How Do Mathematics Teachers Use Technology?
Leong Yong Pak
Universiti
Tungku Link BE 1410
Abstract
Educationists
have said for decades that personal computers, laptops, and hand-held devices
are only vehicles for transporting instructional methods; machines are not what
teachers do in classrooms. Many people do not seem to realize that teachers ask
questions, give examples, lecture, guide discussion, drill, use small groups,
individualize instruction, organize project-based learning, and craft blends of
these teaching practices.
This paper
reports on how teachers teach mathematics in primary and secondary schools in
[Keywords: Technology, primary
mathematics, secondary mathematics]
Introduction
The global
development of technology in education and e-initiatives are costly and include
the introduction of Information and communications technology (ICT) into the
school curricula and teacher education. Many “veteran” teachers are not so
quite oriented toward ICT and the more independent pedagogical orientations
that complement that approach of teaching (Goh & Leong, 2006). Many
decision-makers in education seem to fit Cuban’s (2006) sentiment that the mere
use of technology itself can effect quality teaching and learning. Educationists have said for decades that personal
computers, laptops, and hand-held devices are only vehicles for transporting
instructional methods. Machines cannot replace what teachers can do in
classrooms. Many people do not seem to realize that teachers ask questions,
give examples, lecture, guide discussion, drill, use small groups,
individualize instruction, organize project-based learning, and craft blends of
these teaching practices. Cuban’s commentary drew some responses such as these (Education
Week, 2006. Any improvement in education takes dedication on the part of
teachers, school leadership and parents to learner-centered education, and for
that paradigm shift, there is much good research to point the way. If we truly
wish to empower our students, we must plan learner-centered lessons, put the
tools in our students' hands and coach. Technology has great potential for
raising student achievement. However, a laptop alone will not do it. There are
many more factors that have to be in place. If the teacher knows how to use the
software and can model it effectively, then the technology can make an impact
on student understanding and achievement.
The
quality of teaching and learning interactions can be raised to greater levels
through such ecological uses of technology (Warschauer, 1998). Such benefits
are not just the raising of test scores in some perfectly controlled
experimental research as expounded by Cuban. Technology users get to practice
how to research and analyse information, communicate ideas, and adapt and apply
such information readily available from experts who share their knowledge
unselfishly over the internet. These are essential skills and competences
applied with technology which are needed to excel in this modern world of
increasing challenges for all nations. Schools must rise to such challenges of
educating all students to utilise technology effectively and efficiently. The
fact that some teachers and lecturers in
There are many constraints of
high-stakes testing and examination-oriented curricula, inadequate budgets and
ICT facilities that teachers and students face in schools. These and other
constraints drive teachers to use ICT in very instrumental ways, such as
presenting lessons passively and also delivering drill and practice of
examination questions using technology. All school teachers in Brunei
Darussalam are encouraged to integrate ICT into the teaching and learning of
subjects across the curriculum in pedagogically sound ways. Technology should
be used to support learning activities such as exploration, manipulation and
articulation of what they are learning (speculation, conjecturing, hypothesis
testing, and reflection on what they do). This paper will discuss whether such
elements of enhanced interactive learning of mathematics are practiced.
Background of the Study
Quality use of technology in mathematics and other subject areas in
schools is elusive. Miller, Averis, Door and Glover (2005) in their analysis of the use of technology
such as the interactive whiteboard (IAW) suggested a developmental approach,
with teachers progressing through three stages. Teachers selected as examples
of best practice would ‘demonstrate’ qualities that are identified as enhanced
interactive. The three progressive stages of the IAW or technology teacher
are: (1) Supported didactic: Technology is used only as a visual
support to the lesson and not as an integral tool to conceptual development.
There is little interactivity, pupil involvement or discussion; (2) Interactive:
The teacher makes use of technology to stimulate pupils’ responses from time to
time and to demonstrate some concepts. Elements of lessons challenge pupils to
think, by the use of a variety of verbal, visual and aesthetic stimuli; and (3)
Enhanced
interactive: This approach is a progression from the previous stage,
marked by a change of thinking on the part of teachers who seek to use the
technology as an integral part of lessons, and look to integrate concept and
cognitive development in a way that exploits the interactive capacity of the
technology. These teachers are aware of the techniques available, are fluent in
their use and structure lessons so that there is considerable opportunity for
pupils to respond to technology/IAW stimuli – as individuals, pairs or groups.
With enhanced
interactive learning, technology is used as a means of prompting
discussion, explaining processes and developing hypotheses or structures which
are then tested by varied applications. A wide variety of materials are used
including ‘home-grown’ and internet resources, and IAW specific and commercial
software. The ‘best practice’ teachers selected for their study were all
working at either the interactive or the enhanced interactive stages,
with all of them demonstrating elements of enhanced interactivity. In almost
all cases, they each had an IAW in their classroom and used it all the time.
Oldknow (2004) in an earlier study
reported that the Mathematics Curriculum IT Support
Group from the Department of Education and Skills (DfES) in the
Hennessy
and Ruthven (2003) identified several cases of successful ICT use in secondary
mathematics and developed a model as reference for other teachers. Teachers
should try to use ICT if they realize that ICT could provide students with
opportunities such as i) an interactive learning environment, ii) the
capability for immediate feedback, and iii) possibility of an investigative
approach. The authors posited that the main goal of a teacher is to assist
students to develop cognitively. Once teachers realize the potential of ICT,
they will try to adopt it in their practices.
Many teachers
in
It is
encouraging that there are teachers and educators in teacher education in
Brunei who are continuously exploring innovative, pragmatic and active ways of
using ICT ecologically and effectively (Goh & Leong, 2006; Kam, 2007;
Sallimah & Leong, 2002). These teachers remain focused on students’
understanding, creativity, thinking and performance in examinations as well, while
making use of the technology in their teaching and learning, providing elements
of enhanced interactivity in the classroom and developing higher order thinking
skills. Such teachers should be encouraged to lead others in continuous
professional development activities which appear to be far and in between.
Method
Primary and secondary schools have
been provided with computer laboratories, internet access and interactive
whiteboards for several years. Diploma graduates in computer studies are
employed as ICT teachers in primary schools in
These
student teachers were assigned in small groups of twos and threes to primary
schools to observe mathematics lessons taught in the computer laboratories
using technology. They were asked to take notes of hardware and software used
during the lessons and the kinds of activities, and teacher-pupil and
pupil-pupil interactions that take place during the ICT-mathematics lessons.
The student teachers were also asked to include in their reports their own
comments on the lessons they had observed, and make suggestions of changes in
the lessons they would make if they were to teach the lessons themselves.
The
reports of these student teachers are analysed and discussed in this paper. Key
findings of research into technology use in secondary school mathematics level
teaching of mathematics in
Results and Discussion
Descriptions
of lessons observed by pre-service student teachers, their suggestions and
comments by the writer are summarized in Tables 1 to 5. The lessons
observed were not so motivating. The interactivity of teacher-pupils-technology
was low. Suggestions of the preservice teachers were also not pedagogically
strong nor very interactive and motivating.
Table 1
Technology Use in Primary 1:
Subtraction with regrouping
|
Observations reported by preservice ICT student teachers |
Suggestions by student teachers of
changes |
Comments by researcher |
|
Powerpoint
slides with animation were used to show standard algorithm of 15 – 7. Finger
counting from 7 up to 15 was shown. The teacher focused pupils’ attention on
these similarities: _ + 7 = 15; 7 + 8
= 15; 15 – 7 = 8 |
Only one pupil can do the activity
at a time on the IAW. Pupils found it difficult to do
the subtraction with regrouping. |
Difficulty not addressed.
Alternative methods of counting could be used. (Little interactivity) |
Table 2
Technology Use in Primary 3: Shapes
|
Observations
reported by preservice ICT student teachers |
Suggestions
by student teachers of changes |
Comments
by researcher |
|
Software of basic shapes used by pupils in pairs. Pupils
picked shapes, added colours and patterns, and discussed the shapes on the
IAW. |
More creative for pupils to draw
their own shapes. Teacher could relate shapes to
real objects. |
Discussion could be at a higher level of interactivity. |
Table 3
Technology Use in Primary 4: Place
Value and Addition with 4-Digit Numbers
|
Observations
reported by preservice ICT student teachers |
Suggestions
by student teachers |
Comments
by researcher |
|
Used IAW to explain procedure for
addition of two 4-digit numbers. Used standard algorithm and Hot potatoes. |
Teacher was clear and pupils
understood the teacher’s explanations. |
Understanding
of place value with virtual manipulatives would be useful. (Some
interactivity) |
Descriptions
of lessons observed by inservice student teachers, their suggestions and
comments by the writer are summarized in Tables 6 to 8. The comments of these
inservice teachers reflect better knowledge of pedagogy than the preservice HND
teachers. The three lessons observed were also not so motivating. The
interactivity of teacher-pupils-technology was low. Suggestions of the
preservice teachers were better
pedagogically, more interactive and motivating.
As in primary school mathematics
teaching, there were also a few cases of innovative secondary school
mathematics teachers observed by Kam (2007) in
Although IAWs were employed in many
of the lessons observed, they did not achieve the level of enhanced
interactivity proposed by Miller, Averis, Door and Glover (2005). However, they
were heading in the right direction.
Table 4
Technology Use in Primary 5:
Improper Fractions and Mixed Numbers
|
Observations reported by
preservice ICT student teachers |
Suggestions by student teachers of
changes |
Comments by researcher |
|
IAW used for whole class discussion and try activities on
the IAW individually. Example of five halves of circle
used to show MS Excel activity prepared with
conditional formatting was also used by pupils in pairs filling in the cells,
e.g. Online activities similar to the
Excel activity and other fraction games were also used by the pupils in
pairs. |
Better for teacher to draw the
circles and rectangles while explaining on the IAW. Coloured visual displays of
animation, graphics and text could be clearer. Some PCs could not access
Internet. Activity could have been downloaded and carried out offline. Allow pupils to draw their own
representations using MS Office tools. |
No multiple representations of
fractions used. Problem-solving and problem-posing
not used. More of whole class practice of
not so challenging tasks repeatedly. (Not
sure if pupils understand the concepts. There are websites with good virtual
manipulatives that could be used – some interactivity) |
, 
, 
, 
Table 5
Technology Use in Primary 5: Four
Operations
|
Observations reported by
preservice ICT student teachers |
Suggestions by student teachers |
Comments by researcher |
|
IAW was used for interactive drill
exercises created with Hot potatoes and from websites. Pupils could use the
network in the lab to access the activities. |
Interesting and useful. |
Place
value and number sense lacking. (Some
interactivity, more of drill and practice) |
Table 6
Technology Use in Primary 5:
Geometrical shapes
|
Observations by inservice student
teachers |
Suggestions by trained teachers |
Comments by researcher |
|
Combined different shapes to form
objects on IAW. Whole class discussion/interaction, then pupils worked in
pairs on PCs. Interesting use of ‘Active studio’ program. |
More challenging to learn the
properties of the shapes, e.g. fitting triangles into rectangles, etc. |
Quite good interactivity. Could
explore Euclidean geometry software for drawing. |
Table 7
Technology Use in Primary 4:
Fractions
|
Observations reported by inservice
student teachers in 3s |
Suggestions by trained teachers |
Comments by researcher |
|
Teacher demonstrated answering
worksheet on IAW. Pupils were interested but not attentive Pupils worked in pairs and
manipulate numbers on simple fractions. |
Not enough opportunities for
pupils to explore understanding of fractions. Teaching method is limited to
‘drill-&-practice’ |
Suggestions
of more interactivity by inservice teachers. Virtual manipulatives could be
useful. |
Table 8
Technology Use in Primary 5: Four
Operations
|
Observations reported by inservice
student teachers in 3s |
Suggestions by trained teachers |
Comments by researcher |
|
Math games from www.funbrain.com
were used. Pupils working in pairs could choose the games. Pupils enjoyed the
games and could even surf the Internet for other games. [ICT teacher with no
teacher training yet] |
Pupils improved their reading and ICT skills. Pupils could help each other when working in pairs. |
Concepts to be taught and learned? |
Table 9
Useful Mathematics Websites
Identified by Student Teachers
Conclusion
ICT teachers help subject teachers
with the necessary technology preparations and resources for lessons.of ICT
resources. Subject teachers are learning ICT skills to be more independent.
These two groups of teachers share expertise and experience, and learn from
each other. With the availability of technology, there is a danger of teachers
switching from “chalk-and-talk” with “drill-and-practice” to “show-and-tell”
with “interactive drill-and-practice”. Teachers were seen to be doing and
explaining. Pupils are the ones who need the practice and should be the ones
doing, exploring, explaining and communicating creatively.
The use of
IAW and LCD projection could lead easily to “show and tell” rather than whole
class and small group interactions and activities. Very cleverly, some teachers
have been able to combine various effective strategies in teaching mathematics
with their own resources. Pupils worked (individually, in pairs, or in threes)
on the PCs doing the activities while it was also being demonstrated on the IAW
or LCD projection screen. There could be more open-ended cognitive and
metacognitive tasks and mini-projects/practical investigative activities that
promote meaningful learning and investigations of the content and processes of
mathematics. Many useful virtual manipulative resources are available on the
internet. Demonstration of concepts with the use of a variety of verbal, visual
and aesthetic stimuli helps children to comprehend better and challenges them
to think (Miller, Averis, Door & Glover, 2005).
Computers and technology should take
their place as a natural and powerful part of the teaching and learning
process, affecting both aspects of teaching and learning in three ways. This
new technology influences how information is presented; how students interact
both with the medium and through the medium with the teacher and other
learners; and how knowledge is structured. Brumfit (1998) discussed issues of
bilingual texts generating questions about awareness, the relationship between
control and freedom in language learning, the positive effects of ICT on
motivation, and also the close interaction between the data that we can derive
from our teaching materials and research data that previously had not been
available. All these are possibilities accelerated by new technological
resources. Multimedia technology offers opportunities for creative expression
and exploration in instructional activities that integrate mathematics, science
and technology (Cleland, Wetzel, Zambo, Buss, & Rillero, 1999; Greenberg,
1998; Thomas, Johnson & Stevenson, 1996). With current multimedia,
nonlinear access, autonomy and self-regulation are incorporated into software
design. Learning and teaching should be fun, more interactice and more
independent.
There is an urgency to monitor the
progress and future development of teachers so that they could share and enhance
their skills and achieve higher levels of interactivity in their teaching.
However, this is difficult without a change in curriculum and examination
orientations.
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Copyright © 2007 Dr Leong Yong Pak. The author grants a non-exclusive
license to the organisers of the EARCOME4, Universiti Sains