T. MILFORD ET AL.
Open Access
748
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 (wikispaces.com), mid-term Class-
room Assessment Technique (CAT) (zoomerang.com), 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