Presented by: MA HENDRICKS USAF CoP : Teaching and Learning of Mathematics “Technical Mathematics” UNISA (Pretoria) Bamboo Auditorium 19 February 2019 Presented by: MA HENDRICKS

CAPS ( Curriculum and Assessment Policy Statement) Comparison of the Aims , Structure , Content and Assessment of the Papers for Technical Mathematics & Mathematics CAPS ( Curriculum and Assessment Policy Statement)

TECHNICAL MATHEMATICS CAPS DEFINITIONS TECHNICAL MATHEMATICS MATHEMATICS Mathematics is a LANGUAGE that makes use of symbols and notations describing numerical , geometric and graphical representations.

TECHNICAL MATHEMATICS CAPS DEFINITIONS MATHEMATICS TECHNICAL MATHEMATICS It is a HUMAN ACTIVITY that involves observing, representing and investigating patterns and qualitative relationships in physical and social phenomena and between mathematical objects themselves

TECHNICAL MATHEMATICS CAPS DEFINITIONS MATHEMATICS TECHNICAL MATHEMATICS It helps to DEVELOP MENTAL PROCESSES that enhance logical and critical thinking , accuracy and problem solving that will contribute in decision making.

TECHNICAL MATHEMATICS. CAPS DEFINITIONS MATHEMATICS TECHNICAL MATHEMATICS. Mathematical problem solving enables us to understand the world (physical, social and economic) around us , and, most of all to teach us to think creatively.

TECHNICAL MATHEMATICS CAPS DEFINITIONS MATHEMATICS TECHNICAL MATHEMATICS The aim of Technical Mathematics is to APPLY the Science of Mathematics to the TECHNICAL FIELD where the emphasis is on APPLICATION and not on abstract ideas.

SPECIFIC AIMS DIFFERENCES TECHNICAL MATHEMATICS. To provide the opportunity to develop in learners the ability to be methodical , to generalize , make conjectures and try to justify or prove them.. To provide the opportunity to develop in learners the ability to be methodical , to generalize and to be skillful users of the Science of Mathematics

SPECIFIC AIMS (DIFFERENCES) TECHNICAL MATHEMATICS To provide learners of Technical Schools an alternative and value adding substitute to Mathematical Literacy. To support and sustain technical subjects at Technical Schools

SPECIFIC AIMS (DIFFERENCES) TECHNICAL MATHEMATICS To provide a vocational route aligned with the expectations of labour in order to ensure direct access to learnership/ apprenticeship. To create the opportunity for learners to further their studies at FET Colleges at an entrance level of N4 and thus creating an alternative route to access other HEI’s.

OVERVIEW ASSESSMENT COMMON STRUCTURE PAPER 1 SIMILAR CONTENT PAPER 2 DIFFERENCES ASSESSMENT

STRUCTURE OF THE TWO PAPERS TECHNICAL MATHEMATICS Paper 1 1 Number Systems 2 Algebra 3 Functions & Graphs 4 Finance 5 Differential Calculus & Integration MATHEMATICS Paper 1 1 Algebra 2 Patterns & Sequences 3 Finance 4 Functions & Graphs 5 Differential Calculus 6 Probability & Counting Principle

STRUCTURE OF THE TWO PAPERS TECHNICAL MATHEMATICS Paper 2 1 Analytical Geometry 2 Trigonometry 3 Euclidean Geometry 4 Mensuration 5 Circles, Angles & Angular movement MATHEMATICS Paper 2 1 Statistics 2 Analytical Geometry 3 Trigonometry 4 Euclidean Geometry

STRUCTURE OF THE TWO PAPERS COMMON PAPER 2 PAPER 1 FOUR Topics ALGEBRA FUNCTIONS FINANCE DIFFERENTIAL CALCULUS THREE Topics ANALYTICAL GEOMETRY TRIGONOMETRY EUCLIDEAN GEOMETRY

DIFFERENCES Mathematics Mathematics STRUCTURE OF THE TWO PAPERS Technical Mathematics OTHER NUMBER SYSTEMS - Binary numbers - Complex Numbers INTEGRATION Technical Mathematics CIRCLE (SECTORS /SEGMENTS) RADIAN MEASURE ANGULAR MOVEMENT Mathematics NUMBER PATTERNS PROBABILITY Mathematics STATISTICS

CONTENT OF THE TWO PAPERS Technical Mathematics & Mathematics SIMILAR PAPER 1 ALGEBRA Topics Technical Mathematics & Mathematics 1 Linear Equations and Inequalities 2 Quadratic Equations and Inequalities 3 Simultaneous equations 4 Exponents/ Surds / exponential Equations 5 Logarithms to solve simple exponential equations 6 Remainder & Factor Theorem 7 Nature of roots of quadratic equations

CONTENT OF THE TWO PAPERS Technical Mathematics Additional Content DIFFERENCES PAPER 1 ALGEBRA topics Technical Mathematics Additional Content 1 Binary Number system 2 Complex Numbers 3 Equations involving complex numbers 4 Logarithmic equations 5 Scientific Notation 6 Real Life applications from Technical Field

CONTENT OF THE TWO PAPERS SIMILAR Functions Graphs Technical Mathematics & Mathematics 1 Linear / Quadratic/ Exponential functions 2 Hyperbolic Functions – Technical Mathematics simpler types 3 Cubic Functions – Technical Mathematics simpler types DIFFERENCES Functions Graphs Technical Mathematics Additional Content 1 Graphs of Circle / Semi-circle and Ellipse

CONTENT OF THE TWO PAPERS Technical Mathematics & Mathematics SIMILAR FINANCE topics Technical Mathematics & Mathematics 1 Simple & Compound Growth and Decay 2 Nominal & Effective rates 3 Real life applications DIFFERENCES FINANCE topics Mathematics ONLY 1 ANNUITIES – Future and Present Values

CONTENT OF THE TWO PAPERS Technical Mathematics & Mathematics SIMILAR PAPER 1 CALCULUS topics Technical Mathematics & Mathematics 1 First Principles **** 2 Differentiation Rules 3 Equation of tangents 4 Rates of change 5 Graphs of Cubic functions **** 6 Optimization **** TECHNICAL MATHEMATICS –Simpler examples

CONTENT OF THE TWO PAPERS Technical Mathematics Additional Content DIFFERENCES PAPER 1 CALCULUS topics Technical Mathematics Additional Content 1 Calculus of Motion ( Displacement Formula) 2 Basic Integration 3 Definite Integral 4 Areas bounded by a curve and x-axis

CONTENT OF THE TWO PAPERS DIFFERENCES PAPER 1 SEQUENCES & SERIES Mathematics ONLY 1 Quadratic sequences 2 General terms – Arithmetic & Geometric Sequences 3 Summation of Series & Convergence PROBABILITY Mathematics ONLY 1 Probability 2 Basic Counting Principle

CONTENT OF THE TWO PAPERS Technical Mathematics & SIMILAR PAPER 2 ANALYTICAL GEOMETRY Technical Mathematics & Mathematics 1 Distance / Midpoint / Gradient 2 Angle of inclination 3 Equation of straight lines 4 Equation of circle with centre (0;0) 5 Equation of tangent to circle 6 Points of intersection

CONTENT OF THE TWO PAPERS Technical Mathematics ONLY DIFFERENCES PAPER 2 ANALYTICAL GEOMETRY Mathematics ONLY 1 Equation of circle with centre (a;b) and Applications ANALYTICAL GEOMETRY Technical Mathematics ONLY 1 Equation of ellipse & semi-circle and plotting graph of ellipse and semi-circle

CONTENT OF THE TWO PAPERS Technical Mathematics & Mathematics SIMILAR TRIGONOMETRY Technical Mathematics & Mathematics 1 Sine , Cosine & Tangent functions 2 Basic Sine , Cosine & Tangent Identities 3 Solution of trigonometric equations [0o ; 360o] 4 Graphs of trig functions 5 Reduction formulae 6 Application of Sine , Cosine and Area Rules in 2D & 3D Technical Mathematics restricted to numerical examples . PAPER 2

CONTENT OF THE TWO PAPERS Technical Mathematics ONLY DIFFERENCES TRIGONOMETRY DEGREES & RADIANS Technical Mathematics ONLY 1 Cosecant , Secant & Cotangent functions 2 Basic Cosecant , Secant & Cotangent Identities 3 2D & 3D problems restricted to numerical measurements only. PAPER 2 TRIGONOMETRY DEGREES only Mathematics ONLY 1 Solution of trigonometric equations including negative angles. 2 General solutions of trigonometric equations 3 Proofs of Sine, Cosine and Area Rules examinable.

CONTENT OF THE TWO PAPERS SIMILARITIES PAPER 2 EUCLIDEAN GEOMETRY Technical Mathematics & Mathematics 1 Circle Theorems 2 Proportion and Similarity Theorems 3 Applications DIFFERENCES EUCLIDEAN GEOMETRY Technical Mathematics 1 Proofs of Theorems NOT EXAMINABLE 2 Riders restricted to Calculations only – No proofs

CONTENT OF THE TWO PAPERS Technical Mathematics ONLY DIFFERENCES PAPER 2 SHAPES ANGULAR MEASUREMENT Technical Mathematics ONLY 1 Radian Measure 2 Arcs and Angles / Areas of Sectors and Segments of circle 3 Angular and Circumferential Velocity 4 Surface Areas & Volumes of Prisms, Cylinders, Cones & Spheres 5 Areas of irregular shapes using the Mid-ordinate rule.

CONTENT OF THE TWO PAPERS DIFFERENCES PAPER 2 STATISTICS Mathematics ONLY 1 Measures of central tendency ( Mean , Mode. Median) 2 Measures of dispersion (range , variance) 3 Lines of best fit , correlation 4 Box-whisker plots, scatter plots, ogives, frequency polygons, histograms 5 Frequency tables

ASSESSMENT OF THE TWO PAPERS TECHNICAL MATHEMATICS WEIGHTING OF TOPICS PAPER 1 TOPICS TECHNICAL MATHEMATICS MATHEMATICS ALGEBRA 33,3% 16,6% FUNCTIONS 23,4% FINANCE 10% CALCULUS SEQUENCES & SERIES 0% PROBABILITY

ASSESSMENT OF THE TWO PAPERS TECHNICAL MATHEMATICS WEIGHTING OF TOPICS PAPER 2 TOPICS TECHNICAL MATHEMATICS MATHEMATICS ANALYTICAL GEOMETRY 17% 27% TRIGONOMETRY 33% EUCLIDEAN GEOMETRY MENSURATION , CIRCLES, ANGLES , ANGULAR MOVEMENT 23% 0% STATISTICS 13%

TOPICS WEIGHTING OF TAXONOMY LEVELS ASSESSMENT OF THE TWO PAPERS DIFFERENCES PAPER 1 & 2 TOPICS TECHNICAL MATHEMATICS 2018 Exam Guidelines MATHEMATICS KNOWLEDGE 25% 20% ROUTINE PROCEDURES 45% 35% COMPLEX PROCEDURES 30% PROBLEM SOLVING 10% 15%

TOPICS WEIGHTING OF TAXONOMY LEVELS TECHNICAL MATHEMATICS NOV 2018 Paper WEIGHTING OF TAXONOMY LEVELS ANALYSIS DBE EXAMINING PANEL NOV 2018 PAPER 1 & 2 TOPICS NORM PAPER 1 PAPER 2 KNOWLEDGE 25% 23,3% 26,7% ROUTINE PROCEDURES 45% 46,0% 43,3% COMPLEX PROCEDURES 20% 22,6% PROBLEM SOLVING 10% 7,4%

SOME ACCREDITATION RECOMMENDATIONS FOR HEI’s TECHNICAL MATHEMATICS: TO BE EVALUATED THE SAME AS MATHEMATICS FOR NON- MATHEMATICS PROGRAMMES TO BE EVALUATED THE SAME AS MATHEMATICS FOR PROGRAMMES THAT REQUIRE MATHEMATICS FOR ENTRY, BUT VERY LITTLE PURE MATHEMATICS or SOME SERVICE MATHEMATICS MODULES IS TAUGHT. e.g. Business & Economic Sciences Architecture / Building Sciences Health Sciences Biological Sciences

SOME ACCREDITATION RECOMMENDATIONS TECHNICAL MATHEMATICS: PROGRAMMES WITH MATHEMATICS PRE-REQUISITE PRE 2018 EXAMINATION GUIDELINES: TO BE EVALUATED THE SAME AS MATHEMATICS FOR PROGRAMMES THAT REQUIRE MATHEMATICS FOR ENTRY TO BE CONSIDERED EQUIVALENT TO MATHEMATICS FOR ACADEMIC ACCESS TO HE

SOME ACCREDITATION RECOMMENDATIONS TECHNICAL MATHEMATICS: PROGRAMMES WITH MATHEMATICS PRE-REQUISITE (SCIENCE / ENGINEERING/ ) POST 2018 EXAMINATION GUIDELINES: (CHANGE OF TAXONOMY WEIGHTINGS) TO BE EVALUATED AT ONE LEVEL LOWER AS MATHEMATICS FOR PROGRAMMES THAT REQUIRE MATHEMATICS FOR ENTRY

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