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A year of engaging with the Discipline of Noticing: five mathematics
lecturers’ reflections
Sinead Breena, Aisling McCluskeyb, Maria Meehanc*, Julie O’Donovand
and Ann O’Sheae
aMathematics Department, St Patrick’s College, Dublin, Ireland; bSchool of
Mathematics, Statistics and Applied Mathematics, National University of Ireland,
Galway, Ireland; cSchool of Mathematical Sciences, University College Dublin,
Ireland; dMathematics Department, Cork Institute of Technology, Cork, Ireland;
eDepartment of Mathematics and Statistics, National University of Ireland, Maynooth,
Ireland
In September 2010, five mathematics lecturers set out on a professional
development project with the following aim: to reflect on teaching practice using
John Mason’s Discipline of Noticing. At the end of the academic year, each
lecturer considered her experiences of engaging with the process. In this paper we
describe the observations made and discuss the benefits and challenges of engaging
with the Discipline of Noticing, namely, the benefits of a collaborative approach;
the challenges of ‘noticing in the moment’; and the advantages of, and difficulties
with, writing brief-but-vivid accounts.
Keywords: reflection; discipline of noticing; brief-but-vivid accounts
Introduction
The five authors of this paper are mathematics lecturers from five university-
level institutions in Ireland who embarked on a professional development project with
the aim of developing sustained reflection on, and critique of, their teaching practice
using John Mason’s Discipline of Noticing (2002). It was decided that for the academic
year 2010-2011 each lecturer would keep accounts of moments or critical incidents
from her teaching and periodically circulate these to the rest of the group. It transpired
* Corresponding author. Email: maria.meehan@ucd.ie
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that at the group meetings, held every six to eight weeks, there was discussion about the
Discipline of Noticing itself and due to the predominance of these discussions, each
lecturer reflected on her experiences of engaging with the process at the end of the
academic year. In this paper we describe these experiences and address the following
research question: What are the benefits and challenges for third-level mathematics
lecturers of engaging with the Discipline of Noticing as a means of reflection?
The value of reflection for teachers at all levels has been widely acknowledged
(Bell, Mladenovic, and Segara 2010; National Council of Teachers of Mathematics
2010). The literature on reflection is extensive, with multiple meanings attached to the
term, and references to the concept appearing in a wide range of disciplines (Hatton and
Smith 1995; Moon 2004). While a discussion of reflection can be found in Dewey’s
Democracy and Education published in 1916, most of the literature on the topic dates
from the 1980s onwards with Schön’s work (1983, 1987) on the role of reflection-in-
practice and reflection-on-practice within a variety of professions acting as a catalyst for
study in this area.
In this paper, we report on our experience of using a particular form of
reflection, that is Mason’s Discipline of Noticing. We will describe the Discipline of
Noticing in detail in the next section, but Mason (2002, 59) summarises it as “a
collection of practices which together can enhance sensitivity to notice opportunities to
act freshly in the future”. When considering Mason’s work, Loughran (2006, 46) spoke
of the close relationship between noticing and reflection:
A most important issue that he [Mason] raises relates to the point that if something
is not noticed, then it is unlikely that a response will be forthcoming. Therefore that
which is noticed, how and why, carries influence not only on the nature of
reflection but also on the action(s) as a result of reflection.
He also observed that the purpose of reflection could influence that which is noticed,
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and so noticing and reflection are closely linked.
Researchers have used the term noticing in ways that are slightly different to
Mason’s. For example, van Es and Sherin (2002, 573) defined the aspects of noticing as
follows:
(a) identifying what is important or noteworthy about a classroom situation; (b)
making connections between the specifics of classroom interactions and the
broader principles of teaching and learning that they represent; and (c) using what
one knows about the context to reason about classroom events.
Some authors may consider noticing as a process which only involves aspect (a) above,
but Sherin, Jacobs and Philipp (2011, 5) reported that for most researchers in this field
noticing involves both attending to and making sense of events in a classroom situation.
They advocate the use of noticing by teachers and assert that it can lead to adaptive and
responsive teaching, can allow teachers to learn from teaching (for example by
attending to students’ thinking), and can help them decompose practice into core
activities and develop a language with which these can more readily be discussed.
There have been relatively few studies which involve mathematicians at
university level making use of noticing in their classrooms or reflecting on their own
teaching. Indeed Speer, Smith and Horvath (2010) considered undergraduate
mathematics teaching and noted that
very little research has focused directly on teaching practice - what teachers do and
think daily, in class and out, as they perform their teaching work. (99)
However, some work has been done on this topic recently for example by McAlpine
and Weston (2000); Paterson, Thomas, and Taylor (2011); Hannah, Stewart, and
Thomas (2011); and Jaworski and Matthews (2011). These studies employed a variety
of different conceptualisations of reflection but have at least two features in common -
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firstly, reflection is undertaken as a collective endeavour, and secondly, both
mathematicians and mathematics educators are involved in the process.
The Discipline of Noticing
Mason (2011, 37-38) characterises the Discipline of Noticing as follows:
The discipline of noticing is a collection of techniques for (a) pre-paring to notice
in the moment, that is, to have to come to mind appropriately, and (b) post-paring
by reflecting on the recent past to select what you want to notice or be sensitised to
particularly, in order to pare, that is, to notice in the moment (italics author’s own).
In Mason (2002, 33-34) he distinguishes between three levels of noticing: “ordinary-
noticing” in which one’s memory of something can be jogged if someone else remarks
upon it; “marking” in which one has taken sufficient notice of something to “re-mark”
upon it to someone else; and “recording” where one makes a note of something one has
noticed, usually in writing. He proposes that each level of noticing requires an
additional level of energy in order to enact it. However he suggests that energy is often
dissipated when we grumble about an incident to others, and this energy could be put to
better use in recording the incident. To do this he specifically advocates the writing of
“brief-but-vivid” (46) accounts. These are brief accounts which give an “account-of” a
situation or incident, rather than an “account-for” it. Mason (41) explains:
To account-for something is to offer interpretation, explanation, value-judgement,
justification, or criticism. To give an account-of is to describe or define something
in terms that others who were present (or who might have been present) can
recognise.
A reason for giving an account-of, as opposed to an account-for, is to force “an inner
split between actor and observer” (19), allowing one to re-enter the experience perhaps
more objectively at a later stage, without biasing the account with personal views at the
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time of writing. An account should be vivid in the sense that someone who reads it can
recognise or recollect a similar situation or phenomenon from his or her own
experiences. In particular he stresses that brief-but-vivid accounts are not the data for
professional development: “They are merely entry points to experience. It is the
experience which is the data.” (52)
Mason (2002, 95) summarises the collection of practices involved in noticing
using four headings: systematic reflection, recognising, preparing and noticing, and
validating with others. “Systematic reflection” involves not only keeping brief-but-vivid
accounts, but also examining a collection of accounts to find “threads” (65) or themes
that perhaps highlight, or sensitise you to, some aspects of your practice. Working on
accounts with others can lead to phenomena being identified and labelled (79) as well as
alternative strategies being distinguished. Mason asserts that this process increases the
likelihood of recognition both of choices and of possibilities for acting differently in the
future (70). This is what he describes as “recognising”. To increase the chances of
noticing a possibility during a class, and having an alternative technique come to mind
in-the-moment, Mason advocates vividly imagining oneself carrying out the technique.
He refers to this step in the process as “preparing and noticing”. Finally, an important
action of the Discipline of Noticing is highlighted as the “construction, refinement, and
modification of means to communicate and enrich noticing with others” (90). This can
be achieved via a “task-exercise” (91) which is an account that has been refined or
honed from a brief-but-vivid account or accounts to produce a description of something
that others can instantly recognise and identify with. This is what he describes as
“validating with others”.
The individual hoping to engage in “disciplined rather than sporadic and
serendipitous noticing” (Mason, 2002, 61) must be prepared to work on the collection of
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practices described above in a manner that is “systematic and methodical without being
mechanical” (59). One must discipline oneself to engage in, and develop, these practices
over a sustained period of time, and it is therefore not surprising that Mason states that
the “Discipline of Noticing is aimed at individuals working within a group” (144). He
goes further to say that if the aim of the individual is to experience real change in
practice
it is almost impossible to achieve without a supportive community which develops
a shared language, helps maintain focus and enable individuals to compare and
share experiences, hopes and struggles, so that there is transformation of the social
as well (144).
To summarise, as a professional development tool, the Discipline of Noticing
provides us with a collection of practices that we can engage in, preferably in a group
setting: to enable us to become more sensitive to aspects of our practice that we may
wish to change; to enable us to develop the sensitivity to recognise opportunities to act
freshly as they arise; and, to prepare us to have alternative options come to mind as the
need arises.
Methodology
The five lecturers involved in this project have PhDs in either Pure Mathematics
or Applied Mathematics. While all have engaged in mathematics research, most have
also recently engaged in mathematics education research. Four of the five have over
twelve years experience of teaching mathematics at third-level, while the fifth has been
lecturing for eight years. Most have taught a range of modules from first year to masters
level, and have taught classes ranging in size from single figures up to approximately
300 students.
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The “Noticing Group” first met in September 2010 and decided that for the
academic year 2010-2011, they would bring their teaching and research into closer
relationship by each writing brief-but-vivid accounts of moments or incidents from her
lectures that would be circulated to the other members of the group regularly for
discussion and later analysis. One lecturer took responsibility for setting deadlines for
the accounts to be circulated, and for the coordination of the group meetings. The
number of accounts submitted varied from lecturer to lecturer with some writing an
account of an incident from almost every lecture, while others wrote accounts more
sporadically. The lecturers involved were teaching a range of modules from a first year
mathematics module for Civil Engineers to a masters’ level course in Analytic
Topology. It was also decided that the group meet every six to eight weeks to discuss
any matters relating to the project. In all there were five circulations of accounts and
five meetings between September and May. Topics discussed during meetings varied.
Sometimes there were discussions around a particular account, sometimes there were
similarities drawn between individuals’ accounts, and often the discussion digressed
into some area of mathematics education or some issue concerning classroom practice
or student understanding. At every meeting, there was a discussion on engaging with the
Discipline of Noticing.
Due to the predominance of the discussions on the Discipline of Noticing, it was
decided that each lecturer would write her reflections on the process of engaging with
the discipline for the academic year 2010-2011 and circulate these to the group. To
ensure that each individual’s reflections would be independent of the others, the group
members agreed not to read any other reflections prior to writing her own. No other
criteria were agreed for either the format or content of these reflective pieces. It is these
reflections that we wish to present and discuss in this paper with a view to addressing
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our research question: What are the benefits and challenges for third-level mathematics
lecturers of engaging with the Discipline of Noticing as a process of reflection?
The reflections submitted by each lecturer were between 500 and 1,200 words in
length. Two of the authors independently coded all five sets of reflections using
grounded theory (Strauss and Corbin 1998). In reading each reflection they coded (or
labelled) the points made. When they came across a similar point made by another
person, they used the same code as before or modified the original code so that it would
more appropriately describe all the comments it labelled. Having done this they grouped
the codes into categories with one author using five major categories while the other
used four. However, despite some minor differences in the selection and naming of a
few of the categories (one author had used two categories where the other had used
one), both authors’ codings were very similar. There was agreement on these codes
within the group, and in the next section we present these results. (A brief summary of
these results can be found in Breen et al. (2011).)
Results
Despite being written independently, all five lecturers reflected on most of the
following themes to a greater or lesser extent:
Benefits of collaboration
Challenges of writing brief-but-vivid accounts
Benefits of writing brief-but-vivid accounts
Challenges of noticing in-the-moment
In this section, we describe the lecturers’ reflections under each heading, referring to the
lecturers as Lecturers A, B, C, D and E. These names have been randomly assigned.
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Benefits of collaboration
All five lecturers were united in stating the importance of undertaking the
reflection project as a group. Firstly, working as part of a group provided the necessary
motivation and discipline to keep writing accounts throughout the year. This was the
main practice that all five lecturers engaged with, and the deadlines for accounts to be
circulated meant that the project remained to the fore-front of everyone’s mind.
Personally, I am quite certain nothing would have happened at an individual level
without the group level. There was a “healthy guilt” to have accounts sent in
around the deadline. (Lecturer A)
Working as part of a group also provided the motivation to continue making the effort
to write accounts that were brief-but-vivid.
There is no doubt that I would not have kept writing brief-but-vivid accounts if we
had not been doing it as a group. I had to be disciplined about sitting down to write
them and feel certain that over time, my accounts would have just become logs of
the material I covered in each lecture. (Lecturer B)
Mason (2002, 61) might describe this as being “methodical without being mechanical”.
Secondly, the benefits of meeting up as a group were highlighted. These include
the benefits of discussing one’s classroom practice with others, learning from what
others are doing in practice, clarifying aspects of the Discipline of Noticing with others,
and motivating and supporting engagement in the project.
Regular meetings provided motivation and encouragement. The meetings provided
a forum for discussions of the accounts. I found it very helpful to be able to discuss
and relate similar experiences within the classroom and to listen to others articulate
situations I could relate to. I always left meetings feeling better informed and
enthused about continuing on this project. (Lecturer A)
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Thirdly, working as a group means that each member has access to the accounts
of the other group members. These also provide windows into the ways others deal with
situations in the classroom and think about their teaching. Therefore it is not surprising
that reading the accounts circulated was described by some of the lecturers as being an
interesting and important component of the project.
I found reading other people’s accounts really interesting. I liked finding out about
different teaching styles and hearing how others dealt with problems. I think that
this is a real benefit of a project like this. (Lecturer D)
In addition to providing insights into the practice of others, at least some of the accounts
circulated provided “good” examples of brief-but-vivid accounts. In attempting to
master the art of giving an account-of rather than an account-for an incident, it was
useful to analyse others’ accounts for these qualities. One lecturer who was questioning
how worthwhile providing an account-of an incident was, found that reading the
accounts of others helped her see the benefits of such an approach.
Thus I have struggled with reporting on noticed moments in an ‘account-of’
manner. I have noticed however that through time and particularly with the benefit
of sharing accounts with the rest of the group that it is entirely possible to report
usefully and meaningfully in such a manner. (Lecturer C)
Challenges of writing brief-but-vivid accounts
Not surprisingly, all of the lecturers reflected on the process of writing brief-but-
vivid accounts, and on the challenges involved. As one might expect, one of the first
challenges encountered was that of actually having the discipline to write accounts
(although the group dynamic helped). Most of the lecturers specifically set themselves
the goal of writing an account after each lecture, choosing to focus on a specific event
or incident from the lecture. However sometimes they found it difficult to find the time,
or simply forgot. Interestingly, in relation to actually writing the accounts, two of the
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lecturers commented on the fact that because the account had to be brief and vivid,
and/or provide an account-of an incident rather than an account for, they (initially at
least!) felt the task should be a straightforward one.
I found the idea of “noticing rather than defending, explaining and justifying”
helpful in initiating the report writing in that, all I was required to write down was
what happened and not an indepth analysis. […] However, ironically I think I gave
a considerable amount of personal interpretation in the account and found it rather
difficult to state just what happened without any personal commentary. (Lecturer
A)
Lecturer B reported feeling that the task of writing a brief-but-vivid account seemed
“much less daunting” than that of writing a more reflective piece. Another challenge
arising related to the decision on what to write about and Lecturer D observed that
sometimes it seemed like there was nothing of note to write about, or that a particular
incident which she had already written an account of, kept re-occurring.
Perhaps the two biggest challenges experienced by the lecturers in relation to
brief-but-vivid accounts, were the challenge of writing an account-of, as opposed to an
account-for, an incident; and the challenge of achieving the appropriate levels of brevity
and vividness. The comment above by Lecturer A highlights the difficulty she
experienced in writing an account-of an incident as opposed to an account-for. She was
not alone in this regard and Lecturers D and E echoed her comments. The challenge of
achieving brevity and vividness was experienced differently by members of the group.
Lecturer E struggled with getting the balance right between brief and vivid and even at
the end of the year admitted that she “found, and still finds, the notion of a brief-but-
vivid account difficult to grasp”. Lecturer D and Lecturer B were at opposite ends of the
spectrum when describing the challenges each experienced, with Lecturer D describing
how she felt she was able to write brief-but-not-so-vivid accounts, while Lecturer B
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reflected on how she struggled to tone down the vividness and had to spend significant
time and effort refining her accounts.
I found it easy enough to write brief accounts but hard to write vivid ones. When I
read my accounts now, I remember the experience that I was trying to capture but I
realise that it would be difficult for other people to know what that experience
really was. (Lecturer D)
My first attempt at an account is usually passionate and long and all over the place,
but I find that over several edits it seems to converge to something that isn’t
exactly a brief-but-vivid account by Mason’s standards, but is my attempt at a
compromise account. (Lecturer B)
Finally we discuss a fifth challenge that some of the group experienced in
writing brief-but-vivid accounts: how to write about emotion in accounts. At each group
meeting there was considerable debate over whether emotion was “allowed” in an
account, and if it was, how it should be described. The appearance of the words
“restrain” and “passionate” in Lecturer’s B reflection above alludes to her struggle to
tone down the emotion in her accounts, Lecturer E wrote about writing accounts
“without emotion”, and Lecturer C also noted significant difficulty in this regard. These
lecturers seem to have a particular sense of what a brief-but-vivid account should look
like and may be misinterpreting what Mason says.
Benefits of writing brief-but-vivid accounts
Despite the challenges faced in writing brief-but-vivid accounts, the benefits of
persisting in the process were articulated by most of the group. As noted earlier, one of
the reasons why Mason (2002, 19) advocates giving an account-of an incident, as
opposed to an account-for, is to force “an inner split between actor and observer”. He
also suggests that when frustrated by something that has happened, rather than complain
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about it, one should write an account. Lecturer B and Lecturer E wrote about both of
these benefits in their reflections.
… by writing my whinges down as (bland) accounts instead of just spoofing off, it
somehow enabled me to gain a bit more perspective. Often I found myself thinking
more about where the student might be coming from, and questioning whether
what I was expecting was unreasonable. It helped me stand back and view
incidents in a more measured way. (Lecturer B)
I did find that persisting in trying to write an ‘account-of’ an incident, without
emotion or justification, did help me appreciate the students’ perspective more,
rather than resorting to self-justification. (Lecturer E)
Perhaps most significantly of all, three of the lecturers reflected on what was
emerging for them from their collections of accounts, and had become aware of issues
which needed further investigation and thought:
In previous years, issues that concerned me may have hung around vaguely in the
air and were nothing more than feelings, but by writing the accounts, they have
become more tangible and better articulated. Because of this I now feel I am in a
better position to constructively deal with them. (Lecturer B)
I hoped that the process would help me improve my teaching. I think it certainly
helped me to stand back from it a little and try to analyse it. … I feel that it has
made me aware of some issues but now I need to think about how to change what I
do. This is the hard part. (Lecturer D)
Over the year, I found the same type of critical incident coming to mind a number
of times – indicating, perhaps, an issue I needed to address or had not successfully
addressed. (Lecturer E)
Lecturer E noted an additional benefit of keeping accounts. Her research
interests are in mathematics education and as a teacher, she frequently attempts to
incorporate certain tasks to support student learning into her classes. She found that
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reading her brief-but-vivid accounts enabled her to evaluate these tasks more
objectively. She also observed how her knowledge of the mathematics education
literature influenced her reading of her accounts.
In trying to identify a critical incident and then focusing on it in order to verbalise
it, I found that I could sometimes relate what was happening to
phenomena/constructs described in the literature. (Lecturer E)
Challenges of noticing in-the-moment
As noted previously, Mason (2002, 59) describes the Discipline of Noticing as
“a collection of practices which together can enhance sensitivity to notice opportunities
to act freshly in the future”. We were interested in whether engaging in the practice of
keeping brief-but-vivid accounts had increased the participants’ sensitivity to notice
such opportunities. Four of the lecturers addressed the idea of noticing “in-the-moment”
in their reflections. Three reported little success, especially during the first semester.
Lecturer C in particular felt that noticing in-the-moment and enjoying the flow of the
lecture were mutually exclusive.
For me there was an uneasy tension in trying to enable and then enjoy the flow of a
class against trying to notice various features alongside this. (Lecturer C)
Moreover, Lecturer B reflected that it was precisely when there was not much
happening in class that she remembered to try and notice.
However, these three lecturers stated that they reflected on the lecture
afterwards, with two specifically stating that this is something they would do on the
walk back to their offices immediately after class. Thus if there was an incident of note
to write about, they recalled it easily immediately after the class.
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The fact that I consciously looked for something of note to write about after most
lectures, meant that things I would normally have just “ordinary-noticed”, I then
“marked” and then if I went on to write about them, or “record” them, meant that
they really were to the forefront of my mind throughout the semester. (Lecturer B)
Indeed some of the lecturers did note success at noticing in the second semester of the
academic year. While this could obviously be explained by having already engaged with
the Discipline of Noticing for a semester, the lecturers also conjectured that there were
conditions that may be more conducive to noticing than others. In particular success at
noticing was reported when the lecturer had a small class and/or was very familiar with
the students in the class.
The regularity with which I met with this group of students (seven times each
fortnight) and the resulting regular practice of reflecting and writing accounts
helped me to develop an ability to notice ‘in the moment’. (Lecturer E)
In the second semester, I found it a bit easier to remember to notice during class.
This might be because I was more familiar with the discipline, or maybe the fact
that I had much smaller classes helped. (Lecturer D)
Discussion
Although the five lecturers involved in this study teach mathematics, and indeed
Mason is an eminent researcher in mathematics education, the Discipline of Noticing is
not aimed specifically at mathematics teachers. Mason (2002) promotes it to teachers
who wish to improve their practice, broadly defining a teacher as “anyone working with
others in some caring or supportive capacity which draws upon the exercise of
professional expertise” (1). To the best of our knowledge, this is the first study to
explore the use of the Discipline of Noticing as a professional development tool for
teachers in higher education. In this section we discuss the implications of this study for
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those teaching in higher education that may wish to engage in the Discipline of Noticing
as a means of examining and improving practice.
As noted earlier, Mason (2002) asserts that the Discipline of Noticing is aimed at
people working within a supportive group. He notes (144):
Real change also requires the support of a compatible group of people whose
presence can sustain individuals through difficult patches, and who provide both a
sounding board and a source of challenge for observations, conjectures and
theories.
Our results strongly support Mason’s assertion and highlight specific benefits of
engaging in the Discipline of Noticing as a group. The importance for teachers in higher
education of reflecting on practice within a group setting has also been emphasised by
others. For example, Bell, Mladenovic and Segara (2010) contend that sharing and
discussing experiences (a social model of reflection) is particularly effective for
academic development, while Pereira (1999) also emphasises the need for collaborative
reflection. The group aspect of this project seemed to be crucial to its success in
another way, in that the group dynamic often provided members with the self-discipline
that they needed to persevere.
We noted earlier that most of the mathematics lecturers in the study have
engaged in mathematics education research. This necessarily has an effect on the way
they view and interpret some of the incidents described in their accounts. A study in
New Zealand investigating effective professional development processes for university-
level mathematics lecturers also highlighted the essential role that a supportive
community of practice has to play in enabling reflection and the benefits of this
community being “mixed” (Hannah, Stewart, and Thomas 2011; Paterson, Thomas, and
Taylor 2011). We believe that an education perspective, even if it is not subject specific,
can be beneficial in enabling reflection on practice.
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To summarise we make the following two recommendations to anyone in higher
education wishing to engage in the Discipline of Noticing: do so as part of a group; and,
as a professional development process, the effectiveness of engaging with the Discipline
of Noticing could be enhanced if an education perspective can be provided by one or
more members of this group.
The study also highlights the benefits, and challenges, teachers might expect
from engaging with the discipline. For example the benefits of writing brief-but-vivid
accounts and of perusing a collection of accounts were described. Some of the lecturers
were able to identify themes in their own and others’ accounts and to identify areas of
their own practice on which they would like to improve. The act of writing an account
often gave the author a new perspective on incidents in their classrooms. Furthermore,
sharing the accounts allowed the group members insight into others’ practice and group
discussions gave opportunities for identifying different methods of dealing with
situations in the future. Indeed, Ryan (2012, 3) explains that while reflection has been
variously defined from different perspectives and disciplines, at a broad level there are
generally two key elements: “(1) making sense of experience in relation to self, others
and contextual conditions; and importantly, (2) reimagining and/or planning future
experiences”.
We also caution teachers in higher education engaging with the Discipline of
Noticing not to expect too much too soon. We suggest that systematic engagement over
a long period is necessary before one can see results. In this study the lecturers reported
difficulties with noticing in-the-moment, especially in the first semester. We suggest
that they had unrealistic expectations. Two spoke specifically of how they failed to
notice in-the-moment, but generally reflected on incidents on the way back from the
lecture to their offices. Rather than view this as a failure on their part, we believe this to
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be an extremely useful first step in learning the discipline. Mason (2002, 39) writes that
“Incidents which stay in memory are usually ones in which we have considerable
emotional or intellectual commitment”. We believe that recalling incidents immediately
after a lecture is a useful practice to engage in for those who wish to graduate to
noticing in-the-moment, for as Mason (75) observes: “Noticing something
retrospectively is how most sensitivities begin”.
To conclude we return to the five mathematics lecturers in this study and
examine their next steps in relation to the Discipline of Noticing. As mentioned earlier,
Mason (2002) summarises the processes involved under four headings: systematic
reflection; recognising; preparing and noticing; and validating with others. The
lecturers’ reflections mainly relate to the systematic reflection process – the writing, and
using, of accounts and the examination of a collection of accounts to identify emerging
themes. We suggest that this is because this is the process they had engaged in most
over the year. Significantly though, Lecturers B, D and E had identified themes in their
accounts that they now wanted to address. We believe that the lecturers are now at the
point where they can engage productively with the “recognising” and “preparing and
noticing” stages of the discipline. In relation to the “validating with others” stage, each
lecturer presented a task-exercise to the group for discussion at the end of the academic
year. At this stage it became apparent that two common themes were emerging from the
accounts (namely promoting student engagement and gauging student understanding),
and it was decided to write task exercises on these and to present them to groups of
mathematicians at seminars in the coming year. In this way, we hope to receive
feedback on the task exercises and more importantly, receive others’ perspectives on
dealing with these two issues. We believe that in addition to improving the practice of
the five lecturers involved, the results of this work have the potential to contribute to the
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further understanding of mathematicians’ classroom practices, an area that is not well
researched to date (Speer, Smith and Horvath 2010).
References
Bell, A., R. Mladenovic, and R. Segara. 2010. “Supporting the reflective practice of
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