Creative Education
2011. Vol.2, No.3, 236-243
Copyright © 2011 SciRes. DOI:10.4236/ce.2011.23032
Encouraging the Innovative Use of Geometer’s Sketchpad
through Lesson Study
Chew Cheng Meng, Lim Chap Sam
Universiti Sains Malaysia, Penang, Malaysia.
Received March 10th, 2011; revised April 8th, 2011; accepted April 20th, 2011.
The purpose of this study was to encourage the innovative use of Geometer’s Sketchpad (GSP) in the teaching
and learning of mathematics among secondary school teachers in Malaysia through Lesson Study (LS). Three
LS groups were set up in three secondary schools. Qualitative data were collected through written lesson plans,
video-taped teaching and individual interviews with the participants. Findings of the study show positive
changes in the participants’ knowledge and skills of using GSP to teach the topics of “Lines and Planes in Three
Dimensions,” “Loci in Two Dimensions” and “Plans and Elevations.” These are evidenced in their mathematics
lesson plans, GSP sketches, worksheets and videotaped teaching observations. Analysis of their interview tran-
scripts also reveals positive acceptance and encouraging feedback about LS that promotes peer support and col-
laboration. Thus, the participants have more confidence in using GSP innovatively to teach mathematics at the
secondary school l evel after the LS collaboration.
Keywords: Lesson Study, Geometer’s Sketchpad, Mathematics Teaching and Learning, Secondary School
Introduction
The purpose of this study was to encourage the innovative
use of Geometer’s Sketchpad (GSP) in the teaching and learn-
ing of mathematics among secondary school teachers in Malay-
sia through Lesson Study (LS). We will begin this paper by
discussing the importance of GSP in the teaching and learning
of mathematics in general and geometry in particular. This is
followed by discussing the significance of LS as a potential
model of teacher professional development in schools and as a
potential driving force for encouraging the innovative use of
GSP in the teaching and learning of mathematics among sec-
ondary school teachers.
Importance of GSP
GSP is a dynamic geometry software program for construct-
ing and investigating mathematical objects. It is a dynamic tool
for construction, demonstration and exploration that adds a
powerful dimension to the learning of geometry and many other
areas of mathematics. Further, research has shown that GSP can
be an innovative tool for enhancing students’ learning of plane
geometry (Choi, 1996; Choi-Koh, 1999; Choi-Koh & Sang
Sook, 2000; Driskell, 2004; Elchuck, 1992; Frerking, 1995;
Hannafin, Burruss, & Little, 2001; Abdullah, 2005; Thompson,
2006) and solid geometry as well (Chew, 2007; July, 2001;
McClintock, Jiang & July, 2002).
However, in Malaysian classrooms, the use of GSP in the
teaching and learning of mathematics is still very much at its
infancy state even though the Malaysian Ministry of Education
has purchased the GSP license and supplied the GSP software
to all secondary schools in Malaysia since 2004. While it is
envisaged that this initiative will benefit many teachers and
students as well as teacher educators nationwide, teacher enthu-
siasm and willingness to use GSP remains an issue to be ad-
dressed (Teoh & Fong, 2005). In fact, a study conducted by
Kasmawati (2006) on 151 teachers around Penang state showed
that 26% of the mathematics teachers had gone for the GSP
training courses but only 2% of them used GSP to teach ma-
thematics in their classes. Two major reasons given by these
teachers were 1) lack of time to prepare a GSP lesson and 2)
lack of skills and confidence to use GSP to teach mathematics
in class. Hence, there is an urgent need to set up a collaborative
group effort such as lesson study groups in schools that will
provide helpful support as well as sustain the continuous and
innovative use of GSP in secondary school mathematics teach-
ing.
Significance of LS
LS is a form of teacher professional development practised
decades ago in Japan. From the literature, LS was well estab-
lished since the 1960s (Fernandez & Yoshida, 2004) but claims
were also made that LS had actually started in the late 19th
century (Isoda, Stephens, Ohara, & Miyakawa, 2007). LS is a
process whereby small groups of teachers (usually 4 or 5 teach-
ers) meet at stipulated time to plan, implement, evaluate, and
revise lesson plan collaboratively. It is initiated and organised
by the teachers themselves as study groups at school or district
level with the aim to improve their teaching competency. The
main purpose of LS is to enhance teachers’ pedagogical know-
ledge and skills through peers’ review, critique and collabora-
tion among teachers (Shimahara, 1998). It is an on-going prac-
tice in Japan as a form of teacher professional development
especially in elementary schools. In Japanese teaching career,
teachers would engage in a relentless and continuous process of
improving their teaching by participation in lesson study groups
(Stigler & Hiebert, 1997; Shimahara, 1998; Lewis & Tsuchida
1998; Stigler & Hiebert, 1999; Yoshida, 1999; Lewis, 2000).
As a result, Japanese teachers have well adapted LS as part of

C. C. MENG ET AL. 237
their teaching career and profession. It is the teacher-initiated
and self-directed form of teacher professional development that
makes it a unique type of in-service practice in the teaching
profession. In fact, LS is now practised in many other countries
all over the world (Isoda et al., 2007).
Basically, according to Fernandez and Yoshida (2004: pp.
7-9), a LS cycle consists of the following 6 steps:
Step 1: Collaboratively Planning the Lesson Plan
Teachers come together to plan the lesson in collaborative
nature. They share their teaching knowledge and ideas on how
to design a good lesson drawing on their past experiences, ob-
servations on students’ abilities and ideas from resources and
textbooks. The end product is a lesson plan that describes in
details the process of teaching and learning.
Step 2: Seeing the Lesson Plan in Action
A teacher from the group will implement the lesson plan to
his or her students. Other teachers will act as observers during
the lesson. Occasionally, an expert from an educational institu-
tion is invited to observe the lesson.
Step 3: Discussing the Lesson Plan
The teachers will then come together to reflect on the lesson
that has been taught in a real classroom context. The teachers
share what they have observed during the lesson and comment
on their reflections as well as provide suggestions.
Step 4: Revising the Lesson Plan
Based on the teachers’ observations and reflections of the
lesson, the teachers will decide collaboratively to revise and
update a new version of the lesson plan.
Step 5: Teaching the New Ver sion of the Lesson
Although this step is optional, very often another teacher
from the group will teach the revised version of the lesson in
another classroom. As in the previous observed lesson, other
teachers will again act as observers during the lesson.
Step 6: Sharing Reflections about the New Version of the
Lesson
The teachers will come together again to discuss and reflect
on the revised version of the lesson taught. Again, the teachers
share their observations, comments and suggestions. Following
this, they collaboratively revise the lesson plan.
In fact, a substantial amount of research studies (see Stigler
& Hiebert, 1997; Shimahara, 1998; Lewis & Tsuchida, 1998;
Stigler & Hiebert, 1999; Yoshida, 1999; Lewis, 2000; Fernan-
dez, & Yoshida, 2004) have shown that LS improves teachers’
learning and supports teachers to grow professionally. However,
to date, no related research has yet been found to encourage the
innovative use of GSP in the teaching and learning of mathe-
matics among secondary school teachers in Malaysia through
LS. Therefore, this has spurred our motivation and interest to
adopt LS as a means to encourage the innovative use of GSP
among secondary school mathematics teachers in Malaysia.
Purpose of the Study
The purpose of this study was to encourage the innovative
use of GSP in the teaching and learning of mathematics among
secondary school teachers in Malaysia through LS. More spe-
cifically, this paper discusses the extent to which LS encour-
aged the innovative use of GSP in the teaching and learning of
mathematics among secondary school teachers in Malaysia.
Method
LS is a teacher-led professional development and thus vol-
untary participation from the teachers is an essential factor in
ensuring its success. We began by approaching dedicated and
voluntary mathematics teachers from different schools in the
states of Penang and Kedah to be recruited as participants. They
were then asked to seek three to five mathematics teachers from
their respective schools to form a LS group. Upon their consent,
we sought permission from their respective school administra-
tors to recruit the teachers as participants. Finally, three LS
groups were set up in three secondary schools, two in the state
of Penang and one in the state of Kedah. The two secondary
schools in Penang were named School A and School B while
the secondary school in Kedah was named School C. Schools A
and C are ordinary public secondary schools located in the
mainland of Penang and Kedah respectively. School A had 120
teachers and about 2300 students whereas School C had 77
teachers and about 1000 students including 40 special need
students (deaf and mute) at that time. School B is a secondary
boarding school located in the mainland of Penang with 70
teachers and about 670 students. All the selected students for
admission to School B were above average achievers.
To begin, all the participants attended a one-day workshop
on GSP conducted by an expert in GSP. The aim was to expose
and enhance the participants’ knowledge and skills in GSP.
They were also briefly introduced to the concept and process of
LS as well as the research procedure. Data were collected using
questionnaire to gauge the participants’ knowledge, skills, per-
ceptions and practices of GSP in the teaching and learning of
mathematics.
After the one-day workshop, all the participating schools be-
gan their LS cycle individually from July 2007 till May 2008.
At the end of the project, even though each school managed to
implement at least two LS cycles, the degree of success in en-
couraging the innovative use of GSP in the teaching and learn-
ing of mathematics in each school varied. This is because each
of the LS groups encountered different constraints and chal-
lenges in implementing the study. For each case, qualitative
data were collected through written lesson plans, GSP sketches,
worksheets, video-taped teaching and discussions as well as
teachers’ and students’ interviews.
Findings and Discussion
In this section, the findings of the extent to which LS en-
couraged the innovative use of GSP in the teaching and learn-
ing of mathematics among secondary school teachers in the
three LS groups are discussed. For easy reference, the LS
groups in Schools A, B and C were named Groups A, B and C
respectively.
Group A
Group A consisted of four mathematics teachers. All of them
majored in mathematics and have more than ten years of ma-
thematics teaching experience. GSI is the Senior Teacher of
Science and Mathematics in the school and thus was the LS

C. C. MENG ET AL. 238
group leader. Among the participants, GSI has fairly good
knowledge and skills of using GSP as she had previously at-
tended two GSP related workshops organised by the Penang
State Education Department. Her background knowledge and
skills in GSP has certainly rendered her an advantage in facili-
tating and leading her LS group members who were novice
users of GSP.
The group had completed two LS cycles. During this period,
the group members met at stipulated times after school dis-
missal to engage in the LS cycles. Some of the sessions were
also held during weekends and public holidays. Although partly
due to the busy work schedule of teachers during week days,
the willingness of teachers to sacrifice their weekends and
holidays to learn and practise GSP is clearly an encouraging
reflection of the positive attitudes of these teachers towards the
LS collaboration.
In the first LS cycle, the group members selected a topic in
one of the Form 4 (the fourth year of Malaysian secondary
education) Mathematics chapters, namely Lines and Planes in
3-Dimensions (3-D). The topic briefly introduces lines and
planes in 3-D and students are then required to identify and
calculate: 1) the angle between two lines, 2) the angle between
a line and a plane, and 3) the angle between two planes. Based
on their teaching experiences, students generally have difficul-
ties in identifying and calculating the required angles. Thus
they believed that by using GSP, students might be able to
visualise and identify the required angles through the direct
manipulation of the 3-D objects on the computer screen.
Three LS discussions were held to plan the lesson prior to the
teaching of the topic. During the discussions, GSI discovered
that her group members were struggling to learn how to con-
struct 3-D objects in GSP. Thus, she offered herself to assist
them in the construction of the 3-D objects in GSP whenever
possible as comparatively she has more knowledge and experi-
ence in GSP. In fact, GSI took the role as the leader and facili-
tator of the group in every discussion session and she found that
the interactions with the group members were worthwhile ex-
periences. After the lesson plan was finalised, GSI volunteered
to teach the collaboratively planned lesson in one Form 4 class
in the computer laboratory of the school. The teaching was
observed by all members as well as the second author who
played the role as both a researcher and an external advisor.
An analysis of the lesson plan, GSP sketches, worksheets and
videotaped teaching observation did illuminate GSI’s ability to
use GSP sketches to teach the topic. For example, the lesson
began with a brief explanation of the content and concepts of
Lines and Planes in Three Dimensions by GSI. She then used
the “animated program” as in Figures 1 and 2 for exposition.
The students had the options of selecting the objects in GSP
and they could adjust and rotate the solids by clicking on the
respective buttons so that they could visualize the angles be-
tween lines and planes as well as the angles between two planes
from different perspectives.
Immediately after the teaching, a reflection session of the
lesson was held. The group members reflected that GSP was
effective in enhancing the students’ conceptual understanding
of the 3-D objects. Since all the group members were satisfied
with the lesson, no revision was made to the lesson plan. Al-
though they planned to re-teach the same lesson in another class,
unfortunately it was not implemented as no group member was
Figure 1.
A GSP sketch of a cube.
Figure 2.
A GSP sketch of a pyramid.
willing to have his/her teaching being videotaped and observed
(Goh, 2010).
But, in the second LS cycle, the group members collabora-
tively decided to use GSP merely for revising one of the
mathematics topics that was difficult for the Form 3 students.
Based on their experiences in the first LS cycle, they felt the
constraint to gather the participants for teaching observation at
a particular time. Hence, they chose a topic in one of the Form
2 Mathematics chapters, namely Loci in 2-Dimensions (2-D)
but planned to teach the lesson to the Form 3 students. Another
main reason was that they felt the use of GSP was appropriate
and suitable for teaching the topic as it could help students to
visualise the movement of a point in 2-D through the animation
of the movement of the point. The content of the topic briefly is
about a moving point in equal distance from: 1) a fixed point, 2)
two fixed points, 3) a straight line, and 4) two straight lines.
Three LS discussion sessions which include planning of les-
son plan and hands-on practices with GSP were conducted prior
to the teaching. During the discussions, the group members
collaboratively constructed GSP sketches to be used in teaching
the topic. Once again, GSI facilitated the three discussion ses-
sions. A group member volunteered to conduct the first teach-
ing using one Form 3 class in the computer laboratory as the
students needed to use computers in their group activities. The
lesson also began with a brief explanation of the content and
concepts of Loci in Two Dimensions by the teacher. Then, the
teacher e mployed t he “ani mated program” as in Figures 3 and 4
for exposition. The students had the options of selecting the

C. C. MENG ET AL. 239
Figure 3.
A GSP sketch of a rectangle .
Figure 4.
A GSP sketch of a problem involving loci in 2D.
objects in GSP and they could display the loci of the points by
clicking on the respective buttons.
As in the first LS cycle, a reflection session was held imme-
diately after the observed lesson. During the reflection of the
first teaching, the teacher pointed out that the students were too
eager to explore the GSP sketches by clicking the action but-
tons for the succeeding steps instead of listening to the
teacher’s instructions. Consequently, some of the students
could not follow the instructions half way through the lesson.
To solve this problem, they suggested that the students ought to
try the questions on their own first before checking their an-
swers provided in the GSP sketches.
Based on the suggestion, another group member agreed to
conduct the second teaching using another Form 3 class in the
computer laboratory as the students also needed to use com-
puters in their group activities. The implementation of this
suggestion had made the second teaching to be conducted more
systematically by the second teacher. Nevertheless, they ob-
served that all the students were motivated and actively en-
gaged in the lesson. They acknowledged that the students were
excited with the lesson using GSP.
It was evident from the written lesson plans that the partici-
pating teachers have attempted to make full use of GSP features
such as animation and dynamic capabilities to enable their stu-
dents to acquire better understanding of the geometrical con-
cepts. Another notable observation was that these teachers had
designed in the lessons, especially for the topic of “Loci in Two
Dimensions”, questions that were similar to those in public
examination. These questions and diagrams were collabora-
tively prepared by the participants through the LS collaboration.
Although this was not the explicit goal in the LS collaboration,
this adaptation was positively received by both the teachers and
students. Any approaches that enhance students’ achievement
in public examination are always welcome by all parties in this
examination-oriented culture of Malaysian society.
Group B
Group B also consisted of four mathematics teachers. All of
them majored in mathematics and have more than ten years of
mathematics teaching experience. TKA is the Excellent Mathe-
matics teacher (that is, a title accorded by the Ministry of Edu-
cation to a teacher who is expert in his subject area and excels
in his teaching practice) in the school and thus was the LS
group leader. Among the participants, TKA has fairly good
knowledge and skills in GSP and this has also certainly ren-
dered him an advantage in facilitating and leading his LS group
members who were novice users of GSP.
In the first LS cycl e, Group B members also selected a simi-
lar topic in one of the Form 4 Mathematics chapters, namely
Lines and Planes in 3-Dimensions (3-D). But, in the second LS
cycle, the group members chose a topic in one of the Form 5
Mathematics chapters, namely Plans and Elevations because
they felt that this topic often causes much confusion among
students especially in visualizing the real object in its actual
perspectives. During the first teaching of the second LS cycle,
one of the group members volunteered to teach the topic. First,
he used GSP to demonstrate how 3-D objects could be rotated
to show their plans and elevations. Then, the students were
given 25 minutes to sketch the plan and elevations of the 3-D
objects shown on the screen. Finally, the teacher showed the
plans and elevations of the 3-D objects on the screen by rotat-
ing the 3-D objects in GSP for the students to check their an-
swers. During the reflection session of the lesson, some group
members felt that the learning process was too teacher-centered
and monotonous. A member suggested that a more student-
centered approach ought to be used in line with the LS goal. He
felt that the students would be more engaged in the learning
process if they themselves were to use GSP to find the plans
and elevations of the 3-D objects. However, other members
were sceptical about the students’ ability to use GSP. Finally,
the group members came to a consensus that they would give
the students a training session to learn some basic skills of con-
structing 3-D objects using GSP prior to the second teaching of
the lesson.
During the second teaching of the lesson, the students were
given hand-outs containing figures of 3-D objects (see Figure
5).
The instructions for completing the task in Figure 5 are as
follows:
Look at the solid in the diagram. Sketch on the paper pro-
vided,
1) the plan of the solid
2) the elevation of the solid as viewed from X
3) the elevation of the solid as viewed from Y.
After you have completed your drawings, compare your pic-
tures with your friends beside you.
Now, draw the solid in your computer using the template
provided.

C. C. MENG ET AL. 240
with their peers and busy working on the task in their own
computers. One of the school administrators came to observe
the lesson. He was very pleased with the students’ ability to use
GSP to complete the tasks given. Students also found GSP
useful and interesting. For instance, one of the students re-
sponded that, “I love using GSP very much. Sometimes imagi-
nation cannot be really helpful because we tend to make mis-
takes. But GSP helps to make our imagination work. Love it!”
Another student wrote, “I begin to fall in love with geometry
ever since I use GSP. It is truly useful for those who can’t im-
agine geometrical constructions. It helps a lot in my learning.”
One more student said, “GSP is very useful to all students. It is
an auspicious start to teach students learning mathematics using
GSP.”
Furthermore, the group members managed to administer a
pre-test prior to the first teaching of Plans and Elevations dur-
ing the second LS cycle. The students were asked to draw in
full scale the plans and elevations of four different solid objects.
Each problem was given 12 marks and therefore 48 was the full
mark for the test. The mean score of the pre-test was 13.63.
After the second teaching, a post-test consisting of the equiva-
lent problems were administered to the students on the follow-
ing day. The mean score of the post-test was 28.42. Thus, the
gain score was 14.79 indicating that there was a positive im-
provement in the students’ performance after the second teach-
ing. Figure 6 shows an example of the pre-test questions.
Figure 5.
An example of the task given in the second teaching o f the lesson.
Source: Tan (2010: p. 36).
After you have completed your drawing, rotate the solid in
your computer so as to view it from the direction of Z, X and Y
respectively.
Check to see if you have drawn your plan and elevations cor-
rectly. Group C
Discuss your answers with your friends beside you.
Besides sketching the plan and elevation of the 3-D object
given on the paper, the students were required to rotate the
object on the GSP screen to verify their answers. This time, the
students were rather engrossed in directly manipulating the 3-D
objects on the GSP screen resulting in an obvious change of the
classroom atmosphere as compared with that of the previous
lesson. The students were engaged in learning by discussing
Group C consisted of six mathematics teachers. All of them
majored in mathematics except for one Malay Language teach-
er who also taught mathematics. KS was the LS group leader as
she had attended a GSP workshop previously. She has some
knowledge and skills of using GSP but the other group mem-
bers were novice users of GSP. Her immediate task was to
conduct GSP training sessions for the teachers over several
Figure 6.
ne of the test questions. Source: Tan (2010: p. 36). O

C. C. MENG ET AL. 241
weekends. Although the training sessions went on well as
planned, the teachers were not able to attend the training ses-
sions regularly. It was difficult to record full attendance in any
of the sessions because the teachers had other commitments
such as administrative and extracurricular duties.
In the first LS cycle, Group C also encountered additional
problems such as the group members did not have a good
command of English to teach mathematics in English, insuffi-
cient skills of using GSP to prepare the lesson materials, over
loaded with teaching and administrative work, lack of time to
participate fully in this project, lack of confidence and shy to be
observed by other group members, as well as having students
who were not so competent in English. To overcome the prob-
lems, they decided to use ready-made GSP sketches for teach-
ing “Loci in 2-Dimensions” which were prepared by Group A.
A discussion was held in conjunction with the in-house GSP
training that was scheduled earlier by the school mathematics
committee. The aim of the discussion was to: 1) expose teach-
ers to the ready-made GSP sketches, 2) carry out trial runs of
the ready-made GSP sketches to enhance their skills in using
GSP to teach the topic, and 3) modify the lesson plan to suit
students’ ability. A group member volunteered to implement
the first teaching. Immediately after her lesson a reflection ses-
sion was held. Feedbacks from the group members were very
encouraging. They found it simple to use the ready-made GSP
sketches. Some group members who had never taught the topic
before agreed that the ready-made GSP sketches were useful to
help students to better understand the topic. In addition, the
students found it interesting and easy to follow the lesson (Kal-
som Saidin, 2010).
The next day, another group member used the same ready-
made GSP sketches to conduct the second teaching of the les-
son. During the reflection session after the lesson, the group
members observed that the students were able to understand the
lesson. The teacher also found that it was easier to present the
lesson to her students using the ready-made GSP sketches. As a
result, all the group members and students were so keen to use
GSP so much so that everyone wanted to continue to try using
GSP in another topic in the second LS cycle. This time, they
chose the topic, “Rotation”, because it was a very important
topic which can be enhanced by using GSP. They downloaded
some ready-made GSP sketches related to the topic from the
Internet and used them in their first and second teachings. Dur-
ing the reflection session, all the group members were very
pleased and satisfied with the ready-made GSP sketches be-
cause they could carry out their teaching easily and smoothly.
They observed that their students were also very happy and
actively engaged in learning the topic during the lessons. Some
reflected that they found learning with GSP enhanced their
understanding of the topic and more interesting as well (Kal-
som Saidin, 2010).
Constraints and Implications
Despite the positive feedback from the participating teachers,
the LS groups encountered various constraints which chal-
lenged both the sustainability of the groups and the encourage-
ment of the innovative use of GSP in the teaching and learning
of the geometrical topics in their classes. The main constraints
are discussed next (Lim & Fatimah Saleh, 2010).
Time Constraint
In LS, teachers need to set time for discussions and observa-
tions. They also need time to plan lessons together. In view of
the heavy workload that most teachers face today, it is always a
great challenge to further stress on their limited time for LS.
Very often, they have to sacrifice their weekends and holidays
like the case of Group A. Hence, time constraint remains the
biggest challenge in our effort to promote LS as a means of
encouraging the innovative use of GSP in the teaching and
learning of mathematics among secondary school teachers.
Consequently, this implies the need to have administrators’
support for planning the weekly time table in such a way that
the teachers who are involved in LS can have common free
periods so that they can discuss, observe each other and practise
the skills of using GSP as well.
Commitment
Teachers might not participate in the LS process whole-
heartedly without full commitment. For example, they might
give excuses such as “no time”, “need to fetch my children”
and other family-related reasons to avoid coming for discus-
sions. Some teachers would come late for the meeting but left
early. The lack of commitment of some teachers could demor-
alize the spirit of the LS group members. To gain teachers’ full
commitment, it is important to make teachers realize and ex-
perience the potential benefits of joining the LS group.
Group Leader’s Leadership and Personality
We observed that the degree of success in encouraging the
innovative use of GSP in the teaching and learning of mathe-
matics in each LS group varied. We found that constant moral
support and encouragement from the group leader is especially
important to sustain the group members’ commitment. For
instance, GSI, the group leader of Group A was very keen in
upgrading the professional competency of her group members.
She strongly believed that GSP could be an effective tool for
teaching mathematics in general and geometry in particular and
the innovative use of GSP in mathematics teaching and learning
could be encouraged through LS. Hence, she willingly sacri-
ficed her weekends and holidays to her group members to pre-
pare the GSP sketches. By setting a good role model and hav-
ing fairly good knowledge and skills of using GSP, she was
able to give constant and continuous technological, pedagogical
and content knowledge support to her colleagues. Moreover,
her administrative position as the Senior Teacher of Science
and Mathematics in the school had also given her extra author-
ity to call for meetings and access to administrative support as
well such as the arrangement of the school time table.
Lack of Hardware and Software Support and
Maintenance
As pointed out by one of the teacher participants, one factor
that hindered him from using GSP was the availability and
readiness of the hardware and software support and mainte-
nance as well. For instance, as voiced out by GSI that although
there were 40 desktop computers in the school lab, only seven
of them were in good condition. Hence, she had to borrow lap-
top computers from all mathematics and science teachers to be
used in her lesson. Clearly, the lack of hardware support such

C. C. MENG ET AL. 242
as not enough computers will discourage the teachers to pro-
vide hands-on activities such as using GSP for their students.
Sometimes the teachers might encounter the frustrating experi-
ence that after spending much time and effort in preparing a
lesson using GSP, the computer or the LCD was found not
functioning. Clearly this wasted a lot of teaching and learning
time and resulted in disappointment and frustration among
teachers and students. Hence, it is important for the Ministry of
Education and the school administrators to ensure that there is a
constant maintenance and update of both software and hard-
ware in schools.
Conclusion
In this paper, we only managed to share the experiences of
three LS groups that aimed to encourage the innovative use of
GSP in the teaching and learning of four geometrical topics
among secondary school mathematics teachers through LS. We
acknowledge the limitation of observing significant changes in
the teachers’ knowledge and skills of using GSP. Nevertheless,
we were very much encouraged by the positive attitude and
commitment of the participating teachers as revealed in the
teaching observations and interviews. Further, the findings of
this study show that LS collaboration can be a potential model
of teacher professional development for encouraging the inno-
vative use of GSP in the teaching and learning of mathematics
among secondary school teachers.
Acknowledgement
This project is made possible with funding from the Short
Term Grant of Universiti Sains Malaysia, Penang.
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