A Comparative study of the National Curriculum Statement (NCS) and - PowerPoint PPT Presentation

What’s in the CAPS Package? A Comparative study of the National Curriculum Statement (NCS) and the Curriculum and Assessment Policy Statement (CAPS): FET Phase Mathematical Literacy June 2014 Joan Houston

Rationale Mathematical Literacy is not another level or type of Mathematics . “The ability to use mathematics as a tool to make sense of situations in the environment requires that people model the situations (mentally or formally), bring to bear their mathematical knowledge and work towards a solution.” (John A. Dossey, in Why Numbers count, Steen, 1997)

Documentation NCS (5 subject + 2 general documents)  Organization and some explanations very difficult to digest .  At times language was complex or obscure, or terms were ill-defined.  Difficult to work out how successive versions of documents complemented or related to one another.  Contradictions exist in the documents with respect to the time allocation for teaching Mathematical Literacy and % marks awarded for assessment of Learning Outcomes.

Documentation CAPS (1 subject + 2 general documents)  Extremely specific in design, with well-organized sections and good amplifications  All technical terms used in the documents are clearly defined  Curriculum descriptors are specific, easily understood, concise and measurable  Subsequently an Exam Guideline has been released. CAPS, with its clear and specific format and user- friendliness, is an improvement on the NCS.

Objectives Difficult to compare the NCS and CAPS because NCS: 12 objectives are listed explicitly and in detail. CAPS: Aims and objectives are only implied in The General Aims of the South African Curriculum in the Section called ‘What is Mathematical Literacy?’ However, some of the NCS objectives are idealistic, unmeasurable and vague, e.g. ‘Be sensitive to the aesthetic value of mathematics’ or ‘Explore the importance of mathematical literacy for career opportunities’.

Comparison of the curriculum structure Different terminology and organization of learning process in two curricula. NCS: 4 Learning Outcomes(LOs ) equally weighted for assessment and teaching time. Basic mathematical skills were implied in LOs . Assumption that teacher would know what skill to teach when it was needed. CAPS: Basic Skills (taught explicitly) + 5 Application Topics (ATs), unequall y weighted for assessment and teaching time. Teacher knows when to teach Basic Skills.

Comparison of the curriculum structure

Comparison of approach Besides the difference in terminology of the curricula there is a more essential difference of approach which expresses the difference in the nature of the subject as described in the two curricula. NCS: Mathematical skills and concepts are expressed implicitly in a variety of contexts. CAPS: Important contexts are chosen because they require explicit mathematical skills.

Philosophical difference in approach NCS design: Mathematical skills are expressed in real-life problems and contexts. CAPS design: Real-life problems and situations mathematical skills. require

Philosophical difference in approach  In the NCS, Learning Outcomes suggest mathematica l areas of learning , ‘to enable learners..to handle with confidence the Mathematics that affects their lives ’.  In the CAPS authentic contexts are chosen because they are important (to life) and they require explicit mathematical skills .

Comparison of depth and breadth It was impossible to analyse the depth of topics separately from their breadth because of • the lack of comparability of terminology in the two curricula • the fact that so much of the content of the NCS is implicit and therefore subject to interpretation • the fact that it is often the context of the content/skills that creates the depth of the topics.

Comparison of breadth/depth of Basic Skills CAPS NCS • explicit , clearly listed • little emphasis on and explained in the explicit teaching detail • assumes that the • greater breadth than teacher knows which the NCS. skills to use • specifies a basic • specifies a scientific four-function calculator calculator

Comparison of breadth/depth of Finance NCS CAPS • a scientific calculator • greater breadth results in compound • much more detail in interest problems at financial documents, greater depth tariff systems, • calculated annually, bi- taxation, dealing with annually, quarterly and personal tax, UIF, monthly and calculation pension fund and of time period, interest medical aid. rate and principle amount

Comparison of breadth/depth of Measurement NCS had greater breadth , included calculations to do with • more 2D polygons and 3D solids than CPS • angles  Pythagoras’ Theorem  spheres and cones Highlights the contention that the NCS curriculum emphasised complex mathematical calculations , at the expense of real life problems.

Comparison of breadth/depth in Maps, Plans and Representations of the physical world  CAPS has greater breadth and depth across all three grades.  CAPS has greater depth developing a gradual increase in complexity in all four sections (scale, maps, plans and models).  NCS refers to some of the topics in only one grade , and then in not great complexity.

Comparison of breadth/depth of Data Handling and Probability • CAPS and NCS are of comparable breadth but CAPS diversifies into many more contexts. • NCS goes to a greater depth in some sections in Data handling, e.g. representing data by line of best fit, standard deviation, Ogives and variance. • Greater depth in Probability in CAPS

NCS topics omitted from CAPS Considered an improvement  Line of best fit  Scientific notation  Cumulative frequency and  Financial indices Ogives  Pythagoras’ Theorem  Quadratic functions  Linear programming  Latitude and longitude  Solving equations  Time zones simultaneously using algebraic methods  Trigonometry, including angle from 0º-360 º NEVER ASSESSED in NCS  Transformation geometry  Cones and spheres  Geometrical plane figures  Standard deviation and and tessellations variance

Overall comparison of depth  CAPS goes into greater depth in the areas of application in which the mathematics is involved.  Learners are expected to know more about the topic and to understand the complexity of the authentic real life situation.  CAPS lays great emphasis on the use of correct terminology.  NCS included calculations at a greater depth of mathematical complexity .  NCS defined its depth by the mathematics involved, rather than the depth of problem-solving of a real-life situation.

Overall comparison of breadth  Breadth of the CAPS and the NCS are of a comparable degree.  CAPS is highly specified and explained in great detail  NCS was very abbreviated and breadth was often only implied.

Specification of Content For NCS, specification is low NCS had contracted assessment statements which lacked detailed descriptors of what exactly was to be taught. E.g. Draw graphs as required by the situations and problems being investigated. Only one example given. Teacher had to find other examples and interpret ‘graphs as required’. Difficult for non-mathematically trained teachers (the majority who teach this subject!)

Specification of Content For CAPS, specification is high The scope and purpose of every topic is well defined. All sub-sections contain “work with/identify/determine…”, followed by “in order to…” E.g. Taxation as a topic is divided into Income Tax and VAT, UIF and income tax. For each grade specific source documents are specified. Types of calculations involving VAT and UIF are specified. Set in a time framework within each topic . Very supportive of teachers who lack maths background or confidence.

Overall content/skills coverage  CAPS provides more direction and support for teaching and learning compared to NCS, which lacks clarity and specific detail. Content is comparable.  CAPS has a discipline-based component (Mathematics) in the Basic Skills section, which has provided the essential tools to tackle Application topics.  Mathematical Literacy is not Mathematics, rather it is a facility with quantitative problems in life . In CAPS problems are never contrived for the sake of using the mathematics.  This is an improvement over NCS. This is a clearer and more understandable approach to the teaching and learning of this relatively new subject.

Topic weighting in NCS  All four Learning Outcomes were weighted virtually the same across the phase.  As a single topic Data Handling was weighted the highest in Grade 10. This was inappropriate as it is a relatively easy topic to teach.  Functional Relationships, which is considered conceptually difficult, was slightly under-weighted across the phase and especially in Grade 12.  Space, Shape and Measurement received 26% of teaching time across the phase.

Topic weighting in CAPS  Appropriate emphasis on Basic Skills which are a prerequisite for all the other Application Topics in Grade 10.  As a single topic Finance is weighted the highest (28%) across the phase with the greatest emphasis in Grade 11 and Grade12.  Data Handling and Probability are weighted the least. Considered to be easy topics, therefore appropriate.  Taken together the two spatial topics comprise 37% of teaching time with most emphasis in Grade 12.  Very different emphasis in weighting from NCS.