This document provides an overview and comparison of mathematics curriculum and teacher education systems in Finland, Hong Kong, Singapore, and England. Some key similarities in mathematics curriculum across countries include topics like algebra, geometry, statistics, and probability being taught at both primary and lower secondary levels. Differences include specific topics emphasized, like measurement in Finland and data handling in Hong Kong. Regarding teacher preparation, countries generally require bachelor's or master's degrees, with Finland having the highest educational requirements. Professional development is also emphasized, usually funded through government or school organizations.

1. A COMPARATIVE ANALYSIS OF
MATHEMATICS CURRICULUM AMONG
THE FOUR DIFFERENT COUNTRIES
Presenter: Celestiene Jose C. Claridad
Palawan State University
Graduate School
Ed 210: Comparative Education
Professor: Dr. Erlinda A. Ganapin
SUMMER 2018

2. Learning Objectives:
01 COMPARE
Mathematics Education in every given country
02 EXAMINE
Methods used to prepare prospective teacher
03 INSPECT
Mathematics curricula for each jurisdiction
04 IDENTIFY
Similarities and Differences in terms of Math Education

3. OVERVIEW OF
EDUCATIONAL SYSTEM
Educational System serves as a backbone in
the growth of a nation

4. FINLAND
Educational System
FLAG OF FINLAND

5. 0-6 Early childhood education and care (ECEC)
1 yr Pre – primary education – 6 year old
9 yrs.
Basic education 7 – 16 year olds
(Comprehensive Schools)
3 yrs3 yrs
Matriculation Examination
(General upper secondary schools)
Vocational Qualifications
(also available as apprenticeship training)
3.5 - 4
3 yrs
Bachelor’s degrees
UNIVERSITIES
Bachelor’s degrees
Universities of Applied Sciences
Doctoral Degrees
Licentiate Degrees
Universities 1 – 1.5
2 yrsMaster’s degrees
Universities
Master’s degrees
Universities of Applied Sciences
Work experience 3 years
Work
Exp.
Specialist Vocational Qualification
Further Vocational Qualification

6. HONG KONG
Educational System
FLAG OF
HONG KONG

7. Early Childhood Education
Age 3 – 6 (3 Years)
Primary School
Ages 6 – 12 (6 Years)
Lower Secondary School
Age 12 – 15 (3 Years)
Senior Secondary School
Age 15 – 18 (3 Years)
Hong Kong Diploma of Secondary Education Examination
Minimum Level 3
Pass in All Required
Subjects on HKDS
Minimum Level 2
Pass in Five Subjects on HKDS
University
Post Secondary
Degree Program
(2 Years)
Institute of Vocational
Education (2 – 4 Years)
Bachelor’s Degrees
(4 Years)
Associate’s Degrees
Technical Certificate or
Diploma
Higher Diploma
Master’s Degrees
(2 Years)
Doctoral Degrees
(3 - 4 Years)

8. SINGAPORE
Educational System
FLAG OF
SINGAPORE

9. University
(3 to 5 years)
19 years old and
older
Junior College
(2 years)
Pre - university
(3 years)
Institute of
Technical Ed
Pre-nursery/
Play school
3 years old and
younger
Nursery 4 years old
Kindergarten
1st Year 5 years old
Kindergarten
2nd Year 6 years old
Primary 410 years old
Primary 511 years old
Primary 612 years old
Secondary 113 years old
Secondary 214 years old
Secondary 3 Secondary 3 15 years old
Secondary 4 Secondary 4 16 years old
Secondary 5 17 years old
Polytechnic
(3 years)
17 years old to
20 years old
8 years old Primary 2
7 years old Primary 1
9 years old Primary 3

10. ENGLAND
Educational System
FLAG OF
ENGLAND

11. Nursery School
Primary School
----------------------------------------------------------------------
GCSE
Secondary School
------------------------------------------------------------
College
A-Levels BTEC
College of further education
A-Levels BTEC
HND
------------------------------------------------------------
University or college of futher educationUniversity
HNC
----------------------
Bachelor’s Degree
------------------------------------------------------------
Master Degree
PHD
Primary
Education 3 years
5 years
------------------
16 years
Secondary
Education
17 years
18 years
----------------------------------------------------------------------
Tertiary
Education
21 years
General Education Vocational Education
A
A

13. Source: www.worldtop20.org

14. Mathematics Curriculum

15. GOALS OF MATHEMATICS EDUCATIONThe Mathematics Curriculum in Primary and Lower Secondary Grades
• Develop creative,
mathematical and precise
thinking
• Guide students in finding,
formulating and solving
problems
• Build interest in math.
• Develop creativity
• Enhance lifelong learning
abilities
• Develop math
conceptualization, inquiry,
reasoning, and
communication skills
• formulate and solve
problems in everyday life
• manipulate numbers,
symbols, and other
mathematical objects.
• Develop the students
mathematical abilities
• Develop cognitive and
metacognitive skills
through a mathematical
approach to problem
solving;
• Develop positive attitudes
towards mathematics.
• Become fluent in the
fundamentals of math
• Develop conceptual
understanding
• Develop the ability to
recall and apply
knowledge rapidly and
accurately.
• Reason mathematically
• Conjecture relationship
and generalization
• Develop an argument,
justification or proof
• Apply math in solving
problems
FINLAND HONG KONG SINGAPORE ENGLAND

16. SIMILARITIES
GOALS OF MATHEMATICS EDUCATION
Use Mathematical Approach in
solving real – life problem
Problem Solving
Develop creative thinking through problem
solving
Creative Thinking
Boost interest and positive
attitude towards Mathematics
Interest in Math
Reason out mathematically by
following the line of inquiry
Reasoning Ability
Develop students Mathematical
ability
Mathematical Ability

17. Differences
GOALS OF MATHEMATICS EDUCATION
Develop a lifelong learning abilities
Lifelong Learning
Enable have a reflective thinking or metacognition
Metacognition Skill
Develop the ability to communicate using a
mathematical reasoning .
Communication Skill
01
02
03
Construct arguments, justification and logical proof.
Argument, Justification and Proof
04

18. MATHEMATICS CURRICULUMThe Mathematics Curriculum in Primary and Lower Secondary Grades
Mathematics Topics at
Primary Level, Grade
1 - 5
 Numbers and
Calculations
 Algebra
 Geometry
 Measurement
(Grade 1&2)
 Data Processing and
Statistics
Mathematics Topics at
Primary Level, Grade
1 - 6
 Number
 Shape and Space
 Measurement
 Data Handling
 Algebra (Grade 5)
Mathematics Topics at
Primary Level, Grade
1 - 6
 Numbers and Algebra
 Geometry and
Measurement
Mathematics Topics at
Primary Level, Grade
1 - 6
 Numbers – Number and
place value
 Number – Addition and
Subtraction
 Number – Multiplication
and Division
 Number – Fractions
 Measurement
FINLAND HONG KONG SINGAPORE ENGLAND

19. MATHEMATICS CURRICULUMThe Mathematics Curriculum in Primary and Lower Secondary Grades
Mathematics Topics at
Lower Secondary,
Grade 6 - 9
 Thinking Skills and
Methods
 Numbers and
Calculations
 Algebra
 Functions
 Geometry
 Probability and Statistics
Mathematics Topics at
Lower Secondary,
Grade 7 - 9
 Number and Algebra
 Measurement, Shape,
and Space
 Data Handling
Mathematics Topics at
Lower Secondary,
Grade 7 – 10
 Numbers and Algebra
 Geometry and
Measurement
 Statistics and
Probability
Mathematics Topics at
Lower Secondary,
Grade 7 – 10
 Number
 Algebra
 Ratio, proportion,
and rates of change
 Geometry and
Measures
 Probability
 Statistics
FINLAND HONG KONG SINGAPORE ENGLAND

20. SIMILARITIES
Mathematics Curriculum
Algebra
Geometry
Statistics and Probability
Spiral Progression
Teaching of Numbers
Measurements
Primary Level Lower Secondary Level

21. DIFFERENCES
Mathematics Curriculum
The following are the observed
differences between the math
curriculum of 4 countries.
Mathematics Curriculum
01 02 03 04 05
MeasurementinFinland
AlgebrainHongKong
ThinkingSkillsinFinland
PrimaryMathofEngland
DataHandlinginHong
Kong

22. Curriculum in the Philippines
Grade 1 – 6
 Numbers and Number Sense
 Patterns and Algebra
 Measurement
 Statistics and Probability
 Geometry (Start in Grade 2)
Grade 7 - 10
 Numbers and Number Sense
 Patterns and Algebra
 Measurement
 Statistics and Probability
 Geometry

23. Singapore
VS.
Philippines
Math
Education
Framework

24. TEACHERS
TEACHER EDUCATION
PROFESSIONAL DEVELOPMENT

25. TEACHERS, TEACHER EDUCATION, AND PROFESSIONAL DEVELOPMENT
TEACHERS AND TEACHER EDUCATION
 Teachers in Finland are
highly trained.
 In general education all
teachers are required a
Master’s degree.
 In vocational education
teachers should have a
Master’s degree or
Bachelor’s degree.
 The high level of training
is seen as necessary as
teachers in Finland are
very autonomous
professionally.
 Pre-primary teachers in
schools hold a Master’s
degree.
 Any person who wishes
to teach in a school must
be registered under the
Education Ordinance as
either a registered
teacher or a permitted
teacher.
 Registered teachers are
persons who possess the
approved teacher
qualifications laid down in
the Education Ordinance,
 Permitted teachers are in
possession of academic
qualifications only,
permitted teachers are
given a permit to teach
specified subject(s) in
specified schools.
 For the majority of teac
hing positions in Singap
ore, a Bachelor's degre
e is essential.
 For roles in public and
international schools, a
degree in Education or
your subject area is stro
ngly preferred.
 For ESL positions, a
Bachelor's degree and
a TEFL certification is
usually required.
 GCSE grade C or above in
mathematics and English: for
primary teaching you also
need GCSE science grade C
or above.
 Professional skills tests: in
literacy and numeracy (if trai
ning in England). You must p
ass these before starting you
r teacher training course.
 for primary teaching some IT
T providers prefer you to hav
e a degree in a national curri
culum subject. If you don't, y
ou should talk directly to the t
raining provider to see if they
will accept your degree.
 For secondary teaching you'll
need a degree in, or closely r
elated to, the subject you wo
uld like to teach.
FINLAND HONG KONG SINGAPORE ENGLAND

26. TEACHERS, TEACHER EDUCATION, AND PROFESSIONAL DEVELOPMENT
PROFESSIONAL DEVELOPMENT
 Teachers employers, suc
h as municipalities are re
sponsible for organizing a
nd funding their staff’s pr
ofessional development
 National Bureau of Educa
tion also provide in – serv
ice training/.
 Committee on Profession
al Development of Teach
ers and Principals (COTA
P) is responsible to prom
ote the professional devel
opment of teachers and p
rincipals across the conti
nuum of the teaching prof
ession.
 All teachers are entitled
to 100 hours of PD activ
ities per year.
 Academy of Singapore
Teachers fosters pedag
ogical leadership focus
ed on teacher collabora
tion within schools and
professional networks.
 OPD is well recognized i
n raising teaching and lea
rning standards
 Schools are expected to
offer training and develop
ment opportunities to all s
taff.
FINLAND HONG KONG SINGAPORE ENGLAND

27. Similarities
Teacher and Teacher Education
High Qualification with
regards to teachers
Focuses in Teachers
Training
Professional
Development Among
Teacher is Evident
Teacher’s Autonomy is
needed
Specialization is a
requisite in teaching
Secondary Level
High regards in
teaching
Learning is the focus of
education
Practical applications

28. DIFFERENCE
Teacher and Teacher Education
Each country has its own unique standards in qualifying
a certain person in their teaching force.
Academic requirements varies differently across the
different countries
Teachers
Teacher Eucation

29. INSTRUCTION FOR
MATHEMATICS IN PRIMARY
AND LOWER SECONDARY
GRADES

30. INSTRUCTION FOR MATH IN PRIMARY AND LOWER SECONDARY GRADES
Grade at Which Specialist Teachers for Mathematics are Introduced
 In general, classroom
teachers teach Grade 1
to 6,
 Specialist teachers
Grade 7 to 9.
 Students at the primary
and junior (lower) sec.
level are NOT taught by
general classroom
teachers, they are taught
by teachers of different
subjects.
 In secondary schools,
subject typically are
taught by subject
specialists.
 Primary school teachers
are qualified through
initial teacher training to
teach in English, Math,
Science.
 Secondary School
teachers are qualified in
at most 2 subjects.
 Students are taught by
specialist Math and
Science Teachers from
the 7th Grade.
 At Key Stage 2, students
are typically taught by a
general classroom
teacher
 At Key Stage 3, subjects
typically taught by subject
specialist.
FINLAND HONG KONG SINGAPORE ENGLAND

31. INSTRUCTION FOR MATH IN PRIMARY AND LOWER SECONDARY GRADES
Instructional Materials and Equipment
 Main materials for
teaching Math are
textbooks published by
commercial publishers.
 They widely used
textbook series both for
primary level (Grade 4)
and for the lower
secondary level
(Grade 8)
 Schools and teachers are
free to choose any
textbook series they find
suitable.
 There are NO mandated
instructional materials for
Math, but the EDB
provides lists of
recommended textbooks,
e-textbooks, and teaching
and learning materials for
different subjects.
 EDB encourages the use
of diverse teaching and
learning resources to
enhance learning.
 Materials that provide
experiences beyond
school.
 Commercial publishers
are invited to develop and
published textbooks and
related materials.
 Teaching aids,
manipulatives, and kits
are widely used.
 There are NO centrally
published or mandated
books for teaching
mathematics.
 Nearly all secondary
schools have laboratories
FINLAND HONG KONG SINGAPORE ENGLAND

32. INSTRUCTION FOR MATH IN PRIMARY AND LOWER SECONDARY GRADES
Use of Technology
 Technology use is
common in Math and
Science Instruction.
 ICT is used for
measurement, reporting
results, searching and
processing knowledge.
 Various types of
measurement equipment
and mobile devices are
used in the classroom.
 In math, learning games
are available for training
basic math skills and
concepts in primary
schools
 Information Technology
for Interactive learning is
one of the learning tasks.
 Teachers are expected to
incorporate IT wisely and
critically in math
education.
 Use of computers in
schools is more popular.
 Nearly all classroom have
a computer room with
internet access and
technical support for
e-teaching and e-learning
 Calculators starts in G7
 Electronic Calculators is
introduced in Grade 5.
 At primary level,
calculators are used in
math to enhance
teaching and learning
process.
 At secondary level,
students use a variety of
mathematical tools,
including calculators,
graphing software,
dynamic geometry
software and
spreadsheets.
 Computers are used
widely in schools.
 Most teachers have
access to a computer, but
the number of computers
available for student use
varies.
 It is more common for
secondary school
students to have access
to computers.
 Internet access and
technical support are
available in all secondary
schools
FINLAND HONG KONG SINGAPORE ENGLAND

33. INSTRUCTION FOR MATH IN PRIMARY AND LOWER SECONDARY GRADES
Special Education
 A student who has
difficulties in learning or
in attending school is
entitled to part – time,
special needs education
will be provided with
enhanced support in
accordance with a
learning plan.
 Every student has the
right to study in his or her
own municipal school in
accordance with the
principal of the nearby
school.
 Children with special
needs are enrolled in
ordinary schools where
they can learn with other
children.
 EDB also provides
professional support and
professional dev’t.
courses to teachers with
SPED learners.
 Specialized early
intervention programs for
lower primary students
who are at risk of having
difficulties in literacy and
numeracy.
 Each primary and
secondary schools has a
core group of teachers
trained in special needs.
 Access arrangements are
provided when necessary
depending on student’s
needs (test format).
 At Key Stage 2, Students
who require additional
support have access to
arrangements such as
extra time or in – class
teaching assistance.
FINLAND HONG KONG SINGAPORE ENGLAND

34. SIMILARITIES
Instruction in Teaching Mathematics
English is the widely use
medium of instruction except
in Finland
General classroom teacher
are teaching in Primary Level
Wide use of Technology in
Teaching Math is evident
Special provisions for
students with special needs
is observed.
Calculators is introduced in
earlier grades
Commercial Textbooks is
widely use
01
02
03
04
05
06

35. DIFFERENCE
Instruction in Teaching Mathematics
Every country has a different way of selecting
instructional materials to be used by their public school
system.
Varied technological advances are being used in
mathematics instruction.

36. MONITORING STUDENT
PROGRESS IN MATH

37. MONITORING STUDENT PROGRESS IN MATHEMATICS
PRIMARY AND SECONDARY (LOWER)
 The Finnish National
Board of Education is
responsible for developing
education, and conducts
national assessment of
learning outcomes.
 National assessment are
sample – based and
focus on the central
content of national curr.,
mainly at the end of basic
education.
 Teachers are responsible
for student in the
classroom; teacher made
test, based on textbook,
observation.
 The EDB recommends th
e use of diverse assessm
ent methods for collecting
info. on student learning.
 It focuses on why student
s do not learn well and ho
w to help them improve.
 Common assessment act
ivities in math; discussion
and oral presentations, o
bservation, classwork, ho
mework, and project work
, short quizzes, test and
exam.
 National Exam is adminis
tered in the final years of
primary, secondary, and p
re university.
 Schools assess students
both formally and informa
lly.
 From Grade 3, they cond
uct at least 2 sum. Asses
sment per year –one at th
e end of each semester.
 Formative assessment in
cludes; oral presentation,
written test, and portfolios
 The Standards and Testin
g Agency (STA) which is
under the Department for
Education (DfE) develops
test for Key stage 1 and 2
.
 Statutory Examination is
given at the end of Key st
age 2.
 Test results are provided
to parents and published
at the school level, and ar
e used to evaluate school
and student performance.
FINLAND HONG KONG SINGAPORE ENGLAND

38. MONITORING STUDENT PROGRESS IN MATHEMATICS
NATIONAL EXAMS
 The Finnish Matriculation
Examination is the exami
nation taken at the end of
secondary education to q
ualify for entry into univer
sity.
 The Hong Kong Certificat
e of Education Examinati
on (HKCEE) was a stand
ardized examination con
ducted by the Hng Kong
Examinations and Assess
ment Authority (HKEAA)
 The Singapore Examinati
ons and Assessment Boa
rd, in collaboration with th
e MOE, conducts the foll
owing National Examinati
ons: the PSLE, GCE N-L
evel, GCE O – Level, and
GCE A – Level.
 Primary School Leaving
Exam (PSLE)
 Most students ages 14 to
16 take General Certificat
e of Secondary Education
(GCSEs), GCSEs are gra
ded on a scale of A* thro
ugh G, where A* through
C are GOOD PASS.
 There is no National Curri
culum for students over 1
6, but those who have n
ot yet passed English and
Math must continue to st
udy those subjects.
FINLAND HONG KONG SINGAPORE ENGLAND

39. TEACHING APPROACHES

40. TEACHING APPROACHES
 Inquiry – based teaching
 Structured Problem Solvi
ng Approach
 Individualized Instruction
Model Approach
 Integrative Technique
 Demonstration Approach
 Discovery Approach
 Math – Lab Approach
 Cooperative Learning
 Active Learning
 promoting the
engagement of
students in their o
wn learning
 Cognitive Activation
 stimulate higher-
order skills
 Teacher – directed instru
ction
 rely, to a great
extent, on a
teacher’s ability to
deliver orderly
and clear lessons.
 The teaching style is mainly
practical and you will be en
couraged to communicate fr
om the moment you enter th
e classroom.
 The wide range of creative t
eaching methods includes g
ames, role- playing exercise
s, problem-solving and grou
p discussions. They make u
se of technology to study wi
thout supervision.
FINLAND HONG KONG SINGAPORE ENGLAND

41. BEST PRACTICES IN
MATHEMATICS
EDUCATION

42. BEST PRACTICES IN MATHEMATICS EDUCATION
 Singapore math focuses on children not just
learning but also truly mastering a limited
number of concepts each school year.
 The goal is for children to perform well
because they understand the material on a
deeper level; they are not just learning it for
the test.
SINGAPORE
ENGLAND

43. BEST PRACTICES IN MATHEMATICS EDUCATION
 Finland focuses on the real life application of
concept in teaching mathematics
 Problem solving is basically a main objective
in learning mathematics.
FINLAND
ENGLAND

44. BEST PRACTICES IN MATHEMATICS EDUCATION
 High school math teachers take language as
a big a role in math instruction
 to provide the students with the good
foundation they needed
 engage students in lessons.
ENGLAND
ENGLAND

45. BEST PRACTICES IN MATHEMATICS EDUCATION
 students possessed a high regard for
mathematics and preferred a deep level of
understanding to simple rote memorization.
 The goal of mathematics in hong kong is to
observed the higher order thinking skill by
using constant problem solving approach
HONG KONG
ENGLAND

46. KEY POINTS
Math should focus on children not just learning but also truly mastering a limited
number of concepts each school year;
Our goal should see to it that children to perform well because they understand the
material on a deeper level; they are not just learning it for the test;
We should focus on the real life application of concept in teaching mathematics
Problem solving should be the main objective in learning mathematics;
High school math teachers should take language as a big a role in math
instruction;
Teachers should provide the students with the good foundation they needed;
We should engage students in lessons;
 We should avoid a simple rote memorization; and
We should observed the higher order thinking skill by using constant problem
solving approach.

47. References
 https://worldtop20.org/worldbesteducationsystem
 http://mbctimes.com/english-20-best-education-systems-world/
 https://worldtop20.org/2017-world-best-education-systems-1st-quarter-report
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ml
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Towards_a_More_Holistic_Approach
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u-need-to-become-a-teacher
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48. References
 https://www.teachaway.com/teaching-singapore
 http://www.edb.gov.hk/en/teacher/qualification-training-development/qualification/teacher-training-qualifi
cations/index.html
 http://www.colorincolorado.org/article/math-instruction-english-language-learners
 https://www.teachercreated.com/blog/2014/03/5-best-practices-for-teaching-math/
 https://www.tandfonline.com/doi/abs/10.1080/09575140802020917?src=recsys&journalCode=ceye20
 https://link.springer.com/article/10.1007%2Fs11858-007-0033-4
 http://scholastic.asia/en/scholastic-prime-mathematics/prime-maths-proven-best-practices
 https://fillingmymap.com/2015/04/15/11-ways-finlands-education-system-shows-us-that-less-is-more/
 http://www.pbs.org/parents/education/math/math-tips-for-parents/whats-singapore-math/
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df
 https://link.springer.com/content/pdf/10.1007/978-3-319-12688-3_21.pdf
 https://www.oph.fi/english/education_system
 A Comparative study of mathematics curriculum in Finland
 http://www.edu.helsinki.fi/malu/tutkimus/RMSE2/abstracts/tornroos.pdf

49. Thank you
Celestiene Jose C. Claridad