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

• pportunities’.

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), unequally 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 real-life problems and contexts.

CAPS design:

Real-life problems and situations mathematical skills. are expressed in require

Philosophical difference in approach

 In the NCS, Learning Outcomes suggest

mathematical 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

• explicit, clearly listed

and explained in detail

• greater breadth than

the NCS.

• specifies a basic

four-function calculator NCS

• little emphasis on

the explicit teaching

• assumes that the

teacher knows which skills to use

• specifies a scientific

calculator

Comparison of breadth/depth of Finance

CAPS

• greater breadth
• much more detail in

financial documents, tariff systems, taxation, dealing with personal tax, UIF, pension fund and medical aid. NCS

• a scientific calculator

results in compound interest problems at greater depth

• calculated annually, bi-

annually, quarterly and monthly and calculation

• f time period, interest

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

• f best fit, standard deviation, Ogives and

variance.

• Greater depth in Probability in CAPS

NCS topics omitted from CAPS

Considered an improvement

 Scientific notation  Financial indices  Pythagoras’ Theorem  Linear programming  Solving equations

simultaneously using algebraic methods NEVER ASSESSED in NCS

 Cones and spheres  Standard deviation and

variance

 Line of best fit  Cumulative frequency and

Ogives

 Quadratic functions  Latitude and longitude  Time zones  Trigonometry, including angle

from 0º-360 º

 Transformation geometry  Geometrical plane figures

and tessellations

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

• ften 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

• f 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%

• f teaching time with most emphasis in Grade 12.

 Very different emphasis in weighting from NCS.

Teaching time vs assessment

NCS

• Teaching time of all 4

LOs correlate fairly well with the percentage of marks awarded in assessment.

• Since Functional

Relationship is conceptually the most difficult it is regrettable that this LO received slightly less teaching time than Data Handling.

CAPS

• Teaching time for

Finance (28%) does not correlate well with marks awarded (30-40%)

• Taken together Data

Handling and Probability has 23% of teaching time and is awarded 25-35%

• f the marks in
• assessment. Needs less

teaching time.

Pacing

Specification of pacing

 High in NCS, moderate in CAPS

Actual pacing

• Moderate in NCS and CAPS
• In NCS Functional Relationships is conceptually difficult

and needs a slower pace and more time than allocated. Data Handling is familiar and conceptually easier and does not need as much time as allocated.

• In CAPS Finance and spatial topics need a slower pace.
• There are contradictions in two places in the CAPS

document regarding teaching time.

Sequencing

CAPS is purposeful, introduces a topic in one grade and then develops it in later grade(s). NCS at times has no justification for teaching a topic only

• nce in a grade and then never developing it further.

Progression

In CAPS - clearly evident throughout the Basic Skills and Application topics. In NCS - does not have consistent, clear progression. Little layering of content with respect to difficulty.

Coherence of CAPS

• Overarching logic of the design is the key idea of using basic

mathematical skills to solve and make sense of real life problems which is developed conceptually and contextually across the phase.

• Explicit acknowledgement of the need to teach a wide range of

basic mathematical skills as tools for problem-solving.

• Coherence between the stated objectives and their

implementation.

• Stated integration of the Application Topics. Real problems

include measurement, finance, data and more.

Implications for South African context

CAPS is a great improvement. Extremely helpful to teachers, especially those who are not mathematics teachers, which is a substantial proportion of Mathematical Literacy teachers. For learners the emphasis on basic mathematical skills is empowering and will give them a greater sense of confidence to tackle quantitative and numerical problems in the Application Topics.

Conclusions

A significant shift from NCS to CAPS NCS

• focus is on mathematical skills and concepts and

the Learning Outcomes fit around these mathematical skills.

• tries to find practical contexts in which to use

mathematics.

• defines its depth by the mathematics involved

Conclusions (continued)

CAPS

• Recognises the need for equipping learners with

mathematical tools

• Thrust of the curriculum is to forefront the practical

situations that 21st century people find themselves in that need a solution or effective management.

• Complexity of problems are largely to do with the

complexity of the context and understanding and accessibility of information needed to solve it.

Exit-level attainment

Exit-level attainment

 Greatest emphasis in the type of cognitive skill is the higher

• rder skills. Impossible to comment on the emphasis in terms
• f the cognitive levels specified because in Mathematical

literacy the cognitive demand is evident only in the assessment of the subject.

 It can be clearly seen that the higher order skills of analysis,

comprehension, interpretation, decision-making and drawing conclusions form the greatest emphasis at the exit level. This an appropriate emphasis because it achieves the stated goals of the subject, which is to equip people to live and function in a world that has many quantitative demands and challenges.

 There is no need to shift away from this emphasis.

Recommendations

 The scientific calculator should be re-instated so that

CAPS can give more complex and authentic problems with period changes when dealing with compound interest.

 Aims and objectives of Mathematical Literacy should

be clearly spelt out in the CAPS as they are in the NCS.

 Teaching time of Finance and Data Handling needs

to correlate more closely with the weighting given to the topics in assessment.

 A single outline of the teaching time allocation

rather than multiple versions with contradictions.

“As information becomes ever more quantitative and as society relies increasingly on computers and the data they produce, an innumerate citizen today is as vulnerable as the illiterate peasant of Gutenberg's time.”

(Steen, in Why Numbers Count, 1997)

“It is dangerous for democracy if most of its citizens are quantitatively oblivious.”

(Steen, Calculation vs Context, 2007)