Introduction This syllabus explains the knowledge, skills, attitudes and values that students should achieve in Elementary Prep, 1 and 2 in Cultural Mathematics. These are expressed as learning outcomes and indicators. The learning outcomes are student-centred and written in terms that enable them to be demonstrated, assessed or measured. The outcomes are written to show the progression from one grade to the next. Each learning outcome is illustrated with a list of examples of the kinds of things students should be able to do, know and understand if they are achieving an outcome. These are called indicators. The learning outcomes and indicators will: • give teachers individually or in groups, the flexibility to write programs and units of work, which should be developed to suit local conditions and individual student needs • help teachers assess and report on students’ achievements in relation to the learning outcomes • allow student achievement of the outcomes to be described in consistent ways • help teachers monitor students’ learning • help teachers plan their future teaching programs. In Cultural Mathematics, a manageable number of outcomes are identified for each grade in Elementary Prep, 1 and 2. They are: • organised to show progression from one grade to the next • organised into strands which contain a family of separate outcomes that are related to a particular theme: Space, Measurement, Number, Pattern, Chance • numbered to help track similar outcomes linked to the strands from one grade to the next • written to include all the essential knowledge, skills and understandings a student should achieve in the Cultural Mathematics course • created using an active verb to ensure students actively participate in the learning. The language of instruction at Elementary is the students’ vernacular, which will enable teachers to enhance the students’ understanding of mathematical concepts. Students need to use mathematics in different contexts. Teachers teaching this course must be competent in the language the children speak, so that they can explain the mathematical concepts clearly to their students. Cultural Mathematics is to be timetabled for 180 minutes per week in all Elementary schools. 1 Elementary syllabus Rationale All citizens have the right to participate in the future development of Papua New Guinea. For this reason, students need to develop sound mathematical knowledge, skills and understanding. The mathematics described in this syllabus provides a foundation for this. Students at Elementary will be able to link new mathematical concepts from the five strands in this syllabus to their existing cultural knowledge. The students will integrate this knowledge so that they are can confidently use mathematics in their everyday lives. The Elementary Cultural Mathematics course provides many opportunities for relevant and purposeful learning in an environment that is built on the principles of home life. 2 Cultural Mathematics Curriculum principles Our way of life This course is based on three learning principles: • we learn best when we build new learning on what is already known • we learn well when we recognise an immediate use or need for what is to be learned • we use ideas and skills in a coordinated way to solve real problems. The syllabus continually refers to pre-existing knowledge and skills and teachers need to set the mathematics into contexts that are familiar and of interest to the students. The students need to use concepts and skills from many areas of mathematics to come up with solutions to problems in real-life situations. Integral human development Catering for diversity The Cultural Mathematics curriculum must offer students equal opportunities to participate in class activities and assessment activities. These must be directed and be suitable for girls and boys. To meet the requirements of our National Constitution teachers must ensure that there is no bias in their teaching, learning and assessment methods. All students must be given equal opportunity to achieve success. Teaching and learning In Elementary schools, teachers use an integrated approach to teaching and learning. The teacher creates a program that is meaningful, appropriate and motivating for the students. The use of learning outcomes provides opportunities to integrate the curriculum. Teachers should map out the learning outcomes for those parts of the syllabus that they are intending to teach in the coming term or year. Where there is more than one teacher across a grade, this should be done as a small team. Teachers with leadership responsibilities in the school should be invited to attend and support this planning process. While carrying out this process, links between learning outcomes for different subjects should be noted, as there is scope for combining and using these outcomes in an integrated approach to teaching and learning. 3 Elementary syllabus For example, a Language learning outcome might refer to the use of questionnaires and holding discussions with community members and a Culture and Community learning outcome may also do this. In this way evidence of the achievement of these outcomes can be provided in more than one subject. The education of a child in the past was the responsibility of the family and the local community. Traditional education was integrated with events and seasons and extended over many years depending on the student’s needs. An individual learned about the spiritual, social, economical and political skills necessary for life in the community. These practices have become the foundation of learning for Elementary students. Teaching should build on what students know and should use appropriate local contexts and the community to promote better understanding. Elementary education aims to help students to continue developing an understanding of and identification with their local cultural values and beliefs using the language they already speak. Student-centred learning The teaching approaches required for this syllabus are student- centred. They should promote the philosophy of how to think. Student-centred teaching activities include investigation, problem solving and out-of-class excursions. These approaches provide opportunities for students to work cooperatively, discuss, make decisions, plan, organise, carry out activities, record results and report findings. Teaching activities should also allow students to listen to each other’s opinions, demonstrate their strategies and critically analyse results. Thematic teaching and integration Traditional education was integrated and taught young people to see the world through the eyes of the community, focusing on their needs. Elementary teaching focuses on an integrated curriculum, which is organised into the following subjects: Culture and Community, Language and Cultural Mathematics. A thematic, student-centred, activity-based approach is recommended in Elementary classes. Teaching and learning activities should be based on community themes as much as possible, derived from the community’s calendar and be sensitive to the local culture, traditions and seasons. The development of skills should be emphasised. Cultural Mathematics will be developed with advice from the community. 4 Cultural Mathematics Flexibility and relevance It is important to establish a routine for students. However, teachers need to be flexible with the times allocated to allow for spontaneous learning experiences. Special projects, field trips and unplanned events such as deaths and births and natural disasters such as a volcanic eruption, often provide opportunities for integrated, holistic learning. Teachers should encourage students to take part in local activities to make the curriculum more interesting and relevant. 5 Elementary syllabus Aims Students develop: • a sound foundation for further mathematical learning • confidence in applying mathematical skills • curiosity leading to the understanding of concepts • determination to persist with difficult problems • critical judgment in selecting approaches to problems • an appreciation of the cultural diversity in numeracy. 6 Cultural Mathematics Content overview The content of this syllabus is organised into five strands. A strand such as Space is a useful and convenient way of organising the learning outcomes for a subject. Each strand identifies particular aspects of a subject or a theme such as a set of processes. Each strand displays a typical progression of learning from one grade to the next. Each strand is further organised into a number of substrands to allow the content to be specified and described as learning outcomes. Cultural Mathematics is organised into five strands: • Space • Measurement • Number • Pattern • Chance. Space has two substrands: • Space • Shape. Measurement has three substrands: • Measuring and estimating • Area • Time. Number has four substrands: • Counting • Mathematical language • Operations • Money. Pattern has one substrand: • Patterns. Chance has one substrand: • Chance and information. Space This strand deals with giving information and directions to be followed to move from location to location. It also deals with the concept of shape and the language required to describe various shapes. Measurement This strand concentrates on the units used to describe length, weight, capacity, area and time and how they are measured. The concepts in this strand focus on ways of measuring using local measurements as well as common formal measurements. Students will also estimate and calculate time using traditional ways. 7 Elementary syllabus Number This strand deals with local counting systems using the students’ own language as well as learning the formal language words used in mathematics. The concepts of the four operations, addition, subtraction, multiplication and division are dealt with in a practical way. The value of different traditional money is compared with today’s money of Papua New Guinea. Pattern This strand deals with number patterns and local art patterns such as those used for bilums and pottery. Students are introduced to simple number patterns and their representations as they use numbers to write and to form patterns. The patterns of the local community are found in such things as headdresses for dances and body decoration. Patterns such as tattoos are identified and students learn how to apply rules or make their own rules to produce these patterns. Chance This strand deals with students using information to predict or make guesses about events that will happen, may happen or can never happen. They use simple activities to learn how to explore the concept in this strand. Table of strands and substrands Strand Elementary Prep Elementary 1 Elementary 2 Space • Space • Space • Space • Shape • Shape • Shape Measurement • Measuring and • Measuring and • Measuring and estimating estimating estimating • Area • Area • Area • Time • Time • Timer2 Number • Money • Money • Money • Counting • Counting • Counting • Mathematical language • Mathematical language • Mathematical language • Operations • Operations • Operations Pattern • Patterns • Patterns • Patterns Chance • Chance and information • Chance and information • Chance and information 8 Cultural Mathematics Learning outcomes Numbering of learning outcomes Each learning outcome is numbered with three digits, such as 1.1.1. The first number refers to the grade level. The second number refers to the strand. The third number refers to the outcome in the strand. Thus, 1.1.1 refers to an outcome at Elementary 1, strand 1 and outcome number 1. Strand Elementary Prep Elementary 1 Elementary 2 Space P.1.1 Follow and give 1.1.1 Follow and give 2.1.1 Follow directions simple directions for directions to move from from simple maps moving in a space place to place P.1.2 Identify locally 1.1.2 Compare and 2.1.2 Investigate and known shapes by their group shapes in the describe the features of visual appearance community geometric shapes Measurement P.2.1 Measure the length, 1.2.1 Measure, and 2.2.1 Compare the weight and capacity of compare the length, accuracy of local things using their own weight and capacity of measures of length, informal measuring things using local weight and capacity units informal units P.2.2 Measure how much 1.2.2 Compare and 2.2.2 Estimate the space is covered by measure an area using number of objects objects using their own local ways of needed to cover a informal units measuring surface P.2.3 Use time markers 1.2.3 Tell and use time in 2.2.3 Identify and traditional ways sequence events that occur at different times Number P.3.1 Count objects in 1.3.1 Count groups of 2.3.1 Count objects in vernacular using local objects in vernacular vernacular and English number systems using local and standard number systems P.3.2 Describe the four 1.3.2 Use number 2.3.2 Use vernacular operations using simple symbols that mean the and English words for vernacular words same as vernacular number symbols and number words operational signs P.3.3 Solve simple 1.3.3 Solve problems 2.3.3 Solve problems problems using using two-digit numbers using two-digit numbers concrete materials to 20 or closest to 20 in up to 99 vernacular P.3.4 Describe traditional 1.3.4 Use different 2.3.4 Make and solve money and Papua New amounts of money to money problems Guinean money make up various sums of money 9 Elementary syllabus Strand Elementary Prep Elementary 1 Elementary 2 Patterns P.4.1 Make simple 1.4.1 Recognise various 2.4.1 Collect and patterns local patterns compare various patterns Chance P.5.1 Identify events that 1.5.1 Identify and 2.5.1 Make guesses always happen describe events that about events that will regularly in the sometimes happen in happen, may happen or community the community and the will never happen environment 10 Cultural Mathematics Learning outcomes and indicators Strand: Space Substrand Elementary Prep Elementary 1 Elementary 2 Space P.1.1 Follow and give 1.1.1 Follow and give 2.1.1 Follow directions simple directions for directions to move from from simple maps moving in a space place to place Indicators Students will be Students will be Students will be achieving this outcome achieving this outcome achieving this outcome when they, for example when they, for example when they, for example • give simple directions • give directions to a • talk about direction such as walk three person to find a place in names in vernacular steps forward, stop, the community such as east (sun take three steps left, rises), west (sun sets), turn right, take three north and south steps backward • draw simple maps to • demonstrate using show directions to find directions given the school, villages, • make a list of local gardens, church names for directions • make a list of directions such as east (sun rises) to guide people to • use direction words to certain places play games Sub-strand Prep 1 2 11 Elementary syllabus Strand: Space Substrand Elementary Prep Elementary 1 Elementary 2 Shape P.1.2 Identify locally 1.1.2 Compare and 2.1.2 Investigate and known shapes by their group shapes in the describe the features of visual appearance community geometric shapes Indicators Students will be Students will be Students will be achieving this outcome achieving this outcome achieving this outcome when they, for example when they, for example when they, for example • collect and display • sort shapes according • talk about the features locally known shapes to their differences and of shapes such as in everyday life similarities edges, angles, curves, • name and label locally • make new shapes by faces, sides, corners known shapes in putting simple shapes • group shapes according vernacular together to number of sides, • make a mobile of • display groups of shapes, angles locally known shapes different shapes from • count faces, corners • make a collage of the community such as and edges of locally known shapes baskets, pots, kundus, geometrical figures shells • sort and match shapes • build new shapes using • name features of three-dimensional • make models of locally shapes in vernacular shapes known shapes using such as edges, angles, sand, clay or mud • label using vernacular curves, corners and say English words • identify lines found in • group local shapes for features such as the local environment according to their corners, edges, angles such as roads, rivers, features such as all drawings • identify and discuss objects with curved types of lines that make • draw line drawings of edges up objects such as things such as • build objects using local long, straight, sharp, gardens, houses, materials and label the curved, wavy, thick, thin playing fields shapes used • group lines according to • find things in the local • make line drawings of their differences and community where one regular and irregular similarities half looks exactly the shapes found in the same as the other half • make symmetrical community shapes such as • draw objects from butterfly wings, leaves, different places that are flower petals symmetrical 12 Cultural Mathematics Strand: Measurement Substrand Elementary Prep Elementary 1 Elementary 2 Measuring P.2.1 Measure the length, 1.2.1 Measure, and 2.2.1 Compare the and weight and capacity of compare the length, accuracy of local estimating things using their own weight and capacity of measures of length, informal measuring things using local weight and capacity units informal units Indicators Students will be Students will be Students will be achieving this outcome achieving this outcome achieving this outcome when they, for example when they, for example when they, for example • match and compare • use things such as • measure lengths in lengths and heights hand span, arm different ways and using their own units lengths, pacing, sticks compare their accuracy • measure length, width or other items to • talk about and practise and height using their measure length some traditional own units such as bottle • use comparison words measures from their tops, seeds, leaves for measuring such as local community • collect items of different light, lighter, lightest, • compare local ways of weight and arrange heavy, heavier, measuring weight them in order using heaviest, long, short, • measure capacity using their own units tall, full, empty, not various common much • match and compare containers light and heavy objects • use different containers and other items to • arrange light and heavy measure capacity objects in a simple order • collect containers of different sizes and arrange them in order • use traditional ways to guess and order the amount of liquid such as water, juice 13 Elementary syllabus Strand: Measurement Substrand Elementary Prep Elementary 1 Elementary 2 Area P.2.2 Measure how much 1.2.2 Compare and 2.2.2 Estimate the space is covered by measure an area using number of objects objects using their own local ways of needed to cover a informal units measuring surface Indicators Students will be Students will be Students will be achieving this outcome achieving this outcome achieving this outcome when they, for example when they, for example when they, for example • use items such as • use informal units to • estimate how many leaves, bottle tops, measure regular objects it takes to cover stones or pattern blocks surfaces such as irregular surfaces to cover surfaces such leaves, mats • use different objects to as table top, books • measure and compare estimate the area of a • find out how much areas using traditional given space space is taken up by ways of measuring such things as gardens, • arrange in order things houses, pathways, such as school roads, classrooms gardens, school classrooms, teachers’ houses, tables 14 Cultural Mathematics Strand: Measurement Substrand Elementary Prep Elementary 1 Elementary 2 Time P.2.3 Use time markers 1.2.3 Tell and use time in 2.2.3 Identify and traditional ways sequence events that occur at different times Indicators Students will be Students will be Students will be achieving this outcome achieving this outcome achieving this outcome when they, for example when they, for example when they, for example • name parts of the day • name and list different • discuss their traditional using traditional parts of the day, days calendar measures of time in of the week, months of • list the seasons and vernacular the year activities for each • talk about some annual • list important events of season events and the year such as • make a community celebrations such as feasts, celebrations calendar harvest time, Easter, Independence Day, Christmas Day 15 Elementary syllabus STRAND: Number Substrand Elementary Prep Elementary 1 Elementary 2 Counting P.3.1 Count objects in 1.3.1 Count groups of 2.3.1 Count objects in vernacular using local objects in vernacular vernacular and English number systems using local and standard number systems Indicators Students will be Students will be Students will be achieving this outcome achieving this outcome achieving this outcome when they, for example when they, for example when they, for example • name numbers from • count by grouping • count numbers from zero to the highest objects in many one to a hundred in number that is possible different ways such as English using the in vernacular in twos, fives and tens international number • count common objects • identify how objects system by their own number such as fish, taro, • read and write number words kaukau, banana, words in vernacular up • count using concrete peanuts, betelnuts are to 100 objects grouped in the • count to a hundred in community • talk about where groups of twos, fives numbers are used in • count groups of objects and tens in vernacular their lives to the highest two-digit and English number possible such • match local number • count numbers as count in twos to 98 words to the same accurately in games number of objects • say and write number such as card games, words up to the highest board games and • count local money two-digit number playground activities • talk about some of the possible • write locally used symbols, pictures or position numbers objects used to (ordinal numbers) from represent numbers first to tenth or as far as • use numbers to the language can go participate in traditional and say them in English games such as finding hidden objects 16 Cultural Mathematics Strand: Number Substrand Elementary Prep Elementary 1 Elementary 2 Mathematical P.3.2 Describe the four 1.3.2 Use number 2.3.2 Use vernacular and language operations using symbols that mean the English words for simple vernacular same as vernacular number symbols and words number words operational signs Indicators Students will be Students will be Students will be achieving this outcome achieving this outcome achieving this outcome when they, for example when they, for example when they, for example • talk about vernacular • identify and draw • draw number symbols words for each of the number symbols from (numerals) from zero to operations such as zero to the highest a hundred words that mean putting possible number in • say English and together, taking away, vernacular vernacular words for grouping and sharing • match vernacular words number symbols • use vernacular words with number symbols • identify and draw signs for operations when by playing simple card for addition, subtraction, solving problems games multiplication and • make a set of posters division to match number • make mobiles matching words, symbols and numbers, words and pictures pictures 17 Elementary syllabus Strand: Number Substrand Elementary Prep Elementary 1 Elementary 2 Operations P.3.3 Solve simple 1.3.3 Solve problems 2.3.3 Solve problems problems using using two-digit numbers using two-digit numbers concrete materials to 20 or closest to 20 in up to 99 vernacular Indicators Students will be Students will be Students will be achieving this outcome achieving this outcome achieving this outcome when they, for example when they, for example when they, for example • share whole objects • identify and write units • place and write using concrete and tens numbers in units and materials amongst • work out simple tenths using number friends addition and subtraction sentences and place • talk together in pairs or problems with no value tables small groups to work trading • work out simple out ways of solving • represent a problem addition and subtraction simple problems using concrete problems with trading • put together objects, materials and say it in • make simple number such as counters or vernacular words sentences using stones, to see how • share objects such as numerals, vernacular many objects there are marbles, bottle tops, and English words altogether sweets, peanuts or fruit • use concrete materials • apply counting skills to equally amongst friends to make up number work out how many • group objects into lots, sentences to describe objects, such as such as two lots, three groups of objects such pencils, seeds or lots, four lots to find the as two groups of five marbles, there are product betelnuts altogether in a number • identify and share a • solve simple of containers whole object into equal multiplication and • use counters, such as parts such as into two division problems using stones, leaves, seeds, parts, four parts concrete materials to decide how many without trading objects are left after • identify and share a some are given away whole object into equal • arrange concrete parts such as into three materials in simple parts, five parts games or activities to show understanding of all four operations 18 Cultural Mathematics Strand: Number Substrand Elementary Prep Elementary 1 Elementary 2 Money P.3.4 Describe traditional 1.3.4 Use different 2.3.4 Make and solve money and Papua New amounts of money to money problems Guinean money make up various sums of money Indicators Students will be Students will be Students will be achieving this outcome achieving this outcome achieving this outcome when they, for example when they, for example when they, for example • talk about traditional • show different notes • calculate the cost of money with community and coins used what they intend to buy members and explain • calculate their change • calculate the remaining its value from a given amount amount after their • recognise Papua New after shopping or spending Guinean money and marketing traditional currency • make up given amounts • use different coins to of money make up K1.00 • play ‘shop’ with change to K10.00 19 Elementary syllabus Strand: Patterns Substrand Elementary Prep Elementary 1 Elementary 2 Patterns P.4.1 Make simple 1.4.1 Recognise various 2.4.1 Collect and patterns local patterns compare various patterns Indicators Students will be Students will be Students will be achieving this outcome achieving this outcome achieving this outcome when they, for example when they, for example when they, for example • use numbers to count • talk about different • apply rules to create simple patterns patterns of local their own patterns • recognise, memorise community activities • identify rules in different and use simple such as headdresses patterns patterns for dances, tattoo • find the missing items in patterns, flower patterns • make an object such as a simple pattern a necklace, a drawing • observe an item from • make own rules and using repeating plants or animals, such apply them in forming patterns as finding out if there patterns are patterns in any of • identify repeating them or in the way they • solve simple number patterns of colours in are made up patterns, such as two, objects such as bilums, four, six tapa cloth, clay pots, • use common colours to lime pots, mats make patterns 20 Cultural Mathematics Strand: Chance Substrand Elementary Prep Elementary 1 Elementary 2 Chance and P.5.1 Identify events that 1.5.1 Identify and 2.5.1 Make guesses information always happen describe events that about events that will regularly in the sometimes happen in happen, may happen community the community and the or will never happen environment Indicators Students will be Students will be Students will be achieving this outcome achieving this outcome achieving this outcome when they, for example when they, for example when they, for example • identify daily routines • identify events such as • identify events that will such as getting up, whether it’s going to happen such as going to bed, eating rain, when someone is landslides, volcanic and washing going out to catch fish, eruption, river flooding, • identify daily cycles when fruit is going to be high tides, start and such as the sun comes picked, the day is going finish of school up and goes down, tide to be clear, when yam • identify events that comes in and goes out is planted and might happen such as it harvested will rain, it is going to be • identify events such as windy, wet clothes will the teacher might be dry quickly if the wind is absent, someone may strong, the motor will be sick, their school start team might win • identify events that never happen such as one can find a chest of gold at the end of a rainbow, a chicken that lays a golden egg, a cow that jumped over the moon, that one will live forever 21 Elementary syllabus Assessment and reporting Assessment and reporting practices described here are detailed further in the National Assessment and Reporting Policy and in other support materials produced by the Department of Education. Assessment Assessment is the ongoing process of identifying, gathering and interpreting information about students’ achievement of the learning outcomes described in the subject syllabuses. Assessment in Elementary schooling is the continuous process of finding out what the students have learnt and still need to learn. Elementary teachers should take into account Papua New Guinean cultural values and use local cultural practices where appropriate to assess and report students’ achievement. Assessment at Elementary level should use a range of methods with little emphasis on written tests. It should be based on the learning outcomes and arise from the everyday learning experiences of students. It is a process of: • observing students at work • conferencing or talking and questioning the students about their work and how they are thinking and feeling–their attitude towards work • looking at work samples for information on what students can do. Through these processes teachers gather evidence of students’ learning. Continuous assessment for young students is essential. Their knowledge and skills are continually changing as they learn more. It is important for teachers to be aware of what the students know, can do and understand. When this information is known about the students in the class, programming can be made more relevant and meaningful to match the students’ needs.. Recording and reporting Teachers must keep accurate records of students’ achievement of the learning outcomes and report these achievements in fair and accurate ways to parents and guardians, teachers, students and others. Recording methods may include: • journal, diary or anecdotal notes • portfolios • progressive records • checklists • work samples with comments written by the teacher. 22 Cultural Mathematics Student reports should be based on assessement information collected from ongoing assessment. Schools will decide how reports will be presented to best suit the needs of their communities. When students first start school in Elementary Prep, parents and guardians will be very eager to hear about their child’s progress. Teachers should consider holding a parent-teacher interview either at the end of the child’s first term at school or early second term. In Elementary 1, teachers may decide to hold formal talks with parents and guardians half way through the year and at the end of the year. In Elementary 2, teachers may decide to hold formal talks with parents and guardians in the middle of second term and provide them with a written report at the end of the year. Evaluation Teachers will use assessment information to evaluate the effectiveness of their teaching, learning and assessment programs and to make improvements to their teaching practice in order to improve student learning. Schools may use whole school assessment data to evaluate the effectiveness of teaching and learning in a particular subject or at particular grade levels and make decisions on how to improve student learning. 23 Elementary syllabus References National Department of Education (NDOE) National Department of Education 2003, National Assessment and Reporting Policy, NDOE, Waigani. National Department of Education 2002, National Curriculum Statement, NDOE, Waigani. National Department of Education 1998, Elementary Curriculum Statement, NDOE, Waigani. National Department of Education 1998, Elementary Scope and Sequence, NDOE, Waigani. National Department of Education 1997, Curriculum Overview, NDOE, Waigani. National Department of Education 1997, Resource Book for Cultural Mathematics, NDOE, Waigani. 24 Cultural Mathematics 25 Elementary syllabus Cultural Mathematics Elementary Syllabus Papua New Guinea Department of Education 26 Elementary syllabus Cultural Mathematics Issued free to schools by the Department of Education Published in 2003 by the Department of Education, Papua New Guinea Reprinted with amendments 2005 © Copyright 2003, Department of Education, Papua New Guinea All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher. ISBN 9980–930–68–3 Acknowledgements The Elementary Cultural Mathematics Syllabus was prepared by the Curriculum Development Division of the Department of Education and was coordinated by Barbara Sipou. The Elementary Cultural Mathematics Advisory Committee as well as community members, teachers, inspectors, educators and representatives from government and non-government organisations have developed this syllabus through meetings, workshops and trials. This document was developed with the support of the Australian Government through the Curriculum Reform Implementation Project. 27 ii Elementary syllabus Cultural Mathematics Cultural Mathematics Secretary’s message ..................................................................... iv Introduction .................................................................................... 1 Rationale ........................................................................................ 2 Curriculum principles ...................................................................... 3 Aims ............................................................................................... 6 Content overview ........................................................................... 7 Learning outcomes ........................................................................ 9 Learning outcomes and indicators ................................................ 11 Assessment and reporting ............................................................ 22 References .................................................................................... 24 28 iii Elementary syllabus Cultural Mathematics Secretary’s message The current reforms in education have been in progress since 1992. The Education Reform has emphasised community-based schooling, the use of vernacular languages in schools, the introduction of Elementary schools, the expansion of Primary schooling to Grade 8 and increased access to Grades 9 and 10. This syllabus is to be used by Elementary (Elementary Prep, Elementary 1 and Elementary 2) students in Elementary schools throughout Papua New Guinea. This syllabus develops, links and builds upon concepts, skills and attitudes which flow into Lower Primary (Grades 3, 4 and 5). This syllabus provides a sound foundation for further learning in the reformed school system. Students’ language abilities, already gained in their home environments, must be respected, built on and extended. Vernacular languages have a large part to play in our students’ formative years and their first language should be used to promote a deeper understanding of difficult concepts when this is appropriate. This Cultural Mathematics Syllabus is a significant part of the Education Reform. It presents a coherent view of mathematics at the Elementary level of schooling. Mathematics at this level of schooling is based on the everyday mathematics used in the community. While this syllabus is designed for teachers of Elementary students, it will also be useful for developers of support materials, planners and Lower Primary teachers. Cultural Mathematics provides a sound foundation for future mathematical studies and the mathematical literacy necessary to do other studies. Elementary education is community based. Elementary teachers speak the language of the local children so that they will be able to teach Cultural Mathematics using this vernacular language. With the help of community members and trainers, teachers will be able to develop a relevant community-based curriculum. I commend and approve this syllabus as the official curriculum for Cultural Mathematics to be used in all Elementary schools throughout Papua New Guinea. Peter M. Baki Secretary for Education 29 iv Document Outline
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