Enhancing Professional Learning and Development in the Teaching of Early Childhood Mathematics through Action Research

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The SIJ Transactions on Industrial, Financial & Business Management (IFBM), Vol. 2, No. 3, May 2014

ISSN: 2321-242X © 2014 | Published by The Standard International Journals (The SIJ) 140

Abstract — The objective of this paper is to explore how the kindergarten teacher‟s professional learning and

development as engaged in the teaching of early childhood mathematics can be enhanced through the use of

action research. The focus is drawn on the understanding of how the emergence of the teacher ‟s self-awareness

can be identified through the observation-reflection cycles and the understanding itself as such is a criticalissue that has not yet clearly addressed in the previous study. On the basis of a collaborative action research

approach, a project that contributes to the professional learning and development as engaged by a university

researcher and a kindergarten teacher is described. The project has been undertaken in one Hong Kong

kindergarten class in school. In this project, multiple sources of data have been elicited for triangulation during

the research process. These include school based curriculum guide, teaching plans, teacher journal, interviews,

children works and observation of children learning activities. The findings of this research indicate that the

enhancement of the teacher ‟s professional learning and development grounded in action research perspective

will in turn raise her awareness for helping children learn mathematics in early childhood.

Keywords — Action Research; Early Childhood Mathematics; Professional Development; Professional

Learning; Teaching.

I. INTRODUCTION

HE objective of this paper is to investigate through the

use of action research how the kindergarten teacher‟s

professional learning as well as development can be

enhanced as she engaged herself in the teaching of early

childhood mathematics. The focus is drawn on the

understanding of how the emergence of the teacher ‟s self-

awareness can be seen using the teaching log as a tool for

documenting the change in her practices as identified in the

observation-reflection cycles and we argue that the

understanding itself as such deserves our efforts for it.

1.1. Related Works

Action research has widely been recognised not just as an

essential methodological but a powerful reflective tool for

enhancing research-based practice [see Gore & Zeichner,

1991]. In early childhood setting, attempts at helping young

children (3 to 5 years children) learn high-quality

mathematics (a great concern raised in the joint position

statement by NAEYC and NCTM, 2002) through the

adoption of action research framework have recently been

made [for instance, Haynes et al., 2007]. As advocated, this

usually involves collaboration between the kindergarten

teachers and the university researchers; the latter would

conduct a second-order enquiry [Elliott, 2007] into the

protocols of action research methodology as adopted by the

former who investigate their practices as well as their

knowledge within the domain of mathematics.

The latest move in early childhood education saw an

ambitious attempt to advocate for the notion of

„mathematisation‟ [see Clements et al., 2009; Sarama &

Clements, 2012; Clements & Sarama, 2013] in the classroom

setting through the more explicit use of mathematical

language during the play activities. Sarama & Clements

(2012) argue strongly that teachers should adopt intentionalteaching and sequenced mathematics curricula through the

development of research-based learning trajectories in order

to provide children the necessary „mathematised experiences‟

for their further development of mathematical ability.

However, the advocacy of „mathematisation‟ was no more or

less ambitious than the any other attempts that have claimed

to have their works rested on Freudenthal‟s (1973)

endeavour. It was even unfortunate to see that the notion of

„mathematisation‟ could be misleading when it would be used

to shape the professional practice. The idea of such a notion

T

*Department of Curriculum and Instruction, The Chinese University of Hong Kong, HONG KONG. E-Mail:hylaw{at}cuhk{dot}edu{dot}hk

**Centre for Childhood Research and Innovation, The Hong Kong Institute of Education, HONG KONG.

E-Mail: rhccheung{at}ied{dot}edu{dot}hk

Huk Yuen Law* & Hiu Ching Cheung Rainbow**

Enhancing Professional Learning and

Development in the Teaching of Early

Childhood Mathematics through Action

Research





has been translated either into the teaching of „harder ‟

mathematics requiring more sophisticated level of ability or

into a crude application of mathematics with the absence of

real-life context rather than relating it to Freudenthal‟s

advocacy of seeing mathematics as a human activity through

which the children make sense of their own living

experiences. We cannot agree more on the Final words as

described by Sarama & Clements (2012) that “many adults

have biases against mathematics, and these adults militateagainst mathematics for their children” and these adults

would have also included not just the parents but also many

of the teachers who are working in early childhood settings. It

is not fair, nevertheless, to put blame on the teachers as they

would not find it comfortable with the explicit and concise

use of mathematical language in their actual teaching without

any demand for receiving the more rigor training for such a

purpose.

The learning trajectories as advocated by Clements &

Sarama (2013) in the form of instructional tasks enable

teachers to sketch a curriculum that can help them informing

and guiding their own instructions for the ongoing monitoring

of student learning. Nonetheless, the use of learning

trajectories for specific domains in mathematics requires the

teachers to have their professional autonomy so as to put into

effect of the discernment on the enhancement of children‟s

mathematical thinking and reasoning before the teachers can

chart the developmental progression for the children they are

teaching. The notion of „teachers as researchers‟ and the idea

of action research that entail implications for both the

authorship of practitioners‟ professional autonomy [Elliott,

1990] and the enhancement of their self-awareness in their

own practices [Law, 2009]. According to Elliott (1991),

action research can be regarded as “the study of a social

situation with a view to improving the quality of action within it” (bold italics is our emphases here). In the setting of

early mathematics education, the quality of teachers‟ action

will be examined by looking into the degree of discernment

they can demonstrate in valuing of the social situation (the

classroom) in which they have made conscientious efforts at

making mathematical thinking visible [Law & Cheung,

2014]. In the context of action research [see Elliott, 2007],

the university mathematics educators will adopt a role of

facilitating the teachers to create their pedagogical possibility

for action by validating and theorizing the theoretical

knowledge as adopted and constructed in the actual particular

classroom contexts. In the present study, we would argue that

in the context of action research the use of field experiencelog [Francis et al., 1999] as a powerful research artefact to be

adopted by the kindergarten teachers will enhance their self-

awareness in helping children to elicit the mathematical

thinking in a more visible way.

1.2. The Context of the Study

In Hong Kong, early childhood education and care services

for the pre-primary years are offered mainly in the private

sector and are attended by the majority of two to five year

olds [Chan & Chan, 2003]. Every pre-primary institution has

its own mission, different operation modes and teaching

approaches. As a result, the qualities of pre-primary

curriculum as implemented vary.

In 2006, The Curriculum Development Council

published Guide to the Pre-primary Curriculum aims at

developing a curriculum framework for pre-primary

institutions' reference and adoption. There are four

developmental objectives for young children, namely

“Physical Development”, “Cognitive and LanguageDevelopment”, “Affective and Social Development” and “

Aesthetics Development”. These objectives need to be

achieved through six learning areas, which are “ physical

Fitness and Health”, “Language”, “Early Mathematics”,

“Science and Technology”, “Self and Society” and “Arts”.

Pre-primary institutions need to formulate their own

curriculum based on the guide and transform it in actual

practices so as to provide appropriate learning experiences for

children [CDC, 2006].

It is argued strongly that early mathematics is essential in

pre-primary curriculum as it will be of great promise for

improving later achievement through enhanced mathematical

thinking [Ginsburg et al., 2008]. However, the guide does not

help schools to develop their own mathematics curriculum as

it is too general and inadequate. For example, the guide

suggests “children should build up basic concepts of space

and time through a wide range of activities”; “the activities

should be interesting and should match children's interests”

[CDC, 2006]. In the context of classroom teaching, “What to

teach” and “How to teach?” are still the long existing and yet

unsettling issues in the actual practices of early education.

1.3. The Setting of the Study

The kindergarten curriculum as practiced in Hong Kong is a

theme-based one. There are around 10 themes to becompleted within a school year and each theme normally

lasts for 3 to 5 weeks. In line with the six learning areas

[CDC, 2006], the preschool curriculum based on a certain

theme or topic would then be designed by organising most of

the learning activities around the theme as set.

In early mathematics, the school shave put much

emphasis on helping children grasp preliminary mathematics

concepts such as counting, ordering, sequencing, sorting

through the mastery of a set of skills and procedures. The

school-based curriculum would be adopted and a series of

teaching kits for mathematics instruction and learning

assessment will be used in order to meet the mathematical

learning objectives as specified by the schools themselves. Asa usual practice, children‟s learning will follow a traditional

drill-and-practice approach such that they are provided with

the teaching kits to undergo the repeated practices in the

classroom with minimal guidance from the teacher.

In the kindergarten classroom, mathematics teaching is

integrated and set into one-hour session in the morning,

Mondays through Fridays, in the forms of the circle time and

small group learning. During the circle time, the teacher

introduces various learning activities to help children

understand mathematics concept by demonstrating how the





teaching kits are operated and illustrating what sorts of the

principles and activities rules should be picked up through the

use of the kits. Small group learning that follows the circle

time will enable six to eight children to choose freely from

five to seven learning activities as set at different tables (with

the mathematics teaching kits) around the corners of the

classroom. During the small group period, the teacher

oversees the classroom and encourages children to engage

themselves in different learning activities without anyspecific role as required for the teacher to guide children

learn the mathematics behind the activities.

The project was undertaken through a research

partnership between a university researcher and a teacher at

one Hong Kong kindergarten. The teacher worked as an early

childhood educator for 3 years. This action research project

involved a group of twenty eight children aged 3 to 4 years

old. During the research process, other two kindergarten

teachers who acted as the critical friends of the teacher

researcher taught the same age group of children. They were

invited for interviews as well as doing peer-observation for

data triangulation.

II. THE EMERGENCE OF REFLEXIVITY

2.1. The Use of Research L og

In the action research context, the participant teacher who has

strived at making mathematical thinking visible in the setting

of kindergarten classroom adopted a researcher ‟s role while

doing her teaching. By situating the teacher‟s self in the

experienced context, the data as systematically collected and

recorded in the field experience log during the research

process serve as the source for triggering the emergence of

reflexivity through which the teacher ‟s awareness can be

raised. The teacher used the log to document the dailyhappening of classroom scenario. As included in it, some

critical dialogues during the teaching episodes are to be

identified by both the teacher and the university researcher

during their meeting in the Sharing Seminar. By reflecting on

the critical dialogues, the teacher has expressed a strong

inclination towards re-drafting the action plan for her

teaching while developing the learning trajectories for

helping children learn the counting strategies. In the section

that follows, we will delineate how the teacher ‟s professional

learning can be enhanced through the observation-reflection

cycles as based on the teacher ‟s documentation of her

teaching experiences in the log and the on-going dialogues between the teacher and the university researcher in the

Sharing Seminar.

2.2. The Observation-Reflection Cycles

The collaborative efforts in this project have come from the

dialogues between the participant teacher who want to make

a change in her own pedagogical practices and the university

researcher who desire to advocate the idea of teacher-as-

researcher for the enhancement of professional learning and

development in the teaching early childhood mathematics. As

a researcher, the teacher has a vital role to play to keep up

with the documentation of what she would have observed in

the classroom activities and what she would have reflected

from the observations. As such, the use of the log serves at

least for two major purposes: (1) for the self-reflection of the

teacher; (2) for the facilitating of the conversation exchanges

during the Sharing Seminar. Within the period of the research

process, we have identified four phases of changes in the

observation-reflection cycles as based on the extracts of thelog and the dialogues. These phases are described as follows.

In Phase 1, when the teacher read and re-read what she

had written down in the log of what actually happened in the

classroom, she was beginning to have a self-puzzlement over

her professional role as a teacher in doing the routine

pedagogical practices (see Teacher log 1).

Teacher Log 1

Honestly I don’t know how to teach early maths. As a

teacher, I know each early maths objectives of the

learning kits. I could teach my kids how to manipulate

the learning kits but not the “maths” itself. To

improve maths learning and teaching in myclassroom, I try to be more alert and sensible to maths

learning and teaching, instead of just tell my kids how

to make it or do demonstration for them. I try to

observe my kids carefully….

In Phase 2, that very kind of self-bewilderment led the

teacher to look into her classroom practice through a more

critical lens and for the very first time that she shared with the

children‟s boredom in engaging the mathematics learning

activities. Such an observation enabled herself to take up a

more active role at dialoguing with the children during the

mathematics-related learning activities (see Teacher log 2).

Teacher Log 2 After paying more attention to maths activity in the

classroom, I found my kids felt really boring. Maths

activities were all table tasks and independent

learning kits. In free-choice activities, my children

seldom choose to pick maths activity. To make it more

fun, can maths learning happen in learning corner in

the classroom? Children love to play in learning

corner which is usually for role play, science

discovery…

In Phase 3, the teacher started taking careful notes on the

teacher-children mathematics dialogues as recalled from the

classroom interactions and tried making sense of them

through the conversation exchanges with the university

researcher during the Sharing Seminar (see Teacher log 3).

Teacher Log 3

Apart from observe my kids in the classroom, I started

to write down what happen and what did they say

which is interested me. After reread the notes, It is

surprise that I understand my kids more, I would know

more how they think and how they learn through the

conversation. It is of great value for my teaching.





In phase 4, the teacher started to re-think her role as a

professional teacher on the pedagogical practices through the

critical dialogues as shared during the Sharing Seminar.

2.3. The Cri tical D ialogues as I dentif ied in the Shari ng

Seminar

Here we present two critical dialogues to serve the purpose of

how the teacher ‟s self-awareness has been raised through the

use of these for facilitating her change in the pedagogical practices.

For instance, the following conversations during the

classroom activity at the learning corner have been noted and

shared in the Sharing seminar:

Goal: one-to-one correspondence between counting numbers

1-10 and objects.

Activities: The number cards 1 to 10 are attached to the

baskets. Grouping in pair, the children are asked to pick the

correct number of bears and then put them into the

appropriate basket with the corresponding number card being

attached to it. For example, three bears will be picked and put

into the basket with the number card of 3 being attached to it.

Critical Dialogue 1: Conversations at the Learning Corner

Child 1: (pointing to the basket with number 3) You are

wrong! It is three!

Child 2: (looking closely at the basket and noticed only two

bears inside) Oh! Yes. I need one more bear!

Child 1: No. It is three. Three bears.

Child 2: No. There are two bears already. I need one bear.

(Then putting one more bear into the basket.)

Child 1: Yeah! It is three. Three bears now.

The sharing of this child-child dialogue in the Sharing

Seminar enabled the teacher to make a deeper sense of what

the children had made up their interpretations over the basic

ideas of manipulating the numbers as related to the notion of

quantities as embodied.

Critical Dialogue 2: Conversation at Another Learning

Corner

The scenario: The teacher noticed and wondered why a child

at another learning corner picking one bear each time and put

it one by one into the basket of 10 though finally he had

filled up the basket with the ten bears.

Teacher: Why do you pick one bear only each time?

Child 3: In my worksheet, for ”1”, I stuck one apple (sticker);

for “2”, I stuck one apple (sticker) and one apple (sticker).

Teacher: How about “10”?

Child 3: one apple and one apple and one apple and one

apple… 10 apples!

The teacher had realised from this teacher-child dialogue

how the children were „trained‟ to do with the one-by-one

counting through the use of stickers as the semiotic artifacts

for the making sense of the physical objects

After the Sharing Seminar with the discussion of the

critical dialogues, the teacher made an important remark in

her field experience log:

The children used to learn independently on an

individual basis through the manipulations of the

learning kits over and over again until they got what

the teacher expected to them to achieve. The whole

learning process is rather mechanical! The

conversations inspired me that children can learn

beyond what I have anticipated through mathematical

communication in the form of child-child and child-

teacher interactions.The schematic diagram below summarises the research

process through which the teacher has undergone the

observation-reflection cycles as identified in the four phases

of change in terms of her pedagogical awareness.

Observation-Reflection Cycles

III.

CONCLUDING REFLECTIONS The research project has contributed to raising teacher

awareness in developing her professional learning and

development in early childhood settings by making

mathematical thinking visible not just the physical visibility

but the „visibility‟ of mathematical discourse that constitutes

children‟s mathematical reasoning behind their thinking. The

teacher who has engaged in this study agreed that engaging in

action research had enabled her to recognise that more could

be done by drafting her own sketch of curriculum in order to

help the children learn early childhood mathematics in a

better way. The case study, though in a small scale, justifies

its own purpose if it can have developed an agenda formathematics educators to think seriously of what and how

should be done to enhancing the teachers‟ self -awareness in

undertaking of early mathematics education by articulating

effectively their pedagogical documentation for children,

teachers and even parents. Future research based on the

further investigations on the fostering of children‟s

mathematical thinking through the teacher‟s critical

reflections will throw more light on the enhancement of

effective professional development in the early childhood

education.

O• Observed routine practice of the learning and teaching in classroom

R • Confused about teacher role in children learning mathematics.

O• Observed children being boried in the mathematics learning activities

R

• Seeked ways to improve mathematics learning activities (group work /attractive learning conner)

O

• Observed and took notes of children mathematics conversations in theinnovative new activities

R

• Tried to understand how chlidren think and learn through theirconversations in mathematics activities

O

• Observed children behaviour in the mathematics learning activities and hadconversations with them

R

• Rethink about teacher role and value in children learning mathematics andthe importance of mathematics communication in the learning mathematics





REFERENCES

[1] H. Freudenthal (1973), “Mathematics as an Educational Task ”, Dordrecht: Reidel .

[2] J. Elliott (1990), “Teachers as Researchers: Implications forSupervision and for Teacher Education”, Teaching andTeacher Education, Vol. 6, No. 1, Pp. 1 – 26.

[3] J.M. Gore & K.M. Zeichner (1991), “Action Research and

Reflective Teaching in Preservice Teacher Education: A Case

Study from the United States”, Teaching & Teacher Education,Vol. 7, No. 2, Pp. 119 – 136.

[4] J. Elliott (1991), “Action Research for Educational Change”,

Milton Keynes: Open University Press, Published in Spain by Morata, Madrid.

[5] A. Francis, L. Tyson & M.S. Wilder (1999), “An Analysis ofthe Efficacy of a Reflective Thinking Instructional Module on

the Reflective Thinking Demonstrated in the Filed ExperienceLogs of Early Preservice Teachers”, Action in Teacher

Education, Vol. 21, No. 3, 38 – 44.

[6] National Association for the Education of Young Children and National Council of Teachers of Mathematics (2002), “EarlyChildhood Mathematics: Promoting Good Beginnings”,

http://www.naeyc.org/about/positions/psmath.asp.[7] L.K.S. Chan & L. Chan (2003), “Early Childhood Education in

Hong Kong and its Challenges”, Early Child Development andCare, Vol. 173, No. 1, Pp. 7 – 17.

[8] Curriculum Development Council (2006), “Guide to the Pre-

Primary Curriculum”, Hong Kong: CDC .[9] M. Haynes, C. Cardno & J. Craw (2007), “Enhancing

Mathematics Teaching and Learning in Early ChildhoodSettings”, Teaching & Learning Research Initiative, New

Zealand: Wellingon. Retrieved on 27/8/2013:http://www.tlri.org.nz/sites/default/files/projects/9219_finalreport_0.pdf.

[10] J. Elliott (2007), “Reflecting where the Action is: The Selected

Works of John Elliott”, London & New York: Routledge.[11] H.P. Ginsburg, J.S. Lee & J.S. Boyd (2008), “Mathematics

Education for Young Children: What it is and How to Promoteit”, Social Policy Report: Giving Child and Youth Development

Knowledge Away, Vol. 22, No. 1, Pp. 3 – 22.[12] H.Y. Law (2009), “Learning to Ask: The Role of

Communication in the Teaching and Learning ofMathematics”, Unpublished Doctoral Dissertation, Norwich,UK: University of East Anglia.

[13] D.H. Clements, D.C. Wilson & J. Sarama (2009), “YoungChildren‟s Composition of Geometric Figures: A Learning

Trajectory”, Mathematical Thinking and Learning , Vol. 6, No.2, Pp. 163 – 184.

[14] J. Sarama & D.H. Clements (2012), “Mathematics for theWhole Child”, Editors: S. Suggate & E. Reese, Contemporary

Debates in Childhood Education and Development , London & New York: Routledge, Pp. 71 – 80.

[15] D.H. Clements & J. Sarama (2013), “Solving Problems:

Mathematics for Young Children”, Editor: D.R. Reutzel, Handbook of Research-based Practice in Early Education, New York & London: The Guilford Press, Pp. 348 – 363.

[16] H.Y. Law & H.C. Cheung (2014), “Helping Children LearnMathematics through Action Research: Making Mathematical

Thinking Visible in Kindergarten”, Bangkok InternationalConference on Social Science, Bangkok, Thailand.

Huk-Yuen Law is assistant professor in the

Department of Curriculum and Instruction,Faculty of Education, The Chinese Universityof Hong Kong, where he leads themathematics education team and also holds

the positions of the program director of theMaster of Science in Mathematics Educationand the program coordinator of the B.Ed. ofMathematics and Mathematics Education.

His research interests include action research in education,

communication in the teaching and learning of mathematics, valuesin mathematics education, and mathematics teacher education.

Hiu Ching Cheung Rainbow is an EdD

student of the school of Education, Universityof Bristol. She had been a kindergarten teacherin Hong Kong for three years. Currently, she isa project officer in the Centre for Childhood

Research and Innovation, The Hong KongInstitute of Education. Her research interestsinclude early mathematics and scienceeducation, teacher professional development,

and the improvement of classroom teaching.

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Enhancing Professional Learning and Development in the Teaching of Early Childhood Mathematics through Action Research