Western Cape



Directorate: Curriculum FET

Contents

|Topic |Page |

|The purpose of Mathematical literacy……………………….. |3 |

|Lesson preparation…………………………………………….. |4 |

|Assessment in Mathematical literacy……………………….. |4 |

|Programme of Assessment (PoA) tasks……………………. |6 |

|Questions in PoA tasks…………………………………… |6 |

|Purposes of PoA tasks……………………………………. |8 |

|Guidelines for setting PoA tasks…………………………….. |9 |

|Setting tests, assignments and investigations……….. |10 |

|Setting examinations, grade 10 and 11………………… |11 |

|Setting examinations, grade 12…………………………. |13 |

|Recording and record keeping………………………………. |15 |

|Moderation of learner assessment…………………………… |16 |

|Moderation instruments……………………………………….. |17 |

1. THE PURPOSE OF MATHEMATICAL LITERACY

Mathematical Literacy is intended to develop competencies that allow learners to make sense of, participate in and contribute to the modern world (National Curriculum Statement(NCS); Curriculum and Assessment Policy Statement(CAPS): Mathematical literacy; 2011, Department of Basic Education(DBE)). Information is often presented in various forms such as numbers, charts, graphs and symbols. To be able to participate meaningfully on matters of society one must be able to access and interpret this information.

According to CAPS, Mathematical literacy has FIVE key elements namely; elementary (basic) mathematical content, authentic real-life contexts, familiar and unfamiliar problems, decision making and communication; and integrated content and skills in solving problems.

As a result of this emphasis on both content and contexts Mathematical literacy knowledge has been packaged into TWO types. These are:

❖ Basic skills topics which contain elementary mathematical content learners should master in order to use in exploring contexts.

❖ Applications topics which contain authentic familiar and unfamiliar real-life contexts from which problems arise.

The diagram below shows the structure of Mathematical literacy.

Teaching, learning and assessment in Mathematical literacy takes place within contexts outlined under applications topics. Depending on the learner’s level of development of basic mathematical content, teaching may require revision of these pure mathematical concepts before learners use them to explore contexts.

2. LESSON PREPARATION

Mathematical Literacy involves use of Mathematical and non-Mathematical competencies to solve authentic real-life problems in familiar and unfamiliar contexts. The selection of appropriate contexts to use in a lesson should be based on the Mathematical concepts and skills learners should use to explore the context. Although non-Mathematical considerations are also encouraged in solving problems in Mathematical Literacy these should not be a basis for the selection of contexts - otherwise the subject will be reduced to a general knowledge subject where every answer is correct depending on how one justifies it.

In preparing for a lesson, educators should start with a selection of Mathematical knowledge and skills they want to develop in learners (or learners to use). These are contained in the basic skills topics and some in the applications topics. Once that is done, appropriate activities/ contexts can be chosen to prepare for a lesson.

3. ASSESSMENT IN MATHEMATICAL LITERACY

Learner assessment in Mathematical Literacy takes place informally and formally. Informal assessment is used formatively while formal assessment is used summatively. Examples of informal assessment include classworks, group/pair work, worksheets, short/speed tests, etc. The main purpose of informal assessment is to monitor and support learning. It may be done on a daily or weekly basis depending on the concepts being developed.

Formal assessment on the other hand has a very important purpose- that of progressing the learner from one grade to the next. The decision on whether a learner is ready to move to the next grade or not in the subject should be based on the learner performance in formal assessment.

Formal assessment must be conducted throughout the school year. For this reason formal assessment is referred to as continuous assessment (CASS). Continuous assessment together with the end of the year examinations constitute the subject Programme of Assessment (PoA). Table 1 below shows the minimum number and weighting of assessment tasks required for the grade 10 and 11 programme of assessment (PoA).

TABLE 1: Programme of Assessment, grades 10 and 11

| |PROGRAMME OF ASSESSMENT: GRADE 10 and 11 |

| |Continuous assessment (CASS) |Final |

| |(25%) |Examination |

| | |(75%) |

| |TERM 1 |

| |School – Based Assessment (SBA) |External |

| |(25%) |Examination |

| | |(75%) |

| |TERM 1 |TERM 2 |

|1 |Knowing |±30% |

|2 |Applying routine procedures in familiar contexts |±30% |

|3 |Applying multi-step procedures in a variety of contexts |±20% |

|4 |Reasoning and Reflecting |±20% |

Level 1 and 2 questions are very easy to set as they involve recall of facts (level 1) and or performing routine calculations (level 2) in familiar contexts. Level 3 questions depend mainly on the number of steps performed to get to the final answer and the ability to perform these steps across different contexts. In determining whether a question is at level 4 the following guidelines may be very helpful:

➢ Does the question require the use of integrated content/skills from different topics?

➢ Is the context in which the problem is situated complex and requires careful analysis before performing calculations?

➢ Do non-mathematical considerations have influence on the solution/answer to the question?

➢ Is the learner expected to solve the problem without any guidance?

If the answer to anyone of the above questions is ‘yes’, then the question is at level 4.

2. Purposes of PoA tasks

Tasks in the PoA have different purposes. Assignments are intended to give learners an opportunity to consolidate work or topic already dealt with. They are also most commonly used to prepare learners for tests and examinations.

Investigations are intended to develop higher order thinking skills required to answer level 3 and 4 questions. In these tasks learners are guided towards the discovery of fundamental relationships amongst objects and communicate such relationships in clear and unambiguous terms.

The diagram below shows a summary of the purposes and relationship between the different tasks of a PoA.

As the diagram indicates, it is very clear that all continuous assessment tasks, i.e. assignments, tests, investigations must be set in such a way that they adequately prepare learners to do well in examinations. Some guidelines on setting PoA tasks are given in the next section.

4. GUIDELINES FOR SETTING PoA TASKS

5.1 Setting tests, assignments and investigations: MATHEMATICAL LITERACY

The following table provides some useful guidelines on setting continuous assessment tasks

|Forms of Assessment and |Number required and weighting by end of year |Time allocation per |Length/ Marks | |

|their marking tools | |task | | |

| | | | |Coverage, purpose and |

| | | | |complexity |

| |GR 10 |GR 11 |GR 12 | |

| | | | | |

5.2 Setting examinations: MATHEMATICAL LITERACY, grade 10 and 11

The CAPS document for Mathematical literacy (pages 105 – 110) provides clear guidelines on setting examination papers for grade10 – 12. The table below gives a more specific guidance for each paper and grade.

|Term |Grade 10 |Paper 1 (Basic skills in contexts) |Paper 2 (Applications of basic skills in contexts) |

|2 |TWO Papers |Marks: 100 |Marks: 100 |

| | |Duration: 2 Hours |Duration: 2 Hours |

| | |Paper layout must be similar to that of DBE grade 12 national exam |Paper layout must be similar to that of DBE grade 12 national exam papers |

| | |papers |The question paper should have at least FOUR questions |

| | |The question paper should have at least FOUR questions |The paper should assess ability to use appropriate mathematical and non-mathematical |

| | |The paper should assess understanding of mathematical content(basic |techniques to solve problems in authentic contexts |

| | |skills topics) |ALL topics MUST be covered and mark allocation per topic should be: |

| | |ALL topics MUST be covered and mark allocation per topic should be: |Finance = ± 35 |

| | |Finance = ± 35 |Measurement = ± 20 |

| | |Measurement = ± 20 |Maps, plans and other representations…= ±15 |

| | |Maps, plans and other representations…= ±15 |Data handling = ± 25 |

| | |Data handling = ± 25 |Probability = ± 5 |

| | |Probability = ± 5 |All questions MUST be context based |

| | |All questions MUST be context based |Each question should focus on two or more applications topics(excluding probability) |

| | |Each question should focus on anyone of the FOUR applications |Probability may be assessed in anyone or more of the questions |

| | |topics(excluding probability) |Each question may contain more than one context. |

| | |Probability may be assessed in anyone or more of the questions |Taxonomy levels of questions should be: |

| | |Each question may contain more than one context. |Level 2 = ±25marks |

| | |Taxonomy levels of questions should be: |Level 3 = ±35 marks |

| | |Level 1 = ±60marks |Level 4 = ± 40 marks |

| | |Level 2 = ±35 marks |A memorandum with mark explanation must be used to mark the exam paper |

| | |Level 3 = ± 5 marks | |

| | |A memorandum with mark explanation must be used to mark the exam paper| |

| | | | |

|3 |TWO papers |Marks: 150 |Marks: 150 |

| | |Duration: 3 Hours |Duration: 3 Hours |

| | |Paper layout must be similar to that of DBE grade 12 national exam |Paper layout must be similar to that of DBE grade 12 national exam papers |

| | |papers |The question paper should have at least FIVE questions |

| | |The question paper should have at least FIVE questions |The paper should assess ability to use appropriate mathematical and non-mathematical |

| | |The paper should assess understanding of mathematical content(basic |techniques to solve problems in authentic contexts |

| | |skills topics) |ALL topics MUST be covered and mark allocation per topic should be: |

| | |ALL topics MUST be covered and mark allocation per topic should be: |Finance = ± 50 |

| | |Finance = ± 50 |Measurement = ± 30 |

| | |Measurement = ± 30 |Maps, plans and other representations…= ±20 |

| | |Maps, plans and other representations…= ±20 |Data handling = ± 40 |

| | |Data handling = ± 40 |Probability = ± 10 |

| | |Probability = ± 10 |All questions MUST be context based |

| | |All questions MUST be context based |Each question should focus on two or more applications topics(excluding probability) |

| | |Each question may contain more than one context. |Probability may be assessed in anyone or more of the questions |

| | |Each question should focus on anyone of the FOUR applications |Each question may contain more than one context. |

| | |topics(excluding probability) |Taxonomy levels of questions should be: |

| | |Probability may be assessed in anyone or more of the questions |Level 2 = ±40marks |

| | |Taxonomy levels of questions should be: |Level 3 = ±50 marks |

| | |Level 1 = ±90marks |Level 4 = ± 60 marks |

| | |Level 2 = ±50 marks |A memorandum with mark explanation must be used to mark the exam paper |

| | |Level 3 = ± 10 marks | |

| | |A memorandum with mark explanation must be used to mark the exam | |

| | |paper | |

5. RECORDING AND RECORD KEEPING

Recording

With the exception of examinations, there is no prescribed total mark for other formal assessment tasks for all grades. Only the minimum total mark is suggested (see 5.1 above). Learner performance on each task should be recorded as a mark obtained by the learner in the task out of the total mark for the task. The Western Cape Education Department (WCED) prepares excel mark recording sheets with prescribed weightings for each task. Total marks for examinations are already inserted in the recording sheets.

Educators need to insert total marks for the other formal assessment tasks (assignments, tests and investigations) in the recording sheet before entering each learner’s mark for each task. District offices send these mark recording sheets to their schools.

These recording sheets perform all the necessary mark conversions and give the learner’s final mark for each term of the school year together with the rating code.

Record keeping

Evidence of learner performance (Learner portfolio) must be safely kept (in a file preferably) for record keeping and moderation purposes. This evidence includes ALL marked scripts of formal assessment tasks, including any handwork (e.g. models) that learners might have produced in order to obtain marks

ALL Mathematical Literacy educators must have a portfolio. The educator portfolio should at least contain the following:

• Content page

• Workschedule (Year Plan)

• Programme of assessment

• Assessment tasks and their marking memoranda (tasks in the programme of assessment)

• Mark recording sheets for each class

6. MODERATION OFLEARNER ASSESSMENT

Learner assessment will be moderated at three levels, namely; school, district (cluster) and provincial/national level. The main purpose of the moderation process is to ensure that school based assessment is conducted continuously, fairly and is of acceptable standard. Internal school moderation is the responsibility of the HOD/Subject Head or whoever is appointed to do the moderation and is knowledgeable in the subject. The diagram below shows the relationship between the various stages of moderating school based assessment.

[pic]

All the evidence (learner and educator portfolios) should be made available during moderation.

7. MODERATION INSTRUMENTS

Different moderation instruments are used at each of the stages of school based moderation. Schools are encouraged to develop their internal moderation instruments and should make these available at district moderation level. Districts also develop their own moderation instruments depending on the mode of moderation used in that district.

(Note: Please insert your moderation instruments that you use for school and district level moderation)

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DIRECTORATE: CURRICULUM DEVELOPMENT

PROGRAMME

OF ASSESSMENT (PoA):

PLANNING GUIDE

MATHEMATICAL LITERACY

(GRADES 10 - 12)

CAPS

FET

2015

Basic Skills Topics

(Elementary mathematical content)

Application Topics

(Authentic familiar & unfamiliar real-life contexts)

Probability

Data Handling

Maps, plans & others representations of the physical world

Measurement

Finance

Number and calculations with numbers

Patterns, relationships and representations

Interpret and communicate answers/solutions

Use elementary mathematical content to explore

Assignments

PoA TASK

Purpose

Controlled Tests

Best Performance

In Examinations

(June, Sept, Final)

Development of

Higher Order Thinking Skills

(Level 3 and 4)

INVESTIGATIONS

OR

PROJECTS

UMALUSI

PROVINCIAL MODERATION

(SCP and Curriculum Advisers/Assessment directorate)

DISTRICT MODERATION

(Clusters/Face by Curriculum Advisers)

SCHOOL

(HOD/Subject Head)

Moderation starts

Feedback

Feedback

Feedback

(The moderation process for school based assessment)

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