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Programme for International Student Assessment (PISA) 2015 Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara BAHAGIAN PEMBANGUNAN KURIKULUM KEMENTERIAN.

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Presentation on theme: "Programme for International Student Assessment (PISA) 2015 Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara BAHAGIAN PEMBANGUNAN KURIKULUM KEMENTERIAN."— Presentation transcript:

1 Programme for International Student Assessment (PISA) 2015 Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara BAHAGIAN PEMBANGUNAN KURIKULUM KEMENTERIAN PENDIDIKAN MALAYSIA

2 MasaPerkara 7.30 – 8.50Pendaftaran 9.00 – 10.00Latar Belakang & Kerangka Kerja PISA – 10.15Rehat – Perbincangan tentang bahan & kelas intervensi Pembelajaran secara Hands-on – 2.00Rehat 2.00 – 4.30Perbengkelan & Pembentangan/Gallery Walk 4.30 – 5.00Perbincangan dengan JPN Kandungan Taklimat (1 hari) Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

3 Kandungan Taklimat (2 hari) MasaPerkara HARI PERTAMA – 3.00Pendaftaran 3.00 – 4.30 Latar Belakang & Kerangka Kerja PISA 4.30 – 8.30Rehat 8.30 – Perbincangan tentang bahan & kelas intervensi Pembelajaran secara Hands-on HARI KEDUA 8.00 – 10.00Perbengkelan & Pembentangan/Gallery Walk – 12.30Perbincangan dengan JPN Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

4 APAKAH PISA? Programme for International Students Assessment (PISA) merupakan penyelidikan pendidikan antarabangsa terbesar di dunia Dianjurkan oleh Organisation for Economic Cooperation and Development (OECD) yang berpengkalan di Paris. Bermula pada tahun 2000 dan dijalankan setiap 3 tahun. PISA 2015 merupakan pusingan PISA yang ke-6 Melibatkan lebih 70 buah negara di seluruh dunia. Mengkaji kesediaan murid untuk menempuh kehidupan alam dewasa Mengukur literasi murid dalam sains, matematik, bacaan dan penyelesaian masalah. Mengumpul maklumat dalam konteks amalan pendidikan di negara peserta Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

5 Programme for International Student Assessment

6 6 KEPENTINGAN MENYERTAI PISA Menunjukkan tahap kesediaan murid Malaysia untuk menempuh alam dewasa Membolehkan penggubal dasar mendapat maklumat tepat mengenai sistem pendidikan bagi mengenal pasti ruang untuk penambahbaikan sistem pendidikan Membuat perbandingan prestasi dan persekitaran pembelajaran murid antara negara Menetapkan matlamat polisi seperti yang dicapai oleh negara lain dan belajar daripada polisi dan amalan di negara lain UNIT PENYELIDIKAN ANTARABANGSA (PISA) BPPDP Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

7 Negara Peserta 7 UNIT PENYELIDIKAN ANTARABANGSA (PISA) BPPDP

8 Sampel Kajian PISA 2015 Populasi: Murid berumur 15+ di semua jenis sekolah di Malaysia 9660 org murid: 97% dari Tingkatan 4 & 3% dari Ting. 3 Kerangka Pensampelan: Semua jenis sekolah di Malaysia yang mempunyai murid berumur 15+ tahun Pemilihan Sampel Sekolah: 230 buah sekolah dipilih secara rawak dengan menggunakan kaedah Stratified Multi Stage Cluster Sampling Pemilihan Sampel Murid: 42 murid berumur 15+ dipilih secara rawak dengan menggunakan aplikasi KeyQuest Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

9 Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara Instrumen PISA 2015 UJIAN KOGNITIF Gabungan item-item aneka pilihan dan soalan terbuka Item-item disusun dalam kumpulan berdasarkan teks yang menggambarkan situasi dalam kehidupan sebenar (real - life situation) UJIAN PENYELESAIAN MASALAH SECARA BERKOLABORATIF Murid bekerjasama dengan beberapa agen (komputer) untuk menyelesaikan masalah Menguji kesediaan/kebolehan murid bekerjasama dengan orang lain SOAL SELIDIK MURID Latar belakang murid, persepsi dan sikap murid terhadap sains, matematik dan kemahiran membaca Tahap motivasi dan amalan strategi pembelajaran murid SOAL SELIDIK SEKOLAH DAN GURU Mengumpul maklumat berkenaan sekolah Mengumpul maklumat berkenaan latar belakang dan strategi pengajaran guru

10 KITARAN FOKUS PISA

11 KEDUDUKAN MALAYSIA DALAM PISA 2009

12 Kedudukan Dalam PISA 2012 Matematik 1. Shanghai-China Singapore Hong Kong-China Chinese Taipei Korea Macao-China Japan Liechtenstein Switzerland Netherlands – Estonia Finland Canada – Poland Belgium Germany Viet Nam – Austria Australia Ireland – Slovenia – Denmark – New Zealand – Czech Republic – France U Kingdom Iceland Latvia Luxembourg Norway Portugal Italy Spain Russian Fed. – Slovak Republic – United States – Lithuania Sweden Hungary Croatia – Israel – Greece Serbia – Turkey Romania – Cyprus – Bulgaria – UAE – Kazakhstan – Thailand – Chile – MALAYSIA Mexico – Montenegro – Uruguay – Costa Rica – Albania – Brazil – Argentina – Tunisia – Jordan Colombia – Qatar – Indonesia – Peru – 368 OECD Ave International Ave Kedudukan Dalam PISA 2012 Matematik Kedudukan Dalam PISA 2012 Matematik

13 For the purposes of PISA 2015, mathematical literacy is defined as follows: Mathematical literacy is an individual’s capacity to formulate, employ, and interpret mathematics in a variety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures, facts and tools to describe, explain and predict phenomena. It assists individuals to recognise the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive, engaged and reflective citizens. DEFINISI LITERASI MATEMATIK Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

14 DEFINISI LITERASI MATEMATIK Kapasiti seseorang individu untuk mengenal pasti dan memahami peranan matematik dalam membuat keputusan yang berasas dan dapat memenuhi keperluan kehidupan individu sebagai warga yang konstruktif, prihatin dan reflektif. Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

15 A Model of Mathematical Literacy in Practice Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

16 PISA FRAMEWORK CONTEXT PROCESSES Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara CONTENT CONTENT

17 These four categories characterise the range of mathematical content that is central to the discipline and illustrate the broad areas of content used in the test items for PISA 2015: The four content categories serve as the foundation for identifying this range of content, yet there is not a one-to-one mapping of content topics to these categories. PISA FRAMEWORK Change and RelationshipSpace and ShapeQuantityUncertainty and Data Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

18  Functions: the concept of function, emphasising but not limited to linear functions, their properties, and a variety of descriptions and representations of them. Commonly used representations are verbal, symbolic, tabular and graphical.  Algebraic expressions: verbal interpretation of and manipulation with algebraic expressions, involving numbers, symbols, arithmetic operations, powers and simple roots.  Equations and inequalities: linear and related equations and inequalities, simple second-degree equations, and analytic and non-analytic solution methods  Co-ordinate systems: representation and description of data, position and relationships.  Relationships within and among geometrical objects in two and three dimensions: Static relationships such as algebraic connections among elements of figures (e.g. the Pythagorean theorem as defining the relationship between the lengths of the sides of a right triangle), relative position, similarity and congruence, and dynamic relationships involving transformation and motion of objects, as well as correspondences between two- and three-dimensional objects.

19  Measurement: Quantification of features of and among shapes and objects, such as angle measures, distance, length, perimeter, circumference, area and volume.  Numbers and units: Concepts, representations of numbers and number systems, including properties of integer and rational numbers, relevant aspects of irrational numbers, as well as quantities and units referring to phenomena such as time, money, weight, temperature, distance, area and volume, and derived quantities and their numerical description.  Arithmetic operations: the nature and properties of these operations and related notational conventions.  Percents, ratios and proportions: numerical description of relative magnitude and the application of proportions and proportional reasoning to solve problems.

20  Counting principles: Simple combinations and permutations.  Estimation: Purpose-driven approximation of quantities and numerical expressions, including significant digits and rounding.  Data collection, representation and interpretation: nature, genesis (raw data) and collection of various types of data, and the different ways to represent and interpret them.  Data variability and its description: Concepts such as variability, distribution and central tendency of data sets, and ways to describe and interpret these in quantitative terms.  Samples and sampling: Concepts of sampling and sampling from data populations, including simple inferences based on properties of samples.  Chance and probability: notion of random events, random variation and its representation, chance and frequency of events, and basic aspects of the concept of probability.

21 CONTENT CATEGORY PERCENTAGE OF SCORE POINTS Change and Relationships≈25% Space and Shape≈25% Quantity≈25% Uncertainty and Data≈25% Approximate distribution of score points by content category for PISA 2015 Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

22 PISA FRAMEWORK CONTENT CONTEXT Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara PROCESSES

23 PROCESSES FormulatingEmployingInterpreting Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

24 PROCESSES FormulatingEmployingInterpreting Indicates how effectively students are able to recognise and identify opportunities to use mathematics in problem situations and then provide the necessary mathematical structure needed to formulate that contextualised problem into a mathematical form. Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

25 PROCESSES FormulatingEmployingInterpreting Indicates how well students are able to perform computations and manipulations and apply the concepts and facts that they know to arrive at a mathematical solution to a problem formulated mathematically. Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

26 PROCESSES FormulatingEmployingInterpreting Indicates how effectively students are able to reflect upon mathematical solutions or conclusions, interpret them in the context of a real-world problem, and determine whether the results or conclusions are reasonable. Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

27 PROCESS CATEGORY PERCENTAGE OF SCORE POINTS Formulating situation mathematically ≈25% Employing mathematical concepts, facts, procedures ≈50% Interpreting, applying and evaluating mathematical outcomes ≈25% Approximate distribution of score points by process category for PISA 2015 Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

28 PISA FRAMEWORK CONTENT PROCESSES Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara CONTEXT

29 Contexts An important aspect of mathematical literacy is that mathematics is engaged in solving a problem set in a context. PISA FRAMEWORK

30 CONTEXT CATEGORY PERCENTAGE OF SCORE POINTS Personal≈25% Occupational≈25% Societal≈25% Scientific≈25% Approximate distribution of score points by context category for PISA 2015

31 In PISA 2015, for the first time, the computer will be the main mode of delivery for all tests and questionnaires. Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

32 First, computers are now so commonly used in the workplace and in everyday life that a level of competency in mathematical literacy in the 21st century includes usage of computers (Hoyles et al., 2002). Computers now touch the lives of individuals around the world as they engage in their personal, societal, occupational and scientific endeavours. They offer tools for—among other things— computation, representation, visualisation, modification, exploration and experimentation on, of and with a large variety of mathematical objects, phenomena and processes. The definition of mathematical literacy for PISA 2015 recognises the important role of computer- based tools by noting that mathematically literate individuals are expected to use these in their endeavours to describe, explain, and predict phenomena. in this definition, the word “tool” refers to calculators and computers, as well as to other physical objects such as rulers and protractors used for measuring and construction. Why Computer-based Assessment?

33 A second consideration is that the computer provides a range of opportunities for designers to write test items that are more interactive, authentic and engaging (Stacey and Wiliam, 2013). These opportunities include the ability to design new item formats (e.g. drag-and- drop), to present students with real-world data (such as a large, sortable dataset), or to use colour and graphics to make the assessment more engaging

34 PISA Editor tool Allow students to enter both texts and numbers. Students can enter a fraction, square root, or exponent. Additional symbols such as pi and greater/less than signs are available, as are operators such as multiplication and division signs. The suite of tools available to students is also expected to include a basic scientific calculator. Operators to be included are addition, subtraction, multiplication and division, as well as square root, pi, parentheses, exponent, square, fraction, inverse and the calculator will be programmed to respect the standard order of operations.

35 Computer-based

36 Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

37 1.Multiple-choice Questions (MCQ) 2.Open-constructive 1.Multiple-choice Questions (MCQ) 2.Open-constructive Types of Items Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

38 PISA items in this form comprise a piece of stimulus, one or more questions related to that stimulus (with each question being referred to as an ‘item’) and, for each question, a set of guidelines that define the possible student response options and a proposed scoring scheme based on the defined response codes (the ‘coding guide’). Structure of the Items Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

39 Stimulus Question Scoring scheme HEIGHT There are 25 girls in a class. The average height of the girls is 130 cm Question 1: HEIGHT Explain how the average height is calculated. M421Q01 – PISA ITEMS 1

40 HEIGHT There are 25 girls in a class. The average height of the girls is 130 cm Question 1: HEIGHT Explain how the average height is calculated. M421Q01 – PISA ITEMS 1 Answer the question Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

41 PISA ITEMS 1 Full Credit Code 1: Explanations that include: Sum the individual heights and divide by 25. You add together every girl’s height and divide by the number of girls. Take all the girls’ heights, add them up, and divide by the amount of girls, in this case 25. The sum of all heights in the same unit divided by the number of girls. No Credit Code 0: Other responses. Code 9: Missing.

42 PISA ITEMS 1 StatementTrue or False If there is a girl of height 132 cm in the class, there must be a girl of height 128 cm. True/False The majority of the girls must have height 130 cm.True/False If you rank all of the girls from the shortest to the tallest, then the middle one must have a height equal to 130 cm. True/False Half of the girls in the class must be below 130 cm, and half of the girls must be above 130 cm. True/False HEIGHT SCORING 2 Full Credit Code 1: False, False, False, False. No Credit Code 0: Other responses. Code 9: Missing.

43 PISA ITEMS 1 Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

44 Litter For a homework assignment on the environment, students collected information on the decomposition time of several types of litter that people throw away: Type of litterDecomposition time Banana peel1-3 years Orange peel1-3 years Cardboard boxes0.5 year Chewing gum20-25 years NewspapersA few days Polystyrene cupsOver 100 years A student thinks of displaying the results in a bar graph. Give one reason why a bar graph is unsuitable for displaying these data. Context: Scientific Content: Uncertainty & Data Process: interpreting, applying and evaluating mathematical outcomes PISA ITEMS 2

45 Sample responses for Litter Response 1: “Because it would be hard to do in a bar graph because there are 1-3, 1-3, 0.5, etc. so it would be hard to do it exactly.” Response 2: “Because there is a large difference from the highest sum to the lowest therefore it would be hard to be accurate with 100 years and a few days.” PISA ITEMS 2 Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

46 Question 1 Which pizza is better value for money? Show your reasoning. Pizzas A pizzeria serves two round pizzas of the same thickness in different sizes. The smaller one has a diameter of 30 cm and costs 30 zeds. The larger one has a diameter of 40 cm and costs 40 zeds. QUESTION INTENT: Applies understanding of area to solving a value for money comparison Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

47 Question 1 Which pizza is better value for money? Show your reasoning. Pizzas A pizzeria serves two round pizzas of the same thickness in different sizes. The smaller one has a diameter of 30 cm and costs 30 zeds. The larger one has a diameter of 40 cm and costs 40 zeds. CONTEXT Personal CONTEXT Personal PROCESS Formulating PROCESS Formulating CONTENT Change and Relationships CONTENT Change and Relationships

48 15 cm 20 cm An important part of formulation Employing knowledge from space and shape and Quantity. Formulating a mathematical model to measure value for money Interpreting mathematical result in real world terms.

49 Computer-Based Assessment PISA 2015 Single multiple- choice Reasoning Full credit dependent on both the selection and the reasoning behind it.

50 QUESTION INTENT: Applies understanding of area to solving a value for money comparison Code 2: Gives general reasoning that the surface area of pizza increases more rapidly than the price of pizza to conclude that the larger pizza is better value. The diameter of the pizzas is the same number as their price, but the amount of pizza you get is found using diameter2, so you will get more pizza per zeds from the larger one Code 1: Calculates the area and amount per zed for each pizza to conclude that the larger pizza is better value. Area of smaller pizza is 0.25 x π x 30 x 30 = 225π; amount per zed is 23.6 cm2 area of larger pizza is 0.25 x π x 40 x 40 = 400π; amount per zed is 31.4 cm2 so larger pizza is better value Code 8: They are the same value for money. (This incorrect answer is coded separately, because we would like to keep track of how many students have this misconception). Code 0: Other incorrect responses OR a correct answer without correct reasoning. Code 9: Missing.

51 APARTMENT PURCHASE This is the plan of the apartment that George’s parents want to purchase from a real estate agency. Question 1: APARTMENT PURCHASE PM00FQ01 – 019 To estimate the total floor area of the apartment (including the terrace and the walls), you can measure the size of each room, calculate the area of each one and add all the areas together. However, there is a more efficient method to estimate the total floor area where you only need to measure 4 lengths. Mark on the plan above the four lengths that are needed to estimate the total floor area of the apartment. APARTMENT PURCHASE SCORING 1 QUESTION INTENT: Description: Use spatial reasoning to show on a plan (or by some other method) the minimum number of side lengths needed to determine floor area Mathematical content area: Space and shape Context: Personal Process: Formulate APARTMENT PURCHASE SCORING 1 QUESTION INTENT: Description: Use spatial reasoning to show on a plan (or by some other method) the minimum number of side lengths needed to determine floor area Mathematical content area: Space and shape Context: Personal Process: Formulate

52 A = (9.7m x 8.8m) – (2m x 4.4m) A = 76.56m2 [Clearly used only 4 lengths to measure and calculate required area.] No Credit Code 0: Other responses. Code 9: Missing. Full Credit Code 1: Has indicated the four dimensions needed to estimate the floor area of the apartment on the plan. There are 9 possible solutions as shown in the diagrams below.

53 Stimulus Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

54 Question Question 1: SHAPES M158Q Which of the figures has the largest area? Explain your reasoning. SHAPES SCORING 1 QUESTION INTENT: Comparison of areas of irregular shapes Code 1: Shape B, supported with plausible reasoning. It’s the largest area because the others will fit inside it. Code 8: Shape B, without plausible support. Code 0: Other responses. Code 9: Missing. Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

55 Example responses Code 1: B. It doesn’t have indents in it which decreases the area. A and C have gaps. B, because it’s a full circle, and the others are like circles with bits taken out. B, because it has no open areas: Code 8: B. because it has the largest surface area The circle. It’s pretty obvious. B, because it is bigger. Code 0: They are all the same. Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

56 Question 2: SHAPES Describe a method for estimating the area of figure C. M158Q SHAPES SCORING 2 QUESTION INTENT: To assess students’ strategies for measuring areas of irregular shapes. Code 1: Reasonable method: Draw a grid of squares over the shape and count the squares that are more than half filled by the shape. Cut the arms off the shape and rearrange the pieces so that they fill a square then measure the side of the square. Build a 3D model based on the shape and fill it with water. Measure the amount of water used and the depth of the water in the model. Derive the area from the information. Code 8: Partial answers: The student suggests to find the area of the circle and subtract the area of the cut out pieces. However, the student does not mention about how to find out the area of the cut out pieces. Add up the area of each individual arm of the shape Code 0: Other responses. Code 9: Missing.

57 NOTE: The key point for this question is whether the student offers a METHOD for determining the area. The coding schemes (1, 8, 0) is a hierarchy of the extent to which the student describes a METHOD. Example responses Code 1: You could fill the shape with lots of circles, squares and other basic shapes so there is not a gap. Work out the area of all of the shapes and add together. Redraw the shape onto graph paper and count all of the squares it takes up. Drawing and counting equal size boxes. Smaller boxes = better accuracy (Here the student’s description is brief, but we will be lenient about student’s writing skills and regard the method offered by the student as correct) Make it into a 3D model and filling it with exactly 1cm of water and then measure the volume of water required to fill it up. wrong) Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

58 Code 8: Find the area of B then find the areas of the cut out pieces and subtract them from the main area. Minus the shape from the circle Add up the area of each individual piece e.g., Use a shape like that and pour a liquid into it. Use graph Half of the area of shape B Figure out how many mm2 are in one little leg things and times it by 8. Code 0: Use a string and measure the perimeter of the shape. Stretch the string out to a circle and measure the area of the circle using π r2. (Here the method described by the student is wrong) Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

59 Question 3: SHAPES M158Q Describe a method for estimating the perimeter of figure C. SHAPES SCORING 3 QUESTION INTENT: To assess students’ strategies for measuring perimeters of irregular shapes Code 1: Reasonable method: Lay a piece of string over the outline of the shape then measure the length of string used. Cut the shape up into short, nearly straight pieces and join them together in a line, then measure the length of the line. Measure the length of some of the arms to find an average arm length then multiply by 8 (number of arms) X 2. Code 0: Other responses. Code 9: Missing. Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

60 Question 3: SHAPES M158Q Describe a method for estimating the perimeter of figure C. Example responses Code 1: Wool or string!!! (Here although the answer is brief, the student did offer a METHOD for measuring the perimeter) Cut the side of the shape into sections. Measure each then add them together. (Here the student did not explicitly say that each section needs to be approximately straight, but we will give the benefit of the doubt, that is, by offering the METHOD of cutting the shape into pieces, each piece is assumed to be easily measurable) Code 0: Measure around the outside. (Here the student did not suggest any METHOD of measuring. Simply saying “measure it” is not offering any method of how to go about measuring it) Stretch out the shape to make it a circle. (Here although a method is offered by the student, the method is wrong)

61 Proficiency Scale Description PISA 2015 LEVEL DESCRIPTION 6 At Level 6 students can conceptualise, generalise and utilise information based on their investigations and modelling of complex problem situations. They can link different information sources and representations and flexibly translate among them. Students at this level are capable of advanced mathematical thinking and reasoning. These students can apply their insight and understandings along with a mastery of symbolic and formal mathematical operations and relationships to develop new approaches and strategies for attacking novel situations. Students at this level can formulate and precisely communicate their actions and reflections regarding their findings, interpretations, arguments and the appropriateness of these to the original situations. Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

62 Proficiency Scale Description PISA 2015 LEVEL DESCRIPTION 5 At Level 5 students can develop and work with models for complex situations, identifying constraints and specifying assumptions. They can select, compare and evaluate appropriate problem-solving strategies for dealing with complex problems related to these models. Students at this level can work strategically using broad, well-developed thinking and reasoning skills, appropriate linked representations, symbolic and formal characterisations and insight pertaining to these situations. They can reflect on their actions and formulate and communicate their interpretations and reasoning. 4 At Level 4 students can work effectively with explicit models for complex concrete situations that may involve constraints or call for making assumptions. They can select and integrate different representations, including symbolic, linking them directly to aspects of real-world situations. Students at this level can utilise well-developed skills and reason flexibly, with some insight, in these contexts. They can construct and communicate explanations and arguments based on their interpretations, arguments and actions.

63 Proficiency Scale Description PISA 2015 LEVEL DESCRIPTION 3 At Level 3 students can execute clearly described procedures, including those that require sequential decisions. They can select and apply simple problem-solving strategies. Students at this level can interpret and use representations based on different information sources and reason directly from them. They can develop short communications when reporting their interpretations, results and reasoning. 2 At Level 2 students can interpret and recognise situations in contexts that require no more than direct inference. They can extract relevant information from a single source and make use of a single representational mode. Students at this level can employ basic algorithms, formulae, procedures, or conventions. They are capable of direct reasoning and making literal interpretations of the results. 1 At Level 1 students can answer questions involving familiar contexts where all relevant information is present and the questions are clearly defined. They are able to identify information and to carry out routine procedures according to direct instructions in explicit situations. They can perform actions that are obvious and follow immediately from the given stimuli.

64 Sample Test Items on OECD Website: Sample Test Items on OECD Website:

65 Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara 1)Pentafsiran DataPentafsiran Data 2)PerimeterPerimeter 3)Nisbah 4)Bentuk 3D 5)PolaPola 6)Nombor 7)Keserupaan 8)Teorem Pythagoras 9)Wang 10)Inkuiri dan PenaakulanInkuiri dan Penaakulan 11)Kebarangkalian 12)Kadar

66 Kelas Intervensi Sekurang-kurangnya 10 kelas Sebaik-baiknya 12 kelas  ada 12 bahan intervensi Masa  1 jam Sasaran  semua murid Ting. 3 berumur 15+ thn  semua murid Ting. 4  selepas 15 Feb 2015: murid kajian sebenar Penggunaan komputer oleh murid amat digalakkan  penggunaan adalah wajib pada 2 kelas terakhir  murid dilatih menjawab menggunakan komputer Pembelajaran secara hands-on digalakkan Sekurang-kurangnya 10 kelas Sebaik-baiknya 12 kelas  ada 12 bahan intervensi Masa  1 jam Sasaran  semua murid Ting. 3 berumur 15+ thn  semua murid Ting. 4  selepas 15 Feb 2015: murid kajian sebenar Penggunaan komputer oleh murid amat digalakkan  penggunaan adalah wajib pada 2 kelas terakhir  murid dilatih menjawab menggunakan komputer Pembelajaran secara hands-on digalakkan Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

67 Kelas Intervensi Bincang dengan murid bagaimana menggunakan proses formulating, employing dan interpreting apabila mencari penyelesaian sesuatu masalah yang diberi Aktiviti pembelajaran yang dijalankan dalam taklimat ini perlu dilaksanakan bersama murid Sebaik-baiknya semua guru Matematik dilibatkan Peserta taklimat ini perlu menjalankan kursus dalaman tentang kelas intervensi di sekolah masing-masing Bahan intervensi boleh dimuat turun dari bit.ly/pisamatematik2015 Bincang dengan murid bagaimana menggunakan proses formulating, employing dan interpreting apabila mencari penyelesaian sesuatu masalah yang diberi Aktiviti pembelajaran yang dijalankan dalam taklimat ini perlu dilaksanakan bersama murid Sebaik-baiknya semua guru Matematik dilibatkan Peserta taklimat ini perlu menjalankan kursus dalaman tentang kelas intervensi di sekolah masing-masing Bahan intervensi boleh dimuat turun dari bit.ly/pisamatematik2015 Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

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69 Perbengkelan Teroka bahan yang disediakan. Selesaikan masalah dalam bahan kelas intervensi  tunjukkan kepelbagaian strategi penyelesaian sekiranya berkaitan. Kemukakan cadangan penambahbaikan bahan:  pembetulan untuk sebarang kesilapan dalam bahan, jika ada, dan  Cadangan bahan bantu mengajar untuk aktiviti hands-on, jika berkaitan. Teroka bahan yang disediakan. Selesaikan masalah dalam bahan kelas intervensi  tunjukkan kepelbagaian strategi penyelesaian sekiranya berkaitan. Kemukakan cadangan penambahbaikan bahan:  pembetulan untuk sebarang kesilapan dalam bahan, jika ada, dan  Cadangan bahan bantu mengajar untuk aktiviti hands-on, jika berkaitan. Bahagian Pembangunan Kurikulum Peneraju Pendidikan Negara

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