TUGASAN 3 KAEDAH/PENDEKATAN/TEORI
July 12, 2019 | Author: CpTan | Category: N/A
Short Description
KAEDAH/PENDEKATAN/TEORI DALAM PENGAJARAN MATEMATIK...
Description
SME 6014 PENGAJARAN MATEMATIK TUGASAN 3 KAEDAH/PENDEKATAN/TEORI
AHLI KUMPULAN
NOMBOR MATRI K
AW YING JUAN
M20132002110
TAN CHEW PENG
M20131000648
LOK YIAN LIN
M20141000936
LEE HUEY KUAN
M20141000970
PENSYARAH : PROF. DR. MARZITA PUTEH
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ISI KANDUNGAN
MUKA SURAT 1
Pendahuluan
1
2
Contoh Pengajaran Nombor Nyata
2
2.1
Perbincangan Pendekatan/Kaedah yang digunakan
5
Contoh Pengajaran Geometri Koordinat (Jarak di antara dua titik)
6
3.1
Perbincangan Pendekatan/Kaedah ya y ang digunakan
9
Contoh Pengajaran Geometri Koordinat (Koordinat Titik Tengah)
11
4.1
13
3
4
5
6
7
8
9
Perbincangan Pendekatan/Kaedah yang digunakan
Contoh Pengajaran Logaritma dan Surd
14
5.1
17
Perbincangan Pendekatan/Kaedah yang digunakan
Contoh Pengajaran Trigonometri I
19
6.1
21
Perbincangan Pendekatan/Kaedah yang digunakan
Contoh Pengajaran Trigonometri II
22
7.1
24
Perbincangan Pendekatan/Kaedah yang digunakan
Contoh Pengajaran Vektor
26
8.1
30
Perbincangan Pendekatan/Kaedah ya y ang digunakan
Contoh Pengajaran Nombor Kompleks
32
9.1
35
RUJUKAN
Perbincangan Pendekatan/Kaedah yang digunakan
36
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1
Pendahuluan
Matlamat utama sesuatu sistem pendidikan adalah untuk mempertingkatkan pemahaman pelajar terhadap konsep asas, di samping mengembangkan kebolehan mereka untuk mengenali dan menyelesaikan masalah yang berkaitan (Meor Ibrahim, 2001). Tidak dinafikan, matematik merupakan satu mata pelajaran yang sering menimbulkan masalah kefahaman konsep menyebabkan pelajar kurang minat dalam mata pelajaran ini. Pelajar baranggapan bahawa matematik adalah satu subjek yang abstrak yang memerlukan proses menghafal bagi menyelesaikan sesuatu latihan matematik (Lim, Fatimah dan Munirah, 2004). Kebanyakkan pelajar mendapati matematik merupakan mata pelajaran yang mekanikal, membosankan, tidak mencabar dan tiada kaitan dalam penggunaan harian (Noraini, 2005). Oleh yang demikian, proses pengajaran dan pembelajaran adalah sangat penting untuk merangsangkan minat pelajar terhadap matematik. Terdapat pelbagai pendekatan dan kaedah yang boleh digunakan oleh guru semasa menyampaikan sesuatu pengajaran; sama ada di dalam atau di luar bilik darjah (Abu Hassan dan Meor Ibrahim, 2006). Pemilihan pendekatan dan kaedah yang sesuai dengan tajuk adalah sangat penting kerana pendekatan dan kaedah yang sesuai membolehkan guru menyampaian pengetahuan matematik secara berkesan serta memudahkan pelajar dalam pemahaman konsep matematik serta meningkatkan minat pelajar terhadap matematik. Dalam tugasan ini, pelbagai strategi, pendekatan dan kaedah pengajaran dan pembelajaran matematik telah dibincang. Terdapat lapan contoh pengajaran dan pembelajaran disertakan bersama perbincangan pendekatan dan kaedah yang digunakan.
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2
Contoh Pe Pengajaran No Nombor Ny Nyata
Topik yang
Unit 2 Sistem Nombor Nyata
dipilih
2.2 Garis Nombor
Hasil
Pelajar dapat
pembelajaran
1. Mela Melaka karr gar garis is nomb nombor or 2. Mencari Mencari set set nilai nilai yang yang tertak tertakrif rif bagi bagi sesuatu ketaksamaan dan sebaliknya
Pengetahuan sedia
Pelajar dapat menyatakan set N, W, Z, Q, H dan R serta
ada
perkaitan di antaranya
Alat bantu
Kad-kad nombor nyata, kertas majong, marker pen, pembaris
mengajar
panjang, kertas A4, pen merah, pen hitam, lembaran kerja kerja
Pendekatan
Pendekatan Konstruktivisme
Kaedah
Perbincangan dalam kumpulan kecil dan membuat laporan
Tahap pelajar
Sederhana ke baik
Aktiviti
Set Induksi
1. Guru tampal tampal Kad-kad Kad-kad nombo nomborr nyata nyata di papan tulis. 2
-1.5
∏
2 3
√ 2
2. Pelajar Pelajar menyusun menyusun kad-ka kad-kad d nombor nombor nyata nyata mengikut mengikut tertib menaik (Kalkilator boleh diggunakan untuk membantu pelajar menentukan nilai). 3. Guru Guru bersama bersama pelaj pelajar ar menyem menyemak ak jawapa jawapan. n.
Langkah 1
1. Pelajar Pelajar dibahag dibahagikan ikan kepada kepada bebera beberapa pa kumpu kumpulan. lan. 2. Guru mengedarka mengedarkan n marker marker pen, pen, pembari pembariss panjang panjang dan kertas majung kepada setiap kumpulan. 3. Guru hanya menunjukka menunjukkan n titik titik asalan, asalan, pelajar pelajar diminta diminta melukis garis lurus bagi asalan tersebut serta menandakan
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4. Pelaja Pelajarr membuat membuat perbi perbinca ncanga ngan n dalam dalam kumpul kumpulan an untuk untuk menandakan nombor-nombor nyata di atas garis nombor tersebut. 5. Setiap kumpulan kumpulan mempame mempamerkan rkan hasil perbincang perbincangan. an. Guru Guru bersama pelajar membincangkan hasil kumpulan. kumpulan.
Langkah 2
1. Guru menged mengedarkan arkan kertas A4, pembari pembariss panjang panjang dan pen merah, pen hitam kepada pelajar. 2. Guru menulis menulis satu soalan ketaksamaan ketaksamaan di papan papan tulis. tulis.
>−3 3. Dalam kumpulan, kumpulan, pelajar pelajar diminta diminta melakark melakarkan an satu satu garis garis lurus untuk mewakili ketaksamaan dalam garis nombor.
-3
4. Guru menulis menulis satu soalan ketaksamaan ketaksamaan di papan papan tulis. tulis.
≤3 5. Dalam kumpulan, kumpulan, pelajar pelajar diminta diminta melakark melakarkan an satu satu garis garis lurus untuk mewakili ketaksamaan dalam garis nombor.
3
6. Guru menunj menunjukkan ukkan dua titik titik yang yang berlainan berlainan di di papan papan tulis. tulis.
7. Guru menerangka menerangkan n dua titik ini akan akan di letakkan letakkan di bahagian hujung garisan lurus tersebut. Titik tidak berlorek berlorek akan diletakkan di hujung garisan yang mana nilainya tidak termasuk dalam ketaksamaan, manakala titik berlorak adalah sebaliknya.
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-3
3
9. Pelajar Pelajar membuat membuat garisan garisan putus putus untuk untuk menandakan menandakan bahagian dua garisan itu bertindih. Pelajar diminta diminta melukiskan satu garisan lurus untuk mewakili ketaksamaan ini.
-3
3
10. Guru membimbing pelajar menandakan titik tidak berlorek berlorek dan berlorek di garisan lurus dalam nombor garis yang dihasilkan. 11. Guru bersama pelajar menyemak jawapan bagi setiap kumpulan. 12. Langkah atas diulangi dengan menggunakan soalan yang berlianan.Pelajar menandakan kedudukan kedudukan bagi setiap ketaksamaan yang diberikan
Langkah 3
1. Guru menged mengedarkan arkan lembaran lembaran kerja kerja kepada kepada setiap setiap pelajar, pelajar, pelajar dikehendaki menyiap lembaran kerja kerja dalam masa yang ditetapkan oleh guru. 2. Guru bersama bersama pelajar pelajar menyem menyemak ak jawapan jawapan lembaran lembaran kerja. kerja.
Penutup
1. Guru membimbing membimbing pelajar pelajar membuat membuat refleksi refleksi tentang tentang pembelajaran hari ini.
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2.1 2.1
Perb Perbinc incan anga gan n Pende Pendeka kata tan/ n/Ka Kaed edah ah yang yang digu diguna naka kan n
Pendekatan konstruktivism telah digunakan dalam pengajaran melakar garis nombor dan mencari set nilai yang tertakrif bagi sesuatu ketaksamaan dan sebaliknya. Lima fasa
dalam proses pengajaran pengajaran dan pembelajaran yang berasaskan pendekatan
konstruktivisme yang di cadangkan cadangkan oleh Needham Needham pada tahun1987 telah digunakan iaitu orientasi, pencetusan idea, penstrukturan semula idea dan refleksi (Meor Ibrahim, 2001). Orientasi dijalankan pada set induksi, pelajar menggunakan pengetahuan sedia ada untuk menyusun nombor-nombor nyata mengikut tertib menaik, dalam fasa ini akan mencetus minat pelajar untuk teruskan aktiviti pembelajaran. Fasa pencetusan idea dan penstrukturan semula idea dijalankan pada langkah 1 hingga langkah 3, pelajar menjana idea mereka dengan bimbingan guru. Tanggungjawab guru dalam langkah-langkah ini adalah sangat penting supaya dapat membimbing dan mendorong pelajar membina pengetahuan baru dengan konsep yang betul.Fasa refleksi dilakukan pada penutup iaitu pelajar membuat refleksi refleksi tentang pembelajaran yang telah berlaku. berlaku. Kaedah perbincangan dalam kumpulan kecil dan membuat laporan telah digunakan dalam pengajaran dan pembelajaran ini. Kaedah perbincangan dalam kumpulan juga dikenali sebagai kaedah koperatif yang membolehkan pelajar mencetus idea dan membina idea dalam proses menjalankan aktiviti. Dalam proses membina garis nombor serta menanda kedudukan nombor-nombor nyata, pelajar membuat perbincangan dan setiap pelajar mempunyai peluang untuk memberi idea masing-masin masing-masing. g. Selain itu, membuat membuat lapora laporan n juga juga dilakukan dilakukan dalam proses pembelajaran. Walaupun ia tidak berlaku secara jelas, tetapi pelajar telah membuat laporan secara tidak langsung semasa menyiapkan hasil perbincangan.
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3
Cont Contoh oh Peng Pengaj ajar aran an Ge Geom omet etri ri Koor Koordi dina natt (Jar (Jarak ak di anta antara ra dua dua tit titik ik))
Topik yang
Unit 6 Geometri Koordinat
dipilih
6.2 Jarak di antara dua titik
Hasil
Pelajar dapat
pembelajaran
3. mengenal sistem koordinat Cartesian terdiri daripada pasangan bertertib (a, b).
4. menentukan jarak di antara dua titik. Pengetahuan sedia
Pelajar mengenali Pythagoras Teorem.
ada Alat bantu
Dadu, garisan grid, GSP(Geometry Sketch Pad), lembaran kerja
mengajar Pendekatan
Pen Pendekatan tan Ko Kontek tekstu stual, Pe Pendekatan Pe Permainan da dan Pendekatan Pembelajaran Berasaskan ICT
Kaedah
1. Pengalaman seharian 2. Koperatif
Tahap pelajar
tahap sederhana dan tahap baik
Aktiviti
Set Induksi
4. Setiap Setiap pelaj pelajar ar diberi diberi sekep sekeping ing gamb gambar ar segi tiga tiga denga dengan n pelbagai sudut seperti di bawah:
5. Pelajar Pelajar menghant menghantar ar gambar gambar segi segi tiga tiga kepada kepada pelajar pelajar di
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7. Pelaja lajarr memba membali ling ng dad dadu u kali kali pert pertam amaa untu untuk k berg bergee rak ke ar h timur. 8. Pelajar membalin membaling g dadu kali kali kedua kedua untuk untuk bergera bergera ke arah ut ra.
C ntoh: Pelajar mendapat no nombor 6 ba bagi ba balingan da dadu p rtama dan mendapat nombor 4 bagi balingan kedua. Pelajar perlu melangkah 6 unit ke timur timur dan 4 uni ke utara di atas garisan grid.
9. G ru membimbing pelajar menggunakan rumus P ytagor ytagoras, as, iaitu iaitu sisi miring miring²² = alas² alas² + ting tinggi² gi² unt k m nentukan jarak antara 2 titik.
Contoh: Tentukan jarak antara titik A dan B
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10. Pelajar Pelajar mencari rumus rumus jarak terdekat terdekat dengan dengan menggantikan menggantikan x1,x2,y1,y2 ke dalam teorem teorem Pythagoras Teorem.
Cara pelajar mendapatkan rumus:
a
2
b
2
c
2
AC 2 CB 2 AB 2 AB 2 AC 2 CB 2 AB 2 x2 x1 2 y 2 y1 2 AB
x2 x1 2 y2 y1 2
Langkah 2
13. Pelajar duduk dalam kumpulan dan setiap kumpulan diberi dua dadu dan satu kertas garisan grid. 14. Pelajar dikehendaki membaling dua dadu untuk menentukan koordinat x dan koordinat y. 15. Pelajar diminta memplot titik permulaan (3,4) dan memplot koordinat x dan koordinat y yang diperoleh daripada baling dadu. 16. Pelajar Pelajar diminta menggun menggunakan akan rumus rumus untuk mencari mencari jarak jarak di antara dua titik.
Langkah 3
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2. Pelajar Pelajar yang dapat menyelesaik menyelesaikan an soalan soalan dengan dengan betul betul dan cepat akan menerima hadiah sebagai ganjaran. Penutup
2. Guru membimbing membimbing pelajar pelajar membuat membuat refleksi refleksi tentang tentang pembelajaran hari ini.
3.1 3.1
Perb Perbinc incan anga gan n Pende Pendeka kata tan/ n/Ka Kaed edah ah yang yang digu diguna naka kan n
Set induksi dalam pengajaran dan pembelajaran ini ialah menggunakan kemahiran menganalisis murid untuk membezakan pelbagai jenis segi tiga. Tujuannya adalah untuk memastikan pelajar dapat mengenal pasti ciri-ciri segi tiga bersudut tepat. Bagi langkah pertama, guru menggunakan Pendekatan Kontekstual dengan mengaitkan pengalaman harian pelajar untuk bergerak dari sesuatu tempat ke tempat yang lain. Menurut Nurhadi, dkk (2003: (2003: 4-5), pendekatan kontekstual adalah suatu konsep dimana guru menghadirkan situasi nyata ke dalam kelas. Seterusnya, pelajar menggunakan pengetahuan sedia ada mereka, iaitu Pythagoras Teorem untuk mencari jarak terdekat dengan menggantikan x1 , x2 , y1 , y 2 ke dalam teorem tersebut. Guru membimbing pelajar untuk mendapatkan formula jarak terdekat dengan bantuan gambar gambar segi tiga bersudut bersudut tepat. tepat. Bagi
langkah
kedua,
Pendekatan
Permainan
telah
digunakan
untuk
mengukuhkan pengetahuan mencari jarak terdekat di antara dua titik. Mok Soon Sang (1996), salah satu penyebab kegagalan penguasaan pembelajaran oleh pelajar ialah
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Akhirnya, lembaran kerja diedarkan kepada pelajar sebagai latih tubi bagi langkah penilaian dan fasa refleksi dilakukan bagi penutup iaitu pelajar membuat refleksi tentang pembelajaran yang telah berlaku.
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4
Contoh Pengajaran Geometri Geometri Koordinat Koordinat (Koordinat (Koordinat Titik Tenga h)
Topik yang
Unit 6 Ge metri Koordinat
dipilih
6.3 Koordinat Titik Tengah
Hasil
Pelajar da at
pembelajaran
1. menentukan nentukan koordinat koordinat titik tengah. 2. menentukan jarak di antara dua titik.
Pengetahuan sedia ada
Pelajar da at 1. mengen ngenal al sis sistem tem koor koordi dina natt Cart Cartes esia ian n terd terdir irii dari daripa pada da pasangan be tertib (a, b).
2. menentukan jarak di antara dua titik.n Alat bantu
Kert Kertas as lipa lipa , garisan grid, GSP(Geometry Sketch Pad)
mengajar Pendekatan Kaedah
Pendekata n Penyelesaian Masalah 3. In In uiri penemuan 4. K peratif
Tah Tahap pela pelaja jarr
taha tahap p sed sed rhana rhana dan tahap tahap baik baik
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Titik M terletak segaris dengan AB, dimana jarak AM = MB . Dari gamb r di atas, maka ditemukan bahawa titik M adalah ( ,3)
atas, guru mem emb bimb imbing ing murid rid untuk tuk mene ene mukan 3. Dari gambar di ata rumus untuk mencari titik tengah dari dua buah titik yang diketahui, iaitu:
Langkah 2
1. Pelaja duduk dalam kumpulan. 2. Setiap kumpulan diberi dua set soalan tentang tentang mencar i koordi nat nat titi titik k teng tengah ah di anta antara ra dua dua titi titik k den denga gan n form form la. 3. Pelaja diminta bekerjasama dalam kumpulan untuk k
di nat tersebut di atas garisan grid.
emplot
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Penutup
3. Guru membimbing membimbing pelajar pelajar membuat membuat refleksi refleksi tentang tentang pembelajaran hari ini.
4.1 4.1
Perb Perbinc incan anga gan n Pende Pendeka kata tan/ n/Ka Kaed edah ah yang yang digu diguna naka kan n
Set induksi dalam pengajaran dan pembelajaran ini adalah menggunakan kaedah lipatan kertas untuk mencari titik tengah. Tujuannya adalah untuk memastikan pelajar memahami konsep titik tengah. Bagi langkah pertama, guru menggunakan Pendekatan Penyelesaian masalah dengan meminta pelajar memplot dua koordinat yang diberi dan menggambarkan titik tengah tengah di antara dua titik titik tersebut. tersebut. Pelajar cuba cuba menyelesaik menyelesaikan an masalah yang yang diberikan oleh guru dengan menukarkan soalan kepada bentuk visual dengan garisan grid. Bagi langkah kedua, pelajar dikehendaki bekerjasama dalam kumpulan untuk mencari jawapan bagi soalan-soalan yang diberikan oleh guru. Tujuan aktiviti kumpulan ini adalah untuk meningkatkan kefahaman pelajar untuk menggunakan
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5
Contoh Pengajaran Logaritma dan dan Surd
Topi Topik k yang yang dip dipil ilih ih
Unit Unit 5 log logar arit itma ma dan dan sur surd d 5.4 Persamaan Surd
Hasil
Pelajar dapat
pembelajaran
1. Menyelesaika Menyelesaikan n persamaan persamaan yang melibatkan melibatkan punca kuasa dua. Catatan:
Hasil penyelesaian mesti dalam bentuk persamaan kuadratik.
Menyelesaikan masalah dengan menggunakan kaedah pemfaktoran, penyempurnaan kuasa kuasa dua dan formula.
Pengetahuan sedia ada Alat Bantu
ab
a
b
a b
a b
di mana a dan b adalah nilai positif
Papan putih, pen marker
Mengajar Pendekatan yang
1. Daripa Daripada da spesifi spesifik k kepada kepada umum umum (indukt (induktif) if)
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Pelajar diminta duduk dalam 5 Kumpulan. Aktiviti
Set Induksi 1. Guru Guru men menul ulis is perk perkat ataa aan n ‘SURD’ ( dengan contoh symbol ) di atas papan putih. 2. Kemudi Kemudian an guru guru berta bertanya nya kepa kepada da pelaja pelajarr . Kenapakah Kenapakah kita perlu belajar belajar ‘SURD’? atau Apakah penggunaan ‘SURD’? 3. Sekiranya Sekiranya pelajar pelajar tidak tidak dapat memberi memberi respon respon.. 4. Guru Guru aka akan n memb member erii conto contoh h – cont contoh oh SURD supaya dapat membantu pelajar mendapat idea tentang sebab
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Teknik apakah yang sesuai digunakan untuk menyelesaikan masalah 2? ( pelajar pernah belajar di tingkatan 2 topik 2 dalam matematik) 12. Satu teknik atau idea telah dikenal dikenal pasti untuk menyelesaikan masalah 2.( kuasa dua) 13. Guru menulis menulis soalan masalah masalah 3 ‘ Selesai Selesaikan kan
3 x 1 x 3 ’ 14. Pelajar diberi masa 2 minit minit untuk menjawab masalah 3. 15. Guru minta pelajar tulis jawapan jawapan di atas papan putih. (guru menggantikan nilai untuk semakan jawapan dan buat
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Penutup 24. Guru membimbing membimbing pelajar pelajar menyatakan menyatakan kesimpulan kesimpulan untuk kelas hari tersebut. ( langkah dan idea untuk menyelesaikan masalah persamaan SURD).
5.1 5.1
Perb Perbinc incan anga gan n Pende Pendeka kata tan/ n/Ka Kaed edah ah yang yang digu diguna naka kan n
Saya berpendapat bahawa pendekatan induktif sesuai digunakan (Spesifik kepada umum) kerana pendekatan ini tidak membosankan para pelajar.
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Dengan penggunaan strategi pemusatan pelajar, ujian formatif adalah ditekankan dan keputusan ujian akan digunakan untuk mengkaji kelemahan – kelemahan pelajar. Perbincanga Perbincangan n sub – topik penyelesai penyelesaian an persamaan persamaan SURD diakhiri diakhiri dengan bimbingan para pelajar untuk membuat kesimpulan ketika menyelesaikan soalan persamaan surd.
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6
Contoh Pengajaran Trigonometri I
Topi Topik k yang yang dip dipil ilih ih
Unit Unit 7 Tri Trigo gono nome metr trii 1 7.7 Nisbah Trigonometri untuk Sudut Am
Hasil pembelajaran
Pelajar dapat 1. Mengen Mengenal al pasti pasti simbol simbol posit positif if dan dan 19egat 19egative ive nisbah nisbah trigonometri bagi sesuatu sudut dalam semua sukuan. 2. Mencari Mencari nilai nilai nisbah nisbah trigono trigonometri metri bagi sesuatu sudut dalam semua sukuan.
Pengetahuan sedia ada
1. Pelajar mengetahui mengetahui kedudu kedudukan kan sukuan sukuan 1 hingga hingga 4 (iaitu (iaitu lawan arah jam).
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berikut: Sukuan Sudut
I. (*)
II. (*)
III.
IV.
(*)
(*)
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dibincang pada akhir kelas.
6.1 6.1
Perb Perbinc incan anga gan n Pende Pendeka kata tan/ n/Ka Kaed edah ah yang yang digu diguna naka kan n
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7
Contoh Pe Pengajaran Tr Trigonometri II II
Topik yang
Unit 8 Trigonometri II
dipilih
8.3 Petua Kosinus
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penyelesaian bagi soalan ini. (Guru mengingatkan pelajar bahawa semua sudut dalam segi tiga ini adalah tidak bersudut tepat, pelajar tidak boleh terus menggunakan nisbah trigonometri trigonometri dalam
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60
90
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