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Tuesday, 18 November 2008
PS 2206 Question 2 Use of Spreadsheet in teaching maths
Q2 the Use of Spreadsheet or Microsoft Excel in Mathematics
Thursday, 13 November 2008
PS 4305 3.19 Question 20
LISt the strategies you would use so that the students will not feel bored and depressED.
In teaching and learning mathematics there are many issues that teachers must consider.
1) Teaching methods
2) Resources and teaching aids
3) The language of the learner
4) Multiple intelligences of pupils
Students
Ÿ Young children learn mathematics in different ways and they are not only dependent on the types of learning that requires them to just "sit and listen" to teacher-talk.
Ÿ Students can learn by :-
¬ practicing skills on their own
¬ conducting discussion between them
¬ playing games
¬ doing puzzles
¬ doing practical
¬ problem-solving
¬ finding things by themselves
Ÿ In the classroom context, students need the opportunities to use different kinds of learning as it :-
ð provides motivation
ð improves their learning skills
ð provides variety
ð enabled them to learn things more quickly
Teaching methods
1. Presentation and explanation by the teacher
Ÿ This is a formal teaching method that allows the teacher to present and explain mathematics to the whole class. It can be difficult because you have to ensure that all students understand. This can be a very effective way of :
Ä teaching a new topic to a large number of students
Ä trying to make everyone understand certain stages of the topic
Ä summarizing what has been learnt
2. Drill and practice
Ÿ It is essential that students have the opportunity to practice what they have learnt as well as to develop their understanding by applying new ideas and skills towards the new learning materials.
3. Games
Ÿ Games can help to create an enjoyable, exciting and interesting lesson. Games provide opportunities for the students to take part in learning actively. Moreover, it also allows students to experience success and satisfaction, which later build their confidence and enthusiasm.
Ÿ The benefits of games :
" Help students to understand mathematical concepts
" Enable students to develop mathematical skills
" help students to know mathematical facts
" help students to learn the language and vocabulary of Mathematics
" help students to develop ability in mental mathematics
Ÿ For instance,
i. Go on a Geometry Scavenger Hunt
ii. Sandbox Math Sticks
(Examples of games that can be found in the internet)
4. Practical work (always involve resources)
Ÿ Practical work refers to three things :
a. Using materials and resources to make things which involve using mathematical skills of measuring and estimating as well as the knowledge of making spatial relationships.
b. Marking a solid model of mathematical concept or relationship.
c. Using mathematics in a practical, real-life situation for instance in markets, planning trips and organising event.
Ÿ Benefits of using resources:
a. actively involves students
b. motivates students
c. makes ideas concrete
d. gives hands-on experience
e. makes group work easier
f. gives opportunities for language development
Ÿ According to Huetinck and Munshin (2004) some students are kinaesthetic learners, thus touching objects may enhance their learning needs. An object that can address the concepts in mathematics through visual and kinaesthetic senses is being referred as manipulative.
5. Problems and puzzles
Ÿ This kind of method encourages students to learn mathematics through solving problems and puzzles which have definite answers. The key point of this method is it allows students to work out the solution by themselves.
Ÿ Puzzles develop students’ thinking skills, where problem solving helps to develop the skills of selecting the appropriate method and apply it to the given problem.
6. Investigating mathematics
Ÿ This can be done by setting students with challenge which leads them to discover and practice by themselves. The teacher should find suitable challenges for the students and the challenges should also be matched to the students’ ability.
Ÿ The investigations should encourage students to make their own decisions on :
a. where to start
b. how to deal with the challenge
c. what mathematics they need to use
d. how they can communicate this mathematics
e. how to describe what they have discovered
Portman, J and Richardson, J (1997)
7. Creating a new and fun environment of learning
Ÿ It would be nice if the teacher would bring along the pupils to a mathematic convention or event. This would give them more exposure. Not only that, the children will learn that mathematic is actually fun and very useful in their lives.
8. Active learning
Ÿ Meyers and Jones (1993) define active learning as learning environments that allow “students to talk and listen, read, write, and reflect as they approach course content through problem-solving exercises, informal small groups, simulations, case studies, role playing, and other activities -- all of which require students to apply what they have learnt ”.
Ÿ Many studies show that learning is enhanced when students become actively involved in the learning process. Instructional strategies that engage students in the learning process stimulate critical thinking and a greater awareness of other perspectives
9. Cooperative learning
Ÿ Cooperative Learning is a systematic pedagogical strategy that encourages small groups of students to work together for the achievement of a common goal. The term 'Collaborative Learning' is often used as a synonym for cooperative learning when, in fact, it is a separate strategy that encompasses a broader range of group interactions such as developing learning communities, stimulating student/faculty discussions, and encouraging electronic exchanges (Bruffee, 1993).
Ÿ When integrating cooperative or collaborative learning strategies into a course, careful planning and preparation are essential. Understanding how to form groups, ensure positive interdependence, maintain individual accountability, resolve group conflict, develop appropriate assignments and grading criteria, and manage active learning environments are critical to the achievement of a successful cooperative learning experience.
10. Integrating Technology (use of ICT) in the lesson.
CONCLUSION
In short, by taking into account all of these strategies before starting a lesson, teachers will therefore be able to make students enjoy the lesson and not feel bored and depressed.
Compiled by: Dk Muhyidatul, Nur Farahana, Nur Ridzwannah, Mufidah, Ak Alif
PS 4305 3.18 Question 19
Explain why Malay pupils perform badly in Brunei PSR and PMB examination?
There is no doubt that Bruneian youths are having difficulties in scoring good grades in PSR and PMB examination especially in Mathematics subject.
The main reasons are:
1. The negative classroom environment.
Classroom learning environment refers to the overall climate and culture of the classroom itself - the communication patterns, the design or the classroom layout (the seating arrangement), the organization of physical space and the teacher’s ability to manage students’ behaviour in the classroom.
It can be a powerful teaching instrument to the teacher. The classroom learning environment needs to be supportive so that students will learn to respect each others and their ideas. Moreover, a positive classroom learning environment helps to provide a safe, secure and stimulating climate for children learning and to perform their best (Fraser, 1998). Teachers in Brunei did not find this very important.
The above picture shows the usual seating arrangement that can be found in any Mathematics classroom in Brunei Darussalam. When teachers consciously develop a plan for setting up the classroom and consistently apply this plan by organizing the seating arrangement shown, teaching and learning of Mathematics lesson in the classroom will therefore become ineffective.
Beside, the most common feature of a typical Bruneian classroom is that the walls and bulletin boards are always left empty without posters or pictures being hanged on the wall.
2. Teaching and learning styles -included covering syllabus issue, mixed abilities and language issues.
Most Mathematics teachers in Brunei usually practised “chalk and talk” approach, where it does not emphasize understanding concepts of ‘how’ to get the solution and ‘why’ the rules work. The teachers are only concerned about covering the syllabus and also preparing the students for the upcoming assessments.
Other than that, students of different abilities may have different standard of English. Those who achieve low scores may have problems in understanding English. Thus, teachers need to explain complicated words using simple English so that the whole class may understand the question. This will result in students being too dependent on teachers’ assistance.
In order to overcome this problem, teachers should be creative in their approach. Teachers should teach their students for understanding rather than just using chalk and talk method. Beside that teachers should take into account students’ different ability levels.
Compiled by:
(Dk Muhyidatul Syifa, Nur Farahana, Nur Ridzwannah, Mufidah, Ak Alif Wira Putra)
PS 4305 3.17 Question 18
Language become an issue in the learning and teaching of primary mathematics. Explain.
Many pupils in the primary school level have a problem in understanding the questions in mathematic. They are either confused or misinterpreted. This is due to their lack of mathematical vocabulary. Most of the English words can have different meaning in mathematical context. For example the word “volume” in mathematic context refers to the “space” of something whereas “volume” in daily life means “the level of sound”.
The problem in the acquisition of language does not only occur in word-problem question but also in mathematical problem involving order. The importance of having skills in solving word problems has been strongly emphasized as early as in Primary 1.
According to Kantowski (1977), an individual is faced with a problem when he encounters a problem with question he cannot answer or a situation he is unable to resolve using the knowledge immediately available to him. He must then think of a way to use the information at his disposal to arrive at the solution of the problem” (p. 163). He further differentiates between a problem and an exercise. In the case of a problem, an algorithm which will lead to a solution is unavailable while in an exercise one determines the algorithm and then does the manipulation. For example; “Abdul Rahman bought a television set for $2 985 and a video-recorder for $1 280. How much did he spend on the two items altogether?”(C.D.D, 2004).
Students like mathematics as long as they “understand” and understanding is a major goal of mathematics teaching at all levels in the educational system (Stadler, 2002). An important part of the mathematics subject includes the signs and symbols that are available under the learning and teaching of mathematics. Mathematical understanding is both a linguistic and a conceptual matter (Vergnaud, 1998). In order for the pupils in Brunei to understand mathematics, the pupils must be able to identify relationships between the mathematical symbols and also their relation to everyday language.
Research done by Clements (1999), Gurung (2003), Raimah (2001), Sainah (1998) and Saman (2000) shows that Bruneian pupils both in the upper and lower primary have trouble to cope with mathematics word-problem in English language. Since difficulty in solving word problems has something to do with language, so the study also aims to get insight of the level of language difficulties experienced by the pupils and to identify to what extent it affected their problem solving skills.
From a study being done by Hajah Sainah (1998), it can be concluded that in most cases students find problem-solving tasks more difficult than the symbol manipulation of corresponding computational tasks. A statement by the Cockcroft Report (1982, p6) confirms that Mathematics is a difficult subject both to teach and to learn. Mathematics is more complicated when it is being studied as a second language. A child who cannot understand the language of a mathematics problem cannot possibly find the solution as the Cockcroft Report (1982, p89) claims that language plays an essential part in the formulation and expression of mathematical ideas. Tough (1977, p202) also shares this view that the use of language plays an important part in helping children to establish both the basic mathematical concepts and the terminology that are necessary for mathematical thinking.
Language Difficulties
A student with language problems in Mathematics may :
·have difficulty with the vocabulary of Mathematics
·be confused by language in word problems
·not know when irrelevant information is included or when information is given out of sequence
·have trouble learning or recalling abstract terms
·have difficulty understanding directions
·have difficulty explaining and communicating about math, including asking and answering questions
l have difficulty reading texts to direct their own learning
l have difficulty remembering assigned values or definitions in specific problems
(http://www.pbs.org/wgbh/misunderstoodminds/mathdiffs.html)
References:
- Curriculum Development Department. (2004). Primary Mathematics for Brunei Darussalam. Darjah 5. Singapore: Federal Publication.
- Kantowski, M. G. (1977). Processes involved in mathematical problem solving. Journal for Research in Mathematics Education, 8(3), 163-180.
- Hajah Sainah binti Haji Nayan (1998). Problem-solving errors by primary six children in specialist teachersÂ’ project schools. Unpublished M.Ed dissertation, Sultan Hassanal Bolkiah Institute of Education, Universiti Brunei Darussalam.
- Stadler, E. (2002). Language and understanding of mathematical concepts.Vaxjo University. In English as a second Language. Educational Studies in Mathematics.November 1993 14,4,325-350.Journal for Research in Mathematics Education, 8(3), 163-180.
- Vergnaud, G. ( 1998). Towards a cognitive theory of practice. I.Sierpinska, A. and Kilpatrick, J. Mathematics Education as a Research Domain: A Search for Identiry, 227-240. Kluwer Academic Publishers.
Done by : Ak Alif Wira Putra Bin Pg Awang (06B0410)
Dk Muhyidatul Syifa Binti Pg Mohin (06B0412)
Mufidah Binti Haji Kassim (06B0413)
Nur Ridzwannah Binti Moktar (06B0418)
Nur Farahana Binti Haji Murni (06B0423)
PS 4305 3.16 Question 17 (Malay Ver) Dr Mahathir's Reason of Teaching Maths & Sci in English Current Issue
MENGAJAR SAINS DAN MATEMATIK DALAM BAHASA INGGERIS
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1. Saya mengaku bertanggungjawab berkenaan mengajar Sains dan Matematik dalam Bahasa Inggeris. Kerana itu ramai yang menuduh saya tidak bersemangat kebangsaan Melayu, tidak utamakan bahasa saya.
2. Izinkan saya membuat sedikit penjelasan sebelum saya dihukum.
3. Pendapat saya ialah mereka yang bersemangat kebangsaan Melayu tidak harus utamakan hanya penguasaan bahasa ibunda sahaja tetapi juga melihat bangsanya bediri sama tinggi, duduk sama rendah dengan bangsa-bangsa yang maju di dunia. Hanya dengan fasih bertutur kata dalam bahasa sendiri dengan ilmu pengetahuan yang cetek tidak akan menjadi bangsa kita mulia dan mampu bersaing dengan jayanya dengan bangsa-bangsa maju dan dianggap setaraf dengan mereka.
4. Kita diberitahu Nabi bersabda "Tuntutlah ilmu hingga ke negeri China". Apakah dapat orang Arab tuntut ilmu orang Cina tanpa mempelajari bahasa Cina, lisan dan tulisan, terlebih dahulu?
5. Kita juga tahu orang Arab telah menguasai ilmu Sains, Matematik dan falsafah yang diterokai oleh orang Yunani (Greek) dan menterjemahkan ilmu-ilmu ini ke dalam bahasa Arab sebelum kaji selidik dilakukan untuk memperluaskan ilmu-ilmu ini.
6. Semasa bangsa-bangsa yang beragama Islam iaitu Arab, Turki, Uzbek dan lain-lain berjaya bangunkan tamadun Islam yang gemilang, bangsa-bangsa Eropah berada "di zaman gelap", zaman mereka tidak berilmu dan percaya kepada kuasa-kuasa ghaib terhadap segala kejadian alam.
7. Pada abad ke-15 Masehi, orang Eropah yang berkurun-kurun kagum dengan tamadun orang Islam mula sedar akan ilmu pengetahuan dalam bidang sains, perubatan, matematik, astronomi yang dimiliki orang yang berbahasa Arab serta sumbangan ilmu-ilmu ini kepada tamadun gemilang Islam. Paderi-paderi Kristian Eropah belajar bahasa Arab untuk mendapat akses kepada ilmu-ilmu yang berada dalam kutub-khanah milik Arab dan orang Islam lain.
8. Mereka mempelajari semua ilmu-ilmu ini dalam bahasa Arab dan menterjemahkan kedalam bahasa Latin, dan kemudian kepada bahasa-bahasa Eropah. Kemudian mereka pula membuat kajian dan memperluaskan semua ilmu-ilmu ini. Maka terdirilah tamadun Eropah yang terus maju hingga ke zaman sekarang.
9. Yang jelas daripada sejarah ialah penguasaan ilmu yang ada pada bangsa lain bermula dengan penguasaan bahasa bangsa-bangsa ini.
10. Apakah kita tidak mungkin mengadakan segelintir daripada orang Melayu mempelajari bahasa ilmu di zaman ini, iaitu bahasa Inggeris supaya mereka dapat menterjemahkan ilmu-ilmu ini kepada bahasa Melayu. Dengan itu orang Melayu lain boleh kuasai ilmu-ilmu ini dalam bahasa Melayu, tanpa mempelajari bahasa Inggeris.
11. Malangnya keadaan sekarang tidak seperti abad ke-15 dan sebelumnya. Ilmu di zaman dahulu terhad, dan tidak bertambah dengan pesat.
12. Di zaman ini ilmu Sains dan Matematik yang amat penting untuk membangun dan memajukan masyarakat manusia, kembang dan bertambah dengan pesatnya. Tiap hari, tiap bulan dan tiap tahun ilmu baru yang diperbaharui sepanjang masa, diperkenalkan oleh para saintis dan pengkajiselidik kepada masyarakat dunia. Ilmu matematik terutama algorizmi dan perhitungan yang kompleks digunakan untuk mengetahui apa hasil jangka panjang daripada sesuatu teori dan untuk menentukan gerakan bintang di langit supaya kapal angkasa dapat menemui sasaran setelah berjalan berbulan-bulan.
13. Dimasa yang sama banyak ilmu baru diperkenalkan yang berasas kepada kuasa elektrik, gerakan atom, sains halus atau nano science, asas-asas fisiologi kehidupan tumbuh-tumbuhan dan makhluk Allah dan berbagai-bagai lagi.
14. Hakikatnya ialah jumlah ilmu baru dan kepantasan perkembangannya tidak dapat dikejar oleh penterjemah Melayu yang sedikit yang ada. Harus diingat untuk menterjemah tiap ilmu khusus dalam bidang Sains memerlukan bukan sahaja kefasihan dalam bahasa Melayu dan Inggeris, tetapi juga kepakaran dalam ilmu berkenaan. Kita tidak punyai dengan mencukupi orang yang berkebolehan seperti ini. Jika ada beberapa kerat orang seperti ini mereka tidak mungkin sanggup bekerja sebagai penterjemah seumur hidup mereka.
15. Sebaliknya jika kita belajar Sains dan Matematik dalam bahasa Inggeris kita akan dapat akses secara langsung sendiri semua ilmu yang diterokai dan dibukukan dalam bahasa Inggeris tanpa menunggu pengalih bahasa kita. Tiap-tiap tajuk yang terkini dan yang lama terbuka untuk kita menguasainya. Dengan itu kita tidak akan ketinggalan daripada segi ilmu pengetahuan berbanding dengan bangsa yang maju.
16. Sesungguhnya agama kita menuntut supaya kita kuasai ilmu-ilmu ini. Sebagai orang Islam kita perlu bersedia untuk mempertahankan umat Islam. Di zaman dahulu kuda perang, pemanah, pedang dan tombak memadai untuk pertahanan.
17. Di zaman ini kita perlu kereta perisai, meriam dan roket, pesawat pejuang dan pengebom, kapal perang dan kapal selam. Kita tak mungkin cipta dan bina semua ini tanpa ilmu sains dan matematik. Kita boleh beli daripada orang lain tetapi ini bermakna kita letak diri kita di bawah cengkaman mereka.
18. Jika kita ingin amal ajaran Al-Quran berkenaan dengan keperluan pertahanan bagi umat Islam maka penguasaan ilmu sains dan matematik perlu menjadi sebahagian daripada fardhu kifayah bagi kita. Ia bukan ilmu sekular seperti diperkata sesetengah orang. Ia adalah sesuatu yang diwajib keatas diri kita.
19. Jika kita abaikan ilmu ini semata-mata kerana kita lebih utamakan bahasa kita, dan dengan itu kita jadi bangsa yang kolot dan lemah, dan dihina oleh orang, kita tidak boleh dakwa yang kita adalah pejuang bangsa dan agama. Orang yang rela bangsanya dihina tidak faham akan makna nasionalisme yang sebenar atau tanggungjawab orang Islam terhadap agama mereka.
20. Bagi saya pejuang bangsa yang betul-betul bersemangat perlu bermatlamat untuk menjadikan bangsanya bermaruah, dihormati oleh semua bangsa lain dan berkebolehan bersaing dalam apa juga bidang dengan kemungkinan berjaya.
21. Pemimpin dan pejuang yang hanya ingin disukai ramai dan kerana itu sanggup membiar bangsanya menjadi kolot dan hina, bukanlah pemimpin yang sayang bangsanya. Mereka hanyalah oportunis yang sanggup gadai bangsa sendiri asalkan mereka dapat kekalkan kedudukan mereka. Mereka ini bukan nasionalis dalam erti kata sebenar.
22. Bahasa jiwa bangsa. Tetapi ilmu menentukan keselamatan dan maruah bangsa.
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