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52 Pythagoras 64, December, 2006, pp. 52-61

Reflections on the role of a research task for teacher education in
data handling in a Mathematical Literacy education course

Vera Frith and Robert Prince

Faculty of Higher Education Development, University of Cape Town

vfrith@maths.uct.ac.za and rprince@maths.uct.ac.za

The introduction of the subject “Mathematical Literacy” in the Further Education and Training band
from 2006 has created an urgent need for large numbers of teachers to be educated about the nature of
mathematical literacy and to become effective teachers of it. In this paper we report on an attempt to
contribute to this goal through a curriculum component in an “Advanced Certificate in Education”
course. This curriculum component on data handling was structured around a research task which
required the teachers on the course to practise mathematical literacy in a context where there is close
linkage with other vital competencies, such as verbal reasoning, writing and computer literacy. This
approach articulates well with the kind of teaching envisaged by the curriculum statement for
“Mathematical Literacy”. We report on an initial analysis of the teachers’ reflections on their experience
of the curriculum-embedded research task on this course, the manner in which this task contributed to
their understanding of mathematical literacy as a practice and themselves as practitioners.

Note: We will use the term “Mathematical
Literacy” (in quotes) to denote the school subject,
and mathematical literacy, with lowercase letters,
to denote the practice of mathematical (or
quantitative) literacy.

Introduction
Although “Mathematical Literacy” is being
introduced as a “subject” in the new South African
Further Education and Training (FET) curriculum,
we argue that mathematical (quantitative) literacy
should be understood in the context of the social
practices in which it is embedded. The term
practice is used to include “both what people do
and the ideas, attitudes, ideologies and values that
inform what they do” (Baynham and Baker, 2002:
2). The promotion of any definition of
mathematical literacy will implicitly or explicitly
promote a particular social practice (Jablonka,
2003). The introduction of mathematical literacy as
part of the new school curriculum has the potential
to contribute to the transformation of South
African schooling and society by contributing to
the development of individuals’ ability to
participate fully and critically as citizens (National
Department of Education, 2005a). One of the
consequences of discriminatory educational
policies in South Africa in the past is that
improvements in the general quality of the
mathematical literacy practices in South African
society are urgently needed. We believe the new
curriculum is very welcome as a means towards

promoting this goal. In the medium to long term,
the creation of a more mathematically literate
society will contribute towards the level of
mathematical, scientific and technological
achievement in the country.
The introduction of the new subject of
“Mathematical Literacy” necessitates the training
(or retraining) of teachers to implement this
complex curriculum appropriately. In the same
way that a teacher’s mathematical content
knowledge may be the most important predictor of
learning in the mathematics classroom (Kenschaft,
2005; Ball, Bass and Hill, 2004), so the
development of mathematical literacy by school
learners is likely to be most strongly affected by
the availability of teachers who are highly
mathematically literate themselves.
As part of the preparation for the
implementation of the new curriculum, the four
higher education institutions in the Western Cape
collaborated in developing a number of different
Mathematical Literacy Advanced Certificate in
Education (ACE) courses for delivery in 2004.
These courses were completely new and the
experiences of both the teachers and the teacher
educators on these courses should therefore be
instructive for the design of future courses, which
will no doubt be necessary. In this paper we will
discuss aspects of the design and the experience of
one part of one of these ACE courses. The part of
the course we will focus on consisted of a brief
introduction to mathematical literacy in the context
of the new curriculum, followed by a detailed

Vera Frith and Robert Prince

exploration of the topic of data handling. This will
be referred to as the “data module” in this paper.
In this paper we will first discuss the nature of
mathematical literacy and the approach which sees
it as a practice within a social context. We will
briefly examine the various roles played by an in-
service teacher learning to teach the unfamiliar
curriculum for “Mathematical Literacy”. We will
then outline the design of the “data module” of the
ACE course in the light of these ideas. We will
describe the role of a research task in developing
the teachers’ mathematical literacy practice. In
order to discuss the contribution of the research
task to this development, we examine the teachers’
written reflections on their experience of the task.
This is an initial investigation that is part of a
larger, more long-term research programme
investigating aspects of teacher education for
mathematical literacy.

Mathematical literacy as
contextualised practice
This paper argues for an approach to mathematical
literacy (and other literacies) which sees them as
practices embedded in particular social contexts
(Archer, Frith and Prince, 2002). Baker, Clay and
Fox (1996: 3) refer to “the collection of numeracy
practices that people engage in – that is the
contexts, power relations and activities – when
they are doing mathematics.” Mathematical
literacy should not be seen as only a set of
identifiable mathematical skills that can be learnt
without reference to the social contexts where they
might be applied.
According to Jablonka (2003: 78), “Any
attempt at defining mathematical literacy faces the
problem that it cannot be conceptualised
exclusively in terms of mathematical knowledge,
because it is about an individual’s capacity to use
and apply this knowledge. Thus it has to be
conceived of in functional terms as applicable to
the situations in which the knowledge is to be
used.” This emphasis on the use and application of
knowledge implicitly assumes the importance of
the associated quantitative thinking and reasoning.
We take the view that mathematical literacy
events can be described in terms of the contexts,
the mathematical and statistical content and the
underlying reasoning and behaviours that are
called upon to respond to a situation that requires
mathematical literacy practice. There is a subtle
but important difference between this view, which
sees mathematical literacy as a practice, and the
view expressed in the South African National
Curriculum Statement Grades 10-12 (General)

Mathematical Literacy (National Department of
Education, 2003: 9), which defines mathematical
literacy as a “subject”. However, the emphasis on
problem solving in real contexts is fundamental to
both definitions.
The debate about the meaning of the term
‘mathematical literacy’ (also known as ‘numeracy’
or ‘quantitative literacy’ in different countries) and
its relationship to ‘literacy’ and to ‘mathematics’ is
exemplified by the various articles in the book
Mathematics and Democracy: The Case for
Quantitative Literacy (Steen, 2001). The articles in
this book reinforce the idea that mathematically
literate practice, as opposed to mathematics, is
always embedded within a context. Hughes-Hallett
(2001: 94) summarises the difference between
mathematical (quantitative) literacy and
mathematics as follows: “Mathematics is about
general principles that can be applied in a range of
contexts; quantitative literacy is about seeing every
context through a quantitative lens”.
In thinking about ‘context’, Usiskin (2001)
warns against the use of contrived ‘real-life’
examples masquerading as ‘reality’ in the
mathematics classroom. Teaching “Mathematical
Literacy” requires the use of contexts which are
real for those involved, and which need to be
understood as clearly as the mathematics that is
being applied.
Very often mathematical literacy events (the
situations where mathematical literacy is practised)
require the content, contexts and reasoning that are
usually associated with the use of statistics
(Hughes-Hallett, 2001). Thus data handling is
arguably the most important component in the
“Mathematical Literacy” curriculum and one
which distinguishes it from what is being called the
core “Mathematics” curriculum (National
Department of Education, 2005b).
We adopt the following definition of
mathematical literacy, in which all three
approaches to the description (contexts, content
and reasoning) are embedded:

Mathematical literacy is the ability to
manage situations or solve problems in
practice, and involves responding to
quantitative (mathematical and statistical)
information that may be presented
verbally, graphically, in tabular or
symbolic form; it requires the activation
of a range of enabling knowledge,
behaviours and processes and it can be
observed when it is expressed in the form
of a communication, in written, oral or
visual mode.

Reflections on the role of a research task for teacher education in data handling
in a Mathematical Literacy education course

This definition has been informed by the
discussions and definitions implicit in the
frameworks used by the TIMMS (Mullis et al.,
2003), PISA (Programme for International Student
Assessment, 2003) and ALL (Adult Literacy and
Lifeskills, 2002) studies, but it draws most heavily
on the latter.
The definition of mathematical literacy which
we have adopted implies that being mathematically
literate requires the ability to express quantitative
information coherently in a verbal and visual form.
Kemp (1995) argues that mathematical literacy
includes the ability to communicate clearly and
fluently and to think critically and logically. In
dealing with quantitative or mathematical ideas in
context, students should be able to interpret
information presented either verbally, graphically,
in tabular or symbolic form, and be able to make
transformations between these different
representations. The transformation of quantitative
ideas into verbal messages is the area where a
student’s ability to write coherently about
quantitative ideas will be exercised. Mathematical
literacy also requires the ability to choose the
appropriate form for the expression of a
quantitative idea, and to produce a text that
expresses that idea. Thus the practice of
mathematical literacy must include the ability to
put together a document for a particular purpose in
a particular context.

The teacher as learner in the ACE course
Just as mathematical literacy as a domain can be
usefully conceptualised as a social practice, so has
learning itself been extensively described using a
social practice perspective (Lave and Wenger,
1991; Wenger, 1998). In particular this approach
has been found useful for investigating teacher
learning (Graven, 2004; 2005). Thinking of teacher
learning as taking place within a community of
practice, throws the focus strongly onto the
teacher’s sense of identity and the changes in this
identity that the educational programme brings
about. Graven (2004) also highlights the central
role played by the learner teacher’s confidence. By
examining the teachers’ reflections on their
experience we also emphasise the importance of
these factors.
We have argued that mathematical literacy can
be thought of as a practice within a social context.
Similarly mathematical literacy as experienced by
the learners in educational interventions will be a
different but related practice, which with careful

management by the educator, could be closely
enough related to the practices in broader society
to allow for significant transfer of practices into the
world outside of the educational setting. This
transfer is facilitated by educational practices that
mirror the mathematical literacy practices of
society as closely as possible and assignments
where learners will be required to practise
mathematical literacy outside of the educational
context. This is one of the reasons why, for
example, a research task such as the one described
in this paper is so important.
Although we are focusing in this paper on the
development of the teachers’ mathematical literacy
practices themselves, it is worth pointing out that
the teachers were on the ACE course to develop
their own mathematical literacy practices and to
learn how to teach the subject “Mathematical
Literacy”. In both cases they were subject to the
dichotomy between classroom and “real-world”
practices, and the corresponding confusion of
identities. So not only were they hoping to transfer
their own mathematical literacy practices from the
ACE classroom to their lives as citizens, as
professionals and as “Mathematical Literacy”
teachers in particular, but they were also hoping to
transfer learning about the practice of teaching
from the ACE classroom to their own work
practice in school. The teachers in the ACE
classroom were expected to maintain a dual
identity as learners and as reflective teachers
contemplating implementing a new curriculum, but
without the opportunity to do so until after the
course was completed. Their identity as learners
was further complicated by the fact that they are in
practice already teachers, but not of “Mathematical
Literacy”. So in a sense they were experiencing in-
service teacher education and in another sense it
was pre-service education, given that the new
curriculum had not yet been implemented in the
schools.
So in engaging with the research task in the
course, the teachers had to play and/or reflect upon
various roles (identities). For example, in doing the
research task they were themselves learners within
the context of the course, but were also modelling
the school learners they would be teaching in the
future, by carrying out an assignment identical to
one that might be expected of grade 10 or 11
learners. At the same time as developing their own
mathematical literacy, they were expected to
reflect upon their role as teachers in the classroom,
both in their current practice and in their future
practice as “Mathematical Literacy” teachers.

Vera Frith and Robert Prince

The “Data module” of the Mathematical
Literacy ACE course
The part-time Mathematical Literacy ACE course,
which lasted for two years, consisted of five
modules, each lasting for the equivalent of one
semester (about 14 weeks). Four of the modules
were devoted to the “Learning Outcomes” of the
school “Mathematical Literacy” curriculum. Thus
there was one module on “data handling”, one on
“numbers and operations”, one on “functions and
algebra” and one on “space and shape”. The
teaching and assessment of the material for the
fifth module, which was on “curriculum and
assessment”, was integrated throughout the four
other modules. The students on the course, who
were practicing teachers, were required to attend
scheduled three-hour classes once a week. There
were also additional classes and computer
laboratory sessions for those needing extra
assistance. Students were also expected to do
homework and complete assignments for
assessment in their own time. There was a final
written examination for each of the four modules
that were based on the “Mathematical Literacy”
curriculum learning outcomes.
The first semester of the ACE course was
devoted to data handling (which we call the “data
module” for convenience). The mathematical and
statistical content for this course was the analysis,
representation and interpretation of data. For the
design of the data module we drew upon our
experience in designing curricula for and teaching
on quantitative (mathematical) literacy courses for
first year university students on a variety of study
programmes (Archer, Frith and Prince, 2002; Frith,
Jaftha and Prince, 2005). The principles that
guided our curriculum design (consistent with
seeing mathematical literacy as contextualised
social practice) were:
• that material should be context-based

and make use of real relevant
intrinsically motivating contexts,
wherever possible;

• that curriculum tasks should require the
exercise of several related competencies,
such as writing and using computers, not
just mathematical skills;

• that the production of a (mainly verbal)
product as an outcome of
mathematically literate practice is
important (as well as the understanding
and interpretation of existing
information);

• that students’ confidence should be
promoted;

• that co-operative learning should be
emphasised.

The 14 three-hour classroom sessions were run
as workshops with limited presentation of course
content at the blackboard. Students worked in
groups and engaged with the course materials
while lecturers acted as facilitators. Some sessions
were conducted entirely in the computer laboratory
so that students could develop proficiency in using
a spreadsheet program. The first three sessions
provided an initial orientation to the nature of
mathematical literacy and to the Subject Statement
and Assessment Standards for the subject
“Mathematical Literacy”. The rest of the first
semester was devoted to the study of Learning
Outcome 4: Data Handling from the Subject
Statement (National Department of Education,
2003).
At the beginning of the course the 33 teachers
(of whom 29 completed the ACE course
successfully) wrote an extensive pre-test, designed
to assess their mathematical literacy and reveal
areas of strength and weakness. The use of this test
for similar purposes was described by Prince and
McAuliffe (2005). For those students whose results
on this test indicated the need for additional
instruction in specific mathematical and statistical
concepts, extra workshops were provided. These
workshops were intended to provide these teachers
with a sense of competence and confidence to play
an active and constructive role in the main
classroom sessions. For this module formative
assessments were used and a summative
assessment (final examination) was written at the
end.

The Research task in the data module
Structuring the curriculum of the “data module”
around the execution of an independent research
task provided an ideal environment for the
development of the teachers’ mathematical literacy
practice by realising the curriculum design
principles outlined above. A research task of this
nature is a mathematical literacy event which has
many affordances, such as enriching the
understanding of sampling, bias and uncertainty,
developing data handling techniques, use of
language and technology, and promoting
quantitative reasoning. Similar affordances
provided by graphical representations are explored
in Prince and Archer (2005). It was assumed that
by learning about data handling within the context
of completing an authentic task, the relevance of
the curriculum content was demonstrated and the
motivation of learners was promoted. It also allows

Reflections on the role of a research task for teacher education in data handling
in a Mathematical Literacy education course

for the various literacies (for example, writing and
use of technology in the form of calculators and
spreadsheet applications) to be used in a way that
is less contrived and closer to a ‘real-world’
experience.
Although the research task was done by the
teachers individually mostly in their own time, the
course provided extensive scaffolding exercises
and opportunities for cooperative work with other
students. The task was identical to one presented
using a similar curriculum structure in a grade 10
textbook (Bowie, Frith, Prince and Schauerte,
2005) and similar to the research task in the
companion grade 11 text book (Bowie, Frith and
Prince, 2006). The task was presented at the
beginning of the data module and students were
informed that they would be expected to work
consistently on the execution of the task, in step
with the scaffolding provided throughout the
course. An extract from the statement for the
research task is shown in figure 1.

Research task
For this project you will work on your own and do
your own survey. In this chapter you have seen
two examples of the kind of survey you should do.
All the steps that you have to do to complete a
survey are covered in the units in this chapter.

Suggested example of a survey:
Purpose:
To find out about young people’s attitudes towards
living in South Africa.
Questions:
• Age, gender, grade at school, etc.
• How positive do they feel about their future in

South Africa?
• How important do they think it is to vote in an

election?
• Do they think South Africa has a lot to offer

young people?
• How proud are they to be South African?
• How important is it to them that South African

sportsmen and women should win in
international competitions (such as the
Olympics)?

Figure 1: Abridged extract from a grade 10
textbook presenting the “research task”

Teachers were also free to devise their own
research questions, relating to aspects of the lives
of the school learners they were currently teaching.
For example, one teacher researched learners’
living conditions and another researched learners’
attitudes towards nutrition and exercise.

The scaffolding exercises were structured to
provide support in parallel with the execution of
this task, in a similar manner to the way support
was provided in the textbook. We believe that it is
more effective to provide scaffolding as the task
unfolds (rather than before it is attempted), as
transfer of knowledge is more likely to take place
if the connections are made more explicit in this
way. For example, the first session provided a
framework for understanding the research process
as a whole, while during the second session
students worked together to pilot and refine their
survey questions for the project. At this stage they
were expected to conduct their survey and gather
their data. During sessions two to seven, students
were expected to reflect on the relevance to their
research of the techniques for data analysis and
representation covered in the workshop sessions,
and to apply these techniques to their own data
(including the use of spreadsheets). At the same
time they were told that they should be working on
writing up their report. In the ninth session they
were assisted by a language expert (a lecturer from
the Language Development Unit at the University)
to peer-edit each other’s writing and to provide
constructive criticism, before revising their draft
reports for final submission at the end of the data
module.
In structuring the “data module” this way, the
intention was to provide as authentic as possible an
opportunity to experience and become more expert
in mathematical literacy practice. The intention of
the research task was that the teachers would:
• Become proficient at analysis,

representation and interpretation of data.
• Develop an appreciation for the

processes that comprise quantitative
research and the manner in which they
could influence the research results.

• Recognise through experience the
importance of using relevant contexts as
a vehicle for learning “Mathematical
Literacy”.

• Work cooperatively with peers and other
educators.

• Communicate their findings effectively
in the form of a written report.

• Reflect on the implications of their
experiences for their mathematical
literacy practice.

The Reflection task in the data module
For the discussion of the effectiveness of the
research task in achieving the intentions listed

Vera Frith and Robert Prince

above, in this paper we will focus on the teachers’
reflections on their experience of this task.
As part of the research task (“project”)
statement, students were also asked to reflect on
their experience of the process of completing the
task. To assist them to structure their thoughts,
they were given the following guiding questions
(which are also part of the “project” task in the
school learners’ textbook referred to above):
• Which part of the project did you find

the easiest to do?
• Which part was the hardest?
• What would you do differently next

time?
• Is there any part of the process of doing

a survey that you will need to get help
with before you do a similar survey
again?

• Did you enjoy doing the project?
Explain why or why not.

• Describe the main thing that you think
you learned from doing this project.

Of the 33 teachers on the course, 29 included
written reflections with their project submission.

Teachers’ reflections on the research task
(the “project”)

Parts of the “project” teachers found easiest:
Most teachers said that the easiest part of the
project was the actual collection of the data by
administering their questionnaire to the learners at
their school. Some cited the choice of research
question as the easiest aspect and several others
found the mechanical processes of data analysis
(such as drawing up frequency tables or calculating
statistics) the easiest part.

Parts of the “project” teachers found difficult:
More than half the teachers described their
difficulty in designing the questionnaire for their
survey. Comments like the following were fairly
common: “(The hardest part was) setting and
changing the questions to the questionnaire to
make it appropriate for my survey’s statement and
to minimize ambiguity.”
Many teachers also reflected on the difficulties
they had experienced with the analysis and
interpretation of their data. In some cases they
were aware of difficulties in deciding which kinds
of analysis and representations to use, or
difficulties in actually performing this analysis:
“The analysis of the data was difficult for me as I
was not always sure which tools to use to present

the data and if the choices I made was the
appropriate ones.”
About one third of the teachers reflected
specifically on their difficulty with the writing of
the report and the kinds of reasoning that this
required. The following is typical: “The analyzing
and the reporting of the findings were difficult as
this needed a reflection on the data provided and to
comment on what was evident there. The writing
of the report was also difficult because it needed an
unbiased opinion and the facts stated had to be
always based on the information provided.”

Parts of the “project” teachers would do
differently:
The most frequent observations under this heading
were to do with improving the questionnaire
design and changing the size and nature of the
sample, either to make the task more manageable
or to improve the quality of the information
obtained. Several teachers also commented on the
need for better planning and time management,
particularly to allow for more input from and
interaction with peers. Some mentioned the need
for a more unified approach to the whole research
process and others observed that they would use a
spreadsheet for their data analysis.
The following quotes highlight some of these
issues: “Based on my question, I would get an idea
of what it is that I would like to discuss in the
report and ensure that the questionnaire provides
me with information to be able to do this. In this
way each part of the activity is not seen as isolated
or independent of the other, because the
questionnaire is eventually going to impact on
what you are able to write about in the report.”
And, “The second (thing I would do differently) is
to get constant feedback from fellow class mates so
that I can face the next task with more confidence.”

Parts of the process where teachers would need
more help:
Most teachers who responded to this question said
that they would need help with the questionnaire
design and/or the writing of the report. Thus it
appears that they are least confident about the
ability to communicate quantitative ideas in
writing. A few teachers also indicated a lack of
confidence in their ability to analyse and present
their data graphically in an appropriate way. A few
students identified the need to improve their ability
to interpret the data: “(I would need more help
with the stage where) you have collected the data
and need to make statements about the findings.
The session on writing the report focused on the

Reflections on the role of a research task for teacher education in data handling
in a Mathematical Literacy education course

actual writing of the interpretations. How to make
those necessary interpretations is important and
needs more developing.”

Teachers’ enjoyment of the task:
More than two thirds of the teachers said that they
had enjoyed the research task, in spite of some
having reservations about time pressure and
anxiety about whether they “were on the right
track”. The following quotes illustrate how the
context of the learning task can influence the
affective reaction to it: “I did enjoy doing the
survey. The challenge of designing an applicable
questionnaire was exhilarating. Seeing the results
emerging, analyzing it, seeing a pattern in the
learners’ responses and then writing up the results
kept me curious.” And “… I feel a sense of
achievement. I started something which I took
control of fully and have completed it to the best of
my ability.”

Teachers’ opinions about the main things they
learnt from doing the project:
Teachers mentioned a large variety of topics under
this heading, such as report writing, data analysis
techniques, questionnaire design and the value of
collaboration, for example: “I learned mostly how
to work with people including learners and my
fellow students and lecturers.” However, the most
frequently mentioned topics were to do with an
appreciation of the processes that research entails,
and/or the need for planning and time
management, for instance, “I now have a fairly
good idea of what research entails. I actually
collected the raw data which we only see in books.
We started a process at the very beginning,
processed the data and carried the process through
to the end.”
It is telling that for some teachers the most
significant learning was not about data handling or
the research process, but arose from the context of
the research itself. These teachers cited as most
important insights they had gained about their
school learners, which arose either from their
actual research results or from the experience of
their engagement with the research task.
Reflections like the following illustrate how
relevant the research task was to the teachers’ real
working environments: “I learned to be more
tolerant and patient towards the learners. I now
consciously listen to their reasons for
absenteeism”; “Young people are extremely
willing to be co-operative and helpful. They are
enthusiastic to help adults on condition that their

assistance is acknowledged and they don’t feel
exploited.”

Discussion
We discuss the teachers reflections in the light of
each of the stated intentions of structuring the data
module around the execution of a research task.
These intentions were listed above at the end of the
section under the heading “The Research task in
the data module”.

Becoming proficient in the analysis, representation
and interpretation of data:
Although the analysis and interpretation of data
was a major component of the material covered in
the classroom sessions and some teachers cited it
as the easiest aspect of the project, there were still
many teachers who reflected on the difficulties
they had experienced with the analysis and
representation of their data. Other teachers
commented not so much on the data analysis as on
their difficulties with the more subtle task of
deriving meaningful quantitative information from
their representations of the data.
These difficulties reveal a worrying lack of
competence with tasks which are fundamental to
the achievement of Learning Outcome 4 Data
Handling (National Department of Education,
2003), but which cannot be assumed to be common
knowledge even for a person with a reasonable
level of mathematical education. This points to the
need for extensive training of teachers in data
handling and interpretation, especially as this is a
new component in the Mathematics curriculum as
well.

Developing an appreciation for the processes that
comprise quantitative research and the manner in
which they could influence the research results:
A number of students discussed their growing
awareness of the interdependence of the
components of the research process. In grappling
with their difficulties with questionnaire design,
they developed an awareness of the impact of the
research instrument and method on the quality of
the data that could be collected, and hence the
conclusions that could be drawn. This kind of
insight is valuable both for their own development
as mathematically literate practitioners, and for
making them more able to promote critical
thinking about data in the classroom (which is
heavily emphasised in the “Mathematical Literacy”
FET curriculum). An appreciation for the
dependence of the quality of the data and the
conclusions drawn from it on the research

Vera Frith and Robert Prince

processes (such as possible bias in sampling) is one
of the learning outcomes, which we believe is best
learned in practice.
When they reflected upon the research process,
in terms of their own engagement with it, one of
the strongest themes to emerge was to do with time
management. Teachers developed an appreciation
for the importance of drafting and redrafting
questions and text using input from other people:
“… my concern was the process that I had to
follow. But when I started interacting with my
fellow colleagues, the whole picture became more
clear. I started rephrasing my research questions,
and once this was done, working through the
process step by step became easier. The lectures on
analytical and graphical presentations of data
added more clarity. Hence the knowledge that I
gained in class helped me further to develop my
understanding of my own research project.”
The teachers’ reflections on the process make it
very clear that they feel that it takes considerable
time to communicate with peers and to assimilate
and practise applying the new competencies learnt
in the course. The reflections generally create the
impression that the research task was an effective
vehicle for this, although even more time would
have been appreciated. The implication of this is
that “crash courses” for “Mathematical Literacy”
teachers will probably be less effective at
developing teachers’ mathematically literate
practice.

Recognising through experience the importance of
using relevant contexts as a vehicle for learning
“Mathematical Literacy”:
Most of the teachers reported having enjoyed the
research task. One of the intrinsically motivating
factors was their interest in the information they
were gathering itself. So for these teachers the task
had intrinsic value, not just as an assignment for
the course, but as a task that illuminated and
enriched their teaching experience. Some teachers
also made statements that revealed that completing
the research task gave them a sense of worth and
an identity as a researcher. These experiences
highlight the power of using real, relevant and
intrinsically interesting contexts as a vehicle for
developing mathematical literacy and promoting
learners’ confidence.

Working cooperatively with peers and other
educators:
Just under half the teachers made some comment
reflecting their appreciation of the value of
collaborative work with other teachers (and in

some cases their own school learners) and of
gaining input from the lecturers during the research
process. “Peer assessments of our projects helped a
lot, because you can make the changes as you go
along. Other people’s different perspectives allows
you to broaden your own perspective and enriches
yourself to complete a project with success.” In our
opinion, this aspect of their experience of doing the
research task may be one of the most valuable in
terms of preparing them to be effective facilitators
of learning in the “Mathematical Literacy”
classroom, where they will be expected to motivate
school learners to work collaboratively and to
facilitate this kind of learning.

Communicating findings effectively in the form of a
written report:
More than half the teachers described their
difficulty in designing the questionnaire for their
survey. This highlights the importance of the
“literacy” component of mathematical literacy.
About one third of the teachers reflected
specifically on their difficulty with the writing of
the report and the kinds of reasoning that this
required. The general level of difficulty
experienced in writing about data was also
reflected in the quality of the reports, which
indicated that teachers were probably not
adequately prepared to support school learners
with this kind of writing task, which is a
fundamental component of “Mathematical
Literacy”. Further research will focus on the
insights that can be derived from a close study of
the actual research reports submitted.

Conclusion
In designing a curriculum for “Mathematical
Literacy” teacher training, it is useful to frame
mathematical literacy as contextualised social
practice. Some of the implications of this
framework for the curriculum are that
mathematical and statistical content should be
taught through learners’ engagement with realistic,
relevant contexts; that critical thinking and
communication are important elements and that
collaborative work should be encouraged. The
development of positive attitudes and confidence
should also be promoted. We maintain that
structuring the curriculum of the data handling
component of a “Mathematical Literacy” course
(for teachers or for school learners) around the
execution of a scaffolded research task provides an
effective environment for the realisation of these
principles. This view is supported by the results of
our analysis of the reflections written by the

Reflections on the role of a research task for teacher education in data handling
in a Mathematical Literacy education course

teachers about the research task in the “data
module” of the Mathematical Literacy Advanced
Certificate in Education course.

Acknowledgement
We are very grateful to our late colleague, Stella
Clarke, who assisted us with facilitating the writing
component of the research task, reported in this
paper, at a difficult time in her life. We are also
grateful for the insights and inspiration we have
received from her.

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Mathematics is not only real, but it is the only reality. That is that
entire universe is made of matter, obviously. And matter is made of
particles. It's made of electrons and neutrons and protons. So the
entire universe is made out of particles. Now what are the particles
made out of? They're not made out of anything. The only thing you
can say about the reality of an electron is to cite its mathematical
properties. So there's a sense in which matter has completely
dissolved and what is left is just a mathematical structure.

– Martin Gardner