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BIODATAHONG ENG DING

Additional Mathematics Excellent Teacher (Special Grade C)Master of Education (Maths) University of Malaya

I have been teaching Mathematics and Additional Mathematics in secondary school since 1988. Currently I am teaching in Alam Shah Science School, Kuala Lumpur, Malaysia. Awards Received : Innovative Teacher - National level in year 2000, - State level in years 2000, 2001 and 2003. Creative Teacher - State level in year 2003. Award from Ministry of Science, Technology and Innovation year 2002 Toray Science Education Award in year 2006. School Mathematics text book writer and reference books writer. Currently, I am doing PhD degree (part time) in University of Malaya.

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INTRODUCTIONINTEGRATIONMULTIMEDIA COUSEWAREFEEDBACK FROM TEACHERS AND STUDENTS CONCLUSION

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INTRODUCTIONIntegration is one of the Form 5 topics in Malaysian Additional Mathematics Syllabus.

In this topic, the concepts of Integration, and its application to find the area and volume are introduced.

Students usually find the concepts in this topic abstract especially determining areas under the curves and volumes of revolution.

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INTRODUCTION

The Ministry of Education, Malaysia has developed a teaching courseware to facilitate the teaching and learning of Additional Mathematics.

This section presents how an interactive multimedia environment can be created using the courseware to enhance the conceptual understanding of Integration and its applications.

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SYLLABUS OF INTEGRATION• Integration by Reversing Differentiation• Integrals of axn

• Integrals of Algebraic Expressions• Constants of Integration• Equations of Curves from Gradient

Functions• Integrate of Expressions of the form

(ax+b)n

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SYLLABUS OF INTEGRATIONS

• Definite integrals

• Areas Under the Curves Bounded by the x-axis.

• Areas Under the Curves Bounded by the y-axis.

• Areas Under the Curves Bounded by a straight line.

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SYLLABUS OF INTEGRATIONS

• Volumes of Revolutions When a Curve is Rotated About the x-axis

• Volumes of Revolutions When a Curve is Rotated About the y-axis

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DIFFICULTIES FACED BY STUDENTS IN LEARNING THIS TOPIC

• To understand the abstract concepts of Integration.

• To visualize the area under the curve as the summation of areas of rectangular strips.

• To visualize the volume of revolution as the summation of volumes of cylindrical discs.

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• The teaching courseware is based on the Additional Mathematics Curriculum and it is designed and structured upon the requirements of the National Integrated Curriculum for Secondary Schools (Kurikulum Bersepadu Sekolah Menengah).

MULTIMEDIA COUSEWARE

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• The teaching courseware is developed by the Ministry of Education Malaysia (Curriculum Development Centre) to assist teachers in delivering the teaching content in classroom using English Language.

MULTIMEDIA COUSEWARE

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• The lessons are structured in six main components in the following order:

Introduction Content Activity Exercise Summary Extension

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To arouse the students’ interest and capture their

attentions.

States the learning outcomes

of a particular lesson and sets the stage for the respective lesson.

Good set induction: relates the lesson

to daily life examples, history of

Mathematics.

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Vivid three-dimensional

simulation examples are displayed.

Presents the established concepts contained in

the lesson.

To enhance the conceptual understanding

of Integration.

PHOTOS

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Determine the Volume of Revolution

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Provides features to check the student’s answer step by step.

Contains Interactive activities

for making and testing conjectures.

Discusses and evaluates student’s understanding and

identifies student’s errorsand misconceptions.

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Interactive Activity : Find the volume of revolution

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Enhances understandingof concepts and

mastering of problemsolving skills

Consists of assessment items.

Provides opportunities to practice and develop

newly learned skills.

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Recalls the conceptsand skills learned in the

lesson.

Summarises the entire lesson.

Highlights key points and ideas

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Area under the curve bounded by the x-axis.

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Provides activities outside the classroom

or homework.

Contains additional knowledge

that related to the lessons.

Encourage further exploration and

discovery.

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Module and Swift-Point Player

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• The Teaching Courseware includes other functions which help to enhance the teaching of the subject in the classroom.

MY LESSONS

If the lessons in the CD do not cater to the specific needs of students, teachers can create their own lesson by combining different sections of the lessons in the CD.

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BOOKMARK

When the user wants to stop at a certain page, with the intention of continuing later from that page, they just need to take a bookmark and mark that page.

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TEACHER’S RESOURCES

The Teacher’s Resources contains Teaching Plans and Activity Sheets of each lessons.

All Teacher’s Resources can be printed.

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COURSEWARE PEDAGOGYPre-conceived Idea

Compare with New Idea

Assimilation Accommodation

New

Concept

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ProblematicSituation

Make and Test Conjecture

Satisfy all conditions?

No

New Knowledge

Reflection

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Problem Solving

Mathematical Communication

Reasoning

Making Connection

Use of Technology

PRINCIPLES

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FUN

MEANINGFUL

CHALLENGING

USEFUL

PRINCIPLES

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ConstructivismContextualExploratoryCooperative learning Multiple IntelligentMastery LearningSelf-Access LearningLeaning How to LearnFuture Learning

APPROACHES

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DirectingDemonstratingExplaining and IllustratingQuestioning ConsolidatingEvaluatingSummarising

APPROACHES

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ACTIVE PASSIVE

ABSTRACT

CONCRETE

Manipulates

concrete models

Listen to verbal

explanationDescribes

Concepts

Verbally

Observes demos with concrete models.

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USING THE COURSEWARE

CD ASSISTEDAPPROACH

CD INTEGRATEDAPPROACH

1. Main teaching tool in the classroom.

2. Introduce and present the subject matter, pauses the CD at the appropriate points to check the students’ understanding.

1. Teacher designs his/her own lessons, using a variety of resources.

2. Teacher incorporates the courseware materials, as well as other resources into the lesson at suitable stages.

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The result cannot be generalised to all the populations.

The survey (questionnaire)on teachers was

done on 28 Additional Mathematics

teachers. Experience of

teaching : 1 – 28 years

The interview was carried out with 3

students with performance in Add Maths :Good, Average and Weak.

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FEEDBACK FROM TEACHERS

1. How often do you use the teaching courseware?FEEDBACK PERCENTAGE

Everyday : 0 %

Every week : 17.86%

Once a while : 71.43%

(Certain topics)

Never : 10.71%

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FEEDBACK FROM TEACHERS

2. The benefits of using courseware :

Use for Summary or Revision

Interesting and clear

Make learning process enjoyableTo relate the concept to daily lifeInteractive exercise

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FEEDBACK FROM TEACHERS

2. The benefits of using courseware :

For weak students, the visual can draw their attention. e.g. Integration

Get the attention of students and enhance understanding.

The syllabus can be finished earlier so students can do more drilling exercise.

Deliver the concept in a shorter time (save time).

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FEEDBACK FROM TEACHERS

2. The benefits of using courseware :

It is systematic.

I prepare my own PowerPoint by referring to the content of the CD.

Explaining and introducing the concepts of certain topics better.

Courseware provides good introduction.

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FEEDBACK FROM TEACHERS

2. The benefits of using courseware :

Courseware provides animation to teach certain concepts.

Teaching and learning Add Maths becomes interactive.

To diversify the teaching and learning activities.

Provide more examples for explaining the concepts and skills.

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FEEDBACK FROM TEACHERS3. The reasons why courseware is not used :Take time to set up the laptop and the LCD, needs around 15 minutes. It is time consuming.Some of the courseware are not related to what I want to teach.

For very weak students, they need more explanation, not suitable to use courseware.

Lack of skills to incorporate CD into the PowerPoint.Teachers make their own PowerPoints and teaching resources.

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Do you like the courseware?

FEEDBACK FROM STUDENTS

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FEEDBACK FROM STUDENTS

What are the features in the

coursewareyou like most ?

1. The explanation and problem solving.

2. The examples.

3. The graphics with animations. It creates fun in learning.

4. Easy to understand, I can remember what I have learnt.

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FEEDBACK FROM STUDENTS

What are your suggestions about the use of teaching courseware?

1. All the maths teachers use the courseware to teach to make us understand better.

2. Put in more graphics and give more examples. Add in more music and sound.

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CONCLUSION1. The effective use of the teaching courseware has

transformed abstract and difficult lessons on Integration to stimulating sessions where students can visualize the concepts and enhance their problem solving skills.

2. Thanks Ministry Of Education for the effort of providing this multimedia courseware which enhances the teaching and learning of Additional Mathematics.

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