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Lamp plus pri maths 12 mar
This document outlines the agenda for a 3-day curriculum leadership module on primary mathematics for new heads of department and subject heads. Day 1 will cover the role of mathematics curriculum leaders, lesson planning frameworks, and self-directed learning. Day 2 focuses on higher-order thinking, technology integration, and department planning. Day 3 addresses group discussions on views of mathematics and how the subject has evolved. The objective is to support new curriculum leaders in their role and enable them to understand the mathematics curriculum framework, align programs to student needs, integrate technology, and facilitate teacher professional development.
Lamp plus pri maths 12 mar
- 1. LAMP+ Enhanced Leadership andManagement Programme Curriculum Leadership Module (CLM) Part 2 Primary Mathematics 12 March – 14 MarchCPDD & ETD
- 2. Getting to knowyou… Introduce yourself to your group members • tell your name, school, teaching experience • share something interesting about yourself
- 3. Getting to knowothers… BINGO! Find someone who matches the description in a square. Fill in his/her • Name • School Rules: • Duplication of names not allowed. • Friends from the same table group not allowed. Your Goal: Complete all the 9 squares!
- 4. Overview of LAMP+ Toequip newly-appointed middle managers (MMs) in schools with the “just-in-time” skills to: • deliver their department’s teaching and learning programmes effectively • align it to policy intent and curriculum objectives.
- 5. Objective of CLM(Part 2) To support new HODs/LHs/SHs in their role as Mathematics Curriculum Leaders.
- 6. CLM (Mathematics) At theend of the course, participants will be able to: understand the aim and organisation of the mathematics curriculum in the context of policies and initiatives align Mathematics programmes to the curriculum framework and to cater to the diverse groups of students integrate ICT in teaching and learning in classroom plan and support teacher learning through professional development and sharing for best practices
- 7. Programme • Role ofMathematics Curriculum Leader • Support from CPDD • Sharing by experienced HODs Day 1 • TPACK framework • Lesson Experience • SDL and CoL Day 2 • Higher order thinking • BY(i)TES • Department Planning Day 3
- 8. Group discussion… 2. Whydo you think Mathematics is important? 1. What is Mathematics to you? 3. From your personal experience, how has mathematics education evolved over the years?
- 9. Mathematics Science ofpatterns and relationships Diverse discipline that deals with Data, measurements and observations from science; with inference, deduction, and proof; and with mathematical models of natural phenomena, of human behaviour, and of social systems. Applications of mathematics use these patterns to explain and predict natural phenomena Mathematics relies on logic rather than on observation as its standard of truth (Source : Everybody Counts: A Report to the Nation on the Future of Mathematics Education. ©1989 by the National Academy of Sciences)
- 10. Copyright © Ministryof Education, Singapore. Importance of Mathematics • Highly-skilled, well- educated, scientific manpower needs strong grounding in Mathematics • Individuals who can think logically, abstractly, critically and creatively 10 Nation Individual
- 11. Evolution of Singapore MathematicsEducation 1940s to date
- 12. Evolution of SingaporeMathematics Education 1940s - Math taught in different language medium 2013: Revised Primary Math Teaching and Learning Syllabus (Learning Experiences) 1976: Revised Math Syllabus (Revised Pri Edn System) 1971: Revised Math Syllabus (content reduction) 1970: Math made compulsory in Pri & Sec 1960: 1st MOE designed Math Syllabus introduced 1996: Abacus introduced 1990: Singapore Math Framework 1st introduced 1979: Revised Syllabus (NES); PMP set up at CDIS TSLN, DOE, I&E, ICT MP, TLLM, PETALS, C2015, PERI 2009: PERI (HA) 2008: SBB (Foundation Math) 2007: Revised Math Syllabus (calculator) 2006: PETALS 2005: TLLM 2003: Revised Math Framework 2002: ICT MP2 2001: Revised Math Syllabus (new textbooks) 1999: Interim measure (content-reduced, IT TSLN) 1997: TSLN, ICT MP1
- 13. Initiatives supporting MathematicsCurriculum ...towards our TSLN vision ICT • MP1 - blueprint for the use of ICT • MP2 – harness ICT for learning (2002) 1997 SAIL • Trialled in 7 Pri & 9 Sec • Piloted in 16 Pri & 20 Sec (2003) 2002 SEED • Phase 1 workshops for 24 champion schs • Phase 2 sch-based workshops for pri schs 2004 LSM For P1 students 2007 PETALS Introduced the 5 key principles of engaged learning 2006 2008 SBB For P5 students MP3 Continuum of MP1 & 2 2009 PERI HA Prototype with 16 schools 2011 & 2012 Rollout Resources • P1-P4 • P5-P6 (2013) 2013 Revised Syllabus 21CC, S DL & CoL
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- 15. Your personal thoughts… Howdo you see your role of HOD/LH/SH as a Mathematics Curriculum Leader? Mathematics Curriculum Leader
- 16. Key Roles ofHOD as Curriculum Leader Set directions for the department Plan, implement, monitor and evaluate instructional programmes Develop and model effective teaching strategies Develop evaluation strategies to assess learning effectiveness Plan the professional development of teachers Select, prepare and organise teaching and learning resources
- 17. Curriculum Content What should mystudents learn? Assessment Did my students learn it? Pedagogy How should my students learn? Curriculum CPA
- 18. Set directions forthe department Interpret the aims and objectives of Mathematics Curriculum I. Aims of Mathematics Education II. Mathematics Curriculum Framework Translate them into the instructional programmes for the subject Ensure that the syllabus is understood by all teachers Advise P/VP on the subject Mathematics Curriculum Leader Strategic Planner & Instructional Leader
- 19. Aims of MathematicsEducation in Singapore The broad aims of mathematics education in Singapore are to enable students to: • acquire and apply mathematical concepts and skills; • develop cognitive and metacognitive skills through a mathematical approach to problem solving; and • develop positive attitudes towards mathematics. (Primary Mathematics Teaching and Learning Syllabus, p. 9)
- 20. Overview of Aims acrossthe Levels (Refer also to: Primary Mathematics Teaching and Learning Syllabus, 2012, p. 10) (Mathematics Education in Singapore, 2012, p. 6) Each syllabus expands on the three broad aims of mathematics education
- 21. Syllabus Design Spiral Curriculum ConnectedSyllabuses (Mathematics Education in Singapore, 2012, p. 6; Primary Mathematics Teaching and Learning Syllabus, 2012, p. 11)
- 22. Transition issues Subject BasedBanding (SBB) @ Primary School • Foundation Maths (1 – 4, U) • Standard Maths (A* to E, U) • Download the “From Foundation Maths to NA Maths Handbook” from EduMall http://subjects.edumall.sg/subjects/slot/u1030420/From%20Foundation%2 0Maths%20to%20NA%20Maths.pdf
- 23. Mathematics Curriculum Framework (PrimaryMathematics Teaching and Learning Syllabus, 2012, p. 16)
- 24. PETALSTM Framework Principles ofEngaged Learning Student-centredness is the heart of the framework
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- 26. Standards and Benchmarksfor the Emerging 21st Century Competencies
- 27. 21 Century Competencies OPAL>Gateway>Projects& Programmes 21CC
- 28. 21CC in MathsSyllabus
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- 30. Plan, implement, monitor andevaluate instructional programmes Mathematics Curriculum Leader Strategic Planner & Instructional Leader
- 31. How doesa Mathematics Programme look like? Share on your school’s Mathematics Programme. How do you plan and implement your Mathematics Programme? What must you consider? (3Ps: Purpose – Process - imPact) Group discussion… Why implement How was it implemented How aligned How do you monitor and evaluate your Mathematics Programme?
- 32. Achieve the aimsand objectives of the Mathematics Education Instructional programme in the classroom Includes co-curriculum: outside classroom programme Mathematics programme
- 33. Mathematics programme Instructional Programme Translate syllabus into SOWs Design programmes to cater to students with different learning needs Interpreting aims, objectives, scope and depth Explain rationale for changes Identify strategies and activities to enhance the learning experience
- 34. Mathematics programme Remedial/Supportprogramme Enrichment/Extention activities • Maths trails, Maths Games day, Maths Day • Mathematics Competitions • Maths Camps • Learning journeys Maths newsletter Maths notice board
- 35. Tea Break (15min)
- 36. Curriculum Content What should mystudents learn? Assessment Did my students learn it? Pedagogy How should my students learn? Curriculum CPA
- 37. Content Schemes ofwork for the various levels Interpretation of syllabuses – scope and depth • Communicate aims of maths education • Familiar with the syllabuses (2007 and 2013) and rationale for changes • Supporting resources Syllabus document Teaching and learning guides CPDD Homepage (materials, contacts)
- 38. Communicate aims ofmaths education
- 39. Group discussion… 1. Highlightthe differences between the two syllabuses Compare 2007 & 2013 Syllabuses 2. What are the features of 2013 syllabus 3. What implications does 2013 syllabus have on you as Mathematics Curriculum Leader?
- 40. 3 Principles ofTeaching Principle 1: Teaching is for learning; learning is for understanding; understanding is for reasoning and applying and, ultimately problem solving. Principle 2: Teaching should build on students’ knowledge; take cognizance of students’ interests and experiences; and engage them in active and reflective learning. Principle 3: Teaching should connect to the real world, harness ICT tools and emphasise 21st century competencies.
- 41. 3 Phases ofLearning Effective instruction of a unit typically involves three phases of learning: • Prior Knowledge • Motivating Contexts • Learning Environment • Activity-based Learning • Teacher-directed inquiry • Direct Instruction • Motivated Practice • Reflective Review • Extended Learning
- 42. Learning Experience (LE) What? Describewhat students should do as part of their learning Why? Influence the way teachers teach and students learn so that the curriculum objectives can be achieved Where? Included in textbooks and online TL guide to guide the teaching and learning of the topics How? Students carry out the LE as part of their learning
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- 44. Highlights LE (Primary MathematicsTeaching and Learning Syllabus 2013, p. 56) Numbers up to 100 (Primary One) Teaching and Learning Guide (TLG)
- 45. LE matches theactivities in TLG (Teaching and Learning Guide, 2013) LO1: Count and tell the number of objects in a given set. LO2: Number notation, representation and place value (tens, ones) LO3: Reading and writing numbers in numerals and in words
- 46. LE matches theactivities in TLG
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- 52. Teaching and LearningGuide (TLG)
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- 57. Numbers up to1000 (P2) (Primary Mathematics Teaching and Learning Syllabus 2013, p. 59)
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- 59. Money (P2) (Primary MathematicsTeaching and Learning Syllabus 2013, p. 61)
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- 64. Develop and model effectiveteaching strategies Mathematics Curriculum Leader Strategic Planner & Instructional Leader
- 65. Pedagogy • Suggest specificapproaches for different topics • Share strategies and model how they can be used • Provide references and sources for teaching ideas • Encourage teachers to try out strategies
- 66. Repertoire of TeachingStrategies Share on your teaching strategies which work well for your students. Highlight one example of implementing a teaching strategy. What are the key considerations in implementing a particular teaching strategy? Group discussion…
- 67. Repertoire of Pedagogies Concrete– Pictorial- Abstract Activity -based learning Teacher-directed inquiry Direct Instruction
- 68. Develop evaluation strategies toassess learning effectiveness Strategic Planner & Instructional Leader Mathematics Curriculum Leader
- 72. Developing an AssessmentPlan • The plan should provide information about: • The topics to be assessed • The appropriate assessment methods to use • The schedule of assessment, reporting and feedback • Whether marks are counted towards the final marks for the year • If so, the weighting of the components
- 73. Primary Mathematics AssessmentGuide 2013
- 74. Chapter 3 –Semestral Assessment
- 75. Format for SA2(P2 to P4)
- 76. Format for SA2(P5 to P6)
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- 79. Plan the professional developmentof teachers Mathematics Curriculum Leader People Developer
- 80. Teachers are keyto the success of the instructional programmes “In education, teachers are the intervention. Well-described innovations inform when and how they interact with students and stakeholders, but it is the person (the teacher) who delivers the intervention through his or her words and actions.” (Wallace, Blase, Fixsen, & Naoom, 2008, pp. 54–55).
- 81. Leadership “Leadership is liftinga person’s vision to high sights, the raising of a person’s performance to a higher standard, the building of a personality beyond its normal limitation” - Peter Drucker
- 82. Professional Development Sharingand discussions during Department meetings Protected time Invite external speakers, experts PD Model : Lesson Study Approach Peer observation
- 83. Select, prepare andorganise teaching and learning resources Mathematics Curriculum Leader Resource Manager
- 84. Resources • Identify andbuy suitable resources • Ensure that there are sufficient resources available • Create awareness and build capacity (if necessary) – Variety of resources – Location of the resources (e.g. Maths Room) – Demonstrate/role model the effective use these resources – Loan processes • Monitor the use of these resources
- 85. Resources include • Textbooks •Teaching and Learning Guides (from CPDD) • Teaching aids – e.g. concrete manipulatives, posters, software, geometrical instruments • Reference Books • Publications and journals
- 86. Guide for SelectingApproved Mathematics Textbook and Workbook
- 87. Mathematics Curriculum Leader OtherResponsibilities Other Responsibilities Staff responsibilities • Department culture Administrative duties • Conduct department meetings • Documentation and filing • Review of department action plan • Staff Appraisal • Plan and manage budget • Inventory for resource management
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- 90. Resources given toschools No. Item Year of Distribution 1 Primary Mathematics Syllabus(Year of Implementation: From 2007) 2006 2 A Guide to the Teaching and Learning of Primary Mathematics 2007 – Primary 1 to 4 - File - CD ( Guide, Primary Maths Syllabus 2007 & SAIL package (P3 to P5) 2007) 2007 3 PSLE Mathematics Information Booklet (To be implemented from the Year of Examination 2009) 2007 4 PSLE Foundation Mathematics Information Booklet (To be implemented from the Year of Examination 2009) 2007 5 Information Kit on the Use of Calculators in Primary Mathematics (CD) - powerpoint presentation on Use of Calculators in Primary Mathematics - Poster on Use of Calculators in Primary Mathematics - FAQs 2007 6 A Guide to the Teaching and Learning of Primary Mathematics 2007 – Primary 5 to 6 - File - CD 2008 7 Guidelines for Setting Basic Items in Primary 4 End-Of-Year Examination for Mathematics 2008 8 The Singapore Model Method for Learning Mathematics 2009 9 Pathways to Reasoning and Communication in the Primary School Mathematics Classroom 2009 10 Pedagogy For Engaged Mathematics Learning 2010 11 Diagnostic Package ( Whole Numbers and Fractions) 2010
- 91. Rollout of Resources 2011 P1& P2 2012 P3 & P4 2013 P5 & P6 Early Success…Strong Basics…Steady Progress
- 92. Objectives • To helpstudents build strong foundation in primary Maths through a structured teaching sequence and supporting manipulatives and materials based on the concrete-pictorial- abstract approach. • To raise teachers' pedagogical content knowledge through the provision of instructional guide, teaching resources and professional development activities. Early Success…Strong Basics…Steady Progress
- 93. Resources and Materials Consistsof 2 components • Instructional guide, highlighting teaching and learning sequence, pedagogical approaches and strategies specific to each topic, with a strong emphasis on C-P- A approach • Learning and teaching aids, including a full set of manipulatives for each class Early Success…Strong Basics…Steady Progress
- 94. Professional Development Workshops • Train-the-trainerworkshops, with representatives from each school • Focusing on effective use of the Instructional Materials and on Pedagogical Content Knowledge as well as Problem Solving (Thinking skills and Heuristics) Build capacity in: • Use of Instructional Package. Pedagogical content knowledge (PCK) and content knowledge • Pedagogy. C-P-A, Thinking Skills and Heuristics
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- 97. Professional Development onAssessment Literacy
- 98. Primary Mathematics onlineResources in OPAL Log in to OPAL http://www.academyofsingaporeteachers.moe.gov.sg/ Click GATEWAY Click Subjects & select Mathematics Primary
- 105. Repository of AssessmentItems The Repository of Assessment Items (Mathematics) contains test items that are aligned with the Primary Mathematics Syllabus and are appropriately pitched for the respective levels. This first batch of items is for Primary 4 only (download). When using the items from the Repository, teachers should modify the items to assess students’ learning when setting Semestral Assessment without changing the nature or demand of the items. They should refer to the Table of Specifications (TOS) and format of the paper in the Assessment Guide (Chapter 3, Semestral Assessment) (download). This will help teachers manage the overall difficulty level of the paper and ensure that it is appropriate for the level. In setting the end-of-year Primary 4 examination papers, schools are also reminded to refer to the Guidelines for Setting Basic Items in Primary 4 End-of-Year Examination for Mathematics (download). The guidelines provide further guidance on the setting of the basic items that constitute 30% of the examination paper. This is to help schools to identify more accurately students who would benefit from taking the subject at the foundation level.
- 106. Group online exploration… Share one resource which is you find useful. Highlight why and how it is useful. Explore the Mathematics online Resources in OPAL
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- 108. Sharing by HOD MrsArif Hong CHIJ Kellock
- 109. Sharing by HOD MrLow Yew Fai Springdale Primary School
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Editor's Notes
- #3 5min
- #4 10 min
- #5 This is a 2.5 days’ course. We hope to equip you with ‘just in time skills’ to deliver your department’s teaching and learning programmes effectively, and align it to the policy intent and curriculum objectives.
- #6 This is a 2.5 days’ course. We hope to equip you with ‘just in time skills’ to deliver your department’s teaching and learning programmes effectively, and align it to the policy intent and curriculum objectives.
- #7 By the end of this 2.5 days’ course, we hope that you will:acquire a deeper understanding of the Maths curriculumunderstand the initiatives and policies of MOE supporting the Maths curriculumplan a Maths programme that caters to the needs of the diverse group of pupils in your schoolunderstand how the TPACK framework can be used to develop teachers’ knowledge in designing ICT-enriched learning experiencestake away ready-to-use ICT tools for the teaching and learning of Maths
- #8 For Day 1, we will Look at the evolution of Singapore Math EducationDiscuss on the role of Math Curriculum LeaderDiscuss the Math Framework and use it as a guide to plan the Math programmeLook at the initiatives and policies related to MathsMeet two HODs who will share on how they plan, implement, monitor and evaluate their instructional programmes
- #9 ETD 1Get participants to respond as a group in Google Get representatives from each group to share
- #10 Summarize and emphasize participants’ key pointsMaths is “a diverse discipline that deals with data, measurements, and observations from science; with inference, deduction, and proof; and with mathematical models of natural phenomena, of human behaviour, and of social sciences” and “a science of pattern and order”Maths is fundamentally a social activity, where experts and trained practitioners engage in the science of pattern. It is a science and pattern of relationships. Through its theorems, we have modelling, abstraction, logical analysis, inference, use of symbolsMaths builds mental discipline and encourages logical reasoning, sense makingThere is a strong relationship between Mathematics and the other fields of basic and applied Science. Since Mathematics plays a central role in modern culture, some basic understanding of the nature of mathematics is requisite for scientific literacy. Carl Friedrich Gauss, German Mathematician: “Mathematics is the queen of sciences” (One of the Greatest Mathematicians of All Time) Johann Carl Friedrich Gauss (30 April 1777 – 23 February 1855) was a German mathematician, astronomer and physicist
- #11 For Singapore, Maths is an important subject in the national curriculum. From the time a child enters the formal school system at Primary 1, Maths is a compulsory subject right up to the end of secondary education, giving every child about 10 years of education in the subject.The development of a highly-skilled and well-educated manpower is critical to support an innovation- and technology-driven economy. A strong grounding in Maths and a talent-pool in Maths are essential to support the wide range of value-added economic activities and innovations.The learning of Maths also provides an excellent vehicle to train the mind, and to develop the capacity to think logically, abstractly, critically and creatively. These are important 21st century competencies that we must imbue in our students, so that they can lead a productive life and be life-long learners.
- #13 In 1940s –The existence of medium schools gave rise to various ways Maths was taught by the English, Chinese and Malay medium schools. In those days, Maths was taught in different language medium. Survival Driven 1959 –1960: The 1st MOE designed Maths syllabus was conceived in 1959, and introduced in the Pri and Sec schools in 1960.1970s - Singapore went through a survival-driven education. It was the industrialisation era where the aim was to enable pupils to contribute optimally to the industralising economy. Math was made compulsory for Pri & Sec education due to its importance in industrialisation.1971 -There was a revision of the syllabus in 1971 to reduce content and another revision and reorganisation of the primary math syllabus in 1976.Efficiency Driven:1979 - the Math Syllabus was revised for the New Education System and the Pri Math Project (PMP) team was born and set up at CDIS.1990 - the Singapore Maths Curriculum Framework was first introduced in 1990 in the pri and lower sec Maths syllabuses. 1996 – Abacus was introduced to help pupils consolidate the place value concepts and enhance mental calculation.Ability –Based1997 - MOE adopted the TSLN vision and many initiatives that have an impact on the Maths curriculum have been introduced since 1997 to help realise the vision of TSLN. 1999 - A short term interim measure was implemented in 1999 with the content-reduced syllabus. This syllabus encourages teachers to infuse IT and thinking skills in the lessons.Following the 1999 content-reduced syllabus, the syllabus review team worked on the syllabus and the revised syllabus was implemented in 2001. This was also when we opened up the market to other publishers and gave schools the choice to choose a title that best suit their pupils.In 2002, as part of the ICT Masterplan 2 vision, teaching and learning leveraged on ICT as a tool to customise education to meet the needs and abilities of our students. During the curriculum reviews in 2000 and 2003, the Math framework was updated to reflect new educational emphases and needs in a rapidly changing world. The revised framework was extended formally to all levels in 2003.2007 syllabus was a result of the syllabus review committee that was formed to look into Math in all levels.Some of the key recommendations are:The introduction of the calculatorThe removal of abacus and make it optional for schoolsIntent to strengthen geometrical concepts2008: Subject-Based Banding was implemented in 2008 to P5 cohort in all the primary schools, replacing the merged and EM3 stream. SBB allows students to take subjects at different levels depending on their aptitudes and abilities in these subjects. Hence, students with uneven abilities may be allowed the option to offer their stronger subjects at standard level, or, the option to offer weak subjects at foundation level. Strong professional judgment will be required to determine the course of study that is in the best interest of the student, based on his/her individual needs and strengths2009 – 1st year of PSLE with the use of calculatorRationale on the use of calculator:achieve a better balance between emphasis on computational skills and problem solving skills;widen the repertoire of teaching and learning approaches to facilitate the use of investigations and problems in authentic situations; and help students, particularly those with difficulty learning Mathematics, develop greater confidence in doing Mathematics 2005 – PETALS2008 – Curriculum 2015 Committee: setup to study 21st century skills and mind-sets needed to prepare future generations for a globalised world. 2009 – PERI: More engaging teaching methods, Holistic assessment to support learning2009 – 2010 the syllabus review committee is formed to review the current syllabusesAs in all previous reviews, the 2010 full-term review aims to update the syllabuses so that they continue to meet the needs of our students, build a strong foundation in mathematics, and make improvement in the school mathematics education. It is clear at the start of the review that there is more to be considered than just focussing on the content. More focus has now been given to skills and competencies that will make a better 21st century learner – the process of learning becomes more important than just what is to be taught and remembered. The syllabuses are therefore written with the view that not only will it inform teachers on what to teach, it will also influence the way teachers teach and students learn.
- #14 MOE adopted the TSLN vision in 1997 and many initiatives that have an impact on the Maths curriculum have been introduced since 1997 to help realise the vision of TSLN. Looking at the timeline above, there seemed to be many initiatives introduced.However, we should not see them individually but holistically as continuous journey, little steps and improvement towards our TSLN vision.That is what we have done in each review. The math pentagonal framework which sets the direction for the teaching and learning of math is still relevant but there were minor changes to show the emphasis in each review and to take into account the overarching MOE goals and the subject specific goals.Thus in implementing the math curriculum, you should keep in mind the larger picture.As you play a very important role in implementing the intended curriculum, it is important that you understand the rationale for various changes and how it meets the overarching MOE goals and subject specific goals.
- #16 ETD 2Get participants to write their responses on the online post-its. Use one post-it for every one role/responsibility. Write as many roles/responsibilities as they can think of.ETD Team helps to categorize responses into the 4 key roles of HOD (Curriculum Leader)
- #17 In order to Set directions for the departmentPlan, implement, monitor and evaluate instructional programmesDevelop and model effective teaching strategiesDevelop evaluation strategies to assess learning effectivenessPlan the professional development of teachersSelect, prepare and organise teaching and learning resources
- #18 You need to know the curriculum well.Curriculum is an organised set of formal educational intentions and learning experiences planned for the students in school. It comprises of:Content – What should my students learn?Pedagogy – How should my students learn?Pedagogy refers to the set of instructional strategies that teachers use to help students learnTeachers should exercise a range of pedagogy across various platforms to:Cater to divers range of students with different learning needs/stylesEngage them in different ways so that they have multiple means to access the same info/ideasAnd Assessment – Did my students learn it well?
- #20 The overaching goal of the mathematics curriculum is to ensure that all students will achieve a level of mastery of mathematics that will serve them well in life, and for those who have the interest and ability, to pursue mathematics at the highest possible level.The broad aims of mathematics education in Singapore are to enable students to:acquire and apply mathematical concepts and skills; develop cognitive and metacognitive skills through a mathematical approach to problem solving; anddevelop positive attitudes towards mathematics.
- #21 (Refer also to: Primary Mathematics Teaching and Learning Syllabus, 2012, p. 10)The mathematics curriculum comprises a set of syllabuses spanning 12 years, from primary to pre-university, and is compulsory up to the end of secondary education. Each syllabus has its own specific set of aims to guide the design and implementation of the syllabus. Each syllabus expands on the three broad aims of mathematics education differently to cater for the different needs and abilities of the students.
- #22 (Refer also to: Primary Mathematics Teaching and Learning Syllabus, 2012, p. 11)Mathematics is largely hierarchical in nature. Higher concepts and skills are built upon the more foundational ones and have to be learned in sequence. A spiral approach is adopted in the building up of content across the levels. The mathematics curriculum consists of a set of connected syllabuses to cater to the different needs and abilities of students. This diagram gives an overview of the syllabuses and their connections so that teachers are better able to aappreciate the mathematics curriculum as a whole.The Primary Mathematics syllabus assumes no formal learning of mathematics. However, basic pre-numeracy skills such as matching, sorting and comparing are necessary in providing a good grounding for students to begin learning at Primary 1. The P1-4 syllabus is common to all students. The P5-6 Standard Maths syllabus continues the development of the P1-4 syllabus whereas the P5-6 Foundation Maths syllabus re-visits some of the important concepts and skills in the P1-4 syllabus. The new concepts and skills introduced in Foundation Maths is a subset of the Standard Maths syllabus.The O-Level Maths syllabus builds on the Standard Maths syllabus. The N(A)-Level Maths syllabus is a subset of the O-Level Maths, except that it re-visits some of the topics in Standard Maths syllabus. The N(T)-Level Maths syllabus builds on the Foundation Maths syllabus.The O-Level Additional Maths syllabus assumes knowledge of O-Level Maths content and includes more in-depth treatment of important topics. The N(A)-Level Additional Maths is a subset of the O-Level Mathematics. O-Level Additional Maths together with O-Level Maths content provide the prerequisite knowledge required for H2 Mathematics at the pre-university level. At the pre-university level, mathematics is optional. The H1 Maths syllabus builds on the O-Level Maths syllabus. H2 Maths assumes some of the O-Level Additional Maths content. H3 Maths is an extension of H2 Maths.What does it mean to teachers?Teachers need to have the big picture in mind so that they can better understand the role of each syllabus, the connection it makes with the next level and the dependency relationship between syllabuses. This enables teachers to better understand what they have to do at their level, as well as to plan and advise students in their learning of mathematics. For example, in SBB, teachers need to think carefully before advising students to offer Foundation Maths if they can be guided to learn Standard Maths. Very often, teachers advise students to offer Foundation Maths so that they can easily pass the subject at PSLE. But the repercussion is great: the students will be deprived of higher learning of Maths in future, even though they have the potential to pursue higher level Maths for better prospects. In other words Foundation Maths students are actually doomed to just stagnate at N(T)-Level, and deprived of a better academic qualification, and hence a better job prospects.
- #24 (Refer to Primary Mathematics Teaching and Learning Syllabus, 2012, Chapter 2, p. 16-19)Question: What do you understand about the Math Curriculum Framework?The Singapore Mathematics Curriculum Framework has been a feature of our mathematics curriculum since 1990, and is still relevant to date. The central focus of the framework is mathematical problem solving, ie. Using mathematics to solve problems. The framework sets direction for and provides guidance for the teaching, learning, and assessment of mathematics at all levels, from pri to pre-uni. It also reflects the 21st century competencies.The framework stresses conceptual understanding, skills proficiency and mathematical processes and gives due emphasis to attitudes and metacognition. These five components are inter-related.
- #25 Question: What do you understand about PETALS?How do we infuse PETALS framework into our Math Curriculum?Student-centredness is the heart of the PETALS frameworkStudents are engaged when teachers:Select Pedagogy that considers students’ readiness to learn and their learning styles,Design an Experience of Learning that stretches thinking, promotes inter-connectedness and develops independent learning,Create a Tone of Environment that is safe, stimulating and which engenders trust,Adopt Assessment practices that provide information on how well students have performed and provide timely feedback to improve learning,And select relevant and meaningful Learning Content that makes learning authentic for the students.
- #26 Question: What do you understand about the 21CC Framework? How do we infuse 21cc Framework into our Math Curriculum?Critical and Inventive Thinking Curiosity and Creativity Sound Reasoning and Decision-Making Metacognition Managing Complexities and Ambiguities Learning Experiences:To support the development of collaborative and communication skills, students must be given opportunities to work together on a problem and present their ideas using appropriate mathematical language and methods.To develop habits of self-directed learning, students must be given opportunities to set learning goals and work towards them purposefully.A classroom, rich with these opportunities, will provide the platform for students to develop these 21stcetury competencies….
- #28 ETD 3Get participants to share their school’s maths programme. (Butcher Paper)What is the rationale of having such a programme? How do you ensure that the math programme caters to the needs of all pupils?How do you ensure that the programme is in alignment with the framework?
- #29 Make sure the programme is created for every student. Coherent, Connected, Planned!Customised to the students’ profile and differentiated The programme should help to achieve the aims of maths education – academic and discplinaryAligned to the national policies and initiatives
- #32 You need to know the curriculum well.Curriculum is an organised set of formal educational intentions and learning experiences planned for the students in school. It comprises of:Content – What should my students learn?Pedagogy – How should my students learn?Pedagogy refers to the set of instructional strategies that teachers use to help students learnTeachers should exercise a range of pedagogy across various platforms to:Cater to divers range of students with different learning needs/stylesEngage them in different ways so that they have multiple means to access the same info/ideasAnd Assessment – Did my students learn it well?
- #33 ETD 1Get participants to respond as a group in Google Get representatives from each group to share
- #34 Refer to Primary Mathematics Teaching and Learning Syllabus, 2012, p. 23BELIEFS OF LEARNING:Principle 1: UNDERSTANDINGTeaching is an interactive process that is focused on students’ learning. In this process, teachers use a range of teaching approaches to engage students in learning; students provide teachers with feedback on what they have learnt through assessment, and teachers in turn provide feedback to students and make decisions about instructions to improve learning. The learning of Maths should focus on understanding, not just recall of facts or reproduction of procedures. Understanding is necessary for deep learning and mastery. Only with understanding can students be able to reason mathematically and apply mathematics to solve a range of problems.Principle 2: STUDENT CENTRICITYMathematics is a hierarchical subject. Without understanding of pre-requisite knowledge, foundation will be weak and learning will be shallow. It is important for teachers to check on students’ understanding before introducing new concepts and skills. Teachers need to be aware of their students’ interests and abilities so as to develop learning tasks that are stimulating and challenging. This is important in order to engage students in active and reflective learning where students participate and take ownership on their learning.Principle 3: ICTThere are many applications of mathematics in the real world. Students should have an understanding and appreciation of these applications and how mathematics is used to model and solve problems in real-world contexts. In this way, students will see the meaning and relevance of mathematics. Teachers should infusing ICT to help students learn. ICT tools can help students understand mathematical concepts through visualisations, simulations and representations. They can also support exploration and experimentation and extend the range of problems accessible to students. The ability to use ICT tools is part of the 21st century competencies. It is also important to design learning in ways that promote the development of other 21st century competencies such as working collaboratively and thinking critically about the mathematical solution.
- #35 Refer to Primary Mathematics Teaching and Learning Syllabus, 2012, pp. 24-27.Phase 1 – ReadinessStudent readiness to learn is vital to learning success. In the readiness phase of learning, teachers prepare students so that they are ready to learn. This requires considerations of prior knowledge, motivating contexts, and learning environment.Phase 2 - EngagementThis is the main phase of learning where teachers use a repertoire of pedagogies to engage students in learning new concepts and skills. Three pedagogical approaches form the spine that supports most of the mathematics instruction in the classroom. They are not mutually exclusive and could be used in different parts of a lesson or unit. Teachers at the primary level use the Concrete-Pictorial-Abstract approach together with activity-based learning to help students understand abstract mathematical concepts. The C-P-A approach, introduced in the early 1980s, is a signature pedagogy in the Singapore mathematics classroom. In this approach, students build their understanding of abstract mathematical concepts from relevant everyday experiences and meaningful contexts, using concrete and pictorial representations.In the 1990s, activity-based learning was advocated to encourage active participation by students in the learning process. Activity-based learning is student-centred and involves learning by doing, individually or in groups.Besides activity-based learning, teacher directed inquiry and direct instruction are also used to engage students in learning mathematics. Phase 3 – MasteryThis is the final phase of learning where teachers help students consolidate and extend their learning. I would like to reiterate that this is an ongoing journey. We have introduced the 3 phases in our TL guide in 2007.In the design of some of our resources such as the LSM TRP, we have used the 3 phases to guide developmentMoving on, we will continue our journey to explore working with schools and teachers to make explicit these preliminary ideas.
- #36 Refer to Primary Mathematics Teaching and Learning Syllabus, 2012, p. 22.LE are explicit statements about what students should do as part of their learning. They are described from the perspective of the students as to the kind of opportunities they should have as part of the learning process. They specify and describe Approaches to teaching and learning a topic Contexts to be introduced as part of learning Processes to be emphasizedLearning Experiences for the Primary Maths syllabus provide opportunities for students to:enhance conceptual understanding through the use of the CPA approach and various mathematical tools including ICT tools,apply concepts and skills learnt in real-world context,communicate their reasoning and connections through various mathematical tasks and activities,build confidence and foster interest in mathThe LEs are not exhaustive. Teachers have the flexibility to design the activities according to their students’ abilities and needs.
- #39 Get some groups to share
- #41 Primary Mathematics Teaching and Learning Syllabus, 2012, p. 28 - 29
- #47 The objective of providing all schools with this set of teaching and learning resources, the instructional guide and professional development activities is part of the PERI effort to improve pedagogy and assessment in the primary schools.More specifically, the provision of resources, guidance and professional development activities seeks toHelp students build strong foundation in primary maths through a structured teaching sequence and supporting manipulatives and materials based on the C-P-A approachRaise teachers’ PCK through the provision of instructional guide, teaching resources and professional development activities
- #48 The Instructional package come in the form of an Instructional guide and accompanying teaching aids.The Instructional guide detailed guided teaching steps to scaffold development of conceptual understanding. Teaching activities also emphasise the acquisition of thinking skills and heuristics where appropriate. Accompanying teaching aids are included to enhance understanding of concepts and skills. Where appropriate, simple assessment tools are also suggested to help identify misconceptions, check mastery and monitor progress.
- #49 To build teachers’ capacity, a series of professional development courses are planned:Workshops on Use of Instructional Package with PCKWhile the package is designed for ease-of-use with no specific training, in the initial implementation, there will be a need to help familiarise the teachers with the special features of the package so that they will be able to use it effectively. While familiarising teachers with the package, we will also be running through the PCK associated with the specific mathematics concepts and skills. To prepare teachers adequately, we intend to have 3 workshops stretching from sometime end of the year to next year. We hope to start these workshops in November as the teachers need to understand the key ideas behind the development of this package in order to use it effectively. (3) Workshops on Thinking Skills and HeuristicsThese workshops are to further equip teachers with the skills to teach thinking skills and heuristics that are important for the development of problem solving abilities in the students.
- #50 ETD 5Get participants to share on a useful Maths resource- Poster