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TMP2023TMP2023

TEACHING SECONDARY SCHOOLTEACHING SECONDARY SCHOOL

MATHEMATICSMATHEMATICSbyby

Dr Mohd Uzi bin DollahDr Mohd Uzi bin Dollah

Faculty of Science and TechnologyFaculty of Science and Technology

Universiti Pendidikan Sultan IdrisUniversiti Pendidikan Sultan Idris

Lecture 2Lecture 2

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Objectives of the lecture:Objectives of the lecture:

i.i. IntroductionIntroduction -- Education development inEducation development inMalaysia.Malaysia.

ii.ii. Focus of NEPFocus of NEP

iii.iii. The aims of ISSCMThe aims of ISSCM

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Education Development in MalaysiaEducation Development in Malaysia

The Malaysian mathematics curriculum hasThe Malaysian mathematics curriculum hasundergone several significant changes sinceundergone several significant changes sinceindependent.independent.

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The late of 80The late of 80s KBSM wass KBSM was

implementedimplemented

In the late of 80s, as part of the nationIn the late of 80s, as part of the nation--widewidecurriculum reform based on the Nationalcurriculum reform based on the NationalPhilosophy of Education, the mathematics hasPhilosophy of Education, the mathematics hasundergone some significant changes.undergone some significant changes.

i.e: KBSR (started from 1983) &i.e: KBSR (started from 1983) &KBSM (started from 1989).KBSM (started from 1989).

It is based on the vision that, mathematics is aIt is based on the vision that, mathematics is adynamic subjectdynamic subject,, coherently connected withincoherently connected within

itselfitself and almost all other area of studyand almost all other area of study, and that, and thatthe main purpose of its study isthe main purpose of its study is to solve theto solve theproblemproblem..

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The Integrated Curriculum forThe Integrated Curriculum for

Secondary School (ICSS/KBSM)Secondary School (ICSS/KBSM)

A cabinet committee was formed to study theA cabinet committee was formed to study the

implementation of the education policy in 1979.implementation of the education policy in 1979.

Base on this report, the New Curriculum for theBase on this report, the New Curriculum for thePrimary School (KBSRPrimary School (KBSR-- the acronym in Malay)the acronym in Malay)

was implemented nationally in 1983.was implemented nationally in 1983.

The KBSR was fully implemented from yearThe KBSR was fully implemented from year

one to year six in 1988.one to year six in 1988.

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The committee had acknowledge that:The committee had acknowledge that:

-- Curriculum for the secondary schoolCurriculum for the secondary school(lower and upper) should be continuity of(lower and upper) should be continuity of

the primary curriculum.the primary curriculum.-- This is to ensure that the basic andThis is to ensure that the basic andgeneral education were solid and suitablegeneral education were solid and suitableto enable them to join the work force into enable them to join the work force infuture, or further their study until tertiaryfuture, or further their study until tertiarylevel.level.

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In accordance with the acknowledgementIn accordance with the acknowledgementmade by themade by the Cabinet CommitteeCabinet Committee::

AA National Education Philosophy (NEP)National Education Philosophy (NEP) waswasformulated.formulated.

NEP was formulated with the objective ofNEP was formulated with the objective ofensconcing the national educations aim andensconcing the national educations aim anddirection in producing a good person anddirection in producing a good person andresponsible citizen.responsible citizen.

In 1988 Ministry of Education reshuffled theIn 1988 Ministry of Education reshuffled the

secondary school curriculum.secondary school curriculum. In 1989 the new curriculum for the secondaryIn 1989 the new curriculum for the secondary

school (KBSM) was introduced.school (KBSM) was introduced.

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A -

1979

B -

1983

C -

1988

D -

1989

1

2

1 Primary School

2 Secondary School

A A cabinet committee was formed 1979

B New Curriculum for the Primary School (KBSR) was implementednationally in 1983.

C The KBSR was fully implemented from year one to year six in 1988

D The new curriculum for the secondary school (KBSM) was

implemented in 1989.

Figure: Development of KBSR and KBSM

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The curriculum was proposed based on the NEP thatThe curriculum was proposed based on the NEP that

state:state:Education in Malaysia is an ongoing effort towardsEducation in Malaysia is an ongoing effort towardsfurther developing the potential of individuals in afurther developing the potential of individuals in aholistic and integrated manner so as to producedholistic and integrated manner so as to producedindividuals who are intellectually, spiritually,individuals who are intellectually, spiritually,

emotionally and physically balanced and harmonious,emotionally and physically balanced and harmonious,base on firm belief in God. Such an effort is design tobase on firm belief in God. Such an effort is design toproduce Malaysian citizens who are knowledgeableproduce Malaysian citizens who are knowledgeableand competent, who posses high moral standards, andand competent, who posses high moral standards, andwho are responsible and capable of achieving a highwho are responsible and capable of achieving a high

level of personal welllevel of personal well--being as well as being able tobeing as well as being able tocontribute to the betterment of the family, society andcontribute to the betterment of the family, society andthe nation at large.the nation at large.

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Thus, focus of NEP is on theThus, focus of NEP is on the

development ofdevelopment ofknowledgeable personknowledgeable person

that can contribute toward personalthat can contribute toward personalwellbeing and at the same time beingwellbeing and at the same time being

able to contributeable to contribute as a member of theas a member of the

society and nation at large.society and nation at large.

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Based on the National Educational Philosophy,

the mathematics curriculum in KBSM isplanned to provide students with experiencesthat may consists of the:

a) integration of knowledge, values andlanguage

b) Integration of mathematics with otherbranches of knowledge

c) Integration of various topics in mathematics

d) Integration of mathematics learned in the

classrooms with those experiences outsidethe classrooms (Kementerian Pendidikan,1989).

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Related to the above, several aspects of

mathematics are being given special emphasisin the mathematics curriculum.

These aspects are:

a) The balance between understanding ofconcepts and the mastery of basic skills

b) The use of mathematics in real-lifesituations

c) The development of problem solving skills

d) The appreciation of history of mathematics,

e) Human societal and spiritual valuesinherent in the subject (see also Bishop,1991)

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The mathematics curriculum is general in nature and

is structured as a continuum from Forms 1 to 5. The content of the syllabus is planned in three areas:

number, shape and space, and relations basedon the assumption that generally, in real life situations,a person encounters and thus needs understanding

and the attainment of appropriate skills in the areas of:a) Numbers such as in counting and calculating

b) Shapes, such as recognising and identifying theproperties of shapes and their measurements

c) Relationships, such as to be able to recognise andusing patterns, rules, general principles, laws,

associations and so on in numbers and shapes.

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AIM of ICSSM The mathematics curriculum for

secondary schools aims to developindividuals who are able to think

mathematically, and apply mathematicalknowledge effectively and responsibly insolving problems and making decisions;and

Face the challenges in everyday lifebrought about by the advancement ofscience and technology.

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KBSMs Mathematics CurriculumKBSMs Mathematics Curriculum

Smart Schools Edition (1998)Smart Schools Edition (1998)

In tandem with the rapid development ofIn tandem with the rapid development of

technology and the era of information,technology and the era of information,

the mathematics curricula of the primarythe mathematics curricula of the primaryand secondary schools continued to beand secondary schools continued to be

upgraded to KBSR or KBSM Smartupgraded to KBSR or KBSM Smart

Schools edition.Schools edition.

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The objectives of mathematicsThe objectives of mathematics

curriculum smart schools edition (CDC,curriculum smart schools edition (CDC,1998):1998):

i. Know and understand definitions,i. Know and understand definitions,

concepts, laws, principles and theoremsconcepts, laws, principles and theoremsrelated to Numbers, Shape and Space,related to Numbers, Shape and Space,

and Relationships.and Relationships.

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ii. Enhance and widen the applications ofii. Enhance and widen the applications of

basic fundamental skills such as addition,basic fundamental skills such as addition,

subtraction, multiplication and divisionsubtraction, multiplication and divisionrelated to Numbers, Shapes and Spacesrelated to Numbers, Shapes and Spaces

and Relationships.and Relationships.

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iii. Acquire basic mathematics skills (otheriii. Acquire basic mathematics skills (other

then the four basic operations) such as:then the four basic operations) such as: Making estimation and roundingMaking estimation and rounding

Measuring and constructingMeasuring and constructing

Collecting and handling dataCollecting and handling data

Representing and interpreting dataRepresenting and interpreting data

Recognizing and representing relationshipRecognizing and representing relationshipmathematicallymathematically

Using algorithm and relationshipUsing algorithm and relationship Solving problemsSolving problems

Making decisionMaking decision

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iv. Communicate and reasoniv. Communicate and reason

mathematicallymathematicallyv. Applying knowledge and skills ofv. Applying knowledge and skills of

mathematics in solving problem andmathematics in solving problem and

making decisions responsibly andmaking decisions responsibly andeffectively in daily life.effectively in daily life.

vi. Relate mathematics with other area ofvi. Relate mathematics with other area of

knowledgeknowledge

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vii. Use suitable technologies in conceptvii. Use suitable technologies in concept

building, acquiring skills, solving problembuilding, acquiring skills, solving problemand exploring the field of mathematics.and exploring the field of mathematics.

viii. Cultivate mathematical knowledge andviii. Cultivate mathematical knowledge and

skills effectively and responsively.skills effectively and responsively.ix. Inculcate positive attitudes towardsix. Inculcate positive attitudes towards

mathematics, andmathematics, and

x. Appreciate the beauty and importance ofx. Appreciate the beauty and importance ofmathematics.mathematics.

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Curriculum OrganisationCurriculum Organisation

The content of the curriculum isThe content of the curriculum is

presented in three areas, that is:presented in three areas, that is:

NUMBER, SHAPE & SPACE, andNUMBER, SHAPE & SPACE, andRELATIONSHIP.RELATIONSHIP.

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In everyday situations, an individual generally

needs the following: Knowledge and skills related to numbers such

as counting and computing (NUMBER);

Knowledge and skills related to shapes andspace such as recognising the properties ofshapes and working with measurements(SHAPE and SPACE);

Knowledge and skills related to patterns, rules,general principles, laws, relations and others

for the purpose of recognising andunderstanding relationships involving numbersand shape (RELATIONSHIP)

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The teaching and learning of

mathematics put emphasis on theunderstanding of concepts and the

mastery of skills in the three areas stated

above, as well as the use of mathematicsto solve problems in various situations.

As such, the following areas require

attention during the teaching and learning

process:

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development of problem solving skills that involves four

main steps namely interpreting the problem, planningthe strategy, carrying out the strategy, and reflecting onthe solution obtained so that pupils can effectivelysolve problems in daily life;

development of logical, systematic and creative thinking

skills together with reasoning skills so as to produce anindividual who is able to think logically and rationally;and

inculcation of the intrinsic value of mathematics and thevalues of Malaysian society which include being

systematic, accurate, diligent, confident, not wasteful,moderate and cooperative, all of which contributetowards becoming a responsible citizen.

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Thanks.Thanks.

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Lecture 3Lecture 3

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Objectives of the lecture:Objectives of the lecture:

i.i. The aims of ISSCAM.The aims of ISSCAM.ii.ii. Analyse the ICSSM & ICSSAMAnalyse the ICSSM & ICSSAM

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The KSBMs AdditionalThe KSBMs Additional

Mathematics CurriculumMathematics Curriculum

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Additional Mathematics is an electivesubject in secondary schools, which

caters to the needs of pupils who are

inclined towards Science and

Technology.

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AIM of ICSSAM The Additional Mathematics curriculum

for secondary schools aims to develop

pupils with in-depth mathematical

knowledge and ability, so that they are

able to use mathematics responsibly and

effectively in communications and

problem solving, and are prepared topursue further studies and embark on

science and technology related careers.

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OBJECTIVES:

The Additional Mathematics curriculumenables pupils to:

1. Widen their ability in the fields of

number, shape and relationship as wellas to gain knowledge in calculus, vectorand linear programming,

2. Enhance problem-solving skills,

3. Develop the ability to think critically,creatively and to reason out logically,

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4. Make inference and reasonable

generalisation from given information,

5. Relate the learning of Mathematics todaily activities and careers,

6. Use the knowledge and skills of

Mathematics to interpret and solve real-life problems,

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7. Debate solutions using precisemathematical language,

8. Relate mathematical ideas to the needs

and activities of human beings,9.Use hardware and software to explore

mathematics, and

10. Practice intrinsic mathematical values.

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CURRICULUM ORGANISATION

The contents of the Additional Mathematicscurriculum are organised into two

learning packages:

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The Core Package:

which is compulsory for all pupils comprises

of five components namely:

Geometry

Algebra

Calculus

Trigonometry

Statistics

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The Elective Package:

consists of two application packages:

Science and Technology Application

Social Science Application

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Pupils need to choose only one application

package from the Elective Package based ontheir inclination and field of interest:

The Science and Technology Application Package,

The Social Science Application Package.

In the Core Package, each component consists

of topics related to a branch in mathematics &

each component are organised hierarchicallywith the easier topics followed with more

complex ones.

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ELECTIVE PACKAGE

The Elective Package consists of two application packages (Pupils are to

choose only one application package): Science and Technology Application Package

AST1. Solutions of Triangles

1. Sine rule.

2. Cosine rule.

3.Areas of triangles.

AST2. Motion Along a Straight Line

1. Displacement.

2. Velocity.

3. Acceleration.

Social Science Application Package

ASS1. Index Number

1. Index number.

2. Composite index.

ASS2. Linear Programming

1. Graphs of linear inequalities.

2. Solving linear programming problems.

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Lecture 4Lecture 4

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Objective of the lecture:Objective of the lecture:

Content Organization of the ICSSAMContent Organization of the ICSSAM

Five Aspect Focused in KBSMFive Aspect Focused in KBSMs Mathematics /s Mathematics /

Add Math CurriculumAdd Math Curriculum

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Content OrganisationContent Organisation

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The Additional Mathematics Curriculum

Specifications is prepared in a format

which helps teachers to teach a particulartopic effectively.

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The contents of each topic are dividedinto five columns:

Column 1 : Learning Objectives

Column 2 : Suggested Teaching andLearning Activities

Column 3 : Learning Outcomes

Column 4 : Points To Note; and

Column 5 : Vocabulary.

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i. TheL

earning Objectives: Define clearly what should be taught.

They cover all aspects of the

Mathematics curriculum programme and

are presented in a developmental

sequence designed to support pupils

understanding of the concepts and skill of

mathematics.

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ii. The Suggested Teaching and Learning

Activities: Lists some examples of teaching and learning

activities including methods, techniques,

strategies and resources pertaining to the

specific concepts or skills.

However, teachers are encouraged to look for

other examples or make cross-references,

determine teaching and learning strategiesmost suitable for their students and provide

appropriate teaching and learning materials.

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iii. The Learning Outcomes:

Define specifically what pupils should be

able to do.

They prescribe the knowledge, skills or

mathematical processes and values thatshould be inculcated and developed at

the appropriate level.

These behavioural objectives aremeasurable in all aspects.

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b. Learning outcomeb. Learning outcome

Refer to the skills or mathematical processRefer to the skills or mathematical process

that need to be mastered by students relatedthat need to be mastered by students related

to the Learning Area concerned.to the Learning Area concerned.

They are three level of outcomes:They are three level of outcomes:

Level 1 (Basic)Level 1 (Basic)Encompass basic mathematical skillsEncompass basic mathematical skills

and processes like counting andand processes like counting and

measuring, simple problem solving thatmeasuring, simple problem solving that

can be done directly, andcan be done directly, andcommunicating using simplecommunicating using simple

mathematical symbols.mathematical symbols.

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Level 2: StandardLevel 2: Standard

-- Encompass mathematical skill and processes upEncompass mathematical skill and processes upto the stage of being able to carry out calculation.to the stage of being able to carry out calculation.

-- Students are able to interpret mathematicalStudents are able to interpret mathematicalconcept in the form of statements,concept in the form of statements,

-- Able to solve moderate complex but routineAble to solve moderate complex but routine

problemsproblems

Level 3: AdvancedLevel 3: Advanced

-- encompasses math skills and processes up to theencompasses math skills and processes up to thestage to carry out problem solving.stage to carry out problem solving.

-- able to interpret math concepts.able to interpret math concepts.

-- ability to solve routine and nonability to solve routine and non--routine problem.routine problem.

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Note:Note:

-- complexity of Learning Area obviouslycomplexity of Learning Area obviouslyincrease from level 1 to 3.increase from level 1 to 3.

-- each level, elements of thinking skilleach level, elements of thinking skill

critically and creatively are developed.critically and creatively are developed.-- cultivation of noble values andcultivation of noble values and

positive attitude through teaching andpositive attitude through teaching and

learning.learning.

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iv. Points To Note column:

Attention is drawn to the more significant

aspects of mathematical concepts andskills.

These emphases are to be taken into

account so as to ensure that theconcepts and skills are taught and learnt

effectively as intended.

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v. The Vocabulary:

Consists of standard mathematical terms,instructional words or phrases which are

relevant in structuring activities, in askingquestions or setting tasks.

It is important to pay careful attention to theuse of correct terminology and these need tobe systematically introduced to pupils invarious contexts so as to enable them tounderstand their meaning and learn to usethem appropriately.

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Note:Note:

-- complexity of Learning Area obviouslycomplexity of Learning Area obviouslyincrease from level 1 to 3.increase from level 1 to 3.

-- each level, elements of thinking skilleach level, elements of thinking skill

critically and creatively are developed.critically and creatively are developed.-- cultivation of noble values andcultivation of noble values and

positive attitude through teaching andpositive attitude through teaching and

learning.learning.

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Five Aspect Focused in KBSMsFive Aspect Focused in KBSMs

Mathematics / Add MathMathematics / Add MathCurriculumCurriculum

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i. Problem solving in mathematicsi. Problem solving in mathematics

Become the focus in KBSMBecome the focus in KBSM

Teacher are encourage to stimulate mathematicalTeacher are encourage to stimulate mathematical

problem solving based on their daily experienceproblem solving based on their daily experience

Teacher are expecting to provide students withTeacher are expecting to provide students with

varied experiences through student can workvaried experiences through student can work

individually or in group in tackling math problem.individually or in group in tackling math problem.

Although teacher are free to chose strategy, butAlthough teacher are free to chose strategy, butheuristic strategy as proposed by Polya (1974) areheuristic strategy as proposed by Polya (1974) are

recommended.recommended.

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Four skills involved in problem solving:Four skills involved in problem solving: Understand the problemUnderstand the problem

Devise a planDevise a plan Carry out the planCarry out the plan

Looking backLooking back

Several heuristic strategies have been proposed:Several heuristic strategies have been proposed: Trying a simple caseTrying a simple case

Trial and improvementTrial and improvement

Drawing diagramDrawing diagram

Identifying patternIdentifying pattern

Construct a table or chartConstruct a table or chart

Making a simulationMaking a simulation

Use analogiesUse analogies

Working backwardsWorking backwards

Applying logical reasoningApplying logical reasoning

Using algebraUsing algebra

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ii. Communication in mathematicsii. Communication in mathematics

Communication can act as a means of sharingCommunication can act as a means of sharingideas and clarify the understanding of mathematics,ideas and clarify the understanding of mathematics,and communication can occur through:and communication can occur through:

The process of hearing when responds to what he/her hearThe process of hearing when responds to what he/her hearand encourage him/her to make decision base on his/herand encourage him/her to make decision base on his/herknowledge.knowledge.

The process of reading when the individual collects andThe process of reading when the individual collects andarranges information obtained and then relate it with otherarranges information obtained and then relate it with otherrelevant ideas and concept.relevant ideas and concept.

The process of visualization when observes, analyses,The process of visualization when observes, analyses,interprets and synthesizes the information into concreteinterprets and synthesizes the information into concretematerials like diagrams, representation in the form of tables,materials like diagrams, representation in the form of tables,graphs and other manipulative materials.graphs and other manipulative materials.

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An effective communication can beAn effective communication can be

achieved through the following method:achieved through the following method:a. Oral communicationa. Oral communication

Consider as two way communicationConsider as two way communication

Examples:Examples: Storytelling, asking questions and studentsStorytelling, asking questions and students

answer with their own word.answer with their own word.

Structured and unstructured interviewStructured and unstructured interview

Discussion in the form of forum, seminar, debateDiscussion in the form of forum, seminar, debateand brainstormingand brainstorming

Presentation of the complete taskPresentation of the complete task

Discussion through cooperative learningDiscussion through cooperative learning

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b. Written communicationb. Written communication

A process of channeling ideas and informationA process of channeling ideas and informationabout mathematics in form of writing.about mathematics in form of writing.

The process can encourage student to thinkThe process can encourage student to thinkdeeply about mathematical content anddeeply about mathematical content and

observed relationship between concepts.observed relationship between concepts. Examples:Examples:

ExercisesExercises

JournalsJournals

Scrap booksScrap books

PortfoliosPortfolios

ProjectProject

Written testsWritten tests

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c. Communication through representationc. Communication through representation

Representation is a process of analyzingRepresentation is a process of analyzing

a mathematical problem and interpretinga mathematical problem and interpreting

it from one mode to another.it from one mode to another.

A mathematical representation enableA mathematical representation enablestudents to find relationship betweenstudents to find relationship between

mathematical ideas which are informal,mathematical ideas which are informal,

intuitive and abstract using laymansintuitive and abstract using laymansjargon.jargon.

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iii. Reasoning in Mathematicsiii. Reasoning in Mathematics

The main goal statements clearly statesthe students need to develop the abilityto think logically, systemically, creativelyand critically.

Although this is not clearly stated in thesyllabus, teachers guides and furtherelaboration of the syllabus specially

encourage teachers to use approachesthat can simulate mathematical thinkingor reasoning.

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Logical reasoning is the basis for understanding andLogical reasoning is the basis for understanding anddoing mathematicsdoing mathematics

Logical reasoning in teaching and learning activitiesLogical reasoning in teaching and learning activitiesenables students understand meaningfully the naturalenables students understand meaningfully the naturalphenomena that occur around themphenomena that occur around them

Students in all stages need to be trained inStudents in all stages need to be trained ininvestigating their guesses and predictions by usinginvestigating their guesses and predictions by usingconcrete materials, calculators, computers andconcrete materials, calculators, computers andmathematical representation others.mathematical representation others.

Reasoning can encourage student to make educatedReasoning can encourage student to make educatedguesses or prediction in determining the solution or aguesses or prediction in determining the solution or adiscovery.discovery.

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The use of statistics to critically examine

information as part of the lesson, for

example, can be said to be incorrespondence with the aim of

promoting the above thinking abilities.

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iv. Mathematical connectioniv. Mathematical connection

There is a strong emphasis in makingconnections within mathematics it self andacross other subjects.

Opportunity for students to understandOpportunity for students to understand

concepts meaningfully by making connectionconcepts meaningfully by making connectionwith other concepts or conceptual.with other concepts or conceptual.

Opportunity for student to make conceptualOpportunity for student to make conceptuallink to procedural knowledgelink to procedural knowledge

Relating topics within mathematics to otherRelating topics within mathematics to othergeneral learning areas.general learning areas.

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Link mathematics ideas with conceptsLink mathematics ideas with concepts

and daily experience, students will moreand daily experience, students will moreaware of the importance of mathematics.aware of the importance of mathematics.

Through the introduction of certain factsconcerning historical development in

mathematics, the curriculum hopes thatstudents will be able to see thatmathematics has its origin and in manycultures and is developed as responsesto human needs that are both utilitarianand aesthetic.

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v. Application of technologyv. Application of technology

Used the application of the latest technology to developUsed the application of the latest technology to developand enrich the activities of the topics to be taught.and enrich the activities of the topics to be taught.

Usefulness of the application of technology:Usefulness of the application of technology: Help students understand concepts in depth, meaningful andHelp students understand concepts in depth, meaningful and

precisely.precisely.

Opportunity for students explore mathematical ideas.Opportunity for students explore mathematical ideas. To enhance and diversity the pedagogy in teaching andTo enhance and diversity the pedagogy in teaching and

learning of mathematics through the application of technology,learning of mathematics through the application of technology,such as computers, calculators, software, internet and othersuch as computers, calculators, software, internet and otherexisting learning packages.existing learning packages.

Useful in carrying out activities such as producing materials,Useful in carrying out activities such as producing materials,

drilling, tutorial, revision, remedial and enrichment, simulation,drilling, tutorial, revision, remedial and enrichment, simulation,computation, and learning and teaching aids.computation, and learning and teaching aids.

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Approach in Teaching and LearningApproach in Teaching and Learning

Teachers should use real or concreteTeachers should use real or concrete

material to help pupils to gainmaterial to help pupils to gain

experience, construct abstract ideas,experience, construct abstract ideas,

make inventions, build self confidence,make inventions, build self confidence,encourage independence, and inculcateencourage independence, and inculcate

the spirit of cooperation.the spirit of cooperation.

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The teaching and learning materials usedThe teaching and learning materials used

should contain self diagnostic elements so thatshould contain self diagnostic elements so thatpupils know how far they have understood thepupils know how far they have understood theconcepts and acquire the skills.concepts and acquire the skills.

To assist pupils in having positive attitudes andTo assist pupils in having positive attitudes andpersonalities, the intrinsic mathematical valuespersonalities, the intrinsic mathematical valuesof accuracy, confidence, and thinkingof accuracy, confidence, and thinkingsystematically, have to be infused in teachingsystematically, have to be infused in teachingand learning process.and learning process.

exex-- used of contextused of context promoting moral values,promoting moral values,

group worksgroup works promoting cooperation, andpromoting cooperation, and

used certain topicsused certain topics promoting patriotism.promoting patriotism.

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Various teaching strategies such asVarious teaching strategies such as

direct instruction, discovery learning,direct instruction, discovery learning,

investigation, guided discovery or otherinvestigation, guided discovery or othermethods must be incorporated.methods must be incorporated.

Among the approach that can be givenAmong the approach that can be given

consideration:consideration:

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Amongst the approaches that can be givenconsideration include the following:

Pupils-centered learning that isinteresting;

Different learning abilities and styles ofpupils;

Usage of relevant, suitable and effectiveteaching materials; and

Formative evaluation to determine theeffectiveness of teaching and learning.

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The choice of an approach that is suitable willstimulate the teaching and learningenvironment inside or outside the classroom.

Approaches that are considered suitableinclude the following:

Cooperative learning;

Contextual learning;

Mastery learning;

Constructivism; Enquiry-discovery; and

Future studies.

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Mastery LearningMastery Learning is an instructional method thatis an instructional method thatpresumes all children can learn if they are providedpresumes all children can learn if they are providedwith the appropriate learning conditions wherebywith the appropriate learning conditions wherebystudents are not advanced to a subsequent learningstudents are not advanced to a subsequent learningobjective until they demonstrate proficiency with theobjective until they demonstrate proficiency with thecurrent one.current one.

Mastery learning curricula generally consist of discreteMastery learning curricula generally consist of discretetopics which all students begin together. Students whotopics which all students begin together. Students whodo not satisfactorily complete a topic are givendo not satisfactorily complete a topic are givenadditional instruction until they succeed. Students whoadditional instruction until they succeed. Students whomaster the topic early engage in enrichment activitiesmaster the topic early engage in enrichment activitiesuntil the entire class can progress together.until the entire class can progress together.

based on Benjamin Blooms Learning for Masterybased on Benjamin Blooms Learning for Masterymodelmodel

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Discovery Learning (Bruner)Discovery Learning (Bruner)

Discovery learning is an inquiryDiscovery learning is an inquiry--based, constructivistbased, constructivist

learning theory that takes place in problem solvinglearning theory that takes place in problem solvingsituations where the learner draws on his or her ownsituations where the learner draws on his or her ownpast experience and existing knowledge to discoverpast experience and existing knowledge to discoverfacts and relationships and new truths to be learned.facts and relationships and new truths to be learned.

Students interact with the world by exploring andStudents interact with the world by exploring and

manipulating objects, wrestling with questions andmanipulating objects, wrestling with questions andcontroversies, or performing experiments.controversies, or performing experiments.

As a result, students may be more likely to rememberAs a result, students may be more likely to rememberconcepts and knowledge discovered on their own.concepts and knowledge discovered on their own.

Models that are based upon discovery learning modelModels that are based upon discovery learning model

include: guided discovery, probleminclude: guided discovery, problem--based learning,based learning,simulationsimulation--based learning, casebased learning, case--based learning,based learning,incidental learning, among others.incidental learning, among others.

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InquiryInquiry--based learningbased learning Its core premises include Its core premises includethe requirement that learning should be based aroundthe requirement that learning should be based around

student questions.student questions. PedagogyPedagogy and curriculum requires students to workand curriculum requires students to work

independently to solve problems rather than receivingindependently to solve problems rather than receivingdirect instructions on what to do from the teacher.direct instructions on what to do from the teacher.Teachers are viewed as facilitators of learning ratherTeachers are viewed as facilitators of learning rather

than vessels of knowledge. The teachers job in anthan vessels of knowledge. The teachers job in aninquiry learning environment is therefore not to provideinquiry learning environment is therefore not to provideknowledge, but instead to help students along theknowledge, but instead to help students along theprocess of discovering knowledge themselves.process of discovering knowledge themselves.

InquiryInquiry--based learning is an instructional methodbased learning is an instructional method

developed during thedeveloped during the discovery learningdiscovery learning movement ofmovement ofthe 1960s.the 1960s.

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EVALUATION

Evaluation or assessment is part of theteaching and learning process to ascertain thestrengths and weaknesses of pupils.

It has to be planned and carried out as part ofthe classroom activities.

Different methods of assessment can beconducted.

These maybe in the form of assignments, oralquestioning and answering, observations andinterviews.

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Based on the response, teachers canrectify pupils misconceptions and

weaknesses and also improve their own

teaching skills.

Teachers can then take subsequent

effective measures in conducting

remedial and enrichment activities in

upgrading pupils performances.