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COURSE TITLE: Diploma In Mathematics Education far Secondary Teachers'. INTRODUCTION: In the two-year diploma programme in mathematics far Secondary teachers', a candidate's grade in the examination was the average after marks obtained in mathematics content and mathematics methodology. In the three- year dip lama programme, the two. Components will stand independently. In other words, to. pass the examination candidates will be required to obtain a minimum pass mark of 40% in each camp anent (mathematics content and the mathematics teaching methodology) before the final examination grade is worked out. The two components have separate syllabuses; Part I is Mathematics Content and Part II is Mathematics methodology. Mathematics content will run from first year to third year, while the methodology component will be taught only in the second and third years. RATIONALE: The change of the duration from a two-year pragromme to a three-year pragromme is meant to produce better qualified mathematics teachers who will be able to teach mathematics effectively at bath basic and high school levels. The subject matter that was compressed in two years will now be stretched over a period of three years, with a vertical enrichment in calculus. PART I 1. SUBJECT TITLE: Mathematics Content 2. AIMS: To. enable students develop an in-depth and understanding af Mathematics up to. advanced level. 3. SPECIFIC OBJECTIVES: By the end of the programme students should be able to: Demonstrate mathematical skills of problem salving; Analyse and apply knowledge of Mathematics concepts appropriately; Recognise and apply appropriate mathematical procedures for a given situation; Formulate problems into. Mathematical terms and select and apply appropriate techniques of situation: Organise and present statistical data in graphical, diagrammatic and tabular farms; and apply statistical results of the situation of problems; Recognise and use spatial relationships in two or three dimensions. 4.0 TOPICS: YEAR ONE 1.0 Introduction to Set Theory 1.1 1.2 1.3 1.4 1.5 Definition and notation of sets Subsets; empty and universal sets Intersection and union sets Venn diagrams and Universal sets Sets of numbers (whole, natural, integers, rational, irrational, real and complex numbers) Binary operations, commutative, associative and distributive laws; closure property; identities and inverses of numbers. Identifies and uses De Morgan's laws in simple proofs Complement of a set Sets and logic Boolean algebra Find Cartesian products. Co-Ordinate Geometry 2.1 2.2 2.3 2.4 2.5 Rectangular co-ordinates Midpoint, distance between points. Gradient of a line Equation of a line Parallel and perpendicular lines ALGEBRA Indices, Surds and Logarithms 3.1 3.2 3.3 3.4 3.5 3.6 Laws of indices Rationalization of surds Logarithms of different bases Absolute values Exponential and logarithmic functions Exponential and logarithmic equations Fractions and Partial Fractions 3.7 Factors of expressions both linear and quadratic equation ) 3.8 Multiplication of algebraic expression and fractions 3.9 Long division and synthetic division.} . 3.10 Finding sum of partial fractions or expressing fractions as a sum of partial fractions. Equations and Inequalities 3.11 Linear equations and inequalities 3.12 Quadratic functions and equations; completing the square 3.13 Maximum and minimum .values of quadratic functions and their graphs 3.14 Graphs of linear and quadratic equations 3.15 Quadratic inequalities and inequalities involving absolute value. Theory of Quadratics and Polynomials ~o~ e.. 3.16 Nature of roots 3.17 Open and closed sentences· 3.18 Roots of quadratic equations and symmetrical functions; approximations to roots of equations, 3.19 Roots of polynomials 3.20 Equations involving surds and absolute values and fractional equations 3.21 Theorems of zeros of polynomials 3.22 Factors and remainder theorems. Relations and Functions 3.23 Relations 3.24 Mapping 3.25 Functions 3.26 Inverse functions ,,3.27 Composite functions 3.28 Graphs of y = axn , and sums of such functions; simple rational functions 4.0 Trigonometry 4.1 The radian measure and degree 4.2 Trigonometric ratios of acute and any angle: Sine, cosine, tangent, secant, cosecant, cotangent and their inverse functions. 4.3 Graphs of sine, cosine, tangent, secant, cosecant and cotangent: period of a function. . 4.4 Trigonometric functions 4.5 Sine and cosine rules 4.6 Area of parallelogram and triangle 4.7 Trigonometric equations 4.8 The standard functions 4.9 ex, sinh x, cosh x on R, their properties including basic identities. and graphs; inverse functions. 5.0 Permutations and Combinations 5.1 Arrangements 5.2 The factorial notation 5.3 Permutations 5.4 Combinations 5.5 Partitioning 6.0 Sequences and Series, Binomial Theorem 6.1 Definitions, sequences 6.2 Arithmetic and Geometric Progression 6.3 Arithmetic series 6.4 Geometric series 6.5 Infinite series 6.6 Sigma notation 6.7 Compound interest 6.8 Use of G.P. to recurring decimals 6.9 Pascal's triangle and binomial expansion. 7.0 Elementary Differential Calculus Introduction (review of functions) Limits and continuity The idea of derivatives and differentiation from the first principles Differentiation of powers of x such as ax, ax2+ bx + c, and the general function axn Derivatives of sums, differences, products, quotient and composite functions. Gradient of a line and a curve of a function Tangents and normals Derivatives of trigonometric functions. Derivatives of inverse trigonometric functions Derivatives of exponential functions and logarithm functions [with particular attention to ekx and In(kx)} Higher order derivatives YEAR TWO 8.0 Further Algebra 8. I Mathematical induction; 8.2 Binomial Theorem. 9.0 Further Complex Numbers 9.1 Definition of imaginary and complex numbers. 9.2 Basic operations on complex numbers - addition, subtraction, multiplication ant division. 9.3 Powers and roots of complex numbers (including cubic root of unit) 9.4 Arga d diagram 9.5 Mod1ulus and argument of a complex number 9.6 Polar and rectangular form of a complex number 9.7 De Moivre's theorem 9.8 Applications of partial fraction to complex number. 10.0 Matrices and Determinants (2,3 Dim) 10.1 Definition, notation and order of a matrix 10.2 Addition and subtraction of matrices 10.3 Multiplication of a matrix by a scalar 10.4 Multiplication of matrices 10.5 The double subscript notation 10.6 Some types of matrices: Zero, identity, triangular matrices; inverse and transpose of a matrix 10.7 Singular matrices, matrix up to 3 x 3 10.8 Elementary matrices and a method of finding k'. 10.9 A matrix as a product of elementary matrices 10.10 Determinant and inverse of matrix up to 3 x 3 (As the sum of all signed elementary products; evaluating by cofactor expansion and by row elementary operations); properties of determinants; the minor and cofactor of an element. 10.11 inverse of matrix up to 3 x 3; adjoint of a matrix. 10.12 Application of matrices to solve systems of linear equations (Including Cramer's rule). 11.0 Geometry of Linear Transformation From R2 To R2 11.1 Standard matrices of transformation geometry including trigonometry (Rotation, Reflection, Expansion, Compressions shears, Identity, transformation, Dilation and contractions). 11.2 Composition of transformations 11.3 Single matrix that indicates a succession of transformation. 11.4 Geometric effect of multiplication by a matrix. 11.5 Sketching images (single and succession of images). 12.0 Vectors and Analytic Geometry in 2-Space & 3-Space 12.1 Definition of a vector 12.2 Idea of a vector as a translation 12.3 Addition and subtraction of vectors 12.4 Position of vectors 12.5 Magnitude ofa vector 12.6 Multiplication of a vector by a scalar 12.7 The properties of vector operations 12.8 Parallel and equal vectors 12.9 Unit vectors 12.10 Properties of parallel lines and equal vectors 12.11 Dot product and its properties 12.12 The angle between two vectors 12.13 Cross product and its properties 12.14 Equation of a line 12.15 Plane co-ordinate system 12.16 The particular cases (x, y) and (r, 8), equations of plane curves, loci 12.17 The direction of vectors, direction angles and direction cosines 13.0 Analytic Geometry Inclination of a line Angle between the intersection of lines The distance between a point and a line Circles and equations Tangent to a circle Orthogonal circles Equations of parabola, ellipse and hyperbola 14.0 Further Differentiation Calculus 14.1 Applications of derivatives to gradient of plane curves 14.2 Stationary points (maxima and minima and inflection points) 14.3 Increasing and decreasing functions 14.4 Differentiation and curve sketching 14.5 Differentiation of the implicit functions 14.6 Curve linear motion 14.7 Differentials (approximate incremental) 14.8 Rate of change. 15.0 Integral Calculus 15.1 Differentiation and integration as inverse processes (the idea of an Anti derivative) 15.2 Notation and definition of integration of a function 15.3 Indefinite and definite integrals 15.4 Velocity and acceleration 15.5 Area under a curve 15.6 Velocity-time graphs 15.7 Integration by substitution 15.8 Integration by parts 15.9 Integration of rational function by partial fractions YEAR THREE 16.0 Further Trigonometry 16.1 The equation acos8 ± bsin8 = c 16.2 Trigonometric identities 16.3 Addition and subtraction formulae 16.4 Double and half angle formulae 16.4 Factor formulae 17.0 Further Integration 17.1 Integration of trigonometric functions. 17.2 Integration of exponential and logarithmic functions [with particular attention to ekx and In(kx)] 17.3 Integration by trigonometric functions 17.4 First order separable differential equations and applications 17.5 First order - Exact equations 19.0 Statistics 19.1 Frequency tables for ungrouped and grouped data 19.2 Bar charts, pictograms, pie-charts and histograms 19.3 Frequency polygons and line graphs 19.4 Mean and median from cumulative frequency curves 19.5 Quartiles from ungrouped data and frequency curves 19.6 Range, interquartile, semi-interquartile range from ungrouped data 19.7 Percentiles, variance and standard deviation 19.8 Normal and binomial distributions 19.9 Hypothesis testing 19.10 Scatter diagrams 19.11 Correlation and regression. 20.0 Probability 20.1 Experimental probabilities 20.2 Theoretical probabilities 20.3 Equally likely events 20.4 Mutually exclusive events 20.5 Compound events - independent and dependent (using multiplication rules), Bayes' theorem. 20.6 Tree diagrams 20.7 Expected frequency METHOD OF TEACHING Both Mathematics content and Mathematics methodology shall have 15 hours per week. Mathematics content shall have one-hour periods. The number of periods per week are as follows: Year Lecture Ftesearch/Study Tutorials Total 10 15 I 2 3 2 1 1 4 2 2 1 1 4 3 6. ASSESSMENT a) Continuous assessment Tests shall weigh 90% Assignments shall weigh 10% Two Promotion Examinations - At the end of each of the first two academic years, there shall be a promotion examination. The tests and assignments will contribute 7j to the year's grade and each promotion will contribute YJ of the year's grade. b) Final Examination: At the end of the third year, there shall be one summative final examination that will carry 100 marks. This will contribute 1/3 of final grade. c) Research Paper Research paper is also a separate entity worthy 100%. A student is free to write only one research paper in any of the courses that she/he is taking. Students shall be expected to carry out their research activities independently. 7. PRESCRIBED BOOKS Backhouse, J.K. and Houldsworth, S.P.T. (1996). Pure Mathematics 1 (New Edition), Harlow(U.K.): Longman. Backhouse, J.K. and Houldsworth, S.P.T. (1996). Pure Mathematics 2 (New Edition), Harlow(U.K.): Longman. Graham, D., Graham, C. and Whitecombe, A. (1995). A Level Mathematics, London: Letts Educational. 8. RECOMMENDED BOOKS Farlow SJ and Haggard G .M. (1990). Introduction to Calculus with Applications, New York: McGraw-Hill Publishing Company. Backhouse, J.K. and Houldsworth, S.P.T., Horril PJ. and Wood J.R. (1991). Essential Pure Mathematics, Harlow(U.K.): Longman. Anton, Howard (1991). Elementary Linear Algebra (Sixth Edition), New York: John Wiley & Sons, Inc. • Larson, R.E. and Hostetler, R.P. (1993). Pre-calculus (Third Edition), Toronto: D.C. Health & Company. N.B. Students are encouraged to use recent publications with relevant information. 9. STAFFING SINO NAME SEX QUALIFICATIONS . MBUMWAE B. ED, APe & Primary Teachers' 1 F PATRICIA N. Certificate 2 SHIPOLA JUSTIN K. M MED, DASE & BAED MALAMBO 4 M BAED PRIESTLY PART II 1. SUBJECT TITLE: Mathematics Methodology 2. AIM The aim of this course is to enable students acquire the necessary skills and knowledge to teach mathematics in secondary schools 3. OBJECTIVES At the end of this course the student should be able to: demonstrate an understanding of how children learn mathematics; appraise, choose and execute appropriate instructional strategies; demonstrate and impart mathematical skills of problem solving; identify and appraise the relationship between mathematics and other subjects in the schools curriculum; demonstrate skills in the improvisation and utilisation of mathematics materials; demonstrate skills in various assessment techniques; demonstrate managerial skills and organizational abilities. 4. TOPICS YEAR TWO I. Aims and objectives of teaching mathematics Nature of mathematics Teaching styles and methods; classroom teaching and approaches Questioning techniques Writing of instructional objectives - Apply Bloom's taxonomy Sequencing instructions Lesson planning, schemes and records of work weekly and term forecasts Classroom organisation and management; and roles of mathematics teacher Analysis of secondary mathematics syllabi 10. Teaching facts, skills, concepts and generalisation 1 1. School mathematics Use of teaching aids Use of Mathematics textbooks Preparation of resource materials, \ Learning theories - Brunner, Skemp, Piaget, Skinner, Dienes: concept formations Psychology of learning mathematics Assessment, evaluation and related issues Current views on examinations Problem solving General public perception about mathematics Administration of Mathematics Department and roles of the Head of Department Peer / Micro teaching YEAR THREE Some aspects of the History of Mathematics Modern trends in the development of Mathematics and Mathematics Education Mixed ability teaching - slow and fast learners Gender issues ~n Mathematics Education ',I Clubs and projects - encourage students to produce work unrelated to the syllabus work, but of mathematics nature. Use of calculators and computers in our schools. Departmental library and Mathematics laboratory Peer / Micro teaching (a continuation from Year 2) School Based Teaching Practice Review of School Teaching Practice 5. Methods of teaching Year Lectures Research/Study 2 3 2 2 5 5 Peer/Micro Teaching 4 4 Total 11 11 6. ASSESSMENT 6.1 Continuous Assessment Assignments 50% Tests 30% Peer/Micro teaching 20% Total 100% 6.2 Examination 100% Grading Continuous Assessment 50% Examinations 50% Total 100% 6.3 Teaching Practice Teaching Practice Observations 60% Teaching Practice File 40% 100% 7. PRESCRIBED BOOKS Klkir, Singh Sidhu (1995). The Teaching of Mathematics, (Fourth Edition), New Delhi India: Sterling Publishers Pvt Ltd. Macnab, D. S and Cummine, l.A. (1998). Teaching Mathematics 11-16, Oxford (Great Britain) : Blackwell Ltd. • Orton,A and Wain G. (1994).Issues in Teaching Mathematics, London: CASSEL < (ISBN 0-304-32680- I) 8. RECOMMENDED BOOKS Kalejaiye, Adedoton (1985). Teaching Primary Mathematics, Ibadan (Nigeria): Longman Group Ltd. Marjoram, D.T.E. (1974). Teaching Mathematics, London: Heinemann Educational Ltd. Pimm, David (Editor), (1988). Mathematics, Teachers' and Children, Kent (Great Britain): The Open University. • Capel Susan, Leask Marilyn and Tony Turner (Editors), (2001). Learning to Teach in the Secondary School (Third Edition), Routledge. • Tanner Howard, lones Sonia and Davies Alyson (2002). Developing Numeracy in Secondary Schools, London: David Fulton Publishers. N.B. Students are encouraged to use recent publications with relevant information.