Transcript PPT

INSTITUTE FOR MATHEMATICAL RESEARCH
UNIVERSITY PUTRA MALAYSIA
MALAYSIA
www.inform.upm.edu.my
LEARNING MATHEMATICS THROUGH
UTILIZATION OF TECHNOLOGY
STUDY 1
Rohani Ahmad Tarmizi
([email protected])
Ahmad Fauzi Mohd Ayub
Kamariah Abu Bakar
Royati Saha
BACKGROUND
•
•
•
Technology in education had vast impact on
learners worldwide.
When technology and appropriate teaching
methods are integrated in teaching and learning,
positive impact maybe observe on both cognitive
and affective domain of learning.
Technology as a tool or a support for
communicating with others, allows learners to
play active role in the classrooms.
BACKGROUND



In mathematics, many technological softwares
and hardwares can be used as a tool in
teaching and learning in the classrooms.
With technology students become more active
in thinking about information, making choices,
and executing skills than is typically in a
teacher-led lessons.
In mathematics classrooms, tools such as
Graphing calculators, Autograph, Geometer’s
Sketchpad, e-transformation, Geogebra,
Mathematica, Matlab, Derive, Cabri have been
widely used both at secondary and tertiary
level.
BACKGROUND

In this study, several technological
tools were explored in its efficiency
and utilization at the secondary
level- Graphing calculators,
Autograph
Graphing Calculator Group

Graphing Calculator is a hand-held
mathematics calculator that can
 Draw and analyses graphs,
 Computes the values of mathematical
expression,
 Solve equations,
 Perform symbolic manipulation,
 Perform statistical analyses
ZOOM
To adjust the
windows to a
predefined setting.
WINDOW
TRACE
To move the cursor along the
graph function using ◄ and ►
To set the viewing windows
GRAPH
Y=
Displays the
graph you have
defined.
Display
Y=Editor,where
you can enter
functions.
▲ ► ▼ ◄
2ND
Let you move the cursor
in four directions.
Provides access to
the secondary
function.
CLEAR
ALPHA
Erases the last
entry; erases the
Home screen.
To access the
green letters
above the keys.
X,T,Θ,n
ENTER
Pastes the variable
into the definition
of a function
Executes commands and
evaluates expressions.
Graphing Calculator
Graphing Calculator Group
Graphing Calculator Group
GRAPHING CALCULATOR




GC is considerably a versatile tool for teaching or learning
mathematics.
GC is not only a teaching tool in the hands of the teacher, it
is also a learning tool in the hands of students when used
during classroom investigations, concept development and
guided discovery exercises, explorations, open-ended
homework exercises, and extended modeling projects.
The use of GC in classroom transforms the class to that of a
laboratory.
Students could work in small groups where they can
investigate patterns, analyze results and solve problems,
thereby constructing their own mathematical understanding.
Autograph Group
Autograph Group
Conventional Group
METHODOLOGY
Design of The Study








Experimental design was used for this study.
Students were selected at random and assigned to groups.
The experimental groups underwent learning using graphing
calculator and Autograph technology while the control group
underwent learning using conventional instructional strategy.
Four phases were conducted:
Introduction to software
Introduction to topic
Integrated teaching and learning using software
Testing using achievement test and The Paas Mental Effort
Rating Scale.
Design of the Study
Experimental,
non-equivalent control group
pretest-posttest design
Group
Pretest
Learning
Phase
Posttest
Exp - GC
O1
X
O2
Exp - Auto
O1
X
O2
Conventional
O1
X
O2
Students were assigned to three
groups randomly.
Similar questions as in the posttest.
Learning to use the GC or Autograph
or the traditional learning
EXPERIMENTAL
GROUPS:
Students were
required to solve the
given problems
using paper-pencil
CONTROL
GROUP:
Students were given
problems to solve
using paper-pencil




Introduction to the
technological tools
Induction set phase
Learning and
assessment phase
Test phase
Beginning of a
lesson - to induce in
students an
appropriate set of
behavior and to
spur students to
attack their work
enthusiastically and
diligently.
• Concept development - important
concepts learnt were emphasized
EXPERIMENTAL
GROUPS
Using
GC
Using Autograph
CONTROL
GROUP
Traditional wholeclass instruction

INSTRUMENTS OF THE STUDY
1. Mathematics
Achievement Test
(MAT)
2. Paas Mental Effort
Rating Scale
The MAT was designed
by the researchers to
measure students’
understanding of the
Quadratic Function
topic. It comprised of
three questions based on
the learning outcomes
covered in the learning
phase. The time
allocated to do the test is
30 minutes.
PROCEDURE OF THE STUDY
Randomized assignment of students to the experimental and control
groups and were placed in three different classrooms. A pretest on
Quadratic Functions were then conducted a for all groups.
INTRODUCTION
Use of GC or Autograph followed by
Induction Set for the topic ‘Quadratic Function’
Videotaped sessions
INTERVENTION
GC Strategy, Autograph Strategy &
Conventional Strategy
POSTTEST
Mathematics Achievement & PAAS
mental effort rating scale
METHODOLOGY
Population and Sample




The target population of this study was Form Four
students (grade 10) in National Secondary School in
Malaysia.
The samples selected for this study were Form Four
students from two schools.
The students were brought to the university
(Universiti Putra Malaysia) to participate in the
learning sessions.
The total number of students in the graphic
calculator group was 41 students, groups two
followed the Autograph learning mode was 39 and
the conventional group was 47 students.
RESULTS
Table 1: Comparison of Mathematics Achievement Test
Perfomance
MAT
(Mathematics
Achievement
Test)
Group
N
M
SD
GC
42
15.54
3.14
Autograph
39
10.72
3.47
control
47
13.03
3.65
• Overall mean of MAT scores of GC group was
significantly higher than the conventional group and
Autograph group.
• These findings indicated that the GC strategy group
had performed better in test phase than the conventional
group and Autograph.
RESULTS
Table 2: Comparison of Mental Effort
Variables
Group
N
M
SD
SE
Mental effort
(learning
phase)
GC
31
4.45
1.65
.296
Autograph
22
4.10
2.04
.435
Control
27
3.79
1.96
.378
GC
38
4.79
1.48
.24
Autograph
35
4.95
1.88
.32
Control
28
4.46
1.48
.28
Mental effort
(test phase)
RESULTS
Learning phase
 ANOVA test results indicated that there was no significant
differences in the mean mental effort between the three groups
during learning phase.
 Planned comparison test showed that mean mental effort during
learning phase of GC group was significantly higher from those of
conventional group.
Test phase
 Planned comparison test showed that mean mental effort during
test phase of GC group was significantly lower from those of the
Autograph group.

This finding indicated that the GC strategy group had benefited
from the learning sessions hence their mental effort was lower
compared to the Autograph group during the test phase.
RESULTS
2-D Instructional Efficiency

Table 3: Comparison on instructional efficiency index
Variable
Group
N
M
SD
SE
2-D
instructional
efficiency
GC
38
.3844
.8802
.1428
Autograph
35
-.5125
1.2261
.2072
Control
28
.1613
1.0214
.1930


planned comparison test showed that the mean for GC group
was significantly higher than conventional group followed by
Autograph group
This suggests that learning by integrating the use of GC was
more efficient than using conventional strategy and
Autograph group.
RESULTS

Table 4: Comparisons of selected variables
Variables
Group
N
M
SD
No. of problem
solved
GC
Autograph
Control
42
39
47
6.98
6.64
6.28
.154
1.20
1.08
Total score of
conceptual
knowledge
GC
Autograph
Control
42
39
47
10.12
4.97
7.28
3.06
3.24
3.63
Total score of
procedural
knowledge
GC
Autograph
Control
42
39
47
18.36
16.92
18.06
2.72
3.86
1.36
No. of errors
committed
GC
Autograph
Control
42
39
47
.7937
2.2886
1.5213
.596
2.87
.898
CONCLUSION



The results also showed that the higher performance of
the GC strategy was achieved with a lower mean
mental effort during test phase.
The eta squared indices were .34 and .13 respectively,
a large and moderate effect based on Cohen (1988),
implying that the GC strategy provides effective impact
on cognitive load.
The results also suggested that the higher
achievement was achieved with a reduction in
cognitive load. This contention was supported by the
significantly higher level of 3-D instructional condition
efficiency index reported by the GC strategy as
opposed to the other two strategy.
CONCLUSION



Graphing calculator is instructionally more
efficient compared to conventional method and
Autograph software.
Systematic planning of instructions and good
learning package using graphing calculator and
Autograph will give new views in mathematics
teaching and learning.
This shows that dynamic technological tools,
particularly graphing calculator provide
positive impact upon learners thus becoming
potential tools in teaching mathematics at
Malaysian secondary school level.
CONCLUSION


In conclusion, graphing calculators are
excellent tools which can foster
students to explore and investigate
during mathematical activities besides
enhancing students understanding and
performance.
However, there is a need to conduct
further research on how to integrate
graphing calculators in mathematics
instruction so that students'
mathematical understanding are
enhanced and reinforced.
EXPLORING EFFECT OF UTILIZING
GEOMETER SKETCHPAD ON PERFOMANCE
AND MATHEMATICAL THINKING OF
SECONDARY MATHEMATICS LEARNERS
STUDY 2
Kamariah Abu Bakar
([email protected])
Rohani Ahmad Tarmizi
Ahmad Fauzi Mohd Ayub
Aida Suraya Mohd Yunus
BACKGROUND


The teaching and learning of geometry
utilizing dynamic geometry softwares have
been explicitly indicated in the Malaysian
secondary school syllabus (Ministry of
Education, 2003)
Teachers have been recommended to
utilize such software and one such
dynamic geometry software licensed to be
used in the Malaysian schools is the
Geometer’s Sketchpad (GSP) software.
BACKGROUND
•
•
Geometer’s Sketcpad (GSP) is a software
programme that revolutionized the teaching
and studying of mathematics especially in
geometry.
It is a computer software for creating,
exploring and analyzing a wide range of
mathematics concepts in the field of algebra,
geometry, trigonometry, calculus, and other
areas (Geometer’s Sketchpad, Reference
Manual, 2001).
BACKGROUND
•
•
•
Almeqdadi(2000) in his study had investigated the
effect of using the GSP on students’ understanding of
some of the geometrical concepts.
The sample consisted of 52 students from the Model
School, Yarmouk University, Jordan.
The result of the study indicated that there was a
significant difference between the means of students
on the posttest and more gain in the scores from the
pretest to the posttest in the case of the experimental
group.
BACKGROUND
•
•
•
There are also some studies that showed negative
results.
Teoh Boon Tat & Fong Soon Fook (2005) in their
study to examine the effects of using the GSP and
the graphic calculator (GC) in the learning of the
vertex form of quadratic functions among field
dependent (FD) and field independent (FI) cognitive
style students.
They found that the students performed as well when
using GSP or the GC in the learning of quadratic
function by way of visualization of graphs.
BACKGROUND
•
•
•
A similar research was conducted by Ling (2004)
which compared the use of the GSP software, the
GC and the traditional method to learn on the crosssection of a cone.
Reslts of the study showed that the GSP software
and the GC did not show a significant effect on the
achievement of the students.
From all the findings, it may be concluded that the
utilization of the GSP software has obtained mixed
reviews on its effectiveness.
OBJECTIVES
The purpose of this study is to investigate the effectiveness of integrating a
mathematical software which is Geometer’s Sketchpad compared to the
traditional approach in teaching and learning of form four Additional
Mathematics subject on the topic of ‘Quadratic Functions’.
Specifically, the objectives are:

•
•
To compare students mathematical perfomance utilizing GSP and
conventional instruction in mathematics teaching and learning at the
Malaysian secondary level.
To compare instructional efficiency of learning conditions utilizing GSP
and conventional instruction in mathematics teaching and learning at
the Malaysian secondary level.
To investigate the attitude of students towards learning GSP and
conventional instruction in mathematics teaching and learning at the
Malaysian secondary level.
METHODOLOGY
Design of The Study
•
•
•
A true experimental design randomized posttest only control
group design was used for this study with students randomly
assigned into two groups.
The experimental group underwent learning using GSP
technology while the control group underwent learning using a
conventional instructional strategy.
This study used four phases:
i. Introduction to Geometer Sketchpad
ii. Introduction to Quadratic functions
iii. Integrated teaching and learning using Geometer Sketchpad
iv. Testing using set of Quadratic Equation Test
Design of The Study
Experimental,
non-equivalent control group
pretest-posttest design
Group
Pretest
Learning
Phase
Posttest
Exp - GC
O1
X
O2
Exp - Auto
O1
X
O2
Conventional
O1
X
O2
Students were assigned to two
groups randomly.
Similar questions as in the posttest.
Learning to use the GC or Autograph
or the traditional learning
EXPERIMENTAL
GROUPS:
Students were
required to solve the
given problems
using Geometer
Sketchpad software
CONTROL
GROUP:
Students were given
problems to solve
using paper-pencil




Introduction to the
technological tools
Induction set phase
Learning and
assessment phase
Test phase
Beginning of a
lesson - to induce in
students an
appropriate set of
behavior and to
spur students to
attack their work
enthusiastically and
diligently.
• Concept development - important
concepts learnt were emphasized
EXPERIMENTAL
GROUPS
Using Geometer
Sketchpad
CONTROL
GROUP
Traditional wholeclass instruction
INSTRUMENTS OF THE STUDY
• Mathematics
Achievement Test
(MAT)
• Pass Mental Effort
Rating Scale
• Questionnaire on
Perceived Efficacy of
the technological tools
The MAT was designed by the
researchers to measure students’
understanding of the Quadratic
Function topic. It comprised of three
questions based on the learning
outcomes covered in the learning
phase. The time allocated to do the
test is 30 minutes.
A set of Questionnaire was adapted
from previous studies measuring
perceived efficacy of the instructional
strategy followed by the students
namely the use of Geometer
Sketchpad and traditional learning.
PROCEDURE OF THE STUDY
Randomized assignment of students to the experimental and control
groups and were placed in three different rooms. A pretest on
Quadratic Functions were then conducted a for all groups.
Introduction to the Intervention Mode followed by
Induction Set for the topic ‘Quadratic Function’
Videotapes sessions
INTERVENTION
GSP Strategy &
Conventional Strategy
POSTTEST
Mathematics Achievement & Survey of
Perceived Efficacy of GSP Strategy or
Conventional Strategy
METHODOLOGY
Population and Sample




The target population of this study was Form
Four students (grade 10) in National
Secondary School in Malaysia.
The samples selected for this study were Form
Four students from two schools.
The students were brought to the university
(Universiti Putra Malaysia) to participate in the
learning sessions.
The total number of students in the GSP group
was 45 students whilst the conventional group
was 47 students
RESULTS

Table 1: Comparison of Mathematics Achievements
Variable
MAT score
Group
N
M
SD
GSP
45
11.78
4.10
control
47
13.03
3.65
• Overall mean of MAT scores showed that there was no
significant difference between mean perfomance scores
of the control group compared to scores for the GSP
group.
• In fact, the mean score of the control group is higher
than the result of the experimental group.
…RESULTS

Table 2: Comparisons of selected variables
Variables
Group
N
M
SD
SE
No. of
problem
solved
GSP
Control
45
47
5.98
6.28
1.29
1.08
.19
.16
Total score of
conceptual
knowledge
GSP
Control
45
47
5.99
7.28
4.67
3.63
.70
.53
Total score of
procedural
knowledge
GSP
Control
45
47
18.4
18.06
1.39
1.36
.21
.19
Total score of
the test
GSP
Control
45
47
24.01
25.34
4.74
3.78
.71
.55
…RESULTS

Table 2 (con’t): Comparisons of selected variables
Variables
Group
N
M
SD
SE
No. of errors
committed
GSP
Control
45
47
1.95
1.52
1.54
.898
.23
.13
Mental Load
GSP
Control
45
47
5.61
4.46
2.03
1.48
.30
.28
2D Efficiency
GSP
Control
45
47
- 0.28
0.43
1.22
0.95
.181
.178
3D Efficiency
GSP
Control
45
47
- 0.56
0.61
1.24
0.87
.216
.198
…RESULTS
•
There was no significant difference between procedural steps
when performing each activity like plotting the graphs, were
analyzed.
•
There was also no significant difference between conceptual
skills obtained by the control group as compared to the
experimental group.
…RESULTS
Table 3: Mean and SD of students’ attitutes towards the
teaching and learning approaches.
Control
GSP
Levels
Mean
SD
Mean
SD
Enthuasiasm 3.29
0.612
3.52
0.526
Enjoyment
3.28
0.610
3.40
0.565
Anxiety
1.87
0.386
1.93
0.474
Avoidance
1.77
0.612
1.69
0.526
…RESULTS
•
•
•
•
•
The attitudes of students towards the respective
teaching approaches used was measured according to
the four dimensions of students attitudes.
Level of enthuasiasm refers to the extent students
were enthused to continue learning using the
respective approaches.
Level of enjoyment refers to extent students had
enjoyed the approached used to teach the respective
group.
Level of anxiety refers to the extent the approach had
imposed and created anxiety during learning.
Level of avoidance refers to students perceptions that
the respective approaches were a waste of time and a
fruitless effort.
CONCLUSION




It is crucial to note that the respondents are form four
students selected from a nearby school.
Within six hours, students need to undersatnd the
contents and to familirize with GSP.
For them, GSP is a new and exciting experince as
observed from the attitudinal measures, but they do not
have enough time to explore the GSP and benefited from
its utilization during teaching and learning.
Time’s constraint thus might be one of the factors why
this study came out with negative impact on the use of
technology.
CONCLUSION



Further studies need to be done, especially
on time needed for students to explore and
learning using GSP in learning mathematics.
Furthermore, research also need to be
conducted in normal classroom settings in
Malaysian school in order to explore further
in utilizing GSP in mathematics learning.
However, findings from this study can elicit
ideas to teachers and researchers on the
needs using ICT technology in teaching and
learning mathematics.
Exploring the effectiveness of using
GeoGebra and e-transformation in
teaching and learning Mathematics
STUDY 3
Kamariah Abu Bakara
Ahmad Fauzi Mohd Ayubc
Rohani Ahmad Tarmizi b
a,b,cInstitute of Mathematical Research, Universiti Putra Malaysia, Malaysia
Introduction


Many studies have been conducted to determine the
suitability or effectiveness of the use of computer
software in teaching and learning mathematics.
Research by Rohani Ahmad Tarmizi, Ahmad Fauzi
Md. Ayub, Kamariah, Abu Bakar, Aida Suraya Md.
Yunus (2008) showed that teaching and learning
mathematics utilizing the graphing calculator was
found to be instructionally efficient significantly,
compared to the conventional and Autograph
software.


Findings by Kamariah, Abu Bakar, Rohani Ahmad
Tarmizi, Ahmad Fauzi Mohd. Ayub, Aida Suraya Md.
Yunus (2009). indicated that the use of Gemeters
Sketchpad (GSP) induced higher mathematical
thinking process amongst the GSP group. These
findings showed that the use of GSP had an impact
on both mathematical thinking process and
performance.
Norris (1995) and Penkow (1995) reported that there
was no significant differential effect between
conventional teaching and the use of graphing
calculator.
Purpose



The purpose of this study was to investigate students’
performance score using GeoGebra and e-transformation
in the learning of mathematics by Form two secondary
school students’ on the topic of Transformation.
GeoGebra is an open source software while etransformation is a computer based learning courseware,
specially developed for learning transformation.
Specifically, the objective of this study was to compare the
effects of utilizing the two technologies (GeoGebra and eTransformation) on various performance measures in
learning the topic on transformation.
GeoGebra


GeoGebra is an open source software
under General Public License (GPL) and
freely available at www.geogebra.org.
This software combines geometry,
algebra and calculus into a single easeto-use package for teaching and learning
mathematics from elementary to
university level
GeoGebra
e-transform

e-Transformation (e-Transform) is a courseware
developed by a group of researchers, based on students’
difficulties.
e-transform
e-transform
Methodology



A true experimental design was used for this study with
students being randomly assigned into two groups.
One group used GeoGebra while the other used etransformation. In this study, there is no control group
because both groups underwent computer based learning.
Four phases were conducted:
1) The Pre Testing phase;
2) Introduction to Software (GeoGebra and eTransformation) phase;
3) Integrated teaching and learning phase using each
software and a Learning Activity Module; and
4) the Post Test phase.
Methodology



Purposive sampling was used to select the three
classes of Form two students from a school.
These students were randomly assigned into two
groups, whereby group one followed the GeoGebra
mode of learning and the second group used etransformation.
The total number of students in group one was 40
students, and group two was 30 students.
Results





A. Effects of GeoGebra on Performance score for pre
and post test.
For the group that used GeoGebra, the analysis on the
performance scores for pre and post tests were by using
Wilcoxon T.
Research findings indicated that there was significant
difference in performance scores for the post test (Mdn =
31.00) compared to the pre test (Mdn = 25.00), z = 2.85, p =.004 <.05, r = -0.45).
The results showed that students who learned
transformation using GeoGebra showed increase in their
performance after they used it.
the effect size was medium
Results
B. Effects of e-transformation on Performance score for
pre and post test.
 For the second hyphotesis, analysis using Wilcoxon
T showed that there were significant differences in
post test performance scores (Mdn = 25.00)
compared to the pre test scores (Mdn = 20.00), z = 2.76, p = .006 < .05, r = -0.50).
 This showed that the e-Transformation could help
students to increase their performance.
 the effect size was big.
Results




C. Effects of GeoGebra and e-transformation on Overall
Performance score for pre test
To answer the third hypothesis, the Mann-Whitney test was
conducted on pre test performance scores for the groups
using GeoGebra and e-transformation.
Research findings showed that there was no significant
difference in the pre test performance scores for the
GeoGebra group (Mdn = 25.00) compared to the etransformation group (Mdn= 20:00, U = 478.00, z =- 1.45, p =.
147 > .005, r = 0.173) and the effect size was small [2].
This shows that based on the pre test, students from both
groups were at the same level.
Results
D. Effects of GeoGebra and e-transformation on Overall
Performance score for post test
 For the fourth hypothesis, the Mann-Whitney test was
also conducted on the post test performance scores.
 Findings also indicated that there was no significant
difference in post test performance score for the group
GeoGebra (Mdn= 31.00) compared to the eTransformation group (Mdn = 25.00, U = 494.00, z = 1.262, p = .207 > .005, r = 0.15) and the effect size was
small [2].
 This finding also showed that students who used
GeoGebra and e-transformation did not differ
significantly on the post test.

Results
E.


Effects of GeoGebra and e-transformation on each of the
topics (transformation, reflection and rotation) tested
For the transformation topic, there was no significant
difference in performance scores for the GeoGebra group
(Mdn = 11.00) compared to the e-transformation group
(Mdn = 7:00, U = 483.50, z = -1.407, p = .159 > .005, r =
0.17).
For reflection, the Mann-Whitney test analysis did not
show any significant difference in the performance score
for the GeoGebra group (Mdn = 15.50) compared to the etransformation group (Mdn = 14.00, U = 538.50, z = .767, p = .443 > .005, r = 0.09).
Results



As for rotation topic, findings also indicated that there
was no significant difference in performance scores
for GeoGebra group (Mdn = 7.00) compared to the
e-Transformation group (Mdn = 3.50, U =472.00, z =
-1.543, p = .123 > . 005, r = 0.18).
These findings showed that each topic included in
the post test did not show any significant difference
in terms of the students’ performance scores.
Students who used e-Transformation and GeoGebra
had the same skills when answering questions
related to transformation, reflection and rotation.
Conclusion



Students who used the GeoGebra software and etransformation shows improvement in performance
when comparing the results of the pre and post tests
scores of both groups.
This shows that the use of technology can have a
positive effect on student achievements.
The findings did not show any significant difference
between students who used the GeoGebra software
compared to the e-transformation group.
The Effects of GeoGebra on
Mathematics Achievement:
Enlightening Coordinate Geometry
Learning
STUDY 4
Royati Abdul Saha
Ahmad Fauzi Mohd Ayub
Rohani Ahmad Tarmizi
• Technology Oriented• Business Driven • Sustainable Development• Environmental Friendly
INTRODUCTION
In this rapidly changing environment, education
should change as quickly as the technology does.
The future of Information, Communication and
Technology (ICT) should play as a transformation
role in education rather than integration into
existing subject areas (Fluck,2010).
Malaysian Ministry of Education (MOE) has seen the
application and the use of ICT in education in
Malaysia as the key efforts to create knowledgebased workers which later will generate the
economy(Salbiah Ismail, Director Educational
Technology Division MOE, 2008)
Commercial softwares -Geometer’s Sketchpad, Derive, Cabri,
Matlab, Autograph etc. - need to purchase , some of the
software is really costly
Open Source Software (OSS) allows user to download any
softwares that are available and suitable for the users.
Until August 2010, there are more than 240,000 software
projects that have been registered in SourceForge.net which
is the world’s largest open source software development
site (SourceForge.net, 2010). Example OSS - SAGE, FreeMat,
GeoNet, JLab, Maxima, Axiom, YACAS, JsMath,GeoGebra
etc.
What is GeoGebra?






Dynamic Mathematics
Software
For Learning and Teaching
Mathematics
in Schools
This software was developed by
Markus Hohenwarter in 2001 at the
University of Salsburg
Has been translated to 48
languages. Use in 190 countries.
Geometry, Algebra , Calculus and
Statistics.
Freely available from
www.geogebra.org
GeoGebra is Innovative
It was designed to combine features of
• dynamic geometry software (e.g. Cabri Geometry,
Geometer’s Sketchpad)
• computer algebra systems (e.g. Derive, Maple)
and easy to-use system for teaching and learning
mathematics ( Hohenwarter & Preiner, 2007).
High technical portability
• runs on Windows, Linux,
Solaris, MacOS X
• dynamic worksheets (html)
GeoGebra = Geometry + Algebra
Algebra Window
Geometry & Graphics Window
RESEARCH OBJECTIVES
1
2
3
•To identify differences in the mean posttest scores between
students utilizing GeoGebra and conventional instruction.
• To identify differences in the mean posttest scores of
students utilizing GeoGebra and conventional instruction
among high visual-spatial ability (HV) students.
• To identify differences in the mean posttest scores of
students utilizing GeoGebra and conventional instruction
among the low visual-spatial ability (LV) students.
METHODOLOGY
Students’ Group
Visual-spatial Ability
GeoGebra Group
(GG)
Control Group
(CG)
High Visual-spatial
GGHV
CGHV
Low Visual-spatial
GGLV
CGLV
Table 1: Factorial Design 2 x 2
Use quasi-experimental study with
non-equivalent control group post-test only 2 x 2
(visual-spatial ability x treatment) factorial designs.
Research sample - two homogeneous Form Four
classes in Sekolah Menengah Perempuan Jalan Ipoh,
Kuala Lumpur, aged 16 and 17 years
Group
N
Mean Standard
Deviation
Control Group
26
54.7
GeoGebra
Group
27
65.23
t
DF
Significan
t
2.259
51
0.028
15.660
19.202
Significant difference between mean performance scores of the control
group (M=54.7, SD= 15.660) compared to GeoGebra group (M= 65.23, SD=
19.202; t(51) = 2.259, p = .028 < .05)
The effect size (eta squared, 2) is approximately 0.09, which is
considered to be a moderate effect (Cohen, 1988).
Students who had learned Coordinate Geometry using GeoGebra was
significantly better in their achievement compared to students who
underwent the traditional learning.
Group
N
Mean Standard
Deviation
Control Group
12
61.66
7
GeoGebra
Group
12
67.58
3
t
DF
Significan
t
0.953
22
0.351
13.793
16.489
No significant difference between mean performance scores of the control
group (M=61.667, SD= 13.793) compared to GeoGebra group (M= 67.583,
SD= 16.489; t(22) = 0.953, p = .351> .05)
However, the mean score of the HV students in GeoGebra group is higher
than the result of the HV students in Control Group
Group
N
Mean Standard
Deviation
Control Group
14
48.78
6
GeoGebra
Group
15
64.06
7
t
DF
Significan
t
2.222
27
0.036
15.106
21.569
Significant difference between mean performance scores of the control
group (M=48.786, SD= 15.106) compared to GeoGebra group (M= 64.067,
SD= 21.569; t(27) = 2.222, p = .036< .05)
The effect size (eta squared, 2) is approximately 0.15, which is considered
to be a very large effect (Cohen, 1988)
LV students who had undergone learning Coordinate Geometry using
GeoGebra was significantly better in their achievement rather than students
underwent the traditional learning. GeoGebra software enhanced the LV
students in their mathematics performance.
DISCUSSION & CONCLUSION
The findings showed that computer assisted
instruction as a supplement to traditional classroom
instruction is more effective than traditional
instruction alone.
Consistent with the study by Hennessy, Fung and
Scanlon (2001), Hannafin and Foshay (2008), Ahmad
Fauzi et. al. (2010) and Ahmad Tarmizi et. al. (2010) positive impact of utilizing mathematical learning
softwares thus enhancing students learning and
understanding.
This study gives an alternative to the teachers to
utilize the OSS mathematics software as a tool in their
instructional activities. OSS can solve the problems
whereby there are no cost required
DISCUSSION & CONCLUSION
GeoGebra as a Dynamic Geometry Software can be
used as an effective tool in learning by way of
visualization to promote learning and enhance
understanding.
Therefore, it can be recommended to mathematics
teacher to use DGS GeoGebra in their instructional
process in school.
This software provide teachers and students with a
free new tool, a new way of using technology with
visual aids to help students to interact with the
mathematical concepts individually or in groups, in the
classroom, or at home
This tool can be use as complementary activities to the
regular classroom setting, where students can get
immediate feedback of their findings, in the
classrooms activities as well as in their homework.