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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 Pro FormaProgram Ijazah Sarjana Muda Perguruan Dengan Kepujian
(Matematik Pendidikan Rendah)
Course Title Mathematics Education Curriculum
(Kurikulum Pendidikan Matematik)
Course Code MTE 3102
Credit 3(3+0)
ContactHours
45 hours
Language OfDelivery
English
Prerequisite ToEntry
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
6
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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
Assessment Coursework 50%Examination 50%
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.
AdditionalReferences
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 Pro FormaProgram Ijazah Sarjana Muda Perguruan Dengan Kepujian
(Matematik Pendidikan Rendah)
Course Title Geometry(Geometri)
Course Code MTE 3103
Credit 3(2+1)
ContactHours
60 hours
Language Of
Delivery
English
Prerequisite ToEntry
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
8
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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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Assessment Coursework 60%Examination 40%
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.
AdditionalReferences
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 Pro FormaProgram Ijazah Sarjana Muda Perguruan Dengan Kepujian
(Matematik Pendidikan Rendah)
Course Title Decision Mathematics
(Matematik Keputusan)
Course Code MTE 3104
Credit 3(3+0)
ContactHours
45 hours
Language OfDelivery
English
Prerequisite ToEntry
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
Assessment Coursework 50%Examination 50%
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 Pro FormaProgram Ijazah Sarjana Muda Perguruan Dengan Kepujian
(Matematik Pendidikan Rendah)
Course Title Statistics
(Statistik)
Course Code MTE 3105
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
Assessment Coursework 50%Examination 50%
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.
AdditionalReferences
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.
Smitters, G et. al ( 2000). Advanced Modular Mathematics Statistics 2.2rd ed UK. Harper Collins Publisher Ltd.
Smitters, G et. al ( 2000). Advanced Modular Mathematics Statistics 3.2rd ed UK. Harper Collins Publisher Ltd.
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Course Pro FormaProgram Ijazah Sarjana Muda Perguruan Dengan Kepujian
(Matematik Pendidikan Rendah)
Course Title Resources in Mathematics
(Resos dalam Matematik)
Course Code MTE 3106
Credit 3(3+0)
ContactHours
45 hours
Language OfDelivery
English
Prerequisite ToEntry
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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Assessment Coursework 50%Examination 50%
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.
AdditionalReferences
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/8/3/2019 proforma maths
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Course Pro FormaProgram Ijazah Sarjana Muda Perguruan Dengan Kepujian
(Matematik Pendidikan Rendah)
Course Title Planning and Teaching Mathematics
(Perancangan dan Pengajaran Matematik)
Course Code MTE 3107
Credit 3 (3+0)
ContactHours
45 hours
Language OfDelivery
English
Prerequisite toentry
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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Assessment Coursework 50%Examination 50%
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.
AdditionalReferences
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 Pro FormaProgram Ijazah Sarjana Muda Perguruan Dengan Kepujian
(Matematik Pendidikan Rendah)
Course Title Basic Calculus
(Kalkulus Asas)
Course Code MTE 3108
Credit 3(3+0)
ContactHours
45 hours
Language OfDelivery
English
Prerequisite toentry
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
Assessment Coursework 50%Examination 50%
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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AdditionalReferences
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 Pro FormaProgram Ijazah Sarjana Muda Perguruan Dengan Kepujian
(Matematik Pendidikan Rendah)
Course Title Teaching Of Numbers, Fractions, Decimals and Percentages
(Mengajar Nombor, Pecahan, Perpuluhan dan Peratus)
Course Code MTE 3109
Credit 3(2+1)
ContactHours
60 hours
Language OfDelivery
English
Prerequisite toentry
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.
AdditionalReferences
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 Pro FormaProgram Ijazah Sarjana Muda Perguruan Dengan Kepujian
(Matematik Pendidikan Rendah)
Course Title Linear Algebra
(Aljabar Linear)
Course Code MTE 3110
Credit 3(3+0)
ContactHours
45 hours
Language OfDelivery
English
Prerequisite ToEntry
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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Assessment Coursework 50%Examination 50%
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.
AdditionalReferences
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 Pro FormaProgram Ijazah Sarjana Muda Perguruan Dengan Kepujian
(Matematik Pendidikan Rendah)
Course Title Teaching of Geometry, Measurement and Data Handling
(Mengajar Geometri, Pengukuran dan Pengendalian Data)
Course Code MTE 3111
Credit 3(2+1)
ContactHours
60 hours
Language OfDelivery
English
Prerequisite ToEntry
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 Conversion of units
o Volume of fluids
Mass and weighto Standard and non-standard units
o Conversion of 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
Assessment Coursework 60%Examination 40 %
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.
AdditionalReferences
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 Pro FormaProgram Ijazah Sarjana Muda Perguruan Dengan Kepujian
(Matematik Pendidikan Rendah)
Course Title Assessment Practices in Mathematics(Amalan Pentaksiran dalam Matematik)
Course Code MTE 3112
Credit 3(3+0)
ContactHours
45 hours
Language Of
Delivery
English
Prerequisite toentry
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
Assessment Coursework 50%Examination 50%
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.
AdditionalReferences
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 Pro FormaProgram Ijazah Sarjana Muda Perguruan Dengan Kepujian
(Matematik Pendidikan Rendah)
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
Assessment Coursework 50%Examination 50%
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)
Course Code MTE 3114
Credit 3(2+1)
ContactHours
60 hours
Language OfDelivery English
Prerequisite toentry
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
Assessment Coursework 60%Examination 40 %
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.
AdditionalReferences
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
2 Implement an action research in school and write a draftreport
Implementation of action plan
Data collection methods
6
3 Implement an action research in school and write a draftreport
Analysis of data
Interpretation of data
6
4 Implement an action research in school and write a draftreport
Drawing conclusion
Reflection and implications
6
5 Implement an action research in school and write a draftreport
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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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
14 Documentation and publication procedure of actionresearch
Edit the action research papers based onconstructive feedback from the seminar
6
15 Documentation and publication procedure of actionresearch
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.