Paper for the APEC-Tsukuba International Conference V
held in Tokyo, Japan from 17-21 Feb 2011

Towards a New Normal for Teaching and Learning Mathematics in theMalaysian Classroom: Integrating Thinking, Problem Solving andTechnology
Ui-Hock CHEAH
Southeast Asia Ministers of Education Organization
Regional Center for education in Science and Mathematics(SEAMEO RECSAM)
Penang, Malaysia
Abstract
The Malaysian curriculum specification highlights mathematical thinking, problem
solving and the use of information communication technology (ICT) as its emphases
towards developing students’ learning of mathematics. This paper suggests a practicalteaching approach that integrates these emphases through the use of a dynamic geometry
software and spreadsheet to integrate mathematical thinking problem solving and ICT.

Introduction
The phrase “new normal” was first coined by El-Erian (2010) and was written in response to the2009 world economic crisis. It relates to the things that are likely to happen in the absence ofchanges in policy and business approaches (El-Erian, 2010) to address the world economic crisis.
Applied to the field of mathematics education, the phrase “new normal” appears to have slightly
different meanings particularly because in a sense there has been no crisis of such magnitude inmathematics education when compared to the world economic crisis. In addition, calls forreforms have been regularly mooted by mathematics educators to address weaknesses inmathematics education. Over the last half a century, there have been constant calls from thecommunity of mathematics educators to reform school mathematics. The concern is that without
reforms school mathematics may degenerate into meaningless application of formulas and rules
and subsequently children will not truly appreciate the power of mathematics. Subsequently,
there have been constant revisions to the mathematics school curricula. Since the 1990s there
have been calls for reform to make mathematics more relevant to the learners, to focus onproblem solving and mathematical thinking (National Council of Teachers of Mathematics,
1980, 1991, 2000).
The term “new normal’ in this paper, thus can be taken to refer to the norms that would
emerge should the global calls for reforms are actualized in the classroom. The new normal
connotes the normal practice of teachers and students that promote the learning of mathematics
that is relevant to students. Malaysia too has been caught up with this wave of global reforms inmathematics education. Coupled with the global drive towards problem solving andmathematical thinking, there is also the national agenda of making Malaysia globallycompetitive (National Economic Advisory Council, 2010a, 2010b). In conjunction with thisnational agenda towards making the country competitive, there have also been many educational
initiatives to develop the human capital of the country which is technology savvy. One suchinitiative was the Smart School Project (SSP) to incorporate technology into education (TheSmart School Project Team, 1997; Multimedia Development Corporation, 2005). The Smart
School Project aims to incorporate the use of information communication technologies (ICT)
into schools to enhance teaching and learning. The SSP was not specifically focused on

Paper for the APEC-Tsukuba International Conference V
held in Tokyo, Japan from 17-21 Feb 2011

mathematics but rather targeted in making the whole school technology-smart. Subsequently,
over the last ten years the Ministry of Education in Malaysia (MOE) has put in effort to help
teachers use technology in the classroom. Equipment such as notebook computers, desktopcomputers, LCD computers, computer screens and printers have been supplied to all schools inMalaysia (Muniandy & Mohammad, 2010). Much attention was also given to professional
teacher development in the area of ICT both at pre-service and in-service level.
Following the SSP there has also been initiatives to infuse technology into the teaching
and learning of mathematics. In particular, the (MOE) also embarked into mathematics-related
ICT initiatives by introducing graphing calculators and dynamic geometry softwares intoschools. Graphing calculators were supplied to schools and a national license was acquired in
2002, enabling the Geometer’s SketchPad (GSP), a dynamic geometry software to be installed
into all Malaysian public schools.
The New Normal for the Mathematics Classroom
Curricular Specifications
The inclusion of technology as one of the emphasis in the mathematics classroom has broadened
the scope of teaching and learning. The challenge for the introduction of ICT into themathematics classroom however involves more than just bringing technological equipment into
the classroom. The use of ICT needs to fit into the framework of the content and the nature of thesubject. In the case of mathematics, there is then a need for ICT to become an enabler forlearning mathematics. In the last review of the national mathematics curriculum in 2003, threemain foci were incorporated in the curriculum: problem solving, mathematical thinking and theuse of technology. These three main emphases are evident in the five areas that form the pillarsof the Malaysian mathematics curriculum, namely: a) problem solving in mathematics, b)mathematical communication, c) mathematical reasoning, d) mathematical connections, and e)
application of technology (Curriculum Development Centre, 2006). As a consequence, thechallenge for the mathematics teacher is thus to find ways how these tools can be used inconjunction with problem solving and at the same time encouraging the student to thinkmathematically, emphasizing communication and reasoning.
The new curriculum calls for the teacher to become familiar with new ways to teachmathematics, motivating students and making mathematics more interesting. The vision of the
new normal for the mathematics classroom thus aims to make students more mathematicallyliterate. Students then should be able to acquire mathematical knowledge and reflectively use it
meaningfully in a variety of real world situations. From this perspective teachers need to be
mindful that ICT are the means and not the ends of teaching and learning mathematics in theclassroom. ICT is thus an enabler towards developing students who is mathematically literate.
The introduction of ICT into the classroom poses its own set of challenges. First theteacher needs to become familiar with new technology tools, to understand how these tools workand how they can be used as an enabler of learning mathematics. Second, the teacher then has toincorporate these tools into the lesson mindful that the ICT tools are just enablers. The following
sections in this paper will look at several ways how this enabling can take place through the useof the GSP.
Creating Meaningful Contexts
In the learning of the topic of parabola and conics, often formulas are just quoted without
context. The use of the GSP can enable meaning to be created through the use of vivid visuals

Paper for the APEC-Tsukuba International Conference V
held in Tokyo, Japan from 17-21 Feb 2011

(Kimberling, 2003). Figure 1 shows the task where the perpendicular bisector of two points Aand B are traced. B is a point on the circumference of a circle. Depending on the position of A,
the trace of the perpendicular bisector can yield different forms of conics.

Figure 1. Tracing the perpendicular bisector of AB.
If point A is on the circumference of the circle, the trace is a circle. As shown in Figure 2, if
point A in the circle the trace forms an ellipse, and if point A lie outside the circle then the trace
forms a hyperbola. Similarly, a parabola is formed by the trace of the perpendicular bisector of amoving point on a fixed line and another fixed point not on the fixed line.

Figure 2. Trace showing an ellipse, circle and hyperbola depending on the position of A.

Paper for the APEC-Tsukuba International Conference V
held in Tokyo, Japan from 17-21 Feb 2011

Making Mathematical Connections
One main difficulty of students learning algebra and functions is that often they are unable tovisualize the connections between the mapping as is represented by algebra and thatcharacterized by graphs. The example as shown in Figure 3 and Figure 4 illustrates how theGeometer’s SketchPad can be used to make connections between algebraic functions andgraphical representations (Chanan, Bergosky & Bennet, 2002).

Figure 3. Transforming linear mapping into Cartesian mapping.

Figure 4. Creating graphs using the trace function.
Creating Real-Life Problems
One way of making mathematical ideas relevant to students is to create mathematical problems
that can help the students connect to real-life situations. An example of a mathematical problem
that uses the GSP helps students visualize the problem is shown in Figure 5 (Cheah, 2008).
The problem. Grandfather has a goat farm. He is afraid that the wolf may harm or eat hisgoats. So he uses all his money to buy fences to protect them. However, as he is poor, he canonly afford to buy 24 pieces of fences of 1 metre length each. He wants to build a rectangularfence in a way not only to protect his goats from the wolf, but also to provide as much space forthem. What should the dimensions of the fence be?
Use of ICT. The use of ICT to help students appreciate and visualize the problem better isdone both through the use of the EXCEL spreadsheet and the Geometer’s SketchPad. TheEXCEL file shown in Figure 6 enables students to fill in different values for the length of thePaper for the APEC-Tsukuba International Conference V
held in Tokyo, Japan from 17-21 Feb 2011

rectangle and see how this affects the value of the area while the click-and-drag feature in theGSP enables students to see how the area of the rectangle changes with different values oflengths of the rectangle.

Figure 5. Using ICT to help students understand the problem.

Figure 6. A spreadsheet enabling students to test different variable values.
Conclusion
ICT is a powerful media and if used appropriately in conjunction with problem solving andmathematical thinking creates new ways that can facilitate the learning of mathematics. The
click- and-drag feature in GSP provides not only vivid imageries but also helps students visualize
the meaning of changing variable values. The prime advantage in the use of ICT is that it allows
repetitive calculations to be done quickly and accurately thus freeing up time for mathematical
discourse and thinking. The use of ICT seems to be able to open up new and exciting ways forteachers to teach mathematics.
The examples shown in this paper shows how the GSP and EXCEL spreadsheet can beused meaningfully in problem solving and to visualize mathematical concepts that would be
difficult to do in a traditional mathematics without the aid of ICT.
However for ICT to be sustainably used in the mathematics classroom as envisioned in
the mathematics curriculum in Malaysia, many challenges need to be overcome. Teachers needto be trained and exposed to new technologies. Further, the roles of the teachers in the classroom

Paper for the APEC-Tsukuba International Conference V
held in Tokyo, Japan from 17-21 Feb 2011

need to be reviewed, mindful that the expectations of students and teachers will change throughthe use of ICT. What then is the new normal for the mathematics classroom? What will the newnorms of the classroom be and how can this be integrated with the existing norms of theclassroom? What aspects of the curriculum need to be emphasized and what needs to be deemphasized? A host of questions will arise. Yet there needs to be the courage to create a newnormal for the mathematics classroom. It is therefore critical that teacher professional
development and teacher support be given due prominence, to constantly encourage teachers touse these new ideas, and to cultivate reflective practice while using these new technologies. This
would then enable the teachers to constantly improve their teaching skills and deepen theirknowledge in the subject. Sustaining this new normal of teaching and learning mathematics canthen become a reality.
References
Chanan, S., Bergosky, E., & Bennet, D. (2002). Exploring algebra with the Geometer’sSketchpad. Emeryville, CA: Key Curriculum Press.
Cheah, U. H. (2008, March). A practical framework for technology integration in mathematics
education. Paper presented at the SEAMEO 2008 ICT Conference held in conjunction withthe 43rd SEAMEO Council Conference and the 3rd ASEAN Education Minister Meeting,
Kuala Lumpur, Malaysia
Curriculum Development Centre. (2006). Integrated Curriculum for Primary Schools:Curriculum specifications – Mathematics. Putrajaya, Malaysia: Curriculum Development
Centre, Ministry of Education.
El-Erian, M. A. (2010, October). Navigating the new normal in industrial countries. Paper
presented at the Per Jacobsson Foundation Lecture. Retrieved January, 2011 fromhttp://www.imf.org/external/np/speeches/2010/101010.htm
Kimberling, C. (2003). Geometry in action: A discovery approach using the Geometer’s
Sketchpad. Emeryville, CA: Key College Publishhing.
Muniandy, B., & Mohammad, R. (2010). Malaysia country report. In R.P. Devadason, Wahyudi,U.H. Cheah, & K.T. Ng (Eds.), The state of use of ICT in the teaching and learning ofscience and mathematics among schools in SEAMEO member countries (pp.83-104).
Penang, Malaysia: SEAMEO regional Centre for education in Science and Mathematics.
National Council of Teachers of Mathematics. (1980). An agenda for action: Recommendations
for school mathematics of the 1980's. Reston, VA: National Council of Teachers ofMathematics.
National Council of Teachers of Mathematics. (1991). Professional standards for teachingmathematics. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2000).
National Council of Teachers of Mathematics. (2008). The role of technology in the teaching
and learning of mathematics : A position of the National Council of Teachers ofMathematics. Reston, VA: National Council of Teachers of Mathematics.
National Economic Advisory Council (2010a). New economic model for Malaysia: Part 1
strategic policy directions. Putrajaya, Malaysia: National Economic Advisory CouncilMalaysia
National Economic Advisory Council (2010b). New economic model for Malaysia: Concluding
part strategic policy measures. National Economic Advisory Council Malaysia.

Paper for the APEC-Tsukuba International Conference V
held in Tokyo, Japan from 17-21 Feb 2011

Multimedia Development Corporation (2005). The smart school roadmap 2005-2020: An
educational odyssey. Cyberjaya, Malaysia: Multimedia Development Corporation.
The Smart School Project Team (1997). The Malaysian smart school – An MSC application: Aconceptual blueprint. Kuala Lumpur: The Government of Malaysia.