SA NCS Mathematical Literacy:Learning Outcomes, Assessment Standards, Content and Contexts

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Learning Outcome 1: Number and Operations In Context

The learner is able to use knowledge of numbers and their relationships to investigate a range of different contexts which include financial aspects of personal, business and national issues.

The learner will be involved in life-related problem situations such as those involving finance and quantities. In order to solve such problems, the learner will have to estimate efficiently and calculate accurately while making use of the following concepts and content as well as that from other Learning Outcomes.

Grade 10

Assessments Standards

We know this when the learner is able to:

• Solve problems in various contexts, including financial contexts, by estimating and calculating accurately using mental, written and calculator methods where appropriate, inclusive of:
  • working with simple formulae (e.g. $A=P(1+i{)}^n$ );
  • using the relationships between arithmetical operations (including the commutative, distributive and associative laws) to simplify calculations where possible;
  • working with positive exponents and roots. (The range of problem types includes percentage, ratio, rate and proportion (direct and inverse), simple and compound growth, calculations with very small and very large numbers in decimal and scientific notation.)

For example:

• • • explore compound growth in various situations numerically and work with the compound interest formula;
    • find a percentage by which a quantity was increased;
    • calculate the number of person hours needed for a job if the number of workers is increased;
    • calculate proportional payments for work done by groups of people;
    • calculate the amount of money allocated to education by the budget if it is 8,4% of R36,04 billion;
    • criticise numerically-based arguments.

• Relate calculated answers correctly and appropriately to the problem situation by:
  • interpreting fractional parts of answers in terms of the context;
  • reworking a problem if the first answer is not sensible, or if the initial conditions change;
  • interpreting calculated answers logically in relation to the problem and communicating processes and results.

• Apply mathematical knowledge and skills to plan personal finances (so as to enable effective participation in the economy), inclusive of:
  • income and expenditure;
  • simple interest problems and compound interest situations capitalised annually, half-yearly, quarterly and monthly, including calculation of either rate, principal amount or time when other variables are given or known.

For example:

• • • identify variable expenses and calculate new values to adapt a budget to deal with increased bond repayments due to rising interest rates,
    • adapt a budget to accommodate a change in the price of petrol,
    • calculate the value of the fraction of a bond repayment that goes towards repaying interest or capital,
    • calculate the real cost of a loan of R10 000 for 5 years at 5% capitalised monthly and half yearly.

Proposed content

• Fractions, decimals, percentages.
• Positive exponents and roots.
• The associative, commutative and distributive laws.
• Rate.
• Ratio.
• Direct proportion.
• Inverse proportion.
• Simple formulae.
• Simple and compound growth.
• Scientific notation.

Grade 11

Assessments Standards

We know this when the learner is able to:

• In a variety of contexts, find ways to explore and analyse situations that are numerically based, by:
  • estimating efficiently;
  • working with complex formulae by hand and with a scientific calculator,

For example: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

• • showing awareness of the significance of digits when rounding;
  • checking statements and results by doing relevant calculations;
  • working with positive exponents and roots;
  • involving ratio and proportion in cases where more than two quantities are involved.

For example:

• • • estimate the length of a side if the volume of a cube is 10 cubic units,
    • do calculations to compare different currencies,
    • check a claim that costs of phone calls have risen by 8% by doing relevant calculations,
    • check the effect of rounding on effective repayments on a loan or account (one of the payments will have to be adjusted to reach the total amount to be repaid).

• Relate calculated answers correctly and appropriately to the problem situation by:
  • interpreting fractional parts of answers in terms of the context;
  • reworking a problem if the first answer is not sensible or if the initial conditions change;
  • interpreting calculated answers logically in relation to the problem, and communicating processes and results.

• Investigate opportunities for entrepreneurship and determine profit and sustainability by analysing contributing variables, inclusive of:
  • specifying and calculating the value of income and expenditure items;
  • determining optimal selling prices;
  • estimating and checking profit margins.

For example:

• • • calculate the effect of increased prices of imported vehicle parts on the profit margin of a motor car manufacturer or a small vehicle service workshop,
    • investigate the effect of increasing the number of employees on the profit margin of a small company,
    • investigate the effect of a sales discount on the profit margin.

Proposed content

• Content involved in Grade 10 work but applied to more complex situations.
• Square roots and cube roots.
• Ratio and proportion.
• Complex formulae.
• Cost price and selling price.
• Profit margins.

Grade 12

Assessments Standards

We know this when the learner is able to:

• Correctly apply problem-solving and calculation skills to situations and problems dealt with.

For example:

• • • work with issues involving proportional representation in voting.

• Relate calculated answers correctly and appropriately to the problem situation by:
  • interpreting fractional parts of answers in terms of the context;
  • reworking a problem if the first answer is not sensible or if the initial conditions change;
  • interpreting calculated answers logically in relation to the problem and communicating processes and results.

• Analyse and critically interpret a wide variety of financial situations mathematically, inclusive of:
  • personal and business finances;
  • the effects of taxation, inflation and changing interest rates on personal credit, investment and growth options;
  • financial and other indicators;
  • the effects of currency fluctuations;
  • critical engagement with debates about socially responsible trade.

For example:

• • • calculate the effect of a fixed interest rate against probable variations in interest rates when buying a house or when choosing an investment,
    • calculate the net effect of different interest offerings and bank charges when saving schemes are considered,
    • calculate and compare the projected yields of different retirement options,
    • interpret changes in indices such as the consumer price index or the business confidence index,
    • compare different credit options,
    • calculate the effect of defaulting payments over a period of time,
    • consider different currencies for investment purposes,
    • calculate values in simplified situations in order to discuss the effect of import/export control, levies and rebates, linking the discussion to the way mathematics can be used to argue opposing points of view.

Proposed content

• Content of Grade 10 and Grade 11 but applied to more complex situations.
• Taxation.
• Currency fluctuations.
• Financial and other indices.

Learning Outcome 2: Functional Relationships

The learner is able to recognise, interpret, describe and represent various functional relationships to solve problems in real and simulated contexts.

The learner will be involved in situations that involve relationships between variables depicted graphically, numerically and in tables. These situations can be dealt with through making use of the following content and concepts. Some of the content and concepts more directly related to the other Learning Outcomes will also have to be used.

Grade 10

Assessments Standards

We know this when the learner is able to:

• Work with numerical data and formulae in a variety of real-life situations, in order to establish relationships between variables by:
  • finding the dependent variable;
  • finding the independent variable;
  • describing the rate of change. (Types of relationships to be dealt with include linear, inverse proportion and compound growth in simple situations.)

For example:

• • • critique information about functional relationships in media articles such as telephone costs before and after rate changes,
    • calculate relationships in speed, distance and time.

• Draw graphs in a variety of real-life situations by:
  • point-by-point plotting of data;
  • working with formulae to establish points to plot;
  • using graphing software where available.

For example, draw graphs of:

• • • mass against time when on diet,
    • surface area against side length of a cube,
    • volume against surface area,
    • lengths of a spring against mass added,
    • amount of savings against the investment period.

• Critically interpret tables and graphs that relate to a variety of real-life situations by:
  • finding values of variables at certain points;
  • describing overall trends;
  • identifying maximum and minimum points;
  • describing trends in terms of rates of change.

For example, interpret graphs that:

• • • compare the incidence of AIDS over time,
    • indicate trends in road fatalities,
    • show the expected changes in the mass of a baby with age.

Proposed content

• Tables of values.
• Formulae depicting relationships between variables.
• Cartesian co-ordinate system.
• Linear functions.
• Inverse proportion.
• Compound growth.
• Graphs depicting the relationship between variables.
• Maximum and minimum points.
• Rates of change (speed, distance, time).

Grade 11

Assessments Standards

We know this when the learner is able to:

• Work with numerical data and formulae in a variety of real-life situations, in order to establish relationships between variables by:
  • finding break-even points;
  • finding optimal ranges. (Types of relationships to be dealt with include two simultaneous linear functions in two unknowns, inverse proportion, compound growth [only positive integer exponents] and quadratic functions.)

For example:

• • • interpret and critique quotations for two similar packages given by cell phone providers or car hire companies,
    • use rate of change to offset impressions created by magnification of scales on the axes of graphs.

• Draw graphs as required by the situations and problems being investigated.

For example:

• • • compare costs of cell phone packages for different call intervals by drawing graphs of cost against time.

• Critically interpret tables and graphs depicting relationships between two variables in a variety of real-life and simulated situations by:
  • estimating input and output values;
  • using numerical arguments to verify relationships.

For example:

• • • do spot calculations of the rate of change of population growth in different countries by taking readings from supplied graphs to check figures quoted and to verify estimations of future growth.

Proposed content

• The content of Grade 10 but applied to more complex situations.
• Simple quadratic functions.
• Solution to linear, quadratic and simple exponential equations.
• Solution to two simultaneous linear equations.

Grade 12

Assessments Standards

We know this when the learner is able to:

• Work with numerical data and formulae in a variety of real-life situations, in order to:
  • solve design and planning problems;

For example:

• • • find optimal values for two discrete variables, subject to two or more linear constraints.
  • investigate situations of compound change.

For example:

• • • investigate the rate of depletion of natural resources,
    • investigate the spread of HIV/AIDS and other epidemics,
    • critique articles and reports in the media that are based on graphs or tables.

• Draw graphs as required by the situations and problems being investigated.

For example:

• • • draw graphs of number of AIDS related deaths and deaths caused by malaria over time, on the same system of axes to describe the extent of the AIDS epidemic.

• Critically interpret tables and graphs in the media, inclusive of:
  • graphs with negative values on the axes (dependant variable in particular);
  • more than one graph on a system of axes.

For example:

• • • interpret graphs of temperature against time of day during winter over a number of years to investigate claims of global warming,
    • compare graphs of indices such as the consumer price index and business confidence index to graphs of percentage change in those indices over a particular time interval.

Proposed content

• The content of Grade 10 and Grade 11 but applied to more complex situations.
• Simple linear programming (design and planning problems).
• Graphs showing the fluctuations of indices over time.

Learning Outcome 3: Space, Shape and Measurement

The learner is able to measure using appropriate instruments, to estimate and calculate physical quantities, and to interpret, describe and represent properties of and relationships between 2-dimensional shapes and 3-dimensional objects in a variety of orientations and positions.

Contexts that the learner will deal with here involve space, shape and time. In order to deal with real-life situations in such contexts, the learner will make use of the following and other content and concepts.

Grade 10

Assessments Standards

We know this when the learner is able to:

• Solve problems in 2-dimensional and 3-dimensional contexts by:
  • estimating, measuring and calculating (e.g. by the use of the Theorem of Pythagoras) values which involve:
    • lengths and distances,
    • perimeters and areas of common polygons and circles,
    • volumes of right prisms,
    • angle sizes (0 degrees-360 degrees);
  • checking values for solutions against the contexts in terms of suitability and degree of accuracy.

• Convert units of measurement within the metric system.

For example:

• • • convert km to m, $m{m}^3$ to litres, $k{m}^2$ to $m^2$, $c{m}^3$ to $m^3$.

• Draw and interpret scale drawings of plans to represent and identify views.

For example:

• • • draw and interpret top, front and side views or elevations on a plan.

• Solve real-life problems in 2-dimensional and 3-dimensional situations by the use of geometric diagrams to represent relationships between objects.

For example:

• • • draw floor plans and use symbols to indicate areas and positions taken up by furniture in different arrangements.

• Recognise, visualise, describe and compare properties of geometrical plane figures in natural and cultural forms.

For example:

• • • use the concepts of tessellation and symmetry in describing tilings, Zulu beadwork and other artefacts.

Proposed content

• Measurement of length, distance, volume, area, perimeter.
• Measurement of time (international time zones).
• Polygons commonly encountered (triangles, squares, rectangles that are not squares, parallelograms, trapesiums, regular hexagons).
• Circles.
• Angles (0 degrees-360 degrees).
• Theorem of Pythagoras.
• Conversion of units within the metric system.
• Scale drawings.
• Floor plans.
• Views.
• Basic transformation geometry, symmetry and tessellations.

Grade 11

Assessments Standards

We know this when the learner is able to:

• Solve problems in 2-dimensional and 3- dimensional contexts by:
  • estimating, measuring and calculating (e.g. regular shapes, irregular shapes and natural objects) values which involve:
    • lengths and distances,
    • perimeters and areas of polygons,
    • volumes of right prisms and right circular cylinders,
    • surface areas of right prisms and right circular cylinders,
    • angle sizes (0 degrees-360 degrees);
  • making adjustments to calculated values to accommodate measurement errors and inaccuracies due to rounding.

• Convert units of measurement between different scales and systems.

For example:

• • • convert km to m, $m{m}^3$ to litres, miles to km, kg to lb,
    • work with international times

• Use and interpret scale drawings of plans to:
  • represent and identify views, estimate and calculate values according to scale.

For example:

• • • study a plan of the school building and identify locations or calculate available real area for extensions.

• Use grids, including the Cartesian plane and compass directions, in order to:
  • determine locations;
  • describe relative positions.

For example:

• • • local maps,
    • seat location in cinemas and stadiums,
    • room numbers in multi-levelled buildings.

• Use basic trigonometric ratios (sine, cosine and tangent) and geometric arguments to interpret situations and solve problems about heights, distances and position.

• Recognise, visualise, describe and compare properties of geometrical plane figures and solids in natural and cultural forms.

For example:

• • • use the concepts of rotation, symmetry and reflection in describing decorative Ndebele and Sotho mural designs.

Proposed content

• Grade 10 content but applied to more complex situations.
• Measurement in 3D (angles included, 0 degrees-360 degrees).
• Surface area and volumes of right prisms and right circular cylinders.
• Conversion of measurements between different scales and systems.
• Compass directions.
• Properties of plane figures and solids in natural and cultural forms.
• Location and position on grids.
• Trigonometric ratios: $sinx$, $cosx$, $tanx$.

Grade 12

Assessments Standards

We know this when the learner is able to:

• Solve problems in 2-dimensional and 3- dimensional contexts by:
  • estimating, measuring and calculating (e.g. regular shapes, irregular shapes and natural objects) values which involve:
    • lengths and distances,
    • perimeters and areas of polygons,
    • volumes of right prisms, right circular cylinders, cones and spheres,
    • surface areas of right prisms, right circular cylinders, cones and spheres,
    • angle sizes (0 degrees-360 degrees);
  • making adjustments to calculated values to accommodate measurement errors and inaccuracies due to rounding.

• Convert units of measurement between different scales and systems as required in dealing with problems.

For example:

• • • the dimensions of an imported washing machine are given in inches and must be converted accurately to centimetres for installation purposes,
    • a recipe that is written with imperial measures must be rewritten with accurate metric measures,
    • measures of temperature must be converted between Fahrenheit and Celsius (conversion ratios and formulae given).

• Use and interpret scale drawings of plans to:
  • represent and identify views, estimate and calculate values according to scale, and build models.

For example:

• • • build a scale model of a school building, based on the plan of the building.

• Use grids, including the Cartesian plane and compass directions, in order to:
  • determine locations;
  • describe relative positions.

For example:

• • • understand the use of latitude and longitude in global positioning systems.

• Use basic trigonometric ratios (sine, cosine and tangent) and geometric arguments to interpret situations and solve problems about heights, distances, and position including the application of area, sine and cosine rules.

• Recognise, visualise, describe and compare properties of geometrical plane figures and solids in natural and cultural forms.

For example:

• • • use the concepts of proportion and symmetry in describing local artefacts, art and architecture.

Proposed content

• Content of Grade 10 and Grade 11 but applied to more complex situations.
• Surface areas and volumes of right pyramids and right circular cones and spheres.
• Scale models.
• Sine rule, cosine rule, area rule.

Learning Outcome 4: Data Handling

The learner is able to collect, summarise, display and analyse data and to apply knowledge of statistics and probability to communicate, justify, predict and critically interrogate findings and draw conclusions.

The learner will investigate and interpret situations which can be dealt with using statistical techniques. The following and other content and concepts will assist the learner to do so.

Grade 10

Assessments Standards

We know this when the learner is able to:

• Investigate situations in own life by:
  • formulating questions on issues such as those related to:
    • social, environmental and political factors,
    • people's opinions,
    • human rights and inclusivity;
  • collecting or finding data by appropriate methods (e.g. interviews, questionnaires, the use of data bases) suited to the purpose of drawing conclusions to the questions.

For example, investigate:

• • • substance abuse in the school,
    • water conservation,
    • prevalence of flu during winter,
    • approaches to discipline in the school.

• Select, justify and use a variety of methods to summarise and display data in statistical charts and graphs inclusive of:
  • tallies;
  • tables;
  • pie charts;
  • histograms (first grouping the data);
  • single bar and compound bar graphs;
  • line and broken-line graphs.

For example:

• • • pie charts to show the relative proportions of learners who have flu,
    • compound bar graphs to show the abuse of different substances in the respective Further Education and Training grades.

• Calculate and use appropriate measures of central tendency and spread to make comparisons and draw conclusions, inclusive of the:
  • mean;
  • median;
  • mode;
  • range.

For example:

• • • investigate the cost of a trolley of groceries at three different shops in the area and report the findings by means of mean, median, mode and range.

• Critically interpret a single set of data and representations thereof (with awareness of sources of error) in order to draw conclusions on questions investigated and to make predictions.

For example:

• • • interpret data from the media on the number of stolen and recovered vehicles after a certain tracking device has been installed.

• Work with probability concepts to:
  • compare the relative frequency of an outcome with the probability of an outcome (establishing that it takes very many trials before the relative frequency approaches the value of the probability of an outcome, e.g. to get a 6 when rolling a die);
  • express probability values in terms of fractions, ratios and percentages.

• Effectively communicate conclusions and predictions (using appropriate terminology such as trend, increase, decrease, constant, impossible, likely, fifty-fifty chance), that can be made from the analysis and representation of data on learner-driven issues.

Proposed content

• Construction of questionnaires.
• Populations.
• Selection of a sample.
• Tables recording data.
• Tally and frequency tables.
• Single and compound bar graphs.
• Pie charts.
• Histograms.
• Line and broken-line graphs.
• Mean, median, mode.
• Range.
• Relative frequency.
• Probability.

Grade 11

Assessments Standards

We know this when the learner is able to:

• Investigate a problem on issues such as those related to:
  • social, environmental and political factors;
  • people's opinions;
  • human rights and inclusivity by:
    • using appropriate statistical methods;
    • selecting a representative sample from a population with due sensitivity to issues relating to bias;
    • comparing data from different sources and samples.

For example:

• • • conduct a survey in own school about home languages and comparing that with related data from other sources,
    • identify possible sources of bias in gathering the data,
    • investigate the increase in absenteeism at school (e.g. investigate the correlation between living conditions - squatter camps, houses - and absenteeism),
    • investigate the correlation between distance from school and absenteeism.

• Appropriately choose and interpret the use of methods to summarise and display data in statistical charts and graphs inclusive of:
  • tallies;
  • tables;
  • pie charts;
  • single and compound bar graphs;
  • line and broken-line graphs;
  • ogives of cumulative frequencies.

For example:

• • • interpret the meaning of points on a broken-line graph of house prices in 2002 - does it make sense to assign a monetary value to a point halfway between January and February?

• Calculate, interpret and compare two sets of data using measures of central tendency and spread, inclusive of the:
  • mean;
  • median;
  • mode;
  • range;
  • variance (interpretation only);
  • standard deviation (interpretation only);
  • quartiles.

For example:

• • • conduct a survey in own school about home languages and compare that with related data from other sources,
    • identify possible sources of bias in gathering the data,
    • use concepts of average, mode or median to interpret the data.

• Critically interpret two sets of data and representations thereof (with awareness of sources of error and bias) in order to draw conclusions on problems investigated and make predictions.

For example:

• • • compare data from two providers of tracking devices and draw conclusions about success rates.

• Make and/or test predictions of compound outcomes in the context of games and reallife situations by:
  • designing simple contingency tables to estimate basic probabilities;
  • drawing tree diagrams.

For example:

• • • draw a tree diagram to investigate the probability of getting three heads when tossing three coins.

• Manipulate data in different ways to justify opposing conclusions.

Proposed content

• The content of Grade 10 but applied to more complex situations.
• Selection of samples and bias.
• Cumulative frequencies.
• Ogives (cumulative frequency graphs).
• Variance (interpretation only).
• Standard deviation (interpretation only).
• Quartiles.
• Compound events.
• Contingency tables.
• Tree diagrams.

Grade 12

Assessments Standards

We know this when the learner is able to:

• Investigate a problem on issues such as those related to:
  • social, environmental and political factors;
  • people's opinions;
  • human rights and inclusivity by:
    • using appropriate statistical methods;
    • selecting a representative sample from a population with due sensitivity to issues relating to bias;
    • comparing data from different sources and samples.

For example:

• • • challenge learners to compare claims about preferred TV programmes among teenagers with data from schools in their area,
    • compare preferences across grades or gender.

• Appropriately choose and interpret the use of methods to summarise and display data in statistical charts and graphs including the use of scatter-plots and intuitively-placed lines of best fit to:
  • represent the association between variables (regression analysis not included);
  • describe trends (e.g. a positive linear association).

For example:

• • • Does a positive correlation between age and height necessarily mean that height is dependent on age?
    • Does a positive correlation between mathematics marks and music marks necessarily mean that facility in mathematics is dependent on musical aptitude?
    • Does a positive correlation between pollution levels and TB infections necessarily mean that pollution causes TB?

• Compare different sets of data by calculating and using measures of central tendency and spread, including:
  • mean;
  • median;
  • mode;
  • variance (interpretation only);
  • standard deviation (interpretation only);
  • quartiles;
  • percentiles.

For example:

• • • compare the increase in the cost of a trolley of groceries to the increase in the consumer price food index, and report the findings in terms of variance and standard deviation of specific items,
    • compare academic results in own school to those in the province in terms of quartiles and percentiles.

• Represent and critically analyse data, statistics and probability values in order to draw conclusions on problems investigated and to predict trends.

For example:

• • compare data about stolen vehicles from providers of tracking devices with data provided by official sources like SAPS, and draw conclusions about the trend in vehicle thefts (types of cars most at risk, areas most at risk).

• Critically engage with the use of probability values in making predictions of outcomes in the context of games and real-life situations.

For example:

• • • Investigate claims that the probability of winning a game of chance (e.g. a slot machine) improves if it has not produced a winner for some time.

• Critically evaluate statistically-based arguments, describe the use and misuse of statistics in society, and make well-justified recommendations.

Proposed content

• The content of Grade 10 and Grade 11 but applied to more complex situations.
• Bivariate data.
• Scatter plots.
• Intuitively-placed lines of best fit.
• Percentiles.

About the Proposed Content sections

In this section, content and contexts are provided to support the attainment of the Assessment Standards. The content indicated needs to be dealt with in such a way as to assist the learner to progress towards the achievement of the Learning Outcomes. Content must serve the Learning Outcomes and not be an end in itself. The contexts suggested will enable the content to be embedded in situations which are meaningful to the learner and so assist learning and teaching. The teacher and other educators should be aware of and use local contexts, not necessarily indicated here, which could be more suited to the experiences of the learner. Content and context, when aligned to the attainment of the Assessment Standards, provide a framework for the development of Learning Programmes. The Learning Programme Guidelines give more detail in this respect.

For Mathematical Literacy, the Assessment Standards do indicate progression from grade to grade. However, this progression is not markedly evident in some of the Assessment Standards. The complexity of the situation to be addressed in context, through using the mathematical knowledge and ways of thought available to the learner, is where the extent of the progression needs to be ensured. This is illustrated by the examples given with the Assessment Standards.

Contexts

Contexts are central to the development of Mathematical Literacy in learners. Mathematical Literacy, by its very nature, requires that the subject be rooted in the lives of the learners. It is through engaging learners in situations of a mathematical nature experienced in their lives that the teacher will bring home to learners the usefulness and importance of mathematical ways of thought in solving problems in such situations. To this end it is very important for the teacher to incorporate local and topical issues into the Learning Programmes that they design. The practices of the local community, the home environment and local industry provide a wealth of relevant contexts to explore. The media frequently provide resources that will assist in making what is currently happening locally, nationally and internationally available to the Mathematical Literacy classroom. The approach that needs to be adopted in developing Mathematical Literacy is to engage with contexts rather than applying Mathematics already learned to the context. Research done internationally and in South Africa confirms this approach for young people as well as for adults.

A wealth of contexts can be used to attain the Assessment Standards for Mathematical Literacy in the manner described above. The examples provided in support of many of the Assessment Standards are illustrations of some of these contexts. The possibilities of using such contexts in investigations, projects, assignments and assessment show that Mathematical Literacy is an ideal subject for attaining the authentic education and assessment which is at the core of outcomes-based education. Contexts which have been highlighted are those related to the principles of the National Curriculum Statement, that is, issues which arise in human rights, inclusivity, health (HIV/AIDS) and indigenous knowledge systems.

Being literate in Mathematics is an essential requirement for the development of the responsible citizen, the contributing worker and the self-managing person. Being mathematically literate implies an awareness of the manner in which Mathematics is used to format society and enables astuteness in the user of the products of Mathematics such as hire-purchase agreements and mathematical arguments in the media ­ hence the inclusion of Mathematical Literacy as a Fundamental requirement in the Further Education and Training curriculum.

Many local and international studies have shown the existence of a set of attitudes ­ described as `mathsphobia' ­ in school-going learners and in the population at large. It is the responsibility of the teacher, in implementing this curriculum, to endeavour to win learners to Mathematics. Real-life contexts which lend themselves to mathematical ways of thought are ideal for doing this.

The teacher needs to be sensitive to the manner in which gendered attitudes towards Mathematics play themselves out in the classroom, particularly so in co-educational schools. Stereotyping needs to be guarded against in this respect, where Mathematics is often seen as a male preserve leading to arrogance and domination by the boys in the class. The interests of all need to be taken into account in providing access to mathematical ways of thought so essential to Mathematical Literacy.

Another aspect of providing access and affirmation for learners of Mathematics is to look at examples of Mathematics in the variety of cultures and societal practices that exist in our country. Mathematics is embedded in many cultural artefacts which we experience in our daily lives: the murals of the Ndebele, the rhythm in the drums of the Venda, the beadwork of the Zulu and Vedic art, to name but a few. Architecture, games and music are rich fields to explore through the lenses of Mathematics. Ethnomathematics provides a wealth of more recently developed materials, sensitive to the sacredness of culture, for use in the classroom. The flexibility allowed by the curriculum also promotes the incorporation of local practices as starting points for or applications of the Mathematics to be investigated.

Ethnomathematics also stresses that Mathematics originated in cultures other than the Greek and that it continued to be developed in sophistication by many societies other than the European. Projects in the history of Mathematics can be used to explore this.