Modeling Action Research for Pre-Service Teachers as Part of a Primary Maths Method Class

doi:10.4236/ce.2013.412105

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Creative Education

2013. Vol.4, No.12, 747-751

Published Online December 2013 in SciRes (http://www.scirp.org/journal/ce) http://dx.doi.org/10.4236/ce.2013.412105

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

Email: [email protected]

Received October 8th, 2013; revised Novem b er 8th, 2013; accepted November 15th, 2013

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 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

Introduction

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

T. MILFORD ET AL.

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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

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consistent class that was responsive and sensitive to the needs

of the students that might have otherwise existed.

Wiki

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 zoomerang.com 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

with.

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

Responses

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

Responses

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

Responses

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

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750

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-

tern.”

Common Themes (Key Responses to Action

Research)

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

Responses

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

Responses

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

T. MILFORD ET AL.

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students.

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.

Limitations

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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