways that mixing is accomplished in mixed methods
research.
Integrating the Qualitative and Quantitative Strands
A principal characteristic that distinguishes mixed method from
multi-method research is the extent that a conviction about the co-
mingling of the different strands of the study is embedded in the
methodological assumptions. The multi-method label is the more apt
description when a study has more than one strand but the strands are
only loosely linked. This is referred to in the literature as the concurrent
or parallel design (Creswell & Plano-Clark, 2009). One ready way to
distinguish this type of research is that different individuals often execute
the different strands of the study and analysis is conducted separately.
Another way to distinguish this type of research is that it is readily parsed
into separate publications without any loss of explanatory power. This
could occur, for example, when a team is divided up in to one group that
is responsible for the qualitative phase of a project and a second that is
taking the lead on quantitative data collection and analysis.
Mixing at sampling. The example of research about playground can
also be used to envision classic ways that linkages occur between the
qualitative and quantitative phases in mixed methods research. One of
these is mixing through sampling. In this scenario, researchers often use
quantitative markers to identify a sample for a second phase of analysis.
In the example of the playground information, research might use
quantitative data collection to identify the children that were consistently
active and those that were consistently inactive across the time intervals
studied to organize focus groups to interview the two groups of children.
In this example, the two phases of data collection are quite distinct. It is a
minimal type of mixing because while sampling strategy has a direct role

7
in the claims that can be made about generalizability, it does not have a
direct impact on the explanatory framework that is produced.
Mixing during analysis. A second strategy that might be applied to
the study of playgrounds is to mix during analysis. This is done by
linking qualitatively and quantitatively derived variables in the analysis.
This is the most instrumental type of mixing (Greene, 2007). Willenberg et
al. (2010) mixed during analysis by using a statistical procedure to test for
the relationship between looses and fixed equipment and activity levels.
This generated the conclusion that the most active children were playing
with loose equipment, like soccer balls, and that they preferred soft
surfaces. Results derived from mixing during analysis are often displayed
visually in manuscript through tables or figures (Plano-Clark, 2015).
Because it plays such an instrumental role in constructing the final
conclusions, this is the type of mixing that maximizes the value added of
a mixed method approach.
Mixing during the process of drawing conclusions. Mixing most often
occurs at the inference level (O'Cathain, Murphy, & Nicholl, 2008) where
conclusions from the qualitative and quantitative strand are compared or
linked. While common, this approach does not take advantage of the
explanatory power that can be gained from a more creative interchange
between the qualitative and quantitative strands of a study.
The interplay between the qualitative and quantitative strands has
been depicted in a number of creative ways (Bazeley & Kemp, 2012). In a
recently completed textbook (self cites omitted), I have found it useful to
use the metaphor of an architectural arch to represent key features of a
mixed methods approach.
Mixed Methods and the Metaphor of the Architectural Arch
There are multiple parallels between the way an arch is
constructed and the execution of a mixed methods study with one
qualitative and one quantitative strand. In a perfect arch, each of the
building blocks is wedge shaped and added one at a time, working from a
base toward the apex where the final wedge is dropped into place. This is
like the systematic, step-by-step process of executing a research
procedure, such as occurs by using the constant comparative method to
develop a grounded theory. The metaphor is probably most effective in
capturing the end product of a research study as it is represented in
published form than the actual process of conducting research about
complex questions, which is inevitably far messier and more
unpredictable than textbooks communicate.
Another direct connection between an ideal architectural arch and
the essence of a fully integrated approach to mixed methods research
where mixing occurs through multiple stages of the research process, lies
with the keystone. In the metaphor, the keystone represents the meta-

8
inferences that are drawn by considering the results from the qualitative
and quantitative analysis together. Camouflaged by artistic
embellishments or visible to the naked eye, a keystone is the apex of an
ideal arch. Figure 3 is a photograph of an arch with a keystone taken at
the site of Roman ruins in Lyon, France.
Figure 3: Roman arch in Lyon, France (photograph by author)
Once the keystone is set in place, vertical and horizontal forces
keep the structure erect. Each wedge shaped piece shares the load
equally, which makes it a highly efficient structure. This is like "pure"
mixed methods, where the qualitative and quantitative strands are given

9
equal priority (Johnson, Onwuegbuzie, & Turner, 2007). There are a
myriad of examples of arches dating back thousand of years where the
tension is so well distributed that it remains standing while the building it
supported deteriorated over time.
Acknowledging Paradigmatic Challenges
Mixed method researchers are most decidedly members of the
community who are committed to the idea that empirical qualitative and
quantitative approaches have distinct qualities, but share much in
common. Unlike purists, members of this group take the position that
qualitative and quantitative approaches are not driven by different
paradigms that are inherently incompatible.
Researchers who proclaim pragmatism as their paradigmatic
grounding account for much of the mixed methods research that is
published. As a group, pragmatists are inclined to be interested first and
foremost with what works for the setting and intended audience.
Pragmatists argue that purpose always drives the selection of methods.
They tend to be eclectic in the palette of methods they chose for different
projects. They are driven to finds methods that match the purpose and
context of their research project and inclined to leave arguments about the
incompatibility of qualitative and quantitative approaches to those with a
more philosophical bent.
Sidestepping the argument that qualitative and quantitative
approaches are incompatible, Greene (2007) coined the expression "a
mixed method way of thinking" to refer to a philosophical mindset that
deliberately sets outs to acknowledge complexity and to engage multiple
viewpoints. In contrast to positivist who view reality as singular, a mixed
method way of thinking reflects view of reality as inherently multiple.
This is a perspective implicitly shared by researchers who pull together
members of a team in order to integrate knowledge that emerges from
diverse disciplinary approaches. An axiological or value-driven
commitment to respecting diverse viewpoints is evident in Greene's
position that: "A mixed methods way of thinking aspires to better
understand complex social phenomenon by intentionally include multiple
ways of knowing and valuing and by respectfully valuing differences"
(2007, p. 17).
Greene's mixed method way thinking is highly compatible with a
paradigmatic stance referred to as dialectical pluralism. The most
important feature of this paradigmatic position is its de-emphasis on
consensus and convergence and its emphasis on the knowledge and
insight that can be gained by thinking dialectically and engaging multiple
paradigms and mental models (Greene & Hall, 2010; Johnson &
Schoonenboom, 2016). This can be achieved through negative and

10
extreme case sampling or by the intentional pursuit of what at first
appears to be contradictory, unexpected, or inconsistent.
A dialectical approach readily could be mirrored in initial plan for
sampling employed in a study of children's behavior on school
playgrounds. For example, a study could be designed that purposefully
set out to compare the behaviors and attitudes of the most and least active
children in order to identify the type of equipment and environmental
conditions that promote the highest activity levels.
Expectations for Methodological Transparency
The choice to label one's research as mixed methods comes with an
expectation for methodological transparency that is not applied to work
that is satisfied with a multi-method label. This reflects the mandate to
communicate the results of a study with enough precision and clarity to
allow for reproducibility that is one of the defining features of science
(Open Science Collaboration, 2015). Methodological transparency
promotes replication by reporting details about the steps taken to
complete data collection and data analysis, as well as in specifying which
results came from the qualitative analysis and which came from the
quantitative analysis.
The central role the documentation of methodological procedures
plays in the ability to have confidence in the results of a study is evident
in the most widely used evaluation framework for mixed methods
research publications. That is a six-item set of evaluation criteria proposed
by O'Cathain, Murphy, and Nicholl (2008) and referred to as the Good
Reporting of a Mixed Methods Study (GRAMMS). The criteria identified
in the GRAMMS specify dimensions of the methodological procedures
that should be addressed.
The GRAMMS framework defines quality by stipulating explicit
references in a publication to criteria related to different phases in the
design and execution of a mixed method study. Two criteria are related to
how a study is designed, one is related to sampling, one to an
acknowledgment of limitations, and two to the process and product of
mixing. The criteria in GRAMMS framework are paraphrased in Table 1.

11
Table 1: Summary of the Criteria in the Good Reporting of a Mixed Methods Study
(GRAMMS) Developed by O'Cathain, Murphy, and Nicholls (2008)
Phase of the Research
Process
GRAMMS Criterion
Design Provides a justification or rationale for using a
mixed methods approach.
Specifies a mixed method design and
identifies the timing of the qualitative and
quantitative data collection and their priority.
Procedures Describes the qualitative and quantitative
methods for sampling, data collection, and
analysis.
Mixing Explains when and how mixing occurred.
Explains the value-added of mixing.
Limitations Describes the limitations of each method.
The GRAMMS offers a helpful set of guidelines for anyone trying
to write up the results of a mixed methods study in a way that helps its
readers understand how the results were derived and why they are
significant. Its limitation is that the type of methodological transparency
prescribed offers no assurance of the overall quality of the research and
its results. It does not account, for example, for the very items that lead to
why an article is cited by others. Most importantly, these include the
innovative use of methods, the originality of the insight gained, or the
potential of the results to make a significant contribution to what is
known about a theory or phenomenon.
It is difficult to find a publication that simultaneously meets
standards for transparency put forward by methodologists specializing in
mixed methods research designs while demonstrating the type of
innovation and originality that signals out the authors of a publication for
unusual attention. The Willenberg et al. (2010) article about increasing
physical activity on school playgrounds, for example, is innovative in its
reporting about a mixed methods approach to visual methods and in
providing research with such direct implications for practice. It would,
however, score poorly on a rubric derived from an evaluation rubric, like
the GRAMMS, that rests entirely on methodological transparency.
The discrepancy between the originality evident in the Willenberg
et al. (2010) article and how poorly it would fare under an evaluation
system that rests on mixed methods reporting standard can be attributed
to its purposes and intended audience. Authors of the playground study
had a content-oriented, rather than methodological purpose. All of the 29
items in the reference list are about playgrounds and children's activity

12
levels. They referenced no literature to support their methodological
expertise, but nevertheless managed to demonstrate a a creative and
useful way to use a mixed methods approach that is well worth
replicating.
The criteria in the GRAMMS mirror the authors' guidelines for the
specialized, methodologically oriented Journal of Mixed Methods Research.
Like the shared terminology, the guidelines provide a short hand for
methodologically oriented readers to quickly pinpoint the contribution of
an article. Manuscript writers targeting methodologically oriented
journals or those writing with the purpose of highlighting innovative
approaches using mixed methods, will extend the breadth of their
audience by incorporating the expectations for methodological
transparency evident in the GRAMMS.
Applying the Mixed Method Label
The logic of mixing methods and types of data is inherent in many
research approaches (Sandelowski, 2014) and, consequently, not a
characteristic that is useful to identify them. Rather than to use it to signal
the combination of multiple types of data when the multi-method label is
most apt, affixing a mixed methods label to a publication is a way to
declare that the logic of mixing is central to the purpose of the study and
for understanding its conclusions. The mixed method label is helpful with
the playground study because it communicates that mixing occurred
through multiple stages of data collection and analysis and is essential to
understanding the conclusions.
The intent to engage diverse viewpoints is consistent with Greene's
(2007) mixed methods way of thinking and the paradigmatic assumptions
of dialectical pluralism (Greene & Hall, 2010; Johnson & Schoonenboom,
2016). As noted above, dialectical pluralism is characterized by the belief
that reality is multiple, constructed, and ever changing; a respect for
diverse viewpoints and ways of knowing, and the motivation to pursue
contradictory or unexpected results that is similar to an engagement with
multiple, competing hypothesis that is so central to the scientific method.
This affiliation negates the argument that a mixed methods approach
involves a type of paradigm mixing that is intellectually dishonest. It also
challenges the long standing framing of mixed methods as best
understood simply as the combination of qualitative and quantitative
approach.
Research methods and practice are ever changing (Hesse-Biber,
2010). Adopting the logic that mixed methods produces a synergy or a
quality that is unique beyond its qualitative and quantitative components
makes it possible to be open to new and innovative approaches to
defining it. It creates an openness to the possibility of mixing two types of
qualitative data, that is different from a mindset that, as Creswell (2011)

13
has suggested, a method like content analysis cannot be mixed methods
because it begins with data that is entirely in the form of words. It also
downplays the binary logic that questions the appropriateness of
applying a mixed methods label to a report of a set of results that
emerged unexpectedly. This kind of definitional adaptability is consistent
with Guest's (2012) proposal that a mixed methods label may be a helpful
way to understand a series of inter-linked publications from a larger
research project, even when it is not reflected in an individual publication.
References
Bazeley, P., & Kemp, L. (2012). Mosaics, triangles, and DNA: Metaphors for integrated
analysis in mixed methods research. Journal of Mixed Methods Research 6 (1), 55-
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Creswell, J. W. (2011). Controversies in mixed methods research. N. K. Denzin and Y. S.
Lincoln (Eds.), SAGE Handbook of Qualitative Research (pp. 269-283). Thousand
Oaks, CA. SAGE Publications.
Creswell, J. W., & Plano, C. V. (2007, 2011). Designing and conducting mixed methods
research. Thousand Oaks, CA. SAGE Publications.
Greene, J. C. (2007). Mixed methods in social inquiry. San Francisco, CA.: Wiley Publishers.
Greene, J. C., & Hall, J. N. (2010). Dialectics and pragmatism: Being of consequence. In A.
Tashakkori and C. Teddlie (Eds.), SAGE Handbook of Mixed Methods in Social and
Behavioral Research (Second Edition) (pp. 119-144). Thousand Oaks, CA: SAGE
Publications.
Guest, G. (2012). Describing mixed methods research: An alternative to typologies.
Journal of Mixed Methods Research, 7(2), 141-151.
Hesse-Biber, S. (2010b). Emerging methodologies and methods practices in the field of
mixed method research. Qualitative Inquiry, 16(6), 415-418.
Johnson, R. B., Onwuegbuzie, A. J., & Turner, L. A. (2007). Toward a definition of mixed
methods research. Journal of Mixed Methods Research, 1 (2), 112-133.
Johnson, R. B., & Schoonenboom, J. (2016). Adding qualitative and mixed methods
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O'Cathain, A., Murphy, E., & Nicholl, J. (2008). The quality of mixed methods studies in
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sams.2009.02.011

14
Vol. 15, No. 8, pp. 14-22, July 2016
The Pursuit of „Balance‟ by a Greenhorn
Supervisor
Mark Prendergast
The University of Dublin
Trinity College Dublin, Ireland
Abstract. This article explores the transition process from being a
research supervisee to being a first time doctoral research supervisor.
This is a difficult and trying endeavour. The lack of previous
supervision experience at this level results in many supervisors referring
to their own time as doctoral students and supervising in the same
manner as they experienced. It is important to break this cycle and
realise that just like teaching, there are many different models of
supervision. Much of the research conducted in the area draws
conclusions about the type of characteristics or traits that make a good
supervisor. This article takes a different point of departure and gives a
personal account of the author‟s thoughts and experiences in attempting
to make the transition from supervisee to supervisor. These experiences
are explored with reference to existing literature with the intention of
unearthing and documenting key issues for first-time supervisors to
consider and develop their own understanding of effective supervision
practice. The author hopes that documenting these issues through a
personal, reflective account will help others who decide to continue the
journey and make the transition from supervisee to supervisor.
Keywords: Research Supervision; Higher Education; Reflective Practice;
Research Experiences
Introduction
Insufficient attention has been given to research supervision as a topic requiring
scholarly investigation (Armstrong, 2004; Halse, 2011). This is best summed up
by Park (2007) who described supervision as a secret garden where student and
supervisor engage with limited outside interference or responsibility. This is
regardless of the argument that effective supervision is one of the most
important reasons for the successful completion of research theses (Jonck, &
Swanepoel, 2016; Lee, 2008; Sambrook, Stewart & Roberts, 2008). Given such
importance, the supervision of PhD students‟ needs to be enhanced to reduce
withdrawal rates and improve the quality of research (Maor, Ensor, & Fraser,
2016; Bastalich, 2015). Without doubt I wouldn‟t have been awarded a doctorate
five years ago without the help, support and guidance of my supervisor. Since
then the wheel has turned full circle and I am now at the stage of my academic

15
career where I am supervising a PhD student. However despite the complexities
and challenges of such a role (Stephens, 2013; Hockey, 1997), advice for new
supervisors is scant in the literature (Gordan, 2003). The doctorate is a learning
process for students but also for doctoral supervisors (Halse, 2011). There is a
growing body of research around PhD supervision (Berry & Batty, 2016).
However much of this research draws conclusions about the type of
characteristics or traits that make a good supervisor. This article takes a different
point of departure and aims to give a first-hand account of my personal
thoughts and experiences in attempting to make the transition from supervisee
to supervisor. These experiences will be explored with reference to existing
literature with the aim of unearthing and documenting key issues for first time
supervisors to consider and develop their own understanding of good
supervision practice.
Background
My progress onto the rungs of the supervision ladder have been slow and
unhurried. It began with the supervision of undergraduate students‟ theses,
Masters students and then onto a single Ph.D. student. Each of these steps has
given an insight into the processes involved in thesis completion and the role the
supervisor is expected to play in such processes. Perhaps the most helpful step
of all was my enrolment in a Research Supervision in Higher Education training
course provided in the university where I work. This six week professional
development course broadened my thinking and encouraged me to reflect upon
many alternative aspects to supervision. Up until that point I had considered my
own personal supervision experiences to be the norm. It was enlightening to
hear others recall their own paths, both positive and negative. Everyone has
their own individual journey of research and it is important to learn from each
other (Dash & Ponce, 2005). During the training course the literature around
Ph.D. supervision and the different models of supervision which have been
developed were considered. If I could sum up in three words the most important
thing I learned regarding research supervision thus far, it would be to “find a
balance”. There are an indefinite number of aspects to supervision. However
finding a balance between the key aspects is vital. In this article I aim to outline
and discuss five important aspects to PhD supervision which I have encountered
and which I hope to draw upon to help me become the type of supervisor that I
aspire to be. Each of these aspects will be addressed through the lens of finding a
balance.
Balance of Supervisory Styles
There are many different styles of research supervision (Boche, 2016). At their
broadest these can be referred to as direct (hands-on) and indirect (hands-off)
styles of supervision (Gurr, 2001). A balance in the selection and appropriate use
of these styles is important and should be appropriate to the students overall
level of development. Gurr (2001) argues that at the beginning of the supervision
period a more hands on style is needed. For example at the beginning of my
PhD, my supervisor would organise regular meetings in which he would offer
support and feedback. However in the latter years my supervisor had adapted a
much more hands off approach and it was up to me to organise a meeting if, and

16
only if, I needed some advice. At this stage it was my responsibility to make the
everyday, run of the mill decisions regarding my research.
Although supervisory styles can be further broken down into more
detail, the need for balance is just as important. For example, supervisors need to
find a balance between supporting and challenging and between guiding and
critiquing their students work. In one instance the role of a supervisor is to offer
direction to students on their research. However supervisors are also the
primary critic and are obliged to ensure the student produces work which meets
the requirements of a PhD thesis. This is a difficult balance to strike and
highlights the complexity of the relationship that exists between the supervisor
and the student. Supervisors need to become aware of how to limit the help they
give to their students while at the same time balancing this with support and
constructive critique of their students work (Hockey, 1997). Easterby-Smith,
Thorpe, and Lowe (2002) acknowledge that there is a fine line between
providing feedback, which highlights flaws, and providing praise and
encouragement to try harder. The way in which everyone engages with such
critique and feedback, whether it is the student or the supervisor, is important
and will often depend on the existing relationship between them.
Balance of Relationship between the Supervisor and the Student
This relationship between supervisee and supervisor has been described as one
of the most essential components of successful doctoral completion (Orellana et
al., 2016; Bastalich, 2015; Ives & Rowley, 2005). The development and
maintenance of a helpful, and constructive relationship over time is central in
producing a good quality thesis (Wisker, 2001; de Kleijna et al., 2015). I was
fortunate to have such a relationship with my supervisor. We had very good
rapport, communication and mutual respect. However this seemed to happen
naturally and I had not considered the situation if this was not the case.
Listening to other‟s recall some of their negative experiences of PhD supervision
has led me to believe that very careful consideration must be given to this
relationship. There are two sides to the coin. It is essential that you develop a
good interpersonal working relationship but also ensure that there is a balance
between the professional and social aspects. Perhaps one the most important
aspects here is the selection and allocation of supervisors and students.
Supervisors and students should have a choice of whether they wish to work
together and should not just be matched because they share the same research
topic. In an Australian study carried out by Ives and Rowley (2005) supervisors
and students noted that when it comes to supervisor allocation, it is much more
important to get the interpersonal aspects aligned rather than assigning on the
basis of expertise in the content area. This is backed up by Phillips and Pugh
(1994) who state that the selection of supervisor and student is probably the
most important step that each will take.
Balance of Control
Many supervisors struggle to find a balanced equilibrium in the freedom and
control they express towards the progress and development of their students
work (Hockey, 1997). This is difficult for any supervisor. ‘It is a hard balance to
strike because different students respond so differently’ (Supervisor interviewed in

17
Hockey, 1997). On the one hand it is important that supervisors enable students
to take sufficient control of their own research. This allows them to develop
intellectually and to produce innovative and original research. On the other
hand many students struggle, at least initially, with such freedom. For example
students coming directly from undergraduate programmes often struggle with
the apparent lack of structure within PhD programmes (Gurr, 2001). It is
important to help the students to develop from an initial state of dependency to
relative independence over time (Gurr, 2001). This is where the balance of
control has to be achieved between giving well-timed help in some instances,
and not interfering in others. This balance of control varies from supervisor to
supervisor. Some supervisors have rigid regimes - „we see them monthly and they
produce 500 words before each meeting’ (Supervisor interviewed in Lee, 2008). In
my own experience as a PhD student, there was much a freer rein. Work was
submitted to my supervisor when I had it complete but there were very rarely
any deadlines. While this particular model worked well for me I can see issues
where student motivation begins to falter. Perhaps the findings of Hockey (1997)
are advisable in which supervisors initially impose a strict degree of control over
their student‟s work. The can be relaxed through positive student performance,
with a more balanced input from all parties driving the research forward
(Hockey, 1997).
Balance of Expectations
Similar to any form of teaching and learning, it is important for supervisors to
set high expectations for their students. Research has found that such
expectations can become self-fulfilling prophecies (Muijs & Reynolds, 2001).
However it is also important that such expectations are realistic and achievable.
These expectations might be regarding the standards of academic writing,
critical thinking or even dissemination skills. While I was doing my PhD, my
supervisor also had four other doctoral students at the same stage. He was
aware that we all had our individual strengths and weaknesses and so set
individual, realistic, yet challenging expectations for each of us. For example at
the start of the PhD process the supervisor said he expected each of us to start
presenting our work at conferences as soon as possible. This is a challenging
expectation to some, but perhaps not to others depending on life experience.
However the supervisor, using an array of institutional, regional, national and
international conferences, tactfully pointed us in different directions ensuring
that each of us were challenged sufficiently, without being entirely outside of
our comfort zones. This balance of expectations proved an invaluable experience
for each of us in building confidence while sharing our research and gradually
opening the gates to the academic community.
Balance of Workload
Undoubtedly, the central aim of both the supervisor and the student is thesis
completion and this requires a huge workload. One of the main responsibilities
of the supervisor is to ensure a balance to this workload. There are many
milestones to be met throughout the process and a well-planned and thought-
out workplan can ensure that each of these milestones are reached in a timely
and balanced manner. As a novice researcher, this is an area of concern. More

18
experienced supervisors are more likely to predict the time required for
literature reviews and the collection and analysis of data (Hockey, 1997).
However it is difficult starting out to foresee how much time and output is
needed in each case. The student often looks to their supervisor for guidance in
such matters. In the first year of my PhD, I can recall constantly asking my
supervisor „am I doing enough?‟, „how long should I spend on this section?‟,
„how many words are needed here?‟ Novice supervisors need help and guidance
themselves in answering these queries. This is where the importance of
mentoring and collegial support comes to the fore. It is important that there are
opportunities for informal interactions where novice supervisors can access the
tacit knowledge of their peers on an on-going basis (Stephens, 2012). This will
ensure that there is a balance provided for students not just in workload, but
also in many other aspects of the supervision process.
This balance of workload does not only apply to the students. It is just as
important that supervisors strike a work balance. Many supervisors fall into the
trap of taking on too many PhD students („I know of places where there is a PhD
factory’ - Supervisor interviewed in Lee, 2008). This is not fair to the supervisor
who has an unsustainable workload or to the students as they vie for individual
time and attention.
Discussion and Going Forward
Finding a balance in each of these five aspects to PhD supervision is a complex
endeavour and highlights the difficulties and challenges that lie throughout the
doctoral supervision process. Guthrie (2007) puts forward the notion of a PhD
student embarking on a journey. However I would argue that this journey does
not necessarily end when their PhD has been awarded. For many, this is the first
cycle as they continue into the supervision process. When I completed my PhD I
had no intention of continuing on such a journey. It‟s not that I was against the
idea, simply the thought had not crossed my mind. In my opinion it is
impractical to think you can become an effective PhD supervisor the moment
you make it through your own Viva examination. As mentioned previously I
have worked my way slowly onto the rungs of the supervision ladder. I agree
with Hockey‟s (1997, p.47) assentation that “you cannot learn to be a supervisor
without actually doing it” and in this sense my experience in supervising
undergraduate and Master students theses has been invaluable. It has given me
confidence. Confidence in imparting domain specific knowledge and
methodological guidance, but more importantly confidence in guiding students
through the research process, from the development of a proposal to thesis
submission. There were a plethora of different emotions present when these
students graduated in their respective programmes. Having worked closely with
the students over a number of months, there was obvious joy that the hard work
and endeavour had been rewarded. However as a „greenhorn‟ supervisor my
overarching feeling was one of relief. Relief that the guidance, direction and
feedback I had given students had not been wide of the mark. Relief that an
examiner and external examiner had deemed the work to be satisfactory.
Nevertheless, through these experiences I learned a number of important
supervisory lessons.

19
Perhaps the most important lesson was that I had been overly involved
in the supervision process. I had yet to find a balance in my hands-on
supervisory style and my control in the management of students‟ progress. As
mentioned previously, supervisors need to find a balance between supporting
and challenging and between guiding and critiquing their students work. I must
admit that in the early stages of my supervision journey I found this difficult. I
had an attitude and ethos that is best summed up in a statement from Anderson
(1988) “No that is not the way to do it. Do it this way”. This attitude resulted in
my students developing little autonomy or creativity in their work through my
over involvement. It goes against the advice of Philips (1992) who stated that
supervision is about helping the student to be their own supervisor. Ultimately a
student‟s research thesis is their own work and it is their responsibility for
arriving at the destination (Lee, 2008). Research supervision is a facilitative
process (Pearson & Kayrooz, 2004) and in many cases supervisors need to curb
the assistance they provide and ensure they act as first line examiner of their
student‟s work (Hockey, 1997). This highlights the importance between striking
a balance between intellectual involvement and supervisory styles and control
and is a valuable lesson as I take the next steps in my supervisory journey.
The key for me in recognising this lesson was reflecting on my
experiences as a supervisor. Such reflection was facilitated through my
enrolment in a Research Supervision in Higher Education course. This was a
voluntary training course offered free to charge to staff members by the
university. My only issue with the course is that it was voluntary. It is unnerving
to think that I could have begun doctoral supervision without receiving some
kind of formalised training and broadening my thinking regarding the
supervision process. I signed up to the course with some very clear objectives in
mind. I wanted to know the university supervision policy, its plagiarism policy,
and its preferred referencing style. I wanted sample timeframes that I could
share with students and examples of successful ethical approval applications.
Thankfully the six week course did not provide any of those nuggets of
information. Such information can easily be accessed online. Instead the course
encouraged me to reflect upon my own understanding of supervision and what
alternate understandings were possible. I have since realised that reflection is
one of the key processes of developing an underlying understanding of
supervision. This reflection can take place individually or collectively through
discussion with colleagues (Wright, Murray & Geale, 2007).
The support of experienced colleagues is crucial for the greenhorn
supervisor. Traditionally a supervisor‟s learning process was a solo journey
(Hockey, 1997) and was essentially trail by error (Becher, 1996). Learning from
making mistakes was the norm (Halse, 2011). In recent years there has been
considerable effort to enhance the quality assurance of research supervision
(Maor, Ensor, & Fraser, 2016). Training courses such as the one I attended are
one facet of this effort. Mentorship between experienced and less experienced
colleagues is another. Many issues and concerns be critically analysed through
mentorship (Hockey, 1997). Perhaps the most extreme form of mentorship is
joint supervision with an experienced colleague.
I am currently in the initial few months of supervising my first PhD
student. However again I am doing this taking small steps as I am co-

20
supervising the student with an experienced member of staff in our faculty. This
has provided huge support for me personally. As the focus of the PhD is in my
research area, I have been designated as the „main‟ supervisor. However it is
reassuring to know that there is someone to discuss key decisions with and seek
assistance, when and if required. Co-supervision is becoming more and more
common (Guerin & Green, 2015) and there are lots of advantages, not only for
inexperienced supervisors, but also for the students (Ives & Rowley, 2005). An
Australian study conducted by Pearson (1996) found that students who were
receiving regular supervision from more than one supervisor had higher levels
of satisfaction. The concept of a "developmental niche" for researchers (Dash,
2015) extends mentorship and joint supervision even further and recommends
several people and processes to be involved. Such collaboration would dispel
the myth of supervision as a solo journey and would further lend to the pursuit
of balance in each of the five areas that have been outlined in this article.
Conclusion
Until recently, few researchers have studied the transition from supervisee to
supervisor (Rapisarda, Desmond, & Nelson, 2011). This is an important
transition and many testing and important decisions have to be made by the
supervisor throughout this process. Hockey (1997) determines that the ability to
make many right decisions in PhD supervision is often acquired by previous
experience. Unfortunately for novice researchers such as myself, the main
experience we have is to refer to our own time as a doctoral student. This may be
one of the main reasons why, similar to teachers teaching the way they were
taught (Lortie, 1975), many supervisors tend to supervise in the same manner as
they experienced (Lee, 2008; Doloriert, Sambrook & Stewart, 2012). It is
important to break this cycle and realise that just like teaching, there are many
different models of supervision. These models and decisions relate to each of the
aspects outlined in this article and will vary depending on each individual
supervisor, student and situation.
Thus far, I feel my transition from supervisee to supervisor has gone
relatively smooth. However I am in no doubt that challenges lie ahead. Whether
or not I am equipped to deal with these challenges, only time will tell. Through
completing the training course and reviewing literature for this article I have
acquired valuable knowledge on many aspects of the supervision process.
However I have also learned that perhaps the most valuable and meaningful
knowledge can only be generated through continuing and reflecting on my own
journey of doctoral supervision.
There is no perfect model of supervision which can be applied in all
situations (Beddoe & Egan, 2009). However ensuring that there is a balance of
styles, relationships, control, expectations and workload will go a long way to
improving a greenhorn supervisor‟s experience of supervision, and that of their
students as well. It is my hope that by documenting some of my own thoughts
and experiences, this article will help others who decide to continue the journey
and make the transition from supervisee to supervisor.

21
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© 2016 The author and IJLTER.ORG. All rights reserved
23
Vol. 15, No. 8, pp. 23-34, July 2016
Language Barriers in Statistics Education:
Some Findings From Fiji
Sashi Sharma
The University of Waikato
Hamilton, New Zealand
Abstract. Despite the fact that language plays a crucial role in
mathematics education, not much research has been carried out in
documenting the problems of learning statistics in a second language.
This paper reports on findings from a larger qualitative study that
investigated high school students‟ understanding of statistical ideas.
Data were gathered from individual interviews. The interviews were
audio recorded and complemented by written notes. Two major themes
that evolved from the analysis of data were the confusion among
registers and the interpretation of the tasks. Moreover, students lacked
verbal skills to explain their thinking and interpreted the tasks in ways
not intended by myself. The findings are compared and contrasted with
relevant literature. The paper ends with some suggestions for practice
and further inquiry.
Keywords: English language learners; high school students;
implications; language barriers; mathematical language; socio-cultural
perspective.
Introduction
Imagine a teacher running her fingers across the pages of the textbook and
telling her students, “When numbers or objects are chosen at random they are
chosen freely without any rule or any obvious bias.” The whole class listens in
silence, but one of the shy students is thinking, “I thought it was something that
was rare like the possibility of an earthquake.”
A common view about mathematics is that it is a „universal language‟ and is
„culture free‟ (Barwell, 2012; Bishop, 2002; Borgioli, 2008; Brown, Cady, & Taylor,
2009; Hoffert, 2009; Meaney, 2006). It uses a variety of symbols that are common
across cultures and therefore easily accessible to language learners. From this
perspective, mathematics learners anywhere in the world can access
mathematical concepts using any language (Barwell, 2012; Bishop, 2002).
However, as the text above illustrates, the language of statistics can sometimes
be challenging for students (Bay-Williams & Herrera, 2007; Boero, Douek, &
Ferrari, 2008; Borgioli, 2008; Campbell, Adams, & Davis, 2007; Lavy & Mashiach-
Eizenberg, 2009). Many statistical words are unusual, some terms such as
„random‟ and „normal‟ have a range of interpretations in everyday
communication, and some have more than one meaning in mathematics and

24
statistics (Kaplan, Fisher, & Rogness, 2009; Lesser & Winsor, 2009; Rubenstein &
Thompson, 2002; Watson, 2006; Winsor, 2007).
According to a number of authors (Goldenberg, 2008; Halliday, 1978;
Moschkovich, 2005), mathematics is strongly connected with language and
culture. To be able to do well in mathematics, students must be proficient in the
language of instruction and use language effectively in diverse contexts (Borgioli,
2008; Kotsopoulos, 2007; Morgan, Craig, & Wagner, 2014; Nacarato & Grando,
2014; Xi & Yeping, 2008). This situation may present some unique challenges for
students as they must simultaneously learn ordinary English and mathematical
English, and be able to differentiate between the types of English (Abedi & Lord,
2001; Adler, 1998; Bay-Williams & Herrera, 2007; Kaplan et al., 2009;
Moschkovich, 2005; Winsor, 2007). Students must be able to move between
everyday and academic ways of communicating ideas and relate these
expressions to mathematical symbols and text (Goldenberg, 2008; Kotsopoulos,
2007; Morgan et al., 2014; Salehmohamed & Rowland, 2014). Students in an
English medium classroom may undergo more processing than native English
speakers (Bay-Williams & Herrera, 2007; Bose & Choudhury, 2010; Clarkson,
2007; Latu, 2005; Meaney, 2006; Nacarato, & Grando, 2014; Salehmohamed &
Rowland, 2014). These students can miss out on mathematical learning because
they may be spending too much time trying to understand the problem.
Furthermore, to be able to perform competently, students must understand the
highly technical language used specifically in mathematics (Bay-Williams &
Herrera, 2007; Brown, Cady, & Taylor, 2009; Goldenberg, 2008; Xi & Yeping,
2008). This language is not used in everyday English, and therefore is less likely
to be familiar or understood by English language learners.
The technical language and vocabulary mathematics has is not only essential
for students to be able to understand and access the mathematics they are
learning now, but has a significant influence on their future mathematical
development and careers (Borgioli, 2008; Hoffert, 2009; Morgan et al., 2014;
Neville-Barton & Barton, 2005; Xi & Yeping, 2008). Teachers need to be aware of
issues surrounding mathematical language acquisition and develop pedagogical
strategies to address students‟ difficulties in making sense of mathematical
language (Bay-Williams & Herrera, 2007; Campbell et al., 2007; Salehmohamed
& Rowland, 2014).
The vital role that language plays in mathematics education is evident in a
number of studies (Barwell, 2012; Bose & Choudhury, 2010; Goldenberg, 2008;
Halliday, 1978; Pimm, 1987; Planas & Civil, 2013; Salehmohamed & Rowland,
2014). However, according to Lesser, Wagler, Esquinca and Valenzuela (2013, p.
7) “there have been a few research studies about language issues in statistics
education but these did not involve students learning in a second language”.
The conclusions are consistent with the conclusions reached by Kaplan et al.
(2009) and Lavy and Mashiach-Eizenberg (2009). It is important to gain insights
into how English second language students learn statistics and probability
(Kazima, 2007; Lesser & Winsor, 2009). Moreover, probability context is
“regarded as the biggest challenge for teachers since it has previously belonged
only in the high school curriculum (15-17 years old)” (Nacarato & Grando, 2014,
p. 13). In addition, most of the studies in statistics have been done in western
countries with elementary students rather than secondary students. Like

25
Shaughnessy (2007), Sharma (2012, p. 33) noticed “a lack of research in statistics
education outside of western countries”. Given the lack of research on English
language students learning statistics, Sharma (1997) study addressed these gaps
in literature. It provided an awareness of how other countries and cultures teach
statistical concepts.
This paper has four sections. The first section reviews mathematics and
statistics education research literature to discuss the challenges faced by English
Language Learners. The next section reports on data gathered from a larger
qualitative study that investigated high school students‟ ideas about statistics. It
discusses examples from a Fijian study to explain the impact of language issues
in statistics education. The findings are compared and contrasted with relevant
literature. The final section provides directions for instruction and future studies.
Problems faced by English Language Learners in Mathematics
Language plays an important role in any learning area in the classroom. It is a
tool that can develop student understanding and helps them communicate their
thinking to others. Language also provides a medium by which teachers can
assess student learning (Bay-Williams & Herrera, 2007; Bose & Choudhury,
2010; Kaplan et al. 2009; Mady & Garbati, 2014; Rubenstein & Thompson, 2002).
Indeed there is a growing demand on students' linguistic skills in mathematics
lessons (Bay-Williams & Herrera, 2007; Cobb & McClain, 2004; National Council
of Teachers of English, 2008). Pupils at all levels are not only expected to listen,
talk and to read, but also to write about their work using mathematical language
(Franke, Kazemi & Battey, 2007; NCTM, 2000). However, research shows that
communicating mathematically poses many challenges for students due to
interference from everyday language and within the mathematical register
(Barwell, 2012; Bay-Williams & Herrera, 2007; Boero, Douek, & Ferrari, 2008;
Borgioli, 2008; Cobb & McClain, 2004; Ferrari, 2004; Kotsopoulos, 2007;
Rubenstein & Thompson, 2002). Cruz (2009, p. 1) argues that “one of the goals of
mathematics instruction for bilingual students should be to support the
participation of all students, regardless of their proficiency in English, in
discussions about mathematical ideas poses many challenges for students”.
Some of the challenges of language learning and mathematical understanding
with particular reference to English language learners is explored below.
Language Syntax and Translation
Language is a vehicle through which students learn and communicate
mathematical concepts (Barwell, 2012; Boero et al., 2008; Kaplan et al., 2009;
Moschkovich, 2005). However, English is a complex language with a complex
syntax (sentence structure) and semantic properties (process of making meaning
from the language). Sometimes, the structure of natural English is at odds with
the conventions of mathematical language structures. Students need to be able to
make an appropriate translation from the words of the problem into the
symbolic representation of the solution. Latu (2005) claims that difficulties arise
when the mother tongue does not have the vocabulary to express the idea being
studied. The same points were made by Fasi (1999) and Sharma (1997) in their
studies with Tongan and Fijian-Indian students respectively. Some students in
Sharma‟s study translated the term “sample” into Pasifika Hindi equivalence.

26
Mathematical Register
According to a number of authors (Barwell, 2012; Boero et al., 2008; Bose &
Choudhury, 2010; Goldenberg, 2008) multiple registers are used in mathematics
classrooms. For a student to succeed in a mathematics classroom, they not only
need to be familiar with and competent in their ordinary English register, so
they can communicate with their classmates, but must also have fluency in what
can be multiple mathematical registers (Barwell, 2012; Boero et al., 2008;
Halliday, 1978; Setai & Adler, 2001). The mastery of the mathematical registers,
and the strong ability to switch between them, requires strong linguistic and
metalinguistic skills. This is necessary for students to be able to cope with more
advanced mathematics (Bay-Williams & Herrera, 2007; Boero et al., 2008; Kaplan
et al., 2009; Meaney, 2006; Moschkovich, 2005).
For a student from an English speaking background, mathematical registers
can pose a significant challenge, as a new form of language must be learned and
mastered (Bay-Williams & Herrera, 2007; Meaney, 2006). Not only must an
English language learner try to learn in English whilst concurrently learning to
speak English, they must also be working within the English mathematical
registers without yet having mastery of ordinary English. Furthermore, it is
common for a lot of processing to occur so an English language learner can work
within English and their home language (Moschkovich, 2005; Parvanehnezhad
& Clarkson, 2008; Setai & Adler, 2001). They must be able to understand the
mathematical register, translate it into ordinary English, then translate that into
their own language, before translating it into one of the mathematical registers
used in their home language, before going through the process again in reverse
to enable the student to express their thinking or answer in the appropriate
English mathematical register (Lager, 2006). Therefore, even if an English
language learner is competent in using the ordinary English register, the use of
the mathematical register provides extra difficulties for English language
learners.
Reading Mathematics
The language of mathematics is expressed in mathematical words, graphic
representations and symbols (Kenney, 2005). Reading mathematical texts
provides the learner with an extra challenge over reading English (Latu, 2005).
The learner must simultaneously comprehend and process in both English
language and the discipline language (mathematics) (Kester-Phillips, Bardsley,
Bach, & Gibb-Brown, 2009).
Redundancy is one characteristic of ordinary English that has a significant
influence on how students (mis-) read mathematical English. Ordinary English
has a high degree of redundancy; consequently students learn to skim read,
sampling key words to get the key point, e.g. when reading a novel. In
comparison, mathematical English is concise, each word has purpose with little
redundancy, and a large amount of information is contained in each sentence
(Padula, Lam, & Schmidtke, 2001). Students who transfer their reading skills
from ordinary English to mathematical English texts may be disadvantaged by a
tendency to overlook key information. Cultures with less redundant natural
languages are more likely to pay attention to every word and therefore

27
understand better some forms of mathematical English despite this being their
second language (Mady & Garbati, 2014; Padula et al., 2001).
Code Switching
Code switching involves the movement between languages in a single speech
act and may involve switching a word, a phrase, a sentence or several sentences
(Adler, 1998; Bose & Choudhury, 2010; Salehmohamed & Rowland, 2014; Setati
& Adler, 2001). English language learners may code switch for various reasons,
including to seek clarification and to provide an explanation (Bose & Choudhury,
2010; Moschkovich, 2005). Code switching promotes both student-student and
student-teacher interactions in classrooms involving English language learners
(Salehmohamed & Rowland, 2014; Setati & Adler, 2001).
In the mathematics classroom, English language learners often employ code
switching to clarify their understanding and as a way to express their arguments
and ideas (Bose & Choudhury, 2010; Clarkson, 2007; Moschkovich, 2005;
Parvanehnezhad & Clarkson, 2008; Salehmohamed & Rowland, 2014). Moreover,
in mathematics code switching not only occurs between languages but also
between registers. This can add an extra layer of challenge to the English
language learner, as they may find themselves working between a multitude of
registers in both English and their home language (Bose & Choudhury, 2010;
Lager, 2006). In a study of Australian Vietnamese learning mathematics, in
Australia, Clarkson (2007) found that some of these students switched between
their languages, when solving mathematics problems, individually, because
solving problems in their first language “gave them more confidence” (p. 211).
Sometimes these students switched their languages because they found the
problem difficult to solve in English. This linguistic complexity English language
learners face further demonstrates the need for mathematics teachers to have the
tools and training to effectively work with English language learners.
The Study
The study (Sharma, 1997) took place in Fiji. As mentioned in Sharma (2014, p.
107) “it was designed to explore what ideas form five (Year-11) students have
about statistics and probability, and how they construct these ideas. Twenty nine
students aged 14 to 16 years of which 19 were girls and 10 were boys
participated in the study”. Data was collected using individual interviews.
Students could use both English or vernacular to explain their thinking.
Tasks
As stated in Sharma (2012, p. 36) “the advertisement regarding the sex of a
baby (Item 1) explored students‟ understanding of the bi-directional relationship
between theoretical and experimental probability in an everyday life context”.
Item 1: Advertisement involving sex of a baby
“Expecting a baby? Wondering whether to buy pink or blue?
I can GUARANTEE to predict the sex of your baby correctly.
Just send $20 and a sample of your recent handwriting.
Money-back guarantee if wrong!
Write to…...............................................
What is your opinion about this advertisement?”
Sharma (2012, p. 36)

28
Understanding that a sample from a population can be used to make
estimates of the characteristics of the entire population is key to statistical
inference. Item 2, buying a car (Sharma, 2003) was used to explore students'
understanding of sample size and sampling methods within a meaningful
context.
Item 2: Buying a car
“Mr Singh wants to buy a new car, either a Honda or a Toyota. He
wants whichever car will break down the least. First he read in
Consumer Reports that for 400 cars of each type, the Toyota had more
break-downs than the Honda. Then he talked to three friends. Two
were Toyota owners, who had no major break-downs. The other friend
used to own a Honda but it had lots of break-downs, so he sold it. He
said he would never buy another Honda. Which car should Mr Singh
buy? “(Sharma, 2003, p. 3)
Results and Discussion
This section discusses student responses to the two items mentioned above.
The main focus is on the language challenges faced by these students. Extracts
from individual interviews are used to explain student thinking.
As mentioned in Sharma (2006, p. 48) ”one student explained that Item 1 was
really to do with a doctor charging a $20 consulting fee to inform the parents of
the sex of their unborn baby”. Even when asked to explain how those involved
in putting the advertisement could benefit, the student could not articulate on
the relationship between theoretical and experimental probability.
Three students thought that the advertisement was placed to make money.
When asked to explain their reasoning, “students talked about businesses
putting advertisements to sell their products. There was no evidence of students
integrating theoretical and experimental views of probability”(Sharma, 2014).
It appears that for these English language learners working in different
contexts and registers posed challenges, students were not able to shift between
informal and formal ways of expressing their thinking. The findings resonate
with the conclusions of (Bishton, 2009; Boero et al., 2008). For the students to
succeed in the problem they needed to not only be familiar with both ordinary
English and mathematical registers, but they also needed strong ability to switch
between them in order to cope with different interpretations of probability
(Parvanehnezhad & Clarkson, 2008; Padula et al., 2001). Additionally, not
having the necessary technical, mathematical vocabulary may have hindered
students‟ mathematical communication.
To buy a car based on a report of 800 cases (Item 2) represents the statistically
appropriate response because it represents the population more reliably.
According to Sharma (1996, p. 5) “nine students did not use sample size
information on the car problem (Item 2), they based their responses on their
cultural beliefs and experiences”. Rather than referring to 800 cases in a
consumer report, three students in this study said that Mr Singh could buy
either car because the life of a car depends on how one keeps it (Sharma, 1996).
They did not apply the idea that a larger sample will produce more accurate
estimates of population characteristics. For example, one student explained:
“He should buy any of the cars Honda or Toyota; it depends on
him how he keeps and uses the car … Ah … Because it depends

29
on the person, how he follows instructions then uses it. My father
used to own a car and he kept it for ten years. He sold it but it is
still going and it hasn‟t had any major breakdowns.” (Sharma,
1996, p. 6)
As stated in Sharma (2003, p. 4) four students based their thinking on their
everyday experiences with consumer reports. Students thought that Mr Singh
should take advice from a consumer report because they were the right people
to consult or they felt that Mr Singh should not take advice from the consumer
reports because consumer people often give misleading information.
Two students thought that Mr Singh should buy a Toyota. They drew upon
information given in the consumer report as reflected in the following transcript;
“S; Mr Singh should buy Toyota.
I: Why do you think Mr Singh should buy Toyota?
S: Consumer people did the survey with 400 cars. They used a big
sample.
I: But here it says … Toyota had more break-downs.
S: Sorry, Madame did not read the question properly. He should
buy Honda … Toyota more break-downs.”
The student quote above reinforces to us that students can struggle with
thinking of the sample size in relation to the population, rather than in relation
to the representativeness of the sample. It appears that everyday reading
strategies of skimming and using the context or knowledge of the world to
support comprehension are insufficient for reading statistical English. As a
result, students constructed responses based on these unintended strategies.
The above findings concur with the findings of Padula et al. (2001) and
Kester-Phillips et al. (2009). The authors stated that reading mathematical texts
provides the learner with an extra challenge over reading English “because they
have to simultaneously comprehend and process in both the language of English
and the language of mathematics.”
When asked to define the word sample, five students based their ideas on
previous everyday experiences. They thought that a sample is any small
quantity, or an example of something. For instance, a student explained,
“Eh … sample. Sample is like … in the body you take a small
amount of blood to test whether a person has some disease or not.
If a person wants to give blood to other person, they take out a
sample and test in the lab.”
When asked whether he thought a blood sample is different from a sample
that is selected for research, he said,
“In the maths text book taking a sample means taking small
amount. If you are doing a research like the one you asked me in
the last interview, so you ask each and every student.”
The particular problem here is that the two meanings are not far apart; the
differences are quite subtle. The word sample has a wide general interpretation,
being met in such contexts as a sample survey, free samples of consumer goods,
and samples of blood and urine in medical investigations.
A small number of students used their prior school experiences in
constructing a meaning for range. The students used an algebraic context and
thought of the range as the set of second elements in an ordered pair. They

30
appeared to relate their relations and functions knowledge to this statistics
question.
When asked to find the range from a data set (nine weights recorded in
grams), two students said, “that the range was the second element in the data set.
This is evident in the following interchange” (Sharma, p. 2003, p. 5):
I: What is the range for this data set?
S: 6.0
I: Why do you think so?
S: There are two numbers. First is 6.3 and second is 6.0 and the
first number is domain, the second number is the range.
In the supporting documents, special names are given to the set of first
elements used in a relation and to the set of second elements. The domain is the
set of first elements, and the range is the set of second elements. It seems that the
above student tried to use her previous knowledge about relations and functions
to find the statistical range.
The findings resonate with the findings of a number of authors (Barwell, 2012;
Boero et al., 2008; Bose & Choudhury, 2010; Goldenberg, 2008). These
researchers claim that for students to succeed in a mathematics classroom, they
must have fluency in what can be multiple mathematical registers. The mastery
of the mathematical and statistical registers, and the ability to switch between
them, requires strong linguistic and metalinguistic skills.
The vocabulary and syntactical structure used in statistics can present unique
challenges to all learners, due to the frequent use of familiar English words and
phrases that are assigned different meanings (Kostopolos, 2007). This again is
something that all learners need to learn to understand and work with, but gives
added challenge to English language learners as they must simultaneously learn
and work within both ordinary and mathematical and statistical English (Winsor,
2007).
According to a number of researchers (Bose & Choudhury, 2010; Clarkson,
2007; Moschkovich, 2005; Parvanehnezhad & Clarkson, 2008; Salehmohamed &
Rowland, 2014), English language learners often employ code switching to
clarify their understanding and as a way to express their arguments and ideas.
None of the students in my study used this strategy although they were told
during the individual interviews that they could explain their thinking using
their home language (Hindi) or English language. One reason for this
discrepancy could be the “political role of language and the complexity of the
context in which mathematics is taught and learned”(Planas, 2012, p. 337) in Fiji.
Students are not allowed to use their first language in their mathematics classes
as teachers may think that fluency in English has an impact on students‟ access
to higher education and qualified employment. Hence, any behavior contrary to
the classroom norm may have been seen as a sign of disrespect to the teacher.
Indeed the socio-cultural context can have an impact on students‟ mathematics
learning.
Reflections
When planning a unit in statistics, it is vital for teachers to be aware of the
prior knowledge and linguistic ability of their students. Once this information
has been collected, teachers could build on this understanding. Teachers could
use questions such as Item 2 as a starter for discussion of sample size, method

31
and potential bias. It is likely to generate stories from students‟ family
experiences of buying cars, for example, asking a friend.
In statistics, students need language and statistical skills to relate their
thinking to the real life context and to communicate their ideas both verbally
and in writing. However, teachers may not have the skills to help students
develop communication skills and sound statistical arguments due to a lack of
opportunities to develop their own statistical skills. This has implications for
mathematics teacher educators.
As well as statistical and mathematical knowledge, contextual and statistical
language and English literacy knowledge and skills are important for making
sense of statistical tasks. Students need to have reading, comprehension and
communication skills if they are to achieve statistical literacy. The integration of
these skills can occur in everyday life contexts although a careful choosing of
tasks to accommodate reading abilities is required. Text comprehension support
may be important for helping English learners interpret meaning from the often
unfamiliar, out-of-school contexts and writing styles different to that found in
text books.
Although the range can help provide a more complete picture of a data set, it
has received very little research attention. The findings of this study add to the
research literature. Difficulties may also be caused by students not
differentiating between the meaning of statistics range and function range. It is
evident that students do not properly understand the meaning of the term range
even though they can calculate it using "highest minus lowest".
According to a number of authors (Shaughnessy, 2007; Watson, 2006), context
plays a crucial role in the development of statistical thinking. However,
providing students with an unfamiliar context can make their cognitive loads
more difficult. A child's cognitive load increases when they are exposed to
unfamiliar context whilst also grappling with an unfamiliar language
(Goldenberg, 2008). This has implications in an assessment context, as it further
works to advantage students from English speaking backgrounds who belong to
the dominant culture over English language learners, therefore undermining the
validity of the assessment.
In Sharma study, audiotapes were used to record interview data. However,
this approach did not capture student facial expressions and gestures. In future
research, video recordings could help address these shortcomings.
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