1.3 apparatus & resources in mathematics education

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ABACUS

1 The chronology and development of the application of the abacus in Malaysia

Dates Events

Nov 1993Cabinet ministers decided that abacus should be used in schools.The Ministry of Education should do the implementation.

1994Ministry of Education collaborated with State Education Departmentto organize abacus courses for standard 4 teachers using 5-2 abacus.Duration of implementation in school was from 1994 to 1995

Jan 1995The school division monitored and found 13 schools (N. Sembilan,Melaka and Johor) implementing the Program Pendidikan Sempoa.

Mac 1995The Ministry of Education sent circulars to school to replace the 5-2abacus with the 4-1abacus.

Jun 1995 The first cohort training for resource teachers using 4-2 abacus.

December1995

Second cohort training for resource teachers.

April 1996

Abacus Learning and Speed Calculation Program transferred from

School Division to Curriculum Development Centre.

Jun 1996Proposal of implementing Abacus Learning Program (4-1) andspeed calculation in schools.

Sept 1996Syarikat PM 2020 with Xu Szi Zhong trained 200 resource teachersin the use of abacus.

Feb 1997200 resource teachers completed the course in using abacus for thefour basic mathematical operations

1997Request for allocation of money to train more teachers was notapproved.

Oct 1997The Tecchers Education Division was directed by the Ministry ofEducation to organise Mental Arithmetic Courses for teachers

July 1998 Ministry of Education appointed UCMAS to train teachers in MentalArithmetic using abacus. The coordinator was the TeachersEducation Division.


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2 Technique of using abacus

2.1 Construction and anatomy of abacus

5 2 Abacus

4 1 Abacus


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2.2 Roles of fingers in using abacus

Thumb

Moving lower beads to the beam

for addition

Index

Moving lower beads

away from the beam

Middle

Moving upper beads foraddition and subtraction

Pencil

IndexMoving lower beads

away from the beam for

subtraction

Middle

Moving upper beads for

addition and subtraction

Thumb

Moving lower beads to the beam

for addition


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Middle

Moving upper beads for

addition and subtraction


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Index

Moving lower beads away

from the beam forsubtraction

ThumbMoving beads at the lower

column to the beam


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1 Using abacus as learning resource to show value and mathematical operation

Place value of numbers

Addition

Starting from the rod at the right end

The process include:

- addition without regrouping

- combination of 5

Function Explanation

+ 4 Plus 5 minus 1

+3 Plus 5 minus 2

+2 Plus 5 minus 3

+1 Plus 5 minus 4

- combination of 10

Beads in every rod shows the

value of numbers


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+9 Plus 10 minus 1

+8 Plus 10 minus 2

+7 Plus 10 minus 3

+6 Plus 10 minus 4

+5 Plus 10 minus 5

+ 4 Plus 10 minus 6

+3 Plus 10 minus 7

+2 Plus 10 minus 8

+1 Plus 10 minus 9

- combination of both 5 and 10


+9 Plus 4 minus 5 Plus 10





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Subtraction

Starting from the rod at the right end

The process includes:

- Subtraction without regrouping

- combination of 5


+ 4 Minus 5 Plus 1

+3 Minus 5 Plus 2

+2 Minus 5 Plus 3

+1 Minus 5 Plus 4

- combination of 10


+9 Minus 10 Plus 1

+8 Minus 10 Plus 2

+7 Minus 10 Plus 3

+6 Minus 10 Plus 4

+5 Minus 10 Plus 5

+ 4 Minus 10 Plus 6

+3 Minus 10 Plus 7+2 Minus 10 Plus 8

+1 Minus 10 Plus 9

- combination of both 5 and 10

Function Explanation+9 Minus 10 Plus 5 Minus 4

+8 Minus 10 Plus 5 Minus 3



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Multiplication

Starting from the rod at the left end

Only answers shown on abacus

Division

Starting from the point of reference

Only answers shown on abacus

GlossaryAbacus Abakus

Rod Tiang

Beam Palang pemisah

Point of reference Titik penentu

Bead Manik

Combination Kombinasi

Addition Tambah

Subtraction TolakMultiple Darab

Division Bahagi

Thumb Ibu jari

Index finger Jari telunjuk

Middle finger Jari hantu

Reference

1 Modul latihan abacus untuk jurulatih PPK

2. www.abacus.com

3. www.ucimas.com.my

1.2 CALCULATOR

Objectives of Module

1. Discuss the advantages and disadvantages of using calculator

2. List out 5 functions of calculator

3. Calculate mean, and standard deviation using calculator.


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Content

Advantages

1. fast2. accurate

3. exploring

Disadvantages

1. does not encourage student to think

2. costly

3. does not encourage student to memorise multiplication table

Different types of calculators:-

1 standard

2 scientific

3 graphic

Activity 1 (10 minutes)

1. Divide students into 2 groups - Group A and group B

2. Provide group A with calculators, but not group B

3. Each group is to work out the given questions:

Example; 2583 X 2673 =

9876 X 435 =

781349643 X 2123 =

Which group can answer the questions correctly and fast? State the reasons.

Activity 2 (20 minutes) group activity

Students to complete the table below:

Advantages of using calculator Examples

1.

2.

3.

4.


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Disadvantages of using calculator Examples

1.

2.

3

4.

Students to present their answers

Activity 3(1 hour) - Group Activity

Using calculator in computer

1. Click start, program, accessory, and calculator.

2. Refer to the book Mengenali dan Mengguna Windows 98 page 96.

3. Follow the instructions in that book

Reference

1. Chua Chooi See, Mengenali dan Mengguna Windows 98, Federal Publications,

2000

2. Casio Training Modules for CFX-9850 GB PLUS, Marco Corporation (M) Sdn. Bhd.

3. http://world. Casio.com/edu_e

1.3 THE COMPUTER

Objectives

To describe the benefits of using a computer in a teachinglearning process.

To explain the conditions whereby a computer is beneficial in a teaching-learning

process.

To select and assess the CAI / CAL Program suitable for a mathematics lesson

To define the advantages and disadvantages of the CAI / CAL Program

To list out the softwares which could assist in a teaching-learning process of

mathematics.

Content

I) What is the purpose of using a computer in a teaching-learning process?

Using a computer in a teaching-learning process which is wisely and well planned
http://world/http://world/


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and suitable to the purpose, will enhance efficiency and effectiveness of the teaching-

learning process.

II) What are the benefits of using the computer in a teaching-learning process? To improve students understanding of concept

To provide equal opportunity of learning to all students

To motivate the students

Individualised learning

III) How would you use the computer in a teaching-learning process?

In the context of using the computer in a teaching-learning process, there is no one

method that is the best and therefore ought to be used. The best approach is actually

using the computer suitable to the needs of the students and producing results which

is hoped for, within a reasonable period of time.

The use of the computer can be seen from TWO aspects the teaching aspects (i.e.

teacher using the computer) and the learning aspects (students using the computer)

In the context of learning, the use of the computer can be categorized thus :

- tutorial

-exploratory

- application

- communication

In the context of teaching, the computer is used as an instrument for presentation and

demonstration.

IV) Why Computer Assisted Instruction (CAI) or Computer Assisted Learning (CAL)?

There are many reasons.

-computers have developed rapidly over the past quarter century

- they have become more powerful(that is, able to process and store much more

data),faster, cheaper, smaller, easier to use and more convenient.

- Various computer networks have been connected and have become more

convenient.

- Computers are becoming more compatible with one another

- Computers can be obtained at a lower price.

-

Computers can be used to make classes more effective- Students can work individually


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V) Advantages and Disadvantages of CAI / CAL for Mathematics Teaching

Advantages- CAI / CAL is good for motivating students

- Students can obtain different types of input

- Through simulation and other techniques, computers can present abstract things in

a concrete and easily understood way.

- Learning can be individualized using computers. Students can study materials

related to their individual goals and what they need or are interested in, with

the appropriate difficulty level and at their own pace.

- CAI / CAL can overcome barriers of time and place

- Students can also use computers to work on projects with their classmates

Disadvantages

- requires computers and softwares as well as other equipment, all of which are

expensive

- a special classroom is necessary

- technicians to keep the computers working properly

- if many classes are using the computer room, scheduling would be difficult

VI) Criteria in selecting the CAI / CAL Program

Suitable to the requirements of the syllabus

Suitable to the local needs

Cost of the softwares

Reliability of the program

VII) Suggested Programmes which will help in the teaching-learning process:

Excel

Words

Power point

Publisher


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Strategy

- group discussion

- workshop

-students to select a program and produce a material for a teaching-learning

process

- to present the material produced

Suggested Activities / Tasks

Activity 1

What classroom procedures have you established to ensure that all students are on

task and working productively when using the computer?

1. Log on user name

2. Monitor the usage of computer time

3. Print out a copy as evidence of productive usage

4. Set a time frame for tasks to be completed

5. Prepare a log book to record information regarding the usage of the computer

6. Teacher supervises from time to time

7. Each member of the group is required to write a journal which has to be

confirmed by the other members of the group

Activity 2

What procedures do you have in place to ensure that students who need assistance

when working on the computer get the help they need, without interrupting an

instruction or other activities that may be going on in the classroom?

1. Place a flag on the computer monitor

2. Assign co-facilitators to assist

3. References, etc, to be placed on one corner for easy access

4. Go to help button in the program

5. Place a pencil box on the computer monitor as an indication that help is

needed

6. Enlist the help of classmates who are more skilful and who are seated nearer

to them.


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For the above-suggested activities, students work in-groups of 4 / 5.

Each group will discuss the task selected in about 5 10 minutes.

Each group will then present their products.

The lecturer will form the conclusion.

Reference

1. Intel Teach To The Future (March 2002)

2. Panda Penguin Teknologi Maklumat Dan Komunikasi Dalam P&P

3. Internet


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1.4 INTERNET

MODULE OBJETCIVES

1. Introduction to Internet2. Understanding Directories and Search Engines

3. To get information through internet

4. List out the advantages and disadvantages of using internet.

CONTENT

What is internet?

Internet is a network of networks, linking computers to computers using the same

language ,where communication is almost instantaneous with another.

Basic requirements to connect to the internet

1. A computer which is connected to a telephone line by modem

2. Internet explorer

3. Account with internet service provider;

In Malaysia we have MIMOS Berhad- Jaring, Telekom Malaysia Berhad- TM

Netand Maxis Communications Maxis Net

Search Engine

Search engines are web sites connecting to huge computers having incredible amounts of

indexed information for easy retrieval.

If we seek general information on broad topics, use a Web directory or index. Directories are

arranged by subject and usually include return links to the top level of the directory's Web

site.

Examples of directories are:

Yahoo!

http://www.yahoo.com/

Magellan

http:// magellan. Excite.com/

Yahooligans!

http://www.yahooligans.com

Neo Planets

http://www.neoplanet.com/start

To obtain specific information and the appropriate titles or phrases use a search engine.
http://www.neoplanet.com/starthttp://www.neoplanet.com/start


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Examples of search engine;

Alta Vista

http://www.altavista.com

Google

http://www.google.com

Excite

http://www.excite.com

Interesting and related websites

Topics URL

Fractions

Decimal

Percentage

http://forum.swarthmore.edu/paths/fraction/olympic.fraction.html.

http://www.mathleague.com/help/fraction.html.

http://www.pipeline.com.au/user/matheuse/fraction.html.

http://forum.swarthmore. Edu/dr.math/faq/faq.fractions.html.

http://www.mathleague.com/help/decwholeexp/decwholeexp.html

Place value http://www.arcytech.org/java/b10block/description.htlm

Mixed Numbers http://www.visualfraction.com/multiEasy.html.

Fractions http://www.prerian.on/fraction/default.html.

Whole Number

Addition, Subtraction

Multiplication,Division

Mixed Numbers

http://www.aplusmath.com/Flashcards/index.html.

http://www.kidsmath.com/e int. html.

http://www.mathleague.com/help/wholenumbers/wholenumbers.html

Money, Time,

Measurements :

Measure of length,

weights, liquid

capacity and space

http://www.aplushmath.com/Flashcards/index.html.

http://www.sys.virginia.edu/~wwwle/jun/module.html

http://www.mathleague.com/help/metric/metric.html.

http://www.teachingtime.co.uk

http://www.teachingtime. Co.uk/clockres.html.

Getting Started

(30 minutes)

1. Double click the Internet Explorer icon
http://www.altavista.com/http://www.altavista.com/http://www.google.com/http://www.excite.com/http://forum.swarthmore.edu/paths/fraction/olympic.fraction.htmlhttp://www.mathleague.com/help/fraction.htmlhttp://www.pipeline.com.au/user/matheuse/fraction.htmlhttp://forum.swarthmore/http://www.aplusmath.com/Flashcards/index.htmlhttp://www.kidsmath.com/ehttp://www.aplushmath.com/Flashcards/index.htmlhttp://www.sys.virginia.edu/~wwwle/jun/module.htmlhttp://www.mathleague.com/help/metric/metric.htmlhttp://www.teachingtime.co.uk/http://www.teachingtime/http://www.altavista.com/http://www.google.com/http://www.excite.com/http://forum.swarthmore.edu/paths/fraction/olympic.fraction.htmlhttp://www.mathleague.com/help/fraction.htmlhttp://www.pipeline.com.au/user/matheuse/fraction.htmlhttp://forum.swarthmore/http://www.aplusmath.com/Flashcards/index.htmlhttp://www.kidsmath.com/ehttp://www.aplushmath.com/Flashcards/index.htmlhttp://www.sys.virginia.edu/~wwwle/jun/module.htmlhttp://www.mathleague.com/help/metric/metric.htmlhttp://www.teachingtime.co.uk/http://www.teachingtime/


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2. In the address box type the address you want to visit; example

http://www.ambleside.schoolzone.co.uk/ambleweb/mentalmaths/clock.html ( all in

small letters)

3. Press enter button and wait4. If you do not know the website you want, just type the word you want to search ,

example mathematics in the search box and press enter.

5. The list of URL appears. Choose the related URL and click, then press Enter and

wait.

Workshop

(30 minutes)

Student are divided into groups of 4/5

Every group will discuss one of the following topics

Each group will present the outcome of their discussion

General view and summary by the lecturer.

1. Discuss ways to prevent students from viewing unsuitable website

Suggested answers:

i. Tell student what they can and cannot do online

ii. Used password protection to track user

iii. Filtering computer with Proxy server, firewall, net nanny, etc

iv. Teacher monitors the students using the internet

2. List out the advantages and disadvantages of using internet

Advantages

Suggested answers:

i. Information can be obtained within a few seconds

ii. Accessible to a lot of information with just one click

Disadvantages

Suggested answers:

i. you have to pay for certain information

ii. attract students to visit to XX files
http://www.ambleside.schoolzone.co.uk/ambleweb/mentalmaths/clock.htmlhttp://www.ambleside.schoolzone.co.uk/ambleweb/mentalmaths/clock.html


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3. Many schools have one or two computers for student use. How do you arrange for

equal access?

i. Rotation system

ii. Setup a schedule- during and after school hours

iii. Record usage

Guided Tour

( 1 hour)

1. Divide students into 4 groups.

2. Ask students to link to the following web sites

Group 1 : http:// forum. Swarthmore.edu/paths/fraction/olympic.fractions.html

Group 2 : http://forum.swarthmore.edu/alejandre/frisbie/bricks.html

Group 3 : http://www.visualfractions.com/mixtofrac.html

Group 4: http://www.mathleague.com/help/metric/metric.html

3. Students summarise materials obtained from the various websites.

Reference

1. Intel teach to the Future, Mac2002

2. Poo Kuan Hoong, Pengenalan Kepada Internet Uni-Ed Publication Sdn. Bhd.

3. Palani Murugappan, Internet : Langkah Demi Langkah Venton Publishing.

4. http://www2.moe.gov.my/~mpbp/netweb.htm

Glossary:
http://forum.swarthmore.edu/alejandre/frisbie/bricks.htmlhttp://www.visualfractions.com/mixtofrac.htmlhttp://www.mathleague.com/help/metric/metric.htmlhttp://forum.swarthmore.edu/alejandre/frisbie/bricks.htmlhttp://www.visualfractions.com/mixtofrac.htmlhttp://www.mathleague.com/help/metric/metric.html


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http (Hyper Text Transport Protocol) The rules by which World Wide Web browsers and

servers communicate.

Internet ExplorerMicrosofts World Wide Web browser

URL (Uniform Resource Locator). The address for an internet web site beginning : http://

Web Site Sets of Web pages that can be visited by browsers.

1. general idea about internet

2. Understanding Directories and Search Engines

3. To get information through internet

4. List out the advantages and disadvantages of using internet.

1.5 A TEACHERS GUIDE BOOK

Objectives


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To be able to select a good teacher's guide book

To be able to use a teacher's guide book in planning a lesson

To be able to identify the relevant contents suitable for the lesson

Contents

A) What is a teachers guide book ?

A teachers guide book contains useful information, guidelines and

hints in line with topics found in the students text books, activity and

workbooks. A teachers guidebook also explains the aims of the usage of the various

materials found in the textbooks and the activity workbooks.

B) Objectives of a teachers guide book

i) The teachers guide book is prepared to assist the teacher in planning and

conducting a lesson effectively when using the text book, activity and work book.

The teachers guidebook is also to help a teacher with less experience and lacking in

reference material.

ii) The teachers guidebook is prepared according to the arrangement and progress of

the topics found in the textbooks and activity/work books.

iii) The teachers guidebook is regarded as a reference book, containing notes,

additional materials and resource, so as to assist a teacher to obtain materials to

conduct a lesson.

iv) The teacher's guidebook is also prepared to assist a teacher in planning teaching

strategies.

C) Characteristics

I) a) SkillsThe main aim is to help a teacher, using the textbooks and activity/work book,

when preparing a lesson , to achieve the skills as required in the syllabus.

b) Objectives

Objective here is said to be in the form of behavioral objective.

This is to enable the teacher to expect the basic skills, which the students are

required to acquire.

c) Concept

Concept here refers to understanding, which is built up through skills. This topic isprepared to help a teacher consolidate concept which are found in the textbooks.

d) Values and Attitudes


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This topic lists out examples of moral values, which can be absorbed in a teaching

and learning process. The list does not prevent a teacher from absorbing other

values.

e) Preparation

An activity prepared earlier which is related to the concept or skills to be learnt, will

prepare students in learning new concepts or skills. Such an activity is hoped to

prepare the students mentally and also their psychomotor skills, in order to

encounter a lesson in mathematical concept and skill.

f) Teaching Aids

Various types of teaching aids, including concrete objects, models, charts, diagrams

and others could be used.

g) Suggestions on teaching methods

A teaching method suggested is based on the textbook to help a teacher plan her

lesson. The suggested teaching method needs to take into account the mathematical

concept and skills in the text book.

h) Students Enrichment materials

The teachers guidebook prepares enrichment material for students, in the form of

exercises, activities, mathematical games, and others. Enrichment exercises and

activities have to be challenging to enhance the students thinking power.

i) Resource for the teacher

This suggests further information to help a teacher in preparing for each lesson.

Additional information can be in the form of notes for the teacher, list of reference

books and others.

II) Illustrations

Illustrations in the teachers guidebook should comply with the following:

i i) correct, accurate and function

ii) variety and attractive

III) Language

The language used in the teachers guidebook should be clear and suitable. The

vocabulary used has to be accurate, consistent and up to date.

IV) Presentation


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A teachers guidebook has to be presented with the following characteristics:

a) according to the progress and sequence of the topics in the textbook.

b) contains suggestions of teaching strategies related to the textbook.

c) Systematic and practicald) Attractive and of variety

e) Able to generate creativity and innovative.

Strategy

Group discussion

Workshop

Self assessment

Presentation

Reference

Buku Panduan Guru Matematik Tahun 1- 6

Kementerian Pendidikan Malaysia


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1.6 ACTIVITY / WORK BOOK

Objectives

To be able to select a suitable and good activity / work book

To be able to use the activity / work book in line with the skills taught and the students

capability.

To be able to select activity suitable for a teaching and learning process.

Contents

A) What is the activity / workbook?

The contents in the activity / workbook are divided into chapters, each according to the

topics in Mathematics. Each chapter consists of various units with varieties of exercises

and activities of different levels to consolidate concepts and skills in the textbooks. At

the end of each chapter, there is an exercise to assess the concept and skills acquired.

B) Objectives of the activity / work book

To help students understand and acquired skills in mathematics

To consolidate the students understanding of the concepts and skills acquired.

To help students develop their psychomotor, cognitive and affective skills.

To cultivate the thinking skills in students.

C) Characteristics

I) i) The activity / work book consists of exercises and activities aimed at helping

students to consolidate their understanding of the concept and acquired skills

in mathematics.

ii) All factors used in the activity / workbook must be accurate and up to date.

iii) The activity / work book has to emphasis on mastering learning and thinking

skills

iv) The activity / workbook should contain varieties of activities suitable with the

ability of students at different level of achievement.

II) a) Exercises


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Exercises prepared should meet the following requirements :

Instructions are clear, accurate and easy to understand

Set from easy to difficult

Suitable so as to consolidates concepts and skills at the three different achievement

levels.

To cultivate thinking and learning skills

Contain elements of assessment, consolidation and enrichment.

b) Activities

The requirements needed for activities to be prepared are :

Clear , accurate and easy to understand instructions Can be performed by the students according to their respective level of

achievement

Suitable so as to achieve the objective of the lesson

To create awareness, to discover abilities, to involve students actively and to

attract students interest.

Varieties such as the following could be included :

i) problem solving

ii) mathematical games

iii) simulation games

iv) play act

v) guessing games

III) Illustrations

a) The function of illustrations is to help students understand the questions

b) local situations and materials which are related to the lives of the students are to

be used

c) clear , accurate and the appropriate size suitable for the level of the students.

d) Different forms of graphic such as drawing, photograph and cartoon based on the

local situation.


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IV) Language / Vocabulary

The language used should be :

Simple , clear and suitable for the level

The vocabulary should be :

Consistent, accurate and up to date

V) Values

Insert moral values and elements of patriotism wherever suitable in the activity /

workbook.

VI) Presentation

Questions in the exercises and activities have to be presented based on the

principles of the teaching and learning process. The following are to be considered

According to the progress and sequence of the text book

Easy to understand by students

To be related with the students experiences

Student centered

Style of presentation should be varied.

VII Matters to be avoided

Elements which are sensitive, negative, subversive should be avoided.

Consistent, accurate and up to date

Strategy

Group discussion

Workshop

Presentation

Reference

Buku Panduan Guru Matematik Tahun 1 - 6

Kementerian Pendidikan Malaysia

1.3 apparatus & resources in mathematics education

Documents