BAHAGIAN PEMBANGUNAN KURIKULUM

Transcription

1 Higher Order Thinking Skills in Science & Mathematics ( HOTsSM) BAHAGIAN PEMBANGUNAN KURIKULUM KEMENTERIAN PELAJARAN MALAYSIA

2 khir sesi ini anda akan dapat: emahami apa itu HOTs dalam Matematik. enerapkan HOTs dalam kalangan murid. enyampaikan taklimat berkaitan HOTs kepada uru-guru lain.

3 Sesi Taklimat ini mengandungi DUA komponen: 1) Penerangan & Perbincangan 2) Perbengkelan

4 Apa itu HOTs dalam Matematik?

5 LOWER ORDER THINKING (LOTs) Resnick (1987) Lower-order thinking (LOT) is often characterized by the recall of information or the application of concepts or knowledge to familiar situations and contexts. Schmalz (1973) LOT tasks requires a student to recall a fact, perform a simple operation, or solve a familiar type of problem. It does not require the student to work outside the familiar Senk, Beckman, & Thompson (1997) LOT is involved when students are solving tasks where the solution requires applying a well-known algorithm, often with no justification, explanation, or proof required, and where only a single correct answer is possible Thompson 2008 generally characterized LOT as solving tasks while working in familiar situations and contexts; or, applying algorithms already familiar to the student.

6 IGHER ORDER THINKING SKILLS (HOTs) nick (1987) characterized higher-order thinking (HOT) as -algorithmic. in and Lane (1996) describe HOT as the use of complex, -algorithmic thinking to solve a task in which there is not a ictable, well-rehearsed approach or pathway explicitly itl suggested he task, task instruction, or a worked out example. k, et al (1997) characterized HOT as solving tasks where no rithm has been taught, where justification or explanation are ired, and where more than one solution may be possible. mpson (2008) generally characterized HOT involves solving s where an algorithm has not been taught or using known rithms while working in unfamiliar contexts or situations.

7 IGHER ORDER THINKING SKILLS (HOTs) igher order thinking lls are normally those kills in the top four levels of the revised Bloom s taxonomy: pplying, analysing, luating, and creating.

8 IGHER ORDER THINKING SKILLS (HOTs) Higher-order questions promote learning because these types of questions require students to apply, analyze, synthesize, and evaluate information instead of simply recalling facts.

9 IGHER ORDER THINKING SKILLS (HOTs) Termasuk pemikiran kritikal, pemikiran kreatif, pemikiran logikal, emikiran reflektif dan meta-kognitif kognitif. HOTs dicetuskan melalui masalah bukan rutin, masalah yang tidak jelas atau dilema.

10 Mengapa perlu HOTs dalam Matematik?

11 Menghasilkan modal insan yang cerdas, kreatif dan inovatif bagi memenuhi cabaran abad ke-21 agar negara mampu bersaing di persada dunia. If we want students to develop the capacity to think, reason, and problem solve then we need to start with high-level level, cognitively complex tasks. Stein & Lane 1996

12 s in International Mathematics and Science Studies TIMSS 2007 Average Achievement in the Mathematics Content and Cognitive Domains ysia performed below TIMSS average in both Mathematics

13 Berubah ke arah lebih daripada kefahaman asas dan rote memorization. Meningkatkan tahap kefahaman Meningkatkan kemampuan menjustifikasikan penyelesaian dan dapatan. Konsep matematik dapat dipelajari dengan lebih berkesan melalui l HOTs. Meningkatkan keupayaan murid dalam menyiasat dan meneroka idea matematik memerlukan HOTs.

14 OTs DALAM KURIKULUM MATEMATIK Pernyataan Standard Kurikulum ditulis menggunakan kata kerja mengikut Taksonomi Bloom. Kata Kerja Metaperwakilan Bagi HP yang menggunakan kata kerja seperti menyatakan dan menerangkan turut menuntut guru menyediakan aktiviti kiii yang menekankan HOTs

15 Bagaimana meningkatkan HOTs? rlu kepada transformasi dalam PdP: ru perlu berubah cara: berfikir Mengajar - kurangkan chalk and talk, perbanyakkan hands on Menyoal (ms 4 & 5) Memotivasi Mentaksir Tingkatkan kualiti tugasan yang diberi kepada murid

16 gaging Sikap Positif Pemikiran Reflektif ntukan Masa Membuat & menguji konjektur PELAKSANAAN HOTs MENUNTUT Pelbagai Pendekatan Non-algorithmic Penaakulan & Pembuktian Kritikal & Analitikal Penerokaan & Penyiasatan Kefahaman Mendalam Pelbagai Perkaitan Komunikasi Pelbagai Strategi Kreatif & Inovatif

17 PELAKSANAAN HOTs MENUNTUT ru perlu merancang alan, tugasan dan iviti yang menuntut rid berfikir, berlatih berfikir secara terusan dan menilai ikiran mereka dan ikiran individu lain. Worthwhile and Rich task

18 Different levels of response by Robert Sternberg (American Cognitive i Psychologist) Teacher should answer children's questions in a way that promotes HOTs.

19 Level 1: Reject the question Example: "Why do I have to eat my vegetables?" "Don't ask me any more questions. "Because I said so."

20 Level 2: Restate or almost restate the question as a response Example: "Why do I have to eat my vegetables?" "Because you have to eat your vegetables." "Why is that man acting so crazy?" "Because he's insane. " "Why is it so cold?" Why is it so cold? "Because it's 15 outside."

21 Level 3: Admit ignorance or present information Example: "I don't know, but that's a good question." or, Give a factual answer to the question.

22 Level 4: Voice encouragement to seek response through authority Example: Let's look that up on the internet. Let's look that up in the encyclopedia. Who do we know that might know the Who do we know that might know the answer to that?

23 Level 5: Encourage brainstorming, or consideration of alternative explanations Example: "Why are all the people in Holland so tall? "Let's brainstorm some possible answers." "Maybe it's genetics, or maybe it's diet, or maybe everybody in Holland wears elevator shoes, or " etc.

24 Level 6: Encourage consideration of alternative explanations and a means of evaluating them Example: "Now how are we going to evaluate the possible answer of genetics? Where would we find that information? Information on diet? The number of elevator shoes sold in Holland?

25 Level 7: Encourage consideration of alternative explanations plus a means of evaluating them, and follow-through on evaluations Example: "Okay, let's go find the information for a few days we'll search through the encyclopedia and the Internet, make telephone calls, conduct interviews, and other things. Then we will get back together next week and evaluate our findings. "

26 Bi Bring a closure to Sternberg, so what? Teacher should answer children's questions in a way that promotes HOT, so which level shall the teachers pitched on?

27 INGKATKAN PEMIKIRAN MATEMATIK MURID ) 311)

28 Soalan Bukan Rutin yang memerlukan tahap kognitif yang tinggi dapat membentuk HOTs dalam kalangan murid.

29 RUTIN BUKAN RUTIN Problems can be solved sing methods familiar to students by replicating viously learned methods a step by step fashion. outine problem solving stresses the use of sets of known or prescribed procedures (algorithms) to solve problems Problems that require mathematical analysis and reasoning; many non routine problems can be solved in more than one way, and may have more than one solution.

30 RUTIN BUKAN RUTIN Perlunya keseimbangan antara soalanrutin dengan bukan rutin. Penekanan kepada soalanbukan rutin penting bagi: Membentuk modal insan yang berfikrah. Merealisasikan hasrat negara untuk mencapai satu pertiga teratas dalam TIMSS dan PISA.

31 Contoh Soalan TIMSS & PISA

32 CONTOH SOALAN TIMSS Place either + or - into each box so that t this expression has the largest possible total?

33 CONTOH SOALAN TIMSS Which circle has approximately the same fraction of its area shaded as the rectangle above? A B C D E

34 CONTOH SOALAN TIMSS What is the perimeter of a rectangle whose area is 100 square meters? Answer:

35 CONTOH SOALAN LAIN Antara nombor-nombor berikut, nombor yang mana berbeza? Mengapa? 23, 20, 15, 25

36 TIMSS Population 2 Item Pool (Released Items). Copyright 1994 by IEA, The Hague CONTOH SOALAN TIMSS Brad wanted to find three consecutive whole numbers that add up to 81. He wrote the equation (n 1)+ ) n + (n +1) = 81. What does the n stand for? A) The least of the three whole numbers B) The middle whole number C) The greatest of the three whole numbers. D) The difference between the least and the greatest of the three whole numbers.

37 CONTOH SOALAN TIMSS A car salesman placed this advertisement in the newspaper: Old and new cars for sale, different prices, average price RM 50,000. From the advertisement, which of the following must be true? A) Most of the cars would cost between 68 RM40,000 and RM60,000. B) Half of the cars would cost less than 35 RM50,000, 000 and half would cost more than RM50,000. C) At least one of the cars would cost RM50, D) Some of the cars would cost less than RM 50, Daripada 153 orang pelajar hanya 18%

38 CONTOH SOALAN TIMSS John and Cathy were told to divide a number by 100. By mistake John multiplied the number by 100 and obtained an answer of 450. Cathy correctly divided the number by 100. What was her answer? A B C D. 4.5 TIMSS th-Grade Mathematics Concepts and Mathematics Items

39 CONTOH SOALAN PISA 1) (a) Which of the figures has the largest area? Show your reasoning. (b) Describe a method for estimating the area of figure C. 2) Nick wants to pave the rectangular patio of his new house. The patio has length 5.25 metres and width 3.00 metres. He needs 81 bricks per square metre. Calculate how many bricks Nick needs for the whole patio.

40 CONTOH SOALAN LAIN Mary claims that you can find the area of any triangle given the length of only one side. Is Mary correct or not? Justify your answer.

41 CONTOH SOALAN LAIN Panjang sisi sebuah segiempat sama B adalah empat kali ganda segiempat sama A. Berapa kalilah lebih besar luas B berbanding luas A? Segiempat sama A Segiempat sama B

42 CONTOH AKTIVITI en Pottery erd is part of a piece of pottery that one might dig up at an eological site where pottery making people once lived. aeologists usually want to figure out how big the original piece of ry was, as that can tell them something about who might have the piece and when it was made. the sherd shown on the right, devise a od for determining the diameter of the al plate. : Can you come up with another method?

43 NTOH AKTIVITI Nombor Perdana Bagaimana cikgu mengajar Nombor Perdana?

44 NTOH AKTIVITI Nombor Perdana FAKTOR BIL. FAKTO R KUMP NO. FAKTOR BIL. FAKTO R KUMP

45 NTOH AKTIVITI Nombor Perdana FAKTOR BIL. FAKTO R 1 1 A 1,2 2 B 1,3 2 B 1,2,4 3 1,5 2 B ,2,3,6 4 1,7 2 B 1,2,4,8 4 1,3,9 3 1,2,5, ,11 2 B 1,2,3,4,6,12 6 KUMP NO. FAKTOR BIL. FAKTO R 14 1,2,7, ,3,5, ,2,4,8,16 5 KUMP 17 1,17 2 B 18 1,2,3,6,9, ,19 2 B 20 1, 2, 4,5,10, ,3,7, ,2,11, ,23 2 B ,2,3,6,8,12, 7 24

46 NTOH AKTIVITI How many one by one tiles are required to surround a 5x5 pool? Develop a generalization that predicts the number of tiles required to surround a square pool of anysize size. Explain how your generalization relates to the size of the pool and the number of border tiles.

47 NTOH AKTIVITI

48 Menukarkan k Masalah hrt Rutin kepada Masalah Bukan Rutin

49 MASALAH RUTIN KEPADA BUKAN RUTIN TS TUGASAN 1 Maria membeli sekotak susu dengan harga RM1.55 dan sebungkus biskut dengan harga RM1.70. Berapakah jumlah wang yang dibayar oleh Maria? OTS TUGASAN 2 Maria membeli sekotak susu dengan harga RM1.55 dan sebungkus biskut dengan harga RM1.70. Dia memberikan RM4.00 kepada jurujual. Berapakah bilangan syiling yang diterima oleh Maria sekiranya jurujual itu memberikannya beberapab syiling 5 sen, 10 sen

50 MASALAH RUTIN KEPADA BUKAN RUTIN HOTS TUGASAN 1 ari perimeter segi empat epat yang mempunyai anjang 8 meter dan lebar 17 eter. Cari panjang sebuah segi empat tepat yang mempunyai luas 48 meter persegi dan lebar 6 meter. TUGASAN 2 Mamat ingin membina pagar bagi reban ayam yang berbentuk segi empat. Dia mempunyai 20 meter wayar pagar. 1. Apakah saiz segiempat yang boleh beliau hasilkan? 2. Bentuk manakah yang terbaik? LOTS

51 MASALAH RUTIN KEPADA BUKAN RUTIN SOALAN RUTIN: Satu sisiempat mempunyai sudut-sudut 100, 60, and 130. Apakah nilai sudut yang keempat? Boleh Dikembangkan Kepada: Bolehkah sisiempat mengandungi empat sudut cakah? Bagaimana anda tahu? Bolehkah segitiga mengandungi lebih daripada satu sudut cakah? Terangkan. Bolehkah sisiempat mengandungi dua sudut cakah? Sekiranya boleh, lukiskan rajah. Sekiranya tidak, terangkan. Bolehkah sisiempat mengandungi tiga sudut cakah? Sekiranya boleh, lukiskan rajah. Sekiranya tidak, terangkan.

52 MASALAH RUTIN KEPADA BUKAN RUTIN Bundarkan 726 kepada ratus yang terdekat? LOTS HOTS Apakah nombor yang boleh dibundarkan kepada 700?

53 MASALAH RUTIN VS. BUKAN RUTIN OALAN RUTIN idak memerlukan urid untuk enggunakan emahiran berfikir ada aras tinggi. perasi yang perlu igunakan adalah elas. SOALAN BUKAN RUTIN Memerlukan tahap pemikiran pada aras tinggi. Meningkatkan kemahiran menaakul. Jawapan dan prosedur yang perlu digunakan tidak serta merta jelas. Menggalakkan lebih daripada satu cara penyelesaian dan strategi. Terdapat lebih daripada satu jawapan. Lebih mencabar. Berupaya membentuk murid yang kreatif dan inovatif Penyelesaian memerlukan lebih daripada membuat keputusan dan memilih operasi matematik. Memerlukan masa yang sesuai untuk diselesaikan.

54 Skema Pemarkahan TIMSS & PISA

55 SKEMA PEMARKAHAN TIMSS

56 SKEMA PEMARKAHAN PISA

57 SKEMA PEMARKAHAN PISA

58 Tidak semua tugasan sama, tugasan yang berbeza menggalakkan tahap dan jenis pemikiran yang berbeza. Tahap pemikiran di mana murid melibatkan diri akan menentukan tahap pembelajaran mereka.

59 RBINCANGAN DALAM MPULAN KECIL: ngembangkan Soalan Rutin(LOTs) pada Bukan Rutin(HOTs) 1. Bentukkan kumpulan 2 orang. 2. Tukarkan soalan rutin yang diberi kepada soalan bukan rutin.

60 Kembangkan soalan berikut agar menjadi soalan bukan rutin. 1) = 2) Cari perimeter bagi rajah dibawah. 3 cm 8cm 3) Cari min, median dan mod bagi data berikut: 15, 16, 18, 37, 39 4) Cari isi padu kotak yang mempunyai dimensi 4 cm x 2 cm x 8 cm.

61 CONTOH JAWAPAN 1) Marcella had 825 cupcakes and sold all but 5. If she sold them in packages, what might be the size and number of the packages? How do you know? 2) Is it possible for two rectangles to have an area of 24 sq cm but have different perimeters? Explain how you know. 3) Find five data values so that the mean is 25 and the median is 18. Explain your answers. 4) Can two different boxes have the same area for the base ) but different volumes? Can two different boxes have different dimensions for the base but the same volume? Explain.

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63 Tindakan Susulan Guru Adakan taklimat dalaman di sekolah masing- masing kepada semua guru Sains dan Matematik. Gunakan kandungan dan tempoh masa taklimat seperti yang diterima. i Semua guru Sains dan Matematik menggunakan soalan HOTs dalam pdp. Guru Sains dan Matematik Tingkatan 1 mula menyediakan murid untuk Gerak Gempur HOTsSM pada Jun dan Okt 2013 & 2014 untuk persediaan murid ke TIMSS 2014 dan PISA Soalan dan skema Gerak Gempur akan disediakan secara berpusat dan pelaporan perlu disediakan.

64 TERIMA KASIH