MATHEMATICS CURRICLUM DEVELOPMENT

MATHEMATICS CURRICLUM DEVELOPMET Before World War II After World War II KBSR & KBSM

MATHEMATICS EDUCATION BEFORE THE 2ND WORLD WAR Primary School Mathematics: -Not gazette before 1965. ‘Panduan Untuk Guru’ (Guidance pamphlets) by Pejabat Karang Mengarang, Jabatan Pelajaran Persekutuan Tanah Melayu, Kuala Lumpur (cetakan pertama, 1950) - Mathematics content, basic skills involve simple arithmetics (+, -, ÷, X), trading (jual beli), weighing (timbang menimbang), measurement (ukur mengukur) in everyday life

MATHEMATICS EDUCATION AFTER THE 2ND WORLD WAR Development in USA 1957, lunching of Sputnik I by Soviet Russia –big impact on the Americans National Defense Education Act of 1958 Evaluation of school curriculum – mathematics & Science at school and state level “School Mathematics Study Group” (SMSG) - new mathematics & Science curriculum - Developed by professors from establish universities in USA - to produce scientists

CONT…. 1959, Seminar was held in Royalmount, USA, mathematics educators and mathematician from 8 countries – create impact to other countries “School Mathematics Curriculum Improvement Study” (SSMCIS) - teaching and learning Not only the contents Examples: Teaching Methods: - Cooperative learning - Problem solving - constructivism - inductive and deductive etc......

MATHEMATICS EDUCATION AFTER THE 2ND WORLD WAR Development in UK and Europe In 1961 - “School Mathematics Project” (SMP) Most successful curriculum – teachers and mathematics educator – text book and curriculum guide “Scottish Mathematics Group” “Nuffield Maths” “Midlands Mathematics Experiment”

MATHEMATICS EDUCATION AFTER THE 2ND WORLD WAR Development in Malaysia Primary School (1965) -introduced new topics -development of topics according child psychology -using new approaches and teaching methods In 1968 - “Projek Khas” Special Project– by Ministry of Education -to improve teaching and learning standard in primary school (rural school) 1980 – report on performance of primary school in mathematics by MOE report by Jawatankuasa Kabinet Mengkaji Pelaksanaan Dasar Pelajaran

INTEGRATED CURRICULUM FOR PRIMARY SCHOOL (KBSR) In 1982 – KBSR introduced to primary school Curriculum content ( 4 basic skills and mental arithmetic ) - Recommendations : group learning (cooperative learning) using material using everyday examples in problems solving learning environment

INTEGRATED CURRICULUM FOR SECONDARY SCHOOL (KBSM) Malaysian General Mathematics Modern Mathematics Curriculum KBSM (Integrated Curriculum for Secondary School)

Malaysian General Mathematics Curriculum Mid 1960 to early 1970 5 series of text books new topics: stock exchange arithmetic, density and relative density (share, ketumpatan) Areas : Arithmetic, Algebra, geometry, Trigonometry (Alternative B) Examinations for MGMC syllabus: Cambridge Local Examination Syndicate Oxford Local Examination, Oxford and Cambridge School Examination Board University of London

Modern Mathematics Curriculum (MMC) 1965, Mathematics Seminar at University Malaya Suggestion to form a committee: introduced new teaching methods SPM contents to include in MMC 1969, Peter Whyte (SMG) was invited by MOE 1973 – mathematics modern (from SMP) – Alternative C

INTEGRATED CURRICULUM FOR SECONDARY SCHOOL (KBSM) --Modern Mathematics Curriculum) AIM (MATLAMAT) To develop individuals: who are able to think mathematically who can apply mathematical knowledge effectively responsibly in solving problems and making decision Enable the individual to face challenges in everyday life that arise due to the advancement of science and technology.

INTEGRATED CURRICULUM FOR SECONDARY SCHOOL (KBSM) --Modern Mathematics Curriculum) OBJECTIVES (OBJEKTIF) Understand definitions, concepts, laws, principles and theorems related to Numbers, Shape and Space, and Relationships. Widen applications of basic fundamental skills such as +, -, ÷, and x, related to Numbers, Shape and Space, and Relationships.

INTEGRATED CURRICULUM FOR SECONDARY SCHOOL (KBSM) --Modern Mathematics Curriculum) OBJECTIVES (OBJEKTIF) Acquire basic mathematical skills as: making estimation and rounding; measuring and constructing; collecting and handling data; representing and interpreting data; recognising and representing; relationship and representing using algorithm and relationship; solving problem; and making decision

OBJECTIVES (Continue ...) Communicate mathematically; Apply knowledge and skills of mathematics in solning problems and making decision; Relate mathematics with others areas of knowledge; Use suitable technologies in concept building, acquiring skills, solving problems and exploring the field of mathematics; Cultivate mathematical knowledge and skills effectively and responsibly; Inculcate positive attitudes towards mathematics; and Appreciate the importance and the beauty of mathematics.

Emphases in Teaching and Learning (KBSM) Problem solving in mathematics Communication in mathematics Reasoning in mathematics Mathematics Connections Application of technology

Emphases in Teaching and Learning (KBSM) 1. Problem Solving in Mathematics Main focus in T & L of Mathematics. Involved Polya’s Model (U,D,C,L) Heuristics and strategies

Emphases in Teaching and Learning (KBSM) 2. Communication in Mathematics through the listening process: – individuals respond to what they hear, - encourages individuals to think using their mathematical knowledge in making decisions. through the reading process: - individual collects information and data - rearranges the relationship between ideas and concepts.

Emphases in Teaching and Learning (KBSM) CONT…. through the visualization process when individual: - make an observation, analyses, interprets, and synthesize data, and presents them in the form of geometric board, pictures and diagrams, tables and graphs.

Emphases in Teaching and Learning (KBSM) Effective communication can be developed through: Oral communication two ways of interaction: T-S, S-S, S-O Written communication written work is usually result of discussion brainstorming activities

Emphases in Teaching and Learning (KBSM) 3. Reasoning in Mathematics Logical reasoning To estimate, predict, make intelligent guesses in the process of seeking solutions. Using – concrete materials, calculators, computers, mathematical representation and others.

Emphases in Teaching and Learning (KBSM) 4. Mathematical Connections Opportunities for making connections must be created: can link conceptual to procedural knowledge and relate topics within mathematics and other learning areas in general.

Emphases in Teaching and Learning (KBSM) 5. Application of Technology The Teaching and learning of mathematics should employ the latest technology to help students: understand mathematical concepts in depth, meaningfully and precisely explore mathematical ideas. Examples: Calculators, computers, educational software, websites in internet, relevant learning packages, etc.

Communication in Mathematics Example 1: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 What patterns do you see? You may choose to describe patterns with words, in a table or sequence, or by using mathematics notation.

EXAMPLE Communication in Mathematics Example 2: Write down your description, and then read on ...

EXAMPLE Mathematical Connections Example 1: Connecting New Concepts to Old Concepts Which decimal is equivalent to 12 percent? Which decimal is equivalent to .9 percent? Connected percents to rational numbers, reasoning that 12 percent means 12/100. Then connected the fraction to a decimal: 12/100 = 0.12 .9 percent means 0.9/100, which converts to 0.009

Mathematical Connections Example 1: Connecting Different Models for the Same Concept In mathematics, many concepts can be represented in different ways. Consider the ways of representing 3/4. One of them is NOT a valid representation of what we mean by 3/4 0 ¼ ½ ¾ 1 Do you understand why? Can you express that understanding in words?

Mathematical Connections Example 3: Connecting Conceptual and Procedural Knowledge Variety of standard procedures – called Algorithms Convert a mixed number to an improper fraction: For example: 4¾ = 19/4 Do you know why we multiple the whole number by the denominator, add the numerator, and then put the whole thing over the denominator?

Do you know why we “move over” in whole-number multiplication? Mathematical Connections Example 3 : Connecting Conceptual and Procedural Knowledge 47 X__35 235 141__ 1465 Do you know why we “move over” in whole-number multiplication? Coming to understand why these and many other algorithms work will make you a more powerful problem solver and a stronger teacher.

Reasoning in Mathematics Example: 35 – 9 = The teacher can ask questions like this: “ Do you think it would help to know that 35 – 20 = 15?” “How would it help you to think of 19 as 15 + 4?” “Would it help to count on from 19 to 35?” It is also important for children to recognize invalid arguments, such as: “Would it help to count backward from 19?”

Reasoning in Mathematics Example 2: ( 3, 6, 12, 15, 21, 27, 42, 51) Find a set of these numbers that sums to 100.

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