1. MATHEMATICS CURRICLUM DEVELOPMENT

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

3. 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

4. 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

5. 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......

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

7. 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 “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

8. 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

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

10. 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

11. 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

12. 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.

13. 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.

14. 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

15. 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.

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

17. 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

18. 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.

19. 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.

20. 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

21. 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.

22. 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.

23. 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.

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

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

26. 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

27. 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
Do you understand why?
Can you express that understanding in words?

28. 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?

29. 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.

30. 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 ?”
“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?”

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

32. THANK YOU!
Better than a thousand days of diligent study is one day with a great teacher." --Japanese proverb