spiral approach for mathematics teaching manila jan2010
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Spiral Approach for Mathematics Teaching (High School)Manila, January 2010TRANSCRIPT
Spiral Approach to Teaching Mathematics
The presentation slides are available at
www.mathz4kidz.com
Dr Yeap Ban HarNational Institute of Education
Nanyang Technological University Singapore
Singapore Education System
About Singapore Education System
The vision of Ministry of Education is Moulding the Future of Our Nation .
It focuses on academic as well as non-academic aspects of the students’ education.
About Singapore Education Singapore
It focuses on developing
high-quality workforce as human resource is the only resource in Singapore.
Teaching resources
including textbooks are prepared to facilitate school programmes that can achieve this goal.
About Singapore Education Singapore
Teacher training to coach teachers to bring textbooks to life are conducted by NIE for pre-service and in-service teachers.
University graduates in mathematics and engineering undergo one-year training before they become mathematics teachers in schools where they also teach another subject.
Education System in Singapore
Primary School 6 YearsNational Test: PSLESecondary School 4 or 5 YearsNational Test: GCE O LevelJunior College 2 or 3 YearsNational Test: GCE A Level
We have Independent, Autonomous, Government-Aided and Government Schools.
We also have specialized schools like sports school, school for the arts, science and technology school, mathematics and science high school as well as two schools for struggling students. Some students go polytechnics after secondary school.
Mathematics Curriculum in Singapore
The Singapore mathematics curriculum states that “an emphasis on mathematics
education will ensure that we have an increasingly competitive workforce
to meet the challenges of the 21st century”
The rationale of teaching mathematics is that it is “a good vehicle for the
development and improvement of a person’s intellectual competence”.
Mathematics Curriculum in Singapore
New Syllabus Mathematics is used for
Secondary 1 to Secondary 4.
New Syllabus Additional Mathematics is used by students good in mathematics in Secondary 3 and Secondary 4.
Problem-Solving Curriculum
TEACHING THROUGH PROBLEM SOLVING
Example from NSM Textbooks
ActivityDraw a 4-sided polygon.Cut it into triangles.
How many triangles can you get?
WHAT IS PROBLEM SOLVING?Example from National Test in Singapore
National Test Grade 10
A fly, F, starts at a point with position vector (i + 12j) cm and crawls across the surface with a velocity of (3i + 2j) cm s-1. At the instant the fly starts crawling, a spider, S, at the point with position vector (85i + 5j) cm, sets off across the surface with a velocity of (-5i + kj) cm s-1, where k is a constant. Given that the spider catches the fly, calculate the value of k.
(1, 12)
(4, 14)
(7, 16)
(1+3t, 12+2t)
At time t, the fly is at (1+3t, 12+2t)
And the spider is at (85-5t, k+5t)
Given that the fly caught the spider:
1 + 3t = 85 – 5t and 12 + 2t = k + 5t
8t = 84 or t = 10.5
k = 12 – 3 (10.5) = …
Spiral Curriculum
TEACHING AS EXTENDING STUDENTS’ KNOWLEDGE (PIAGET)
Example from NSM Textbooks
Spiral Curriculum
Spiral Approach
• Primary 6– Writing expressions in one variable
• Secondary 1– Writing expressions in more than one variables– Factorisation
• ax + by • ax + bx + kay + kby
Spiral Approach
• Secondary 2– Factorisation
• a2x2 – b2y2 • a2 + 2ab + b2 • ax2 + bx + c
• Secondary 3 – 4– Factorisation
• cubic expressions* • other expressions* (e.g. trigonometric expressions
reducible to quadratic or cubic expressions)
Meaningful Learning
Grade 8 Lesson on Volume of PyramidA class in Semarang, Indonesia doing a lesson from NSM 2
TEACHING AS DEVELOPING CONCEPTUAL UNDERSTANDING (SKEMP)
Example from NSM Textbooks
21st Century Curriculum
WHY STUDENTS LEARN MATHEMATICS?
Example from NSM Textbooks
Visualization
Modelling
Connection
Communication
Outcomes
Learning Outcomes: Achievement & Attitude
HOW WELL HAVE THE STUDENTS LEARN?
Findings from TIMSS
International Benchmarks
Advanced
Intermediate
Low
High
2 4031
15 7064
46 8885
75 9794
Grade 8
Telok Kurau Primary School
TIMSSTrends in International Maths and Science Studies
4540
7171
8690
9598
Advanced
Intermediate
Low
High
2 30
15 124
46 4414
75 6648
Grade 8
Effective Methods in Teaching Mathematics
TIMSSTrends in International Maths and Science Studies
402
7018
8850
9782
Advanced
Intermediate
Low
High
41
74
92
98
Singapore
Catholic High School (Primary)
TIMSSTrends in International Maths and Science Studies
40
70
88
97
Advanced
Intermediate
Low
High
10
40
77
95
U S A
Catholic High School (Primary)
TIMSSTrends in International Maths and Science Studies
6
31
67
92
Advanced
Intermediate
Low
High
16
48
79
94
England
Catholic High School (Primary)
TIMSSTrends in International Maths and Science Studies
8
35
69
90
Advanced
Intermediate
Low
High
5
26
67
90
International
Catholic High School (Primary)
TIMSSTrends in International Maths and Science Studies
2
15
46
75