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Course Pro FormaProgram Ijazah Sarjana Muda Perguruan Dengan Kepujian

(Matematik Pendidikan Rendah)

Course Title Knowing Numbers

(Mengenal Nombor)

Course Code MTE 3101

Credit 3(3+0)

ContactHours

45 hours

Language OfDelivery

English

Prerequisite ToEntry

Nil

Semester One/ Two

LearningOutcomes

1. Compare the development of various number systems

2. Generate one set of numbers to another set of numbers

3. Characterize natural, rational, irrational and real numbers

4. Perform fundamental operations on the various sets of numbers

5. Extend knowledge innumber concepts through number recreationactivities

6. Determine the modulus, argument and conjugate of a complexnumber

7. Convert complex number from coordinate form to polar form andvice versa

8. Apply number concepts in problem solving activities

Synopsis In this course students are exposed to the various numeration systemsand also the elementary number theory. In addition, there is a furtherexploration into natural, rational, irrational and real numbers. Thecharacteristics and theorems related to these sets of numbers will alsobe highlighted. Appreciation of Fibonacci Numbers and Golden Ratio in

nature is emphasized. In the process, students will apply theirknowledge of numbers in number recreations and problem solving.

Kursus ini akan memberi pendedahan kepada pelajar tentangsistem nombor dan asas teori nombor. Pelajar juga akan menerokaidengan lebih mendalam tentang ciri dan teorem yang berkaitandengan nombor asli, nombor nisbah dan nombor bukan nisbah sertanombor nyata. Perkaitan antara Nombor Fibonacci dengan GoldenRatio dan alam semula jadi juga akan dibincangkan dan akandiaplikasikan dalam rekreasi nombor dan penyelesaian masalah .

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Topic Content Hours

1 Numeration Systems

Early numeration systems

Hindu-Arabic Numeration System Different numeration systems

o Number of symbols and grouping in various

baseso Changing base b to base 10 and vice versa

6

2 Elementary Number Theory

Number systemso Definition

o Classifications within the set of real

numberso Number representation

6

3 Natural numbers

Prime Numberso Divisibility

o Prime Factorization -The Euclidean

Algorithm

Modular Numbers

The Fundamental Theorem of Arithmetic

Number recreationso Fibonacci Sequence and Golden Ratio

o Magic Squares

o

Problem solving

12

4 Rational Numbers

Basic properties

Cardinality of the rational numbers

Complex fractions and continued fractions

Problem solving

6

5 Irrational Numbers

Basic properties

Square roots and surdso Product rule

o Quotient ruleo Problem solving

6

6 Complex Numbers

Modulus, argument and conjugate of aComplex Number

Operations involving Complex Numbers

Complex Numbers in polar form

6

7 Estimation of quantities

Rounding off numberso whole Numbers

o fraction and decimalso standard forms

3

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o square roots and surds

Total 45

Assessment Coursework 50%Examination 50%

Main References Groves, Susie. (2006). Exploring number and space: Study guide.Victoria: Deakin University.

Musser, Gary L.; Burger, William F. & Peterson, Blake E. (2006).Mathematics for elementary teachers. A contemporary approach. 7th ed.NJ: John Wiley and Sons.

Smith, K. J. (2001). The nature of mathematics. 9th ed. Pacific Grove,

CA: Brooks/Cole.

AdditionalReferences

Bennett A.B. and Nelson L.T., (1998). Mathematics for elementaryteachers: An activity approach. 4th ed. NY:McGraw-Hill.

Brodie, Ross and Swift, Stephen. (2002). New QMaths II. Australia:Nelson Thomson Learning.

Byrne, J. Richard. (2000). Number systems: An elementary approach.New Jersey: Prentice Hall.

Groves, Susie. (2006). Exploring number and space: Reader. Victoria:

Deakin University.

Humble, S. (2002). The experimenters A-Z of mathematics: Mathsactivities with computer support. London: David Fulton.

Miller, C. D.; Heeren, V. E. & Hornsby, E. J. Jr. (1990). Mathematicalideas. 6th ed.USA: Harper Collins.

Mullan, E. et.al. (2001). Maths in action: Mathematics 2. USA: NelsonThornes Limited.

Nicholson, W. Keith. (2003). Linear algebra with applications. 4th ed.

Singapore: McGraw Hill.

Shakuntala Devi (1984). The book of numbers. Delhi, India: OrientPaperbacks.

Shakuntala Devi (1986). The joy of numbers. Delhi, India: OrientPaperbacks.

Sullivan, Michael. (1999).Algebra and trigonometry. 5th ed. New Jersey:Prentice Hall.

Tipler, M.J. et.al.(2003). New national framework mathematics. USA:Nelson Thornes Limited.

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Course Title Mathematics Education Curriculum

(Kurikulum Pendidikan Matematik)


Credit 3(3+0)

ContactHours

45 hours

Language OfDelivery

English


Nil

Semester One/ Two

LearningOutcomes

1. Explain the roles of mathematics, mathematicians and mathematicsteacher

2. Describe the development of mathematics education and curriculumin Malaysia

3. Interpret the national mathematics curriculum

4. Participate in the professional development of mathematics teachers

5. Integrate and develop interest and values in mathematics education

Synopsis This course allows students to acknowledge the history and roles ofmathematicians. They are exposed to the meanings and roles ofmathematics and values in mathematics on top of being familiar with theroles as a mathematics teacher. It also requires students to explore thedevelopment of the Malaysian Mathematics Curriculum and to study theMalaysian Mathematics Curriculum: KBSR and KBSM.

Kursus ini memberikan pendedahan kepada pelajar untuk menghayatisejarah dan peranan ahli matematik. Pelajar juga didedahkan kepadamakna, peranan dan nilai dalam matematik serta peranan gurumatematik. Pelajar akan meneliti perkembangan Kurikulum Matematikdi Malaysia dan juga mengkaji Kurikulum Matematik KBSR dan KBSM.

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Topic Content Hours

1 Mathematics Education

Meanings and roles of mathematics

History and roles of mathematicians Nature of mathematics

Values in mathematics

9

2 Development of Mathematics Curriculum

Development of Mathematics Curriculum inMalaysia

The influence of other countries MathematicsCurriculum on Malaysian MathematicsCurriculum

Policies and programs for developing childrens

Mathematics

9

3 Study of Malaysian Mathematics Curriculum

Five pillars in teaching and learningmathematicso Problem solving in mathematics

o Communication in mathematics

o Mathematical reasoning

o Mathematical connections

o Application of technology

KBSRo Philosophy of KBSR Mathematics

Educationo Primary mathematics curriculum

o Content organization of mathematical

concepts in primary school education andrelationship to pre-school education

oCurriculum specifications for Year 1 to Year

6

KBSMo Philosophy of KBSR Mathematics

Educationo Secondary Mathematics Curriculum

o Study of connection of topics from primary

to secondary mathematics

18

4 Professional development of MathematicsTeachers

Academic discourseo Seminar, workshops, conferences,

books and journals

Academic bodieso Mathematics Teachers Association:

NCTM, NUTP,PESAMA

Roles of mathematics teacher

Life-long education

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5 Issues and trends

Teaching Mathematics and Science in EnglishLanguage

Mathematics in smart schools

ICT in mathematics education

3

Total 45


Main References Dosey, John et. al. (2002). Mathematical methods and modelling fortodays mathematics classroom. UK: Brooks/ Cole.

Pritchard, Alan (2005) .Ways of learning. (pp. 1-107).USA: David FultonPublishers.

Smith, K.J. (2001). The nature of mathematics. 9th ed. CA:ThompsonLearning.


Cathcart , W. G. et. al.(2006). Learning mathematics in elementary andmiddle schools. (pp. 1-107). USA: Pearson Prentice Hall.

Day, C. (1999). The challenge of lifelong learning. UK: Taylor & FrancisInc.

Gates, P. (2001). Issues in mathematics teaching. UK: Taylor &Francis Group.

Kementerian Pendidikan Malaysia. Kurikulum BersepaduSekolah Rendah. Sukatan Pelajaran Matematik(2001). PPK.KPM.

Kementerian Pendidikan Malaysia. Kurikulum Bersepadu SekolahMenengah. Sukatan Pelajaran Matematik(2000). PPK.KPM.

Kementerian Pendidikan Malaysia. Kurikulum Bersepadu SekolahRendah. Sukatan Pelajaran MatematikTahun 6(2001). PPK.KPM.

Ministry of Education Malaysia. Integrated Curriculum for SecondarySchool. Curriculum Specifications Mathematics Form 1 - 4 (2005)2006).CDC. MOE.

Ministry of Education Malaysia. Integrated Curriculum for SecondarySchool. Curriculum Specifications Mathematics Form 5(2006).

Ministry of Education Malaysia. Integrated Curriculum for PrimarySchool. Curriculum Specifications Mathematics Year 1-5 (2002-2006).CDC. MOE.

National Council of Teachers of Mathematics (1991).Professional standards for teaching mathematics. NCTM. Reston,Virginia.

Orlich, Donald C. et. al. (2001). Teaching strategy: A guide for effectiveinstructions. (pp. 75-229). USA: Houghton Mifflin.

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Course Title Geometry(Geometri)


Credit 3(2+1)

ContactHours

60 hours

Language Of

Delivery

English


Nil

Semester One/ Two

LearningOutcomes

1. Apply the theory of transformation and isometrics in planegeometry: rotation, translation, glide reflections in art and design

2. Use ICT e.g. Geometer Sketchpad to explore and createtessellations; investigate isometry and symmetry and exploreconics

3. Integrate basic techniques to construct geometric models

SynopsisThis course provides an opportunity for the students to explore theapplications of geometry. It discusses concepts in plane geometry-tessellations, symmetries and transformations. Students will also discoverpatterns in art and design. In addition, exposure to dimensional geometryof the Platonic solids is also highlighted. The use of ICT e.g. GSP isapplied as a tool to investigate and construct projects in geometry.

Kursus ini memberi peluang kepada pelajar untuk menerokai aplikasi

geometri. Kursus ini juga membincangkan konsep dalam satah geometri,teselasi, simetri dan transformasi. Pelajar akan mempelajari corak dalamseni dan reka bentuk. Selain itu, pelajar juga akan didedahkan kepadageometri dimensi bagi pepejal Platonic. Teknologi Maklumat danKomunikasi seperti Geometer Sketchpad akan digunakan sebagai alatuntuk menyiasat dan membangunkan projek geometri.

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Topic Content Hours

Theory

1Plane tessellations

Types of tessellations

Tessellation and art

Fractal geometry

5

2 Plane symmetries and transformations

Isometry of the planeo rotation

o reflection

o translation

o glide reflection

Plane symmetry

Finite symmetry groups and the seven Friezepatterns

6

3 Regular and Semi-regular solids

Five platonic solids

Vertices, faces & edges

Archimedean solids

Kepler-Poinsot solids

5

4 Geometric Modeling

Paper Engineering- pop-up models

- pop-up techniques- art and design

6

5 Conics

Locus

Parabola

Ellipse

Ellipse and parabola

Parabola, ellipse and hyperbola

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Sub Total30

Practical

1Geometer Sketchpad

explore and create tessellations

familiarization with basic commands of GSP

explore and create basic transformations

develop a tool kit for tessellation, isometry of theplane and conics

10

2 Construction of platonic solids paper construction of 5 platonic solids

paper construction of Archimedean solids

construction of Kepler-Poinsot solids

photographs of the solids constructed

6

3 Paper Engineering Project

explore and analyse the mathematics of some

basic paper folding techniques analyse a collection of paper engineering in

cards, books and packaging

produce a pop-up card

6

4 Exploring Conics Using ICT e.g. GSP

Locus

Parabola

Ellipse and hyperbola

6

5 Exhibition

GSP toolkit for tessellation and isometry

Potato printing

Paper engineering project

2

Sub Total 30

Total60

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Main ReferencesGrayson, R. (1995). Using Geometer's Sketchpad to explore combinedtransformations. Micromaths. vol.11, no 2, pp 6-13.

Parks, H. et.al. (2000). Mathematics in life society and the world. 2nd ed.USA: Prentice Hall.

Russell,J. (1996). Nets with polyhedra. Mathematics Teaching, vol.154,pp.12-13.

Smith, K. J. (2001).The nature of mathematics. Glencoe : McGraw Hill.

Tannenbaum, P. (2004). Excursions in modern mathematics. 5th ed. NJ:

Pearson Prentice Hall.


Budden, F.J. (1972). The fascination of group. London: CambridgeUniversity Press.

Crowe, D. (1986). Symmetry, rigid motions andpatterns. Arlington, MA:COMAP, Inc.

Johnson,P. (1992). Pop-up paper engineering. London: Falmer Press.

Pugh, A. (1976). Polyhedra: A visual approach. Berkeley,CA.: Universityof California Press.

Schattschneider,D. (1990). Visions of symmetry: Notebooks,periodic drawings and related works of M.C. Escher. New York: W.H.Freeman.

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Course Title Decision Mathematics

(Matematik Keputusan)


Credit 3(3+0)

ContactHours

45 hours

Language OfDelivery

English


Nil

Semester One/ Two

LearningOutcomes

1. Define the various tools in decision mathematics

2. Apply mathematics algorithms, heuristic algorithms, sorting,searching, graphs, linear programming and critical paths analysisin decision making

3. Select appropriate tools for making decision in mathematics

4. Integrate knowledge and understanding of Decision Mathematicsand mathematical modeling in daily life

Synopsis This course introduces students to another useful branch ofmathematics. It provides information about introduction to decisionMathematics, types of searches, linear programming, graphs,networks, critical path analysis, algorithms, heuristic algorithms andmethods of sorting.

Kursus ini memperkenalkan pelajar kepada satu lagi cabangmatematik yang berguna. Kursus ini menyediakan maklumat tentang pengenalan kepada Matematik keputusan, jenis-jenis carian, pemprograman linear, graf, rangkaian, analisa laluan kritikal,algoritma, algoritma heuristik dan kaedah mengisih.

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Topic Content Hours

1 Introduction

What is Decision Mathematics?

Tools in Decision Mathematics

1

2 Types of searches

Linear search algorithm

Indexed sequential search algorithm

Binary search algorithm

4

3 Linear Programming

Types of Linear Programming problemso Infinitely many solutions

o Empty feasible regions

o Unbounded feasible regionso Degeneracy

o The Simplex Method in Linear

Programming

10

4 Graphs

Definitions of graph, edge, degree

Types of graphso simple graph

o walk, trail, path, cycle

o Hamiltonian cycleo digraph

o incidence matrix

o planar graph

o bipartite graph

3

5 Networks

Kruskals Algorithm

Prims Algorithm

Dijkstras Algorithm

6

6 Critical Path Analysis Introduction and definition of Critical Path

Analysis

The elements of a network diagram :dummies, events, key even, symbols.

Constructing a network diagram

Analyzing a network diagram

Resource Management

11

7 Algorithms

Introduction and definition of Algorithms Ways of communicating algorithms

2

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8 Heuristic Algorithms

First-fit Algorithm

First-fit decreasing Algorithm

Full bins

4

9 Methods of Sorting

Interchange sort

Bubble sort

Shuttle sort

Quick sort

4

Total 45


MainReferences

Parramore, K. et. al (2004). Decision Mathematics 1 D1. 3rd ed. UK.British Library Publication.

Parramore. K. et. al (2004). Decision Mathematics 2 and C. 3rd ed. UK.British Library Publication.

AdditionalReferences Hebborn , John (2000). Decision mathematics. UK : Paperback.

Savage, Sam L. (2002). Decision making with insight. UK : Paperback.Smith, K.J. (2001). The nature of mathematics. 9th ed. CA:ThompsonLearning.

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Course Title Statistics

(Statistik)


Credit 3(3+0)

ContactHours

45 hours

Language OfDelivery

English

Prerequisite toentry

Nil

Semester One/Two

Learningoutcomes

Explain the theoretical and empirical aspects underpinningprobability

Apply sampling and estimation theory in estimating the mean of apopulation

Use inferential statistics such as Chi-Square test, ANOVA andlinear regression in hypothesis testing

Apply their knowledge and understanding of these areas instatistics to relevant real life problems

Synopsis In this course, students will revisit the concepts of probability andexplore inferential statistics such as t-test, Chi-Square test, analysis ofvariance (ANOVA) in hypothesis testing and linear regression inanalyzing linear relationship in bivariate variables. The importance ofusing the appropriate statistical methods in solving real life problemsis emphasized.

Dalam kursus ini, pelajar akan mengimbas kembali konsep yangberkaitan dengan kebarangkalian dan menerokai statistik inferensseperti ujian-t, ujian Chi-Square, analisis varians (ANOVA) dalam pengujian hipotesis dan regresi linear dalam menganalisisperhubungan linear dalam dua pembolehubah (bivariate). Kepentinganmenggunakan kaedah statistik yang sesuai dalam penyelesaianmasalah harian adalah dititikberatkan.

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Topic Content Hours

1 Probability

Introduction to probabilityo

Theoriticalo Empirical

Compound Eventso Independent Events

o Mutually Exclusive

The Addition and Multiplication Rule

Probability Treeo Theoretical

Conditional Probabilities

3

2 Sampling and estimation theory

Elementary sampling

Sampling distribution

Point estimation and interval estimation

Confidence level

Reading Statistic Tables

Estimating the Mean of Population when STDof the Population is Known

Estimating the Mean and STD of PopulationFrom Sample Data

Estimating the mean of a population basedon a small sample size

9

3 Hypothesis testing Introduction

Methodology for hypothesis testing.

Testing one mean

Testing the difference between two populationmeans

Testing a population proportion

Testing a population variance (standarddeviation)

Testing the ratio of two populationvariance(standard deviation)

12

4 The Chi-square hypothesis test

The general procedure for the test

The goodness of fit test

The test of association

9

5 Analysis of variance ( ANOVA )

Introduction on one way Independent ANOVA

Calculating ANOVA by hand

Calculating ANOVA using EXCEL

6

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6 Linear Regression

Introductiono Independent variables

o Dependent variables

o Scatter diagram

The least squares straight lineo Interpolation and extrapolation

6

Total 45


MainReferences

Eccles, A. et. al (2004). Statistics 1. 3rd ed UK: Martins the PrintersLtd.

Davies, M et. al ( 2005). Statistics 2. 3rd ed UK. Hodder Murray

Davies, M et. al ( 2005). Statistics 3. 3rd ed UK. Hodder Murray

Mann, Prem S. ( 2003 ). Introductory Statistics. 5th ed. NY: Wiley.

Rowntree, D. (2004). Statistics without tears: A primer for nonmathematicians. Boston, MA: Pearson Education.

Spielgel, R. M (2000). Statistics crash course. USA: Mc Graw Hill.


Cook, Upton, G. I. (2000). Introducing Statistics. 2nd ed. NY: OxfordUniversity Press.

Norusis, M. J. (1985). SPSS X: Advanced statistics guide.NY:McGraw-Hill Book Company.

Smitters, G et. al ( 2000). Advanced Modular Mathematics Statistics 1.2rd ed UK. Harper Collins Publisher Ltd.



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Course Title Resources in Mathematics

(Resos dalam Matematik)


Credit 3(3+0)

ContactHours

45 hours

Language OfDelivery

English


Nil

Semester One/ Two

LearningOutcomes

1. Choose appropriate and relevant mathematics resources

2. Demonstrate their understanding in using the resources

3. Produce creative manipulative materials to support teaching andlearning in mathematics

4. Display effective management skills in planning and handlingmathematics resources

Synopsis This course provides an opportunity for students to explore the

applications of various resources in teaching and learningMathematics. Students will be introduced to printed materials, teachingand learning aids, technology in Mathematics, Mathematics facilitiesand management of resources.

Kursus ini memberi peluang kepada pelajar untuk menerokai aplikasi pelbagai resos dalam pengajaran dan pembelajaran matematik.Pelajar akan diperkenalkan dengan bahan bercetak, alat bantu pengajaran dan pembelajaran, teknologi dalam Matematik,kemudahan-kemudahan Matematik dan pengurusan resos.

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Topic Content Hours

1 Printed materials

Bookso

text, referenceo Literature books

Integrating literature in teaching andlearning Mathematics

Journals and articles

6

2 Teaching and learning aidso Manipulative kits: geoboard, Dienes

blocks, Cuisenaire rods, Base ten blockso Nets and solids

o Measuring instrument : weighing scale

o Computing tools: calculators, abacus, rods

& sticks

12

3 Technology in Mathematics

Hardwareo Computers, LCD

Software packageso Teaching packages

o Teaching software and courseware

Internet and online instructions

15

4 Mathematics Facilities Mathematics Laboratory Mathematics garden

Mathematics corners

6

5 Management of resources

Inventory and records

Monitoring and maintenance

Planning and budgeting

6

Total 45

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Main

References

Foresman, Scott (2000). Interactive mathematics: Lessons and tools.

NJ: Prentice Hall.Jennings, Sue and Dunne, Richard (2003). I see maths books. vol 1-3.UK: Mashford Colour Press.

National Curriculum Council. (1991). Prime calculators: Children andmathematics. UK: Simon and Schuster.


Burns, Marilyn (1992).About Teaching Mathematics. Maths Solution.

Haylock, D. (2003). Understandingmathematics in the lower primaryyears. UK: Paul Chapman.

Publication.

Trautman, Andria P. & Lichenberg, Betty K (2003). Mathematics: Agood beginning . 6th ed. UK: Wadsworth/ Thompson Inc.

Websides http://www.ulm.edu/~esmith/250/31/repbase10.htmlhttp://homepage.mac.com/efithian/Geometry/Activity-03.htmlhttp://mathforum.org/trscavo/geoboards/intro1.htmlhttp://en.wikipedia.org/wiki/Geoboardhttp://www.cuisenaire.co.uk/cuisenaire/products/history/algebra.htmhttp://www.teachingenglish.org.uk/think/resources/rods.s

htmlhttp://en.wikipedia.org/wiki/Cuisenaire_rodshttp://www.etacuisenaire.com/cuisenairerods/cuisenairerods.jsphttp://www.innovationslearning.co.uk/subjects/maths/activities/year3/number_deans/question.asphttp://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/assets/pdf/literacyy7/s4placevalue2.pdfhttp://www.arcytech.org/java/b10blocks/description.htmlhttp://www.mathsisfun.com

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http://www.ulm.edu/~esmith/250/31/repbase10.htmlhttp://homepage.mac.com/efithian/Geometry/Activity-03.htmlhttp://homepage.mac.com/efithian/Geometry/Activity-03.htmlhttp://mathforum.org/trscavo/geoboards/intro1.htmlhttp://en.wikipedia.org/wiki/Geoboardhttp://www.cuisenaire.co.uk/cuisenaire/products/history/algebra.htmhttp://www.cuisenaire.co.uk/cuisenaire/products/history/algebra.htmhttp://www.teachingenglish.org.uk/think/resources/rods.shtmlhttp://www.teachingenglish.org.uk/think/resources/rods.shtmlhttp://en.wikipedia.org/wiki/Cuisenaire_rodshttp://www.etacuisenaire.com/cuisenairerods/cuisenairerods.jsphttp://www.etacuisenaire.com/cuisenairerods/cuisenairerods.jsphttp://www.innovationslearning.co.uk/subjects/maths/activities/year3/number_deans/question.asphttp://www.innovationslearning.co.uk/subjects/maths/activities/year3/number_deans/question.asphttp://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/assets/pdf/literacyy7/s4placevalue2.pdfhttp://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/assets/pdf/literacyy7/s4placevalue2.pdfhttp://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/assets/pdf/literacyy7/s4placevalue2.pdfhttp://www.arcytech.org/java/b10blocks/description.htmlhttp://www.mathsisfun.com/http://www.ulm.edu/~esmith/250/31/repbase10.htmlhttp://homepage.mac.com/efithian/Geometry/Activity-03.htmlhttp://homepage.mac.com/efithian/Geometry/Activity-03.htmlhttp://mathforum.org/trscavo/geoboards/intro1.htmlhttp://en.wikipedia.org/wiki/Geoboardhttp://www.cuisenaire.co.uk/cuisenaire/products/history/algebra.htmhttp://www.cuisenaire.co.uk/cuisenaire/products/history/algebra.htmhttp://www.teachingenglish.org.uk/think/resources/rods.shtmlhttp://www.teachingenglish.org.uk/think/resources/rods.shtmlhttp://en.wikipedia.org/wiki/Cuisenaire_rodshttp://www.etacuisenaire.com/cuisenairerods/cuisenairerods.jsphttp://www.etacuisenaire.com/cuisenairerods/cuisenairerods.jsphttp://www.innovationslearning.co.uk/subjects/maths/activities/year3/number_deans/question.asphttp://www.innovationslearning.co.uk/subjects/maths/activities/year3/number_deans/question.asphttp://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/assets/pdf/literacyy7/s4placevalue2.pdfhttp://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/assets/pdf/literacyy7/s4placevalue2.pdfhttp://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/assets/pdf/literacyy7/s4placevalue2.pdfhttp://www.arcytech.org/java/b10blocks/description.htmlhttp://www.mathsisfun.com/


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Course Title Planning and Teaching Mathematics

(Perancangan dan Pengajaran Matematik)


Credit 3 (3+0)

ContactHours

45 hours

Language OfDelivery

English


Nil

Semester One/ Two

Learningoutcomes

1. Produce a well- organized Mathematics lesson plan with correctformat

2. Select the appropriate method and technique in carrying outteaching and learning mathematics

3. Apply the relevant mathematical learning theories and ideasthroughout the lesson

Synopsis This course will provide an opportunity for students to begin planning

an effective Mathematics lesson. Students are taught and guided toincorporate appropriate methods and techniques in their planning,using relevant Mathematical ideas. In addition, applications ofMathematics learning theories are highlighted in the teaching andlearning of Mathematics.

Kursus ini memberi peluang kepada pelajar untuk merancang suatupelajaran Matematik yang efektif. Pelajar diajar dan dibimbing untukmenggunakan kaedah dan teknik yang sesuai dalam perancangandengan menggunakan idea Matematik yang relevan. Selain itu,aplikasi teori pembelajaran Matematik diberikan perhatian dalampengajaran dan pembelajaran Matematik.

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Topic Content Hours

1 Planning Mathematics Lessons

Revisit Primary Mathematics

Curriculum Preparing Scheme of Work

o yearly/term, weekly and daily lesson

plano format : its components

o guidelines

Classroom management andcommunication

Micro and macro teaching

9

2 Mathematics Teaching Methods and Techniques Induction and deduction

Discovery and investigation Questioning and discussion Practical work Expository Laboratory Demonstration Cooperative and collaborative learning Student centered, teacher centered, media

centered approach

12

3 Learning mathematics Behaviourism

Cognitive and constructivist Humanistic approach

9

4 Mathematical knowledge of teaching Factual information Concept Algorithm

Doing mathematics

6

5 Enhancing learning mathematics Learning styles and individualdifferences Social context of teaching and learningmathematics Creative arts in mathematics

o stories, poems, music and dramas

Recreation mathematics Project based learning

9

Total 45

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MainReferences

Hollands, Roy (1987). The development of mathematical skills. UK:Blackwell.

Mooney, Claire et.al. (2002). Primary mathematics :Theory andpractice. UK: Learning Matters.

Post, Thomas R. (1992). Teaching mathematics in grades K-8:Research-based methods. UK: Allyn and Bacon.


Cohen, Alan Louis (1987). Early education : The school years. Asource book for teachers. USA: P.C.P Education series.

Hopkins, Christine.(1999). Mathematics in the primary school. USA:David Fullton.

Rays, Robert E. et. all (2001). Helping children learn mathematics.NY: John Wiley and Sons Inc.

Wall, W. D (1975). Constructive education for children. London: TheUnesco Press.

Freiberg & Driscoll (2005). Universal teaching strategies. 4th ed.USA:Pearson.

Bobis, J. (2004). Mathematics for Children: Challenging Children ToThink Mathematically(2nd Ed). Australia: Pearson.

Kennedy, L. M. at. al(2004) .Guiding Childrens learning ofMathematics(10th ed). USA: Thomson.

Bottle, G. (2005).Teaching Mathematics in The Primary School.

London: Continuum.

Lang, H. R. & Evans, D. N. (2006) Models, Strategies and Methods forEffective Teaching. USA: Pearson.

Sgroi, L. S. (2001).Teaching Elementary and Middle Schoolmathematics - Raising the Standards. USA: Wadsworth/ThomsonLearning

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Course Title Basic Calculus

(Kalkulus Asas)


Credit 3(3+0)

ContactHours

45 hours

Language OfDelivery

English


Nil

Semester One/ Two

Learningoutcomes

1. Differentiate between functions and non- functions

2. Sketch graphs of elementary functions manually and/or usinggraphing calculator

3. Determine the inverse of a function

4. Recognise patterns and relationships

5. Find the first and second derivatives of functions

6. Apply the concepts of derivatives and integrals in problem

solving

Synopsis This course focuses on the key concepts of Calculus which includesfunctions and graphs, basic understanding of limits and limittheorem, derivatives and integrals, and patterns and relationships. Atthis point, students are able to find the first and second derivatives offunctions and minimum and maximum points of graphs. Theapplications and use of technology is also emphasized throughgraphing calculator and software such as Geometers Sketchpad tosketch and interpret the graphs of functions.

Kursus ini memfokuskan kepada konsep utama dalam Kalkulus;

fungsi dan graf, kefahaman asas mengenai had dan teorem had,derivatif dan integral serta pola dan perhubungan. Pelajar bolehmencari derivatif pertama dan kedua bagi fungsi serta titik minimumdan maksimum bagi graf. Penggunaan dan aplikasi teknologidijelaskan melalui kalkulator grafik dan perisian seperti GeometerSketchpad untuk melakar dan membuat interpretasi graf fungsi.

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Topic Content Hours

1 Functions and graphs

Patterns and relationships

Use of variables to express relationships Pattern recognition

Concepts of functionso Composition of functions

Domain and range

Inverse of functions

Graph sketchingo by hand

o graphing calculator

o GSP

9

2 Limits and continuity

Definition of limits

Properties and theorems of limit

One-sided and two-sided limits

Concepts of continuity

Properties and theorems of continuousfunction

12

3 Derivatives

Definition: Slope of a tangent to a curve at apoint

Definition of a differentiable function at a

point First derivatives

The first principle

Formula

Second derivatives

Applications of derivatives

12

4 Integrals

The concept of anti-derivatives

Indefinite and definite integrals

Applications of integrals

12

Total 45


MainReferences

Bittinger, M. L. (2004). Calculus and its applications. 8th ed. Boston:Pearson/Addison-Wesley.

Clements, C., Pantozzi, R. & Steketee, S. (2002). Exploring calculuswith the Geometers Sketchpad. Emeryville, CA: Key CurriculumPress.

Finney.et.al. (2000). Calculus : A Complete Course. 2nd

ed. USA:Addison Wesley.

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Barnet et.al. (2000). Precalculus: A graphing approach. NY:Mc GrawHill.

Berlinski, D. (1995).A tour of the calculus. New York: Pantheon Books.

Brodie, Ross (2002).. New Mathematics IIB. USA: Thomson & Nelson.

De Temple, D., & Robertson, J. (1991). The CALC handbook:Conceptual activities for learning the calculus. Palo Alto, CA: DaleSeymour Publications.

Foerster, P. A. (1998). Calculus concepts and applications.Emeryville, CA: Key Curriculum Press.

Key, Stewart. J. (2005). Single variable calculus: Concepts andcontexts. Belmont, CA: Thomson Higher Education.

___ _____ (2001).The Geometers sketchpad: Dynamic geometrysoftware for exploring mathematics. Version 4.[Computer software]

Emeryville, CA: Key Curriculum Press.

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Course Title Teaching Of Numbers, Fractions, Decimals and Percentages

(Mengajar Nombor, Pecahan, Perpuluhan dan Peratus)


Credit 3(2+1)

ContactHours

60 hours

Language OfDelivery

English


Nil

Semester One/ Two

Learningoutcomes

1. Relate the mathematical learning theories into the childrensframework of learning numbers

2. Study the development of childrens understanding in mathematics

3. Reinforce childrens mathematical concepts in numbers, fractions,decimals and percentages through various activities

4. Plan effective teaching lessons incorporating appropriateresources, approaches and strategies

Synopsis This course exposes to the students that children learn mathematicsby constructing their own ideas at different levels and stages.Discussions cover topics related to teaching of numbers, fractions,decimals and percentages, also construction of teaching aids, microand macro teaching sessions.

Kursus ini memberi pendedahan kepada pelajar bahawa kanak-kanakbelajar matematik dengan membina idea sendiri pada aras dan peringkat yang berbeza. Perbincangan meliputi perkara berkaitandengan mengajar nombor, pecahan, perpuluhan dan peratus sertamembina alat bantu mengajar, sesi pengajaran mikro dan makro.

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Topic Content Hours

Theory

1Numbers

Whole numberso Early number developmento Numbers sense

o Counting

o The role of algorithms

o Place value representation of numbers

Number operations and basic factso Addition and subtraction

o Multiplication and division

Operation sense and computationso Calculators and abacus

o Mental computations

o Computational estimation Key issues in teaching whole numbers

15

2 Fractions, decimals and percentages

Fractionso Meaning of fractions and equivalent

o Mixed number and improper fraction

o Fractions operations

Decimalso Common fractions and decimals :relationship

and conversion

o Place value, ordering and roundingo Decimal operations

Percentageso Percentage

Key issues in teaching fractions, decimals andpercentages

15

Sub Total 30

Practical

1Construction of teaching aids

Numbers

Fractions, decimals and percentages

15

2 Micro/macro teaching

Preparing an effective lesson plan

Carry out micro/macro teaching

15

Sub Total 30

Total 60

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Assessment Coursework 60%Examination 40 %

MainReferences

Howett , Jerry (2000). Numbers Power: A real world approach to maths.USA: Contemporary Books.

Kennedy, Leonard M. and Tipps, Steve (2000). Guiding childrenslearningmathematics. USA: Wadsworth Thomson Learning.

Tucher, Benny F. et.al. (2002). Teaching mathematics to allchildren:designing and adapting instruction to meet the needs of diverselearners. USA: Prentice Hall.


Afonso, Fiona et.al. (2002). Maths for WA : Homework and books. UK:Longman.

Bobis, J, Mulligan. J. Lowrie, T., & Taplin, M. (2004). Mathematics forchildren: Challenging children to think mathematically. 2nd ed. Sydney:

Prentice Hall.

Booker, G,, Bond, D., L., & Swan, P. (2004). Teaching primarymathematics. 3rd ed. Sydney: Pearson Education Australia.

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Course Title Linear Algebra

(Aljabar Linear)


Credit 3(3+0)

ContactHours

45 hours

Language OfDelivery

English


Nil

Semester One/ Two

LearningOutcomes

1. Find the determinant and inverse of a matrix

2. Calculate the length of a vector, the dot product and angle betweentwo vectors

3. Determine a given vector as a subspace or independent vector

4. Apply concepts of linear equations and linear inequalities to solverelated problems

5. Integrate knowledge of matrix algebra and vector space in daily

applications

Synopsis This course provides students with the knowledge of linear equationsand inequalities, matrix algebra and vector space. The idea isextended to using Elimination, Substitution, Gauss-Jordan Method andCramer Rule in solving linear systems. In addition, students are taughtto find the inverse of a singular matrix using the adjoint method orelementary row operations. Concepts of vector space in R2and R3 arealso discussed.

Kursus ini membekalkan pelajar dengan pengetahuan tentangpersamaan dan ketaksamaan linear, aljabar matriks dan ruang vektor.Idea ini dilanjutkan kepada Kaedah Penghapusan, Penggantian, danGauss-Jordan serta Hukum Cramer dalam penyelesaian sistem linear.Selain itu, pelajar diajar mencari songsang matriks dengan kaedahadjoin atau operasi baris elementari. Konsep ruang vektor dalam R2

dan R3 juga dibincangkan.

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Topic Content Hours

1 System of Linear Equations and Inequalities

Solving linear equationso

Elimination Methodo Substitution Method

o Gauss-Jordan method

Linear Inequalities and Linear Programmingo Homogeneous systems

o Applications of Linear Equations and

Inequalities

15

2 Matrix Algebra

Matrix arithmetic

Systems of linear equations( up to 4 unknowns)o Elementary row operationso Determinant and its properties

The Cramers rule

Singular and non-singular matrix

Inverse of a matrixo Adjoint method

o Elementary row operations method

10

3 Vector Space

Vectors in Plane R2

o Introduction to vectors

o Vector Operationso Properties of Vector Operations

o Length of vector

o Dot product

o Angle between two vectors

Vectors in Space R3

o General vector space

o Subspace

o Linear independence

o Basis, dimension and rank

Applications of vector space in daily life

20

Total 45

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Main References Dugopolski . (2002). Precalculus: Functions and graphs. USA :Addison and Wesley.

Howard, A. & Rorres, C. (2000). Elementary linear algebra:Applications version . 8th ed. NY: John Wiley.

Stewart, J. et.al. (2001).Algebra and Trigonometry. USA : Thompsonand Learning.


Goodman , Arthur and Hirsch, Lewis. (2000). Precalculus:Understanding functions. Pacific Grove, CA:Brooks/Cole PublishingCompany.

Herstein, I.N. (1975). Topics in algebra. 2nd ed. Lexington, MA: XeroxCollege Publishing.

ONan, M. & Enderton,H.B.(1990). Linear algebra. 3rd ed. NY:Harcourt Brace Jovanovich.

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Course Title Teaching of Geometry, Measurement and Data Handling

(Mengajar Geometri, Pengukuran dan Pengendalian Data)


Credit 3(2+1)

ContactHours

60 hours

Language OfDelivery

English


Nil

Semester One/ Two

LearningOutcomes

1. Demonstrate an understanding of current primary practice relatedto teaching of geometry, measurement and data handling

2. Plan for progression in the teaching of geometry, measurementgraphs and data handling effectively

3. Reflect on classroom practice in these areas

4. Apply the knowledge gained in real life situations whereappropriate

Synopsis In this course, students will learn the key concepts in geometry,measurement and data handling. They will be introduced to a range ofrelated teaching and learning strategies, effective planning andteaching, the use of technology, micro and macro teaching sessions.

Dalam kursus ini, pelajar akan belajar konsep utama geometri, pengukuran dan pengendalian data. Pelajar akan diperkenalkandengan strategi pengajaran dan pembelajaran, perancanganpengajaran efektif, penggunaan teknologi, sesi pengajaran mikro danmakro.

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Topic Content Hours

1 Geometry

2D Shapeso

Vocabulary, properties andcharacteristics:Triangle, quadrilateral,polygon, circle

o Classification of 2D shapes

o Key issues in teaching 2D shapes

3D Shapeso Vocabulary, properties and

characteristics: cube, cuboid, cones,pyramid, cylinder, sphere

o Classification of 3D shapes

o Nets of 3D shapes

o Key issues in teaching 3D shapes

Applications of geometry in real lifeo 2D: shape and space (plane

geometry)o 3D: volume (three dimensional)

o Use of technology in geometry

10

2 Measurement

Lengtho Standard and non-standard units

o Conversion of units

o Area and Perimeter

Liquid capacity and volumeo Standard and non-standard units


o Volume of fluids

Mass and weighto Standard and non-standard units


Timeo Hour system

Key issues in teaching measurement

Applications of measurement in real life

14

3 Data handling

Data manipulationo Collecting data

o Displaying data

o Interpreting data

Averageo Deriving formula

o Use formula to calculate

Key issues in teaching graphs and average

6

Sub Total 30

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1Practical2-D and 3-D shapes

Construct geometrical shapes

Analyse the properties of the geometricalshapes

Classify the geometrical shapes

10

2 Data handling

Collect data on the followingo Length

o Liquid capacity and volume

o Mass and weight

o Time

Display and interpret data in graphical formusing appropriate technology

Oral presentation

10

3 Micro/macro teaching

Prepare effective lesson plan

Carry out micro/macro teaching

10

Sub Total 30

Total 60


MainReferences

Askew, M. (1998). Teaching primary Mathematics. London: HodderArnold.

Cathcart, W.G., Pothier,Y.M., Vance, J.H. & Bezuk, N.S. (2006).Learning mathematics in elementary and middle school: A learnercentered approach. 4th ed. New Jersey: Pearson Education.

Haylock, D. (2006). Mathematics explained for primary teachers.London: Sage Inc.


Bennett, D. (1999). Exploring geometry with The GeometersSketchpad. Emeryville,CA: Key Curriculum Press.

Killen, R. (2005). Effective teaching strategies: Lessons from research

and practice. 5th ed. Wentworth Falls: Social Science Press.

Rowntree, D. (2004). Statistics without tears: A primer for nonmathematicians. Boston, MA: Pearson Education.

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Course Title Assessment Practices in Mathematics(Amalan Pentaksiran dalam Matematik)


Credit 3(3+0)

ContactHours

45 hours

Language Of

Delivery

English


Nil

Semester One/ Two

Learningoutcomes

1. Identify pupils ability, difficulty, misconception and learning needsin mathematics

2. Plan suitable activities for remedial, enrichment and special needspupils when applicable

3. Apply acquired knowledge in planning and implementing

assessment4. Integrate the applications of technology in assessment

Synopsis Students will be exposed to the skills of carrying out testing andevaluation. The topics discussed are testing and evaluation,mathematical difficulties and diagnostic test, special needs inMathematics education and applications of technology in assessment.

Pelajar akan didedahkan tentang kemahiran menjalankan pengujiandan penilaian. Topik-topik yang turut dibincangkan ialah mengenaipengujian dan penilaian, kesukaran Matematik dan ujian diagnostik,

keperluan khas dalam pendidikan matematik dan aplikasi teknologidalam pentaksiran.

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Topic Content Hours

1 Testing and Evaluation

Definition

Assessment Designo Principles of item construction

o Solo / Bloom Taxonomy

o Curriculum specification and Planning

of test (test blue print) School based and classroom assessment

o Formative and summative

o Formal and informal evaluation

o Alternative assessment

Interpretation of assessmento Item analysis and interpretation of

items

(difficulty and discrimination index)o Evaluation of reports and reporting

o Monitoring

recording progress and monitoring ofstudents achievement

Assessment administrationo Test administration

o Test moderation and marking scheme

o Test reliability and validity

o Bank items

15

2 Mathematical Difficulties and Diagnostic test Diagnostic testo standard IQ test,

o school based test

o classroom test

Diagnostic assessment and administrationo principles of item construction

o implementation and administration

o analysis of results

Misconception and Mathematical Difficultieso Misconception

o Newman Error Analysis reading

comprehension

transformation skills

process Skills

encode

carelessness

motivation

15

3 Special needs in Mathematics Education

Effective teaching skills for special needso

exhibit a range of creative andeffective teaching for special needs

10

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o learning strategies for special

educationneeds

Enrichment activities

Remedial activities

Other types of learning disabilitieso Dyslexia

o Dyspraxia

o Dyscalculia

o Dysphasia

4 Applications of technology in assessment ICT in assessment Item construction(software e.g. Hot potatoes, J-Quizzes) Item analysis (Quest-2, Excel)

5

Total 45


MainReferences

Clemson, D. & Clemson, W. (1995). Maths assessments. UK: StanleyThomas Publishers Ltd.

Hopkins, Christine (1999). Mathematics in the Primary school. UK:David Fullton.

Yudariah Mohamad Yusof et.al. (2005). Diagnostik & pemulihan:Kesalahan lazim bagi beberapa tajuk matematik sekolah menengah.Malaysia: UTM Skudai.


Kementerian Pendidikan Malaysia (1993). Buku panduan pengayaandalam KBSR/matematik. KL: Pusat Perkembangan Kurikulum.

Kementerian Pendidikan Malaysia (1993). Buku panduan pemulihandalam KBSR/matematik. KL: Pusat Perkembangan Kurikulum.

Troutman, A.P. and Lichtenberg, B.K. (2003). Mathematics a goodBeginning. 6th ed. Wadsworth/Thompson Inc.

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Course TitleAction Research I Primary Mathematics (Methodology)

(Penyelidikan Tindakan I Matematik Sekolah Rendah (Kaedah)

Course Code MTE3113

Credit 3 (3+0)

Contact Hours 45 hours

Medium ofInstruction English

Pre-requisite toentry

None

Semester One/Two

Learning Outcomes

1. Describe the educational research methods and their usein education.

2. Explain the basic of research including types ofeducational research, research designs, procedure and ethics.

3. Analyse and discuss current issues in education that can

be investigated through action research.4. Discuss what is action research and its process.5. Acquire the skills of planning and implementing an action

research in school.

6. Acquire the skills of writing an action research proposal,report and journal article.

Synopsis This course provides knowledge about the various researchmethods in education and the basic of educational research. It willalso explore ways of acquiring the skills of planning an action

research, implementing the research, analysing and interpretingthe research data, and documenting the action research findings ina report or article.

Kursus ini memberi pengetahuan tentang pelbagai kaedah penyelidikan dalam pendidikan dan asas penyelidikan. Ia jugameneroka cara-cara memperolehi kemahiran merancang danmelaksana satu kajian tindakan, menganalisis danmenginterpretasi data penyelidikan, dan kaedah mendokumentasihasil penyelidikan tindakan dalam bentuk laporan atau kertas kerjakajian.

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Topic Content Hours

1 An Introduction to research methods in education

The aims of educational research

The characteristics of educational research

Approaches in educational researchThe positivist approach (quantitative)The interpretive approach (qualitative)

Ethics of educational research

- The important aspects of research ethics- Ethical codes

3

2 Types of educational researchBasic researchApplied researchAction researchEvaluation research

Introduction to various types of education researchdesign

Quantitative researchExperimentalQuasi-experimentalSurveyCorrelational

Qualitative researchEthnographyCase studyHistorical

3

3 Educational research procedure

Choosing a research problem Determining the research objective Determining the research questions Determining the research hypotheses Reviewing the literature Planning the research design Determining the sampling procedure Constructing the research instrument Constructing the validity and reliability of the

instrument

Determining the data collection procedure

Collecting data Analysing and interpreting the data

3

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Reporting the results and findings

4 Action research

Definition and concept The characteristics of action research

The importance of action research Issues related to action research

Models of action research- Stephen Kemmiss model- John Elliotts model- Dave Ebbutts model- Jack Whiteheads model- Jean Mcniffs model- Kurt Lewins model

3

5 Action research: The process

Adapted from the models of Lewin, 1946 andLaidlaw,1992:

Identifying an aspect of the educational practice toimprove

Planning an action Implementing the action Collecting the data Reflecting on the action (before, during and after

the action)

Taking further actionDeveloping the second cycle of action research

3

6 Action research: Planning and proposal

Context Focus / aspect of practice to improve Research questions Literature review Subjects of the study Action plan Implementation of action plan

Data collection methods Reflection: Data analysis and interpretation Work schedule Budget Sources of reference

3

7 Action research: Data collection methods

Observation: : observer, participant-observer,participant

Document analysis checklists

Interview: structured, semi-structured, unstructured

3

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8 Action research: Data collection methods

Questionnaires Video and cassette recordings Logs

Field notes Photographs Portfolios Anecdotal records Slides Journals Diaries

3

9 Action research: Data collection considerations

Sampling, validity, reliability, bias

Sampling and bias Validity:

- External critics (originality of thedata)

- Internal critics (accuracy of thedata)

- Data triangulation

Reliability- The generalisability of findings Ethics

3

10 Action research: data analysis

Qualitative data

Content analysis Categorising the data Coding the data Arranging the data into analysis grids Identifying the issues/assertions Further research activities

3

11 Action research :data analysis

Quantitative data Descriptive analysis: Frequency, percentage,mean, mod, median, standard deviation,correlation coefficient

3

12 Interpreting the action research data

Integrating various sources of data Connecting the data with literature review Summarising the results and drawing conclusions

3

13 Writing an action research report

The context/background of the study Literature review

3

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Focus/ aspect of the practice to improve The action plan Implementation of action plan Data collection methods Data analysis and interpretation

Reflection and implications Plan for further action Citation of references :American Psychological

Association (APA)

14 Writing an action research article

Abstract The context Research focus Action plan

Implementation of action plan Data collection methods Data analysis and interpretation Reflection and implications The next step Bibliography

3

15 Ways of making action research data public

Seminars Publications

Action research networks

3


Main Reference Cohen, L. , Manion, L. & Morrison, K. (2001). Research Methodsin

Education (5th. Eds.). London: Routledge Falmer.

Creswell, J. W. (2005). Educational Research. Planning,Conducting, and Evaluating Quantitative And QualitativeResearch. Ohio: Prentice Hall.

AdditionalReference

Fraenkel, J.R. & Wallen, N.E.(1990). How to Design and EvaluateResearch in Education. USA, McGraw-Hill

Gillham, B. (2003). The Research Interview. London: Continuum.

Jones, J. (2005). Management Skills in School. London: PaulChapman Publishing.

Kembar, D. (2000).Action Learning and Action research. London:Kogan Page.

Mills, G. E. (2000).Action Research. A guide for the TeacherResearcher. Ohio: Prentice Hall.

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Macintyre, C. (2000). The Art of Action Research in the Classroom.

London: David Fulton Publishers Ltd.

Course Pro Forma

Program Ijazah Sarjana Muda Perguruan Dengan Kepujian(Matematik Pendidikan Rendah)

Course Title Applications of Mathematics(Aplikasi Matematik)


Credit 3(2+1)

ContactHours

60 hours

Language OfDelivery English


Nil

Semester One/ Two

Learningoutcomes

1.Explore the role of mathematics in modern technologies.

2. Investigate mathematics as an ongoing cultural activity

3. Demonstrate an understanding of the nature of mathematics

and its applications

4. Apply the various mathematical processes and problem solvingtechniques

Synopsis This course relates students to the earlier mathematics courses. Itscontents cover mathematics in every day life, classical codes andciphers, codes and cryptography, use of mathematical modeling inbiology and ecology, and some key mathematical ideas related tocalculus.

Kursus ini dikaitkan dengan kursus-kursus matematik yang sebelumini. Isi kandungannya meliputi matematik di dalam kehidupan harian,kod klasik dan nombor rahsia, kod dan kriptografi, penggunaan modelmatematik dalam biologi dan ekologi, serta sebahagian idea utamamatematik berkaitan dengan kalkulus.

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Topic Content Hours

1TheoryMathematics in every day life

Role of mathematics in modern technologies

Mathematics as an ongoing cultural activity

Bases for contemporary mathematics

4

2 Classical codes and ciphers

The development of classicalcodes and ciphers using the followingtechniqueso Transposition

o Substitution

4

3 Codes and cryptography

Error correcting codes:repetition codes, parity check codes,Hamming codes, Hadamard codesand the 1969 Mariner spacecraft

Linear codes: solution spacesfor systems of linear equations andtheir use in error correcting codes

Public-key cryptography,including the use of elementary

number theory to producecomputationally intractable systems ofcodes, the RSA algorithm

6

4 Use of mathematical modeling in biology andecology

Predator-prey models:separate and non-separategenerations, the logistic equation,interactions between species,simulations

The use of simple differentialequations in modeling safe andeffective drug dosages

Modeling the spread ofdiseases such as AIDS, bird flu etc

10

5 Some key mathematical ideas related to calculus

Archimedes approximation of

Archimedes determination ofthe area of a circle

Zenos paradox

Newtons investigation of cubiccurves

6

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Sub Total 30

1PracticalMathematics in everyday life

Investigate the followingo Role of mathematics in modern

technologies

o Mathematics as an ongoing culturalactivity

o Bases for contemporary

mathematics

Compile the findings

Submit a written report

10

2 Mathematical modeling

Conduct a mathematicalmodeling activity based on thefollowing stepso Specify a real problem

o Formulate a mathematicalmodelo Solve the mathematical

problemo Interpret the solution

o Compare with reality

o Communicate the results

Group presentation

Submit a written report

10

3 Some key mathematical ideas related to calculus

Group projecto Explore applications and relations of the

following

Archimedes approximation of

Archimedes determination ofthe area of a circle

Zenos paradox

Newtons investigation of cubiccurves

o Presentation of project

10

Sub Total 30

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Total 60


Main

References

Coutinho, S. C. (1999). The mathematics of ciphers: Number

theory and RSA Cryptography. Natick, MA: A. K. Peters.

Dym, C. L. (2004). Principles of mathematical modelling. 2nd ed.Boston: Elsevier Academic Press.

Haydock, R. (1991). Information and coding. UK: Cambridge.

Stacey, K. & Stillman, G. (2002). Modelling trends in numbers ofdeaths due to HIV/AIDS infection in USA and Australia. Melbourne:University of Melbourne, CAS-CAT Project.

Wilf, H. S. (1986). Algorithms and complexity. Englewood Cliffs, NJ:

Prentice-Hall.


Fazekas de St Groth, C., & Solomon, P. J. (1990). Short-termprediction of the AIDS epidemic using empirical models. In P. J.Solomon, C. Fazekas de St Groth, & S. R. Wilson (Eds.),

Projections of acquired immune deficiency syndrome in Australiausing data to the end of September 1989 (Working Paper No. 16,pp. 11-17). Canberra, ACT: Australian National University,National Centre for Epidemiology and Population Health.

Full Singh, S. (2002). The cracking codebook: How to make it, break it,

hack it, crack it. London: Harper Collins.

Hellman, M. E. (1979). The mathematics of public-keycryptography. Scientific American, 241(8), 146157.

Humphreys, J. F., & Prest, M. Y. (2004). Numbers, groups andcodes. 2nd ed. Cambridge: Cambridge University Press.

Jackson, M. B., & Ramsey, J. R. (1993). Problems for studentinvestigation. MAA Notes. Volume 30. Washington: MathematicalAssociation of America.

Jackson, T. H. (1987). From number theory to secret codes. Bristol:IOP Publishing.

Malevitch, J., Froelich, G., & Froelich, D. (1991). Codes galore Module#18. Lexington, VA: Consortium for Mathematics and Its Applications(COMAP).

Maynard Smith, J. (1968). Mathematical ideas in biology. London:Cambridge University Press.

Posamentier, A. A., & Lehmann, I. (2004). : A biography of the

world's most mysterious number, Amherst, NY: Prometheus Books.

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Trappe, W., & Washington, L. C. (2006). Introduction to cryptographywith coding theory. 2nd ed. Upper Saddle River, NJ: Pearson PrenticeHall.

Welsh, D. J. A., (1988). Codes and cryptography. Oxford: Oxford

University Press.

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Course Pro Forma

Program Ijazah Sarjana Muda Perguruan Dengan Kepujian(Matematik Pendidikan Rendah)

Course Title Action Research II Primary Mathematics (Implementation andReporting)[Penyelidikan Tindakan II Matematik Pendidikan Rendah(Implementasi dan Pelaporan)]

Course Code MTE3115

Credit 3 (0+3)

Contact Hours 90 hours

Medium of Instruction English

Pre-requisite to entry None

Semester One/Two

Learning Outcomes 1. Implement an action research in a school.

2. Write an action research report based on the research

data collected.

3. Organise an action research seminar.

4. Present an action research paper in the seminar.

5. Document and publish the action research paper in a

journal.

Synopsis This course involves skills of carrying out an action research in a

school. It will also provide opportunities for students to organise an

action research seminar and to present their action research findings

during the seminar. The students will also apply their skills on how to

document and publish their research papers in a journal.

Kursus ini melibatkan kemahiran melaksanakan penyelidikantindakan di sekolah. Ia juga akan memberi peluang kepada pelajarmengorganisasi satu seminar penyelidikan tindakan dan

membentang kertas penyelidikan tindakan dalam seminar itu. Pelajarjuga akan menggunakan kemahiran mereka untuk mendokumentasidan menerbit kertas penyelidikan dalam jurnal.

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Topic ContentHours

1 Implement an action research in school and write a draftreport

The context/background of the study Literature review

Focus of the study / identify the aspect of thepractice to improve

The action plan

6


Implementation of action plan

Data collection methods

6


Analysis of data

Interpretation of data

6


Drawing conclusion

Reflection and implications

6


Plan for further action Citation of references :American Psychological

Association (APA)

6

6 The final action research report

Read the draft report

Revise the draft

Edit the draft

Proof-read the draft

Final report

6

7 Organisation of action research seminar Theme of seminar

Working committee

Venue of seminar

Costing of seminar

Publicity

6

8 Organisation of action research seminar

Selection and editing of action research papers6

9 Organisation of action research seminar

Selection and editing of action research papers6

10 Organisation of action research seminar Planning of presentation of action research papers

6

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54/54

in the seminar

11 Action research seminar

Presentation of action research reports in theseminar

6

12 Action research seminar

Presentation of action research reports in theseminar

6

13 Documentation and publication procedure of actionresearch

Collect action research papers6


Edit the action research papers based onconstructive feedback from the seminar

6


Document findings of action research papers6

Jumlah 90

Assessment Course work 100%

Main Reference Fraenkel, J.R.; Wallen, N.E.(1990). How to Design and EvaluateResearch in Education. USA, McGraw-Hill

Jones, J. (2005). Management Skills in School. London: PaulChapman Publishing.

Additional Reference McNiff, J. (1995). Teaching as Learning: An Action ResearchApproach. London: Routledge.

Miles, M.B. and Huberman,A.M. (1994). Qualitative DataAnalysis. Second Edition, London: Sage Publications.

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