Download Mathematics_Syllabus_3_year

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.