Creative Education
2013. Vol.4, No.12, 747-751
Published Online December 2013 in SciRes (
Open Access 747
Modeling Action Research for Pre-Service Teachers as Part of a
Primary Maths Method Class
Todd Milford, Lyndal Hellaby, Rebekah Strang
School of Education and Professional Studies, Griffith University, Brisbane, Australia
Received October 8th, 2013; revised Novem b er 8th, 2013; accepted November 15th, 2013
Copyright © 2013 Todd Milford et al. This is an open access article distributed under the Creative Commons
Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the
original work is properly cited. In accordance of the Creative Commons Attribution License all Copyrights ©
2013 are reserved for SCIRP and the owner of the intellectual property Todd Milford et al. All Copyright ©
2013 are guarded by law and by SCIRP as a g uardian.
How does an early academic, who has specialized training in educational statistics and measurement, ap-
proach the teaching of a primary mathematics methods course for first and second year pre-service teach-
ers? The research study presented here explores the design and delivery of a newly developed, single-
semester (36 hours over 9 weeks), course for a combined first and second year pre-service teachers in
primary mathematics in a Bachelor of Education (BEd) program. Over the nine week period, the course
lecturer and tutorial instructors used action research methodologies to collect and analyze data from the
course. Through these data collection and analysis, the authors identified students’ common concerns and
apprehensions and utilized them as a basis for efforts to enact change for the betterment of the students
involved in the class. The collection and analysis of the data as well as the specific actions taken by the
authors to these identified concerns and apprehensions are the focus of this paper.
Keywords: Action Research; Mathematics Education; Teacher Education
The purpose of this study was to research the impact of the
design and delivery of a newly developed, single-semester,
course in primary school mathematics in a Bachelor of Edu-
cation (BEd) program at a university located in a major urban
centre on the east coast of Australia. Over a nine week period,
we (the authors—who consisted of the course designer and
lecturer as well as the tutorial instructors) used as well as
modelled an action research approach to this class. By this, we
mean that we actively collected and analyzed data gathered
from this class in an effort to adjust delivery and better meet the
needs of the students. Neither the instructor nor the tutors had
ever taught maths methods classes previously. The first author,
the course designer and lecturer, holds a PhD in educational
measurement and the second and third authors, the tutorial in-
structors, hold Graduate Diplomas in Learning and Teaching.
On top of this challenging starting position, mathematics is a
content area that is typically viewed by pre-service teachers less
favorably than their other content classes (Rech, Hartzell &
Stephens, 1993). Lastly, this course represented the combina-
tion of both first year and second year pre-service teachers into
a single methods class for administrative reasons. This also
presented a challenge as although the entire group was early in
their respective programs there was a difference between the
two groups in terms of experience and growth as pre-service
teachers. Taking these three factors into account, it seemed
reasonable and worthwhile (as well as necessary) to begin
ongoing, systematic data collection and analysis that allowed
reflection and adjustment of our teaching to make delivery
more effective and impactful for the students. The three authors
worked together in concert to actively collect data, comment on
the course and course delivery and make necessary changes as
the semester progressed.
In this paper we 1) document the data we collected over the
course of this nine week semester, 2) discuss how we went
about both ongoing and post hoc analysis, 3) suggest ways in
which the students may have benefited from seeing and ex-
periencing the action research process and 4) reflect on what we
might do to improve our teaching in the future. We describe our
experiences of teaching mathematics pedagogy as well as mod-
eling reflective teaching practice to this group of first and sec-
ond year students. As stated, we employed an action research
approach to the exploration and analysis of data in this class.
Specifically, we worked under the umbrella of what Ferrance
(2000) refers to as “a disciplined inquiry done by a teacher with
the intent that the research will inform and change his or her
practice in the future.” (p. 1). Through the analysis of the class
data and our own action research, we have come to recognize
some of the common concerns around mathematics and
mathematics instruction for beginning teachers which helped to
inform our concurrent delivery of the class as well as future
iterations. It is our identification of the common concerns and
our efforts to address these that will be the focus of this paper.
Theoretical Framework
In planning our approaches to delivering course content, we
were aware that a body of research existed regarding teacher
instructional beliefs in mathematics and the influence of those
Open Access
beliefs on instructional practice (e.g., Thompson, 2002; Handal,
2003). We also recognized that pre-service teachers have well
established and long held attitudes which may be coupled with
beliefs about mathematics instruction, beliefs which have de-
veloped after spending hundreds of hours in classrooms learn-
ing mathematics. Additionally, pre-service teachers might well
possess limited conceptual understanding of (Quinn, 2001) and
high anxiety and apprehension around (Uusimaki & Nason,
2004) mathematics. Together, these factors can impact nega-
tively pre-service teachers’ beliefs about their ability to teach
mathematics and their eventual effectiveness as teachers in this
area (Huinker & Madison, 1997; Quinn, 1997). In light of this
potential impact, we were also mindful of the identified need to
better prepare pre-service teachers for the realities of their
classroom experiences when they begin practicum teaching
(Stuart & Thurlow, 2000). However, it is one thing to be aware
of an issue and another thing entirely to address it.
The initial planning for this class which provided the context
for our action research was an evolutionary one. There were a
wealth of resources available in terms of a standard assigned
text (Booker, Bond, Sparrow, & Swan, 2010), a course outline
which was designed and written by the Senior Course Conve-
nor prior to our being assigned this class to teach and which
was accepted in its entirety (the three of us were new to this
course, institution and content area so acceptance seemed like a
wise choice), and a resource and tutorial room stocked with a
wealth of math supplies such as manipulatives and games.
However, we lacked a clear idea on our path of how to deliver
content clearly and effectively and about what exactly one was
to do with all these resources. Our main goal was to create a
classroom experience that would help reduce students’ anxiety
around maths and that would help these same students to un-
derstand how to apply these resources in their own primary
(prep to year 6) maths classrooms. To achieve this goal, we first
had to determine how to best use these materials and resources
in the typical school classroom and then to apply them to the
university one with pre-service teachers. An additional chal-
lenge was the actual class sizes (lectures to more than 200 stu-
dents across two campuses) with numerous tutorials to be
planned as well as monitored. In all, the class involved 39 hours
of contact time with 26 hours full class lecture and 13 hour long
tutorials all over a condensed nine-week semester. On top of
this, the first author was unfamiliar with the concept of tutorial
at the university level at this point. He had taken lecture and
laboratory classes in his undergraduate degree but never had
taught within this type of system. It was at this point that the
research li terature (i.e., English & Halford, 1995; Grouws, 1992)
and other textbooks on mathematics (i.e., Jorgeson & Dole,
2011; Van de Walle, Karp, & Bay-Willimas, 2013) proved in-
valuable to expand our knowledge, confidence and overall di-
rection for this class.
Methods of Inquiry
To better meet the needs of this class, identify the potential
apprehensions these students might be facing and to better pre-
pare them for the realities of teaching, we decided early in the
planning stages for this class to take an action research ap-
proach to instruction (Ferrance, 2000). We embedded a cyclical
design of identifying a problem around these apprehensions
(anticipated or recognized), gathering data on that problem,
analyzing this data, acting on the data collected (done among
the instructor and tutors and explained to the entire class), and
ultimately re-evaluating. The course data collection included an
instructor and tutor wiki (, mid-term Class-
room Assessment Technique (CAT) (, and fi-
nal class evaluations (Blackboard).
The data were interpreted by the instructor and in conjunc-
tion with conversations among the tutorial staff, decisions were
made as to how best to address the perceived and expressed
needs of students. Those decisions typically resulted in the
implementation of pedagogical changes, with the results of
those changes monitored. For example, assignments quickly
emerged as a concern for this group of students so to better
explain both the assignment and the accompanying assessment
rubric the instructor attended half of all tutorials in the fourth
week, providing clarification and answering any questions by
the students. Having the instructor complete these sessions,
rather than the tutorial instructors provided students with a
higher level of consistency across all tutorials. This action was
recognized by students as a positive helpful service in both the
midterm (i.e., CAT) and final class (i.e., Blackboard) feedback.
In an effort to model what we perceive to be good practice in
teaching, and to prepare students to undertake similar reflective
teaching in their own classrooms, we discussed these steps in
our action research and our overall rationale to the students.
This was done initially at the beginning of the course, and pe-
riodically in lectures as part of ongoing dialogue. For instance,
there were feelings of inconsistency between the tutorials as
expressed by comments made to tutors as well as emails ad-
dressed to the lecturer (e.g., “I attended tutorial this week on
Tuesday but found it difficult to learn in the way this tutor
teaches and coming from a not so strong mathematics mind I
think it’s better that I change.”). To address this perception of
inconsistency—and avoid an administrative nightmare of stu-
dents switching tutorials—it was decided that because one of
the tutors was already making her own PowerPoint’s for tutori-
als, these PowerPoint’s would be extended to all sessions to
ensure reliability improved to the benefit of all students. The
change was explained to the students as a direct result of their
feedback. Data was collected anonymously from the online tool
to measure their reaction. It was hoped students could see the
process, understand the changes and see that effective sensitive
teaching—instead of a linear and pre-set exercise—is an itera-
tive, constantly changing and adjusting practice.
Data Collection and Methods of Interpretation
As this was a single semester course delivered over the span
of nine weeks, the study included data collected over this brief
time period. In total there were 317 who were enrolled in this
course and who submitted assignments for both tasks. All of the
data collected for this study has been done in the context of
normal teaching practices and allowed us to consider issues
related to the delivery of the course and to students reactions to
it. The course data collection included an instructor and tutor
wiki, mid-term Classroom Assessment Technique (CAT), and
final class evaluations. Throughout the entire semester as well
as the research process, all authors strived for open lines of
communication and analysis of the class delivery by sharing
thoughts, findings and potential strategies with each other as
well as with students in a regular and open manner both inside
and outside of regular class and tutorial sessions. Engaging in
this level of open discussion resulted in the delivery of a more
Open Access 749
consistent class that was responsive and sensitive to the needs
of the students that might have otherwise existed.
The class wiki was used as a repository and place for reflec-
tion on how the class and the tutorials were unfolding as the
semester progressed. It was initially envisioned as a place that
all staff could share ideas, issue and concerns and potentially
work to some resolution. Although other forms of communica-
tion among staff (i.e. texting, phone, emails and face-to-face
conversations) replaced some of the purpose of the wiki, some
useful and potentially beneficial comments and themes did
emerge from it. For example, 1) engagement and attendance
was identified as positive (e.g., “Most of the students were en-
gaged”); 2) that the first and second year classes responded
differently (e.g., “There is a growing difference between the
first and second years in terms of engagement”, “There was a
significant difference in understanding between the first and
second years”); 3) how to teach maths; 4) that students did not
want as much theory in tutorial but more application (e.g.,
“Encourage students to have a go at teaching some of the ex-
amples”); and, 5) how ACARA (Australian Curriculum) and
the QSA (Queensland Curriculum) needs to be brought into the
content coverage and linked for their understanding.
Classroom Assessment Techniques
Classroom Assessment Techniques are formative evaluation
methods that serve two purposes. They can help instructors to
assess the degree to which students understand the course con-
tent and they can provide information about the effectiveness of
teaching methods (Haugen, 1999). Most are designed to be
quick and easy to use and each CAT provides different kinds of
information. This CAT was administered in the fourth week of
the course and was placed on-line via and a
link was sent out to the entire class. A week was given for stu-
dents to respond to three prompts 1) So far in the course I am
most satisfied with? 2) So far in the course I am most least
satisfied with; and, 3) So far in the course I am having trouble
All responses were downloaded anonymously and coded by
theme. Approximately a third of the class responded to the
CAT and results from the three prompts are provided below in
Tables 1-3.
Table 1 offers an overview of what had been working well in
the class to this point. Almost 75% of respondents indicated
that lecture, the critical reflection upon pedagogical content and
the overall learning environment were working to their satisfac-
tion. Examples of comments from these areas of satisfaction
include 1) “The lecturer and the lectures—the delivery is en-
gaging an interesting”; 2) “the critical way your address the
textbook and provide alternative ideas”; and, 3) “the learning
environment that lowers the stress level by 10%—if you can
measure stress level?”
Table 2 offers an overview of what had up to that point in
the class not been working well. Over 80% of respondents in-
dicated that they were not satisfied with four areas: the tutorial,
the class structure, nothing and lectures. Examples of comments
from these areas of dissatisfaction include 1) “I feel the tutorials
need to include more content” and “I feel I am not getting any-
thing from tutorials”; 2) “dislike double lectures and tutorials in
a week”; and, 3) “the lectures seems to go on forever!”
Table 1.
Student response to initial classroom assessment technique to question
“So far in the course I am most satisfied with?”
CodeValueDescription Number of
Responses Percentage o f
1 L Lectures 56 43.75
2 CR/CCritical
Reflection/Content 24 18.75
3 LE Learning Environment 18 14.1
4 T Tutorial 9 7
5 ADAssignment Details 8 6.25
6 V Videos 5 3.9
7 L@GWebboard Discussions 3 2.3
8 S Surveys 1 .8
9 Nt Notes 1 .8
10 M Misc. 3 2.3
Total 128 99.9
Table 2.
Student response to initial classroom assessment technique to question
“So far in the course I am least satisfied with?”
CodeValueDescription Nu mber of
Responses Percentage o f
1 T Tutorial 37 39.4
2 CS/AClass Structure/Admin 20 21.2
3 N Nothing 13 13.8
4 L Lectures 12 12.7
5 TATalking 6 6.4
6 MCMaths Content—Maths Is
Hard 3 3.2
7 AS Assignment Structure 2 2.1
8 G Games to Teach 1 1.1
Total 94 99.9
Table 3.
Student response to initial classroom assessment technique to question
“So far in the course I am having trouble with?”
CodeValueDescription Number of
Responses Percentage of
1 N Nothing 32 33.8
2 L Lecture 17 17.5
3 C Content 16 16.4
4 T Tutorial 12 12.3
5 AS Assignment 7 7.2
6 R Readings 5 5.2
7 TA Talking Students 4 4
8 M Motivation 4 4
Total 128 99.95
Lastly, Table 3 offers student comments on what they were
having trouble with. Almost 35% of respondents indicated
Open Access
nothing and another 45% indicated lecture, content and tutorial.
Examples of these identified difficulties included 1) “The lec-
tures go too fast”; 2) “taking in and absorbing all the informa-
tion”; and, 3) “the tutorials seem like a waste of time”.
Final Evaluations
As part of the University policy, all classes (lecture and tuto-
rials) are to be evaluated at the end of term via an online survey
format similar to the CAT done previously for this class. Al-
though the questions were slightly different, they did capture
some of the same aspect of the class. As with the CAT, all re-
sponses were downloaded anonymously and coded by theme.
Again, approximately a third of the class responded to this sur-
vey and results from the two prompts are provided below in
Tables 4 and 5. Table 1 offers an overview of students’ atti-
tudes at the completion of the lecture and tutorials.
Table 4 offers students a second opportunity to comment on
what was good about this course. Almost 90% of respondents
indicated that lecture, the tutorials, the support from staff and
the content were good. Examples of comments from these areas
of satisfaction include 1) “The lecturer was excellent and the
tutors were there to help you learn”; 2) “During tutorials we
were able to get involved in experiences by actually teaching”;
and, 3) “I was hoping for more maths than how to teach maths.”
Table 5 offers an overview of the feedback from students on
how the class could be improved in the future. In this case, 95%
of respondents indicated that tutorials, the assessments and the
content (along with nothing) could be improved for future itera-
tions of the class. Examples of comments from these areas in-
clude 1) “Tutors seemed unsure at times, which lead to confu-
sion and contradictions to lectures”; 2) “The assessment tasks
could have been worded better and more specific”; and, 3) “The
layout of the course as to what was taught was in a weird pat-
Common Themes (Key Responses to Action
Early on in the delivery of this class (primarily from data via
tutorial instructors through the wiki and conversations and
supported through the initial CAT) it became apparent that
there was a substantial amount of student concern around the
usefulness of tutorials, the value of teaching maths pedagogy
over maths content and the general approach and delivery of the
lecturer. From an action perspective, these were positive as they
allowed for potential adjustments (i.e., either offering a better
rational for the approach to pedagogy or in simply talking
slower in lecture) based upon this feedback, Additionally, they
also offered a demonstration for student on how these are being
made as well as an opportunity to measure near the end of the
class on how these were received.
Initial responses to the tutorial. During the first series of
lectures and tutorials, it became apparent both through our con-
tact with the students as well as through our internal conversa-
tions (informally and via the wiki) that there was some concern
with the delivery of the tutorial. For example, at the initial CAT
only 7% of students responded that the tutorial was the most
satisfying aspect of the class while almost 40% indicated that it
was the most dissatisfying. Based upon this feedback and our
own conversations, the tutorials were adjusted and expanded to
include more application as well as student teaching. In support
for this adjustment, there was a discernible change in the tuto-
Table 4.
Student response to final class evaluations to question “What was good
about this course?”
CodeValue Description Number of
Responses Percentage of
1 L Lectures 62 57.4
2 T Tutorials 14 12.8
3 SS Supportive Staff 11 10.1
4 C Content 10 9.3
5 V Videos 2 2
6 M Materials 1 1
7 T Text 1 1
Total 108 100
Table 5.
Student response to final class evaluations to question “How could this
course be improved?”
CodeValueDescription Number of
Responses Percentage of
1 T Tutorials 34 43
2 AS Assessment 15 19
3 C Content 14 17.7
4 NA Nothing 13 16.5
5 M Mixture and Atmosphere 3 3.7
Total 79 99.9
rial ranking as a positive or worthwhile learning experience
from 7% initially to almost 13% at course conclusion.
Content vs. pedagogy. There has been a long running di-
lemma among mathematics educators of how to teach mathe-
matics (i.e. how much time should be devoted to teaching ac-
tual maths and how much to strategies for teaching these con-
cepts) (Gurganus, 2007). We had thought about how to ap-
proach this class from the very beginning and although there
was some concern among the students about their lack of con-
tent knowledge throughout the delivery, we were encouraged
that close to 60% of respondents indicated that lecture and con-
tent were working to their satisfaction at both points in the
feedback cycle. This was perhaps best articulated by one stu-
dent who commented that “I feel I gain valuable information of
attending (lectures) and find I am able to walk away from them
questioning past teaching methods and starting to form new
more effectives ones that are my own.”
Educational Significance
We began this process with the task of presenting an educa-
tional methods class in mathematics to a group of pre-service
teachers early in their teaching development. Recognising many
of these students would approach mathematics with some de-
gree of reticence if not outright anxiety and consternation, we
sought to find a way to offer a meaningful and worthwhile
learning experience while simultaneously modelling reflective
practice and allow students to offer feedback and adjust the
direction of the class to better meet their learning needs. Over-
all, we identified the amount of content that was covered, the
long lecture format and the ways that tutorials were structured
and the as common concerns and apprehensions among the
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We also hoped that this would model good pedagogy for
these students and allow them to leave with new ideas and ap-
proaches to teaching primary mathematics as well as general
approaches to their own current and future classroom behaviour.
To this end we hope and believe we were successful on both
fronts. The data demonstrated that students would offer feed-
back on how to adjust the course delivery and would respond to
these changes and that despite some concern with their own
content knowledge in this area students were able to recognise
some learning in terms of how they might go about teaching
this content area in their own classes. However, this research
also reflects how complex trying to measure the delivery of a
class such as this is and how difficult it is to measure if we have
or have not been effective.
We continue to ask questions of our own actions: Could
more informal data collection have improved our delivery?
Would background knowledge of students be something to
collect at the onset to guide our instruction? Should students be
required to do more content classes prior to methods classes?
With the help of our students we can continue to ask such ques-
tions and to uncover more learning.
The major limitation concerning this study relates to the re-
sponses rates of the Classroom Assessment Techniques (CATs).
Although the authors were happy with the overall response
rates (approximately 35%), there is some concern that this 35%
response rate captures the same students for both sessions.
These students may have been a biased group who were moti-
vated to respond for specific reasons and who might have not
been representative of the entire class.
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