Different teaching strategies in mathematics by Rutchel T. Regarido

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PALAWAN STATE UNIVERSITY
Puerto Princesa City, Palawan
College of Graduate School
Prepared by:
RUTCHEL T. REGARIDO
Master of Education in Mathematics
Submitted to:
PROF. ERLINDA A. GANAPIN
Professor in Ed. 610- Comparative Education
School year: Summer 2018

AUSTRALIA CANADA DENMARK TAIWAN

OBJECTIVES:
1. Determine the education system of each country.
 Overview of education curriculum
 Curriculum goals of each country
2. Determine the performance standard of mathematics in each
country in PISA result.
3. Determine the different teaching strategies of teaching mathematics
of the different countries of Australia, Canada, Denmark, Taiwan and
Japan.
4. Determine the best practices that can be apply in Philippines.

What is MATHEMATICS?
1. Mathematics is practical.
2.Mathematics is a language.
3. Mathematics is derived from real life.
4. Mathematical knowledge is abstract.

I. Educational system of each country
*Overview of Education system
 A national curriculum for all
primary and secondary schools
in Australia under progressive
development, review, and
implementation
 In the late 1980s a significant
push for a national curriculum in
Australia was mounted by the
Hawke Federal Labor
government.
 Curriculum will support teachers
and schools to make full use of
key values education resources
to meet new requirements in the
first four learning areas (English,
science, mathematics and
history)
 Focuses on an entitlement for all
students while acknowledging
that the needs and interests of
students may vary.
 The most part provided publicly,
funded and overseen by federal,
provincial, and local
governments.
 Generally divided into primary
education, followed by
secondary education and post-
secondary.
 Curriculum development in
Canada has gone from teaching
survival skills, both practical and
cultural, to emphasizing self-
fulfilment and standards-based
achievements.
 A province-run system of public
education provided, funded and
administered by federal,
provincial, and local
governments.
 The Minister of Education is
responsible for setting the targets
of achievement for each subject
taught in the folkeskole.
 The Ministry of Education
provides curriculum guidelines for
each subject; the guidelines are
merely recommendations, and
the schools are allowed to
formulate their own curricula as
long as they are in accordance
with the overall target levels.
 Danish higher education features
innovative teaching methods and
an informal learning environment
designed to promote creativity,
self-expression, analytical and
critical thinking.
 Curriculum intended to foster key
competencies in future
generations and in part to bolster
and enhance Taiwan’s economic
competitiveness.
 The new curriculum’s vision
statement, titled “Facilitate Self-
actualization, Adaptive Learning to
Individual Fulfilment, and Life Long
Learning,” is then presented and
the new curriculum’s theme
“Spontaneity, Interaction, Common
Good”.
 Nine-year compulsory education
was implemented in Taiwan in
1968. As society and the economy
have changed, a 12-year
compulsory curriculum was
developed and in 2010 the
Ministry of Education announced
that its development was
completed and ready to
implement.

 Have greater attention can be
devoted to equipping young
Australians with the skills,
knowledge, understandings and
capabilities necessary to enable
them to effectively engage with
and prosper in society, compete in
a Globalized world and thrive in
the information-rich workplaces of
the future.
 The curriculum provides the
content, and a set of achievement
Standards which state the expected
quality of learning, in year levels.
 The school year for elementary
and secondary schools in
Canada extends from the first
week of September to mid-June
or the last week of June,
yielding roughly 185 to 200
teaching days.
 Education in Denmark usually
starts in early September and ends
in the end of June. The first
semester usually ends in
December with examinations in
January and the second semester
ends in May, exams - in June.
 Danish education aims to ensure
that all young people acquire
knowledge and competencies
which will qualify them to take an
active part in society and contribute
to its further development.
Education is open to all and
generally free of charge.
 Principles discriminate against
none and cater to the specific
nature of the individual, embrace
the spirits of humanities and
sciences, respect for values of
humanity, strive for the
development of potential in the
individual while cultivating
sociability, and help the individual
in his/her pursuit of self-
realization.”
I. Educational system of each country
*Overview of Education system

The Australian Curriculum
September 2015 all education ministers endorsed the Australian Curriculum:
Foundation to Year 10 in:
• eight key learning areas—English, Mathematics, Science, Humanities and
Social Sciences, Health and Physical Education, Languages, Technologies and
the Arts
• seven general capabilities—literacy, numeracy, information and
communication technology capability, critical and creative thinking, personal
and social capability, intercultural understanding, and ethical understanding
• three cross-curriculum priorities—sustainability, Asia and Australia's
engagement with Asia, and Aboriginal and Torres Strait Islander histories and
cultures.

What are the key principles for effective teaching of
mathematics ?Principle 1: Articulating goals
Identify key ideas that underpin the concepts you are seeking to teach, communicate to students that these are the goals of the teaching,
and explain to them how you hope they will learn.
Principle 2: Making connections
Build on what students know, mathematically and experientially, including creating and connecting students with stories that both
contextualise and establish a rationale for the learning.
Principle 3: Fostering engagement
Engage students by utilising a variety of rich and challenging tasks that allow students time and opportunities to make decisions, and which
use a variety of forms of representation.
Principle 4: Differentiating challenges
Interact with students while they engage in the experiences, encourage students to interact with each other, including asking and answering
questions, and specifically plan to support students who need itand challenge those who are ready.
Principle 5: Structuring lessons
Adopt pedagogies that foster communication and both individual and group responsibilities, use students’ reports to the class as learning
opportunities, with teacher summaries of key mathematical ideas.
Principle 6: Promoting fluency and transfer
Fluency is important, and it can be developed in two ways: by short everyday practice of mental processes; and by practice, reinforcement and
prompting transfer of learnt skills.

CANADIAN EDUCATION CURRICULUM
The Canadian education system is ranked among the best in the world, with our
nation’s students coming seventh overall in a new international study of school systems
To OPTIMIZE students’ full potential, to WIDEN their horizons through learning,
cooperating and sharing and finally to CREATE an environment that will empower
students to successfully exist in a global society.
In a safe, homely atmosphere we SUPPORT students’ individual gifts, creating conditions
in which they can develop their interests and talents.
We GIVE our students tools to pursue their dreams and to influence the world we live
in.
We OFFER education that inspires the development of the whole child.
We HELP our students discover the way to succeed in a global, ever-changing society.

DANISH EDUCATION SYSTEM
Danish education aims to ensure that all young people acquire knowledge and competencies which will qualify
them to take an active part in society and contribute to its further development. Education is open to all and generally free
of charge. Other characteristic features of the Danish education system include:
1. High standards
The quality of Danish education is assured in many ways. It is mainly regulated and financed by the State, and all
public educational institutions are approved and evaluated on an on going basis.
2. Relevance
Danish educational institutions must provide their students with knowledge and competencies for them to use in
their future job and in life in general.
3. Lifelong learning
Lifelong learning is a key principle in Denmark. The idea goes back all the way to the 19th century Danish
clergyman and philosopher N.F.S. Grundtvig, who argued that a prerequisite for active participation in a democratic society
is education for all citizens on a lifelong basis.
4. Active participation
Treating pupils and students as independent people with a right to form their own opinion and a duty to
participate actively in discussions is a matter of course in Danish education.
5. Project work
At all levels of the education system, pupils and students attend classes, however, they also carry out project
work, either on an individual basis or in small groups.

TAIWANESE EDUCATION SYSTEM
 The following are areas of concerns of the current curriculum.
1. A need for better understanding of “empowering the learners to learn
2. Problems of testing-oriented education
3. Too much lecturing, not enough action
4. Gap between learning and the real world
 A number of factors must be considered and challenges overcome in finalizing and implementing the
12-year Curriculum for Basic Education. These include:
1. Continuity and Integrity
2. The curriculum structure
3. Experimenting on the new curriculum
4. Pedagogy and instruction resources
5. Support systems

MISSION AND VISION OF EDUCATION CURRICULUM OF EACH
COUNTRY
(Curriculum Goals)
AUSTRALIA: Two major goals
Goal 1:
Australian schooling promotes Equity
and excellence.
Goal 2:
All young Australians become
successful Learners, confident and
creative individuals, and active and
informed citizens.

CANADA: Four major goals
1. Achieving Excellence: Children and students of all ages will achieve high levels of
academic performance, acquire valuable skills and demonstrate good citizenship. Educators
will be supported in learning continuously and will be recognized as among the best in the
world.
2. Ensuring Equity: All children and students will be inspired to reach their full potential,
with access to rich learning experiences that begin at birth and continue into adulthood.
3. Promoting Well-Being: All children and students will develop enhanced mental and
physical health, a positive sense of self and belonging, and the skills to make positive
choices.
4. Enhancing Public Confidence: Ontarians will have confidence in a publicly funded
education system that helps develop new generations of confident, capable and caring
citizens.

DENMARK: Three general goals
Danish education aims to ensure that all young people acquire knowledge and competencies which will
qualify them to take an active part in society and contribute to its further development. Education is open to all
and generally free of charge.
3 General goals
1. The Folkeskole shall - in cooperation with the parents - further the pupils’ acquisition of knowledge, skills,
working methods and ways of expressing themselves and thus contribute to the all-round personal
development of the individual pupil.
2. The Folkeskole shall endeavour to create such opportunities for experience, industry and absorption that
the pupils develop awareness, imagination and an urge to learn, so that they acquire confidence in their own
possibilities and learn how to commit themselves and take action.
3. The Folkeskole shall familiarise the pupils with Danish culture and contribute to their understanding of other
cultures and of man’s interaction with nature. The school shall prepare the pupils for participation, joint
responsibility, rights and duties in a society based on freedom and democracy. The teaching of the school and
its daily life must therefore build on intellectual freedom, equality and democracy."

TAIWAN: Goals both Nine and Twelve –year
curriculum
The Nine-year Curriculum (MOE, 2000)
1. To enhance self-understanding and explore individual potential;
2. To develop creativity and the ability to appreciate beauty and present
one’s own talents;
3. To promote abilities related to career planning and lifelong learning;
4. To cultivate knowledge and skills related to expression, communication,
and sharing;
5. To learn to respect others, care for the community, and facilitate
teamwork;
6. To further cultural learning and international understanding;
7. To strengthen knowledge and skills related to planning, organizing, and
implementing;
8. To acquire the ability to utilize technology and information;
9. To encourage the attitude of active learning and studying; and
10. To develop abilities related to independent thinking and problem-solving.
The Twelve-year Curriculum
(MOE, 2014d)
1. To inspire potential;
2. To foster life knowledge and skills;
3. To advance career development; and
4. To cultivate civic responsibility.

II. PISA RESULTS OF EACH COUNTRY IN
MATHEMATICS, SCIENCE AND READING

III. The different teaching strategies of
teaching mathematics of each country.
1. AUSTRALIA
1. Behaviourism - learning and teaching is essentially about changing behaviours through stimulus
materials and consequent rewards/punishments
2. Constructivism - learning and teaching is about designing activities that enable students to build
upon prior knowledge to construct internally consistent mental models
3. Socio-constructivism - learning is a collaborative, negotiated experience that is most effectively
achieved through peer and group interaction
4. Authentic learning - learning is best facilitated through realistic, relevant, complex, and
problematized tasks
5. Face-to face-delivery technologies-The most popular technologies for delivering lectures via
computer (on Windows operating systems) are Microsoft PowerPoint presentations and LaTeX-based
documents.
6. Online delivery technologies- Vital for distance education, but has also become very popular to
complement traditional face-to-face teaching in a "blended" approach.
7. Group tasks-Learn through interaction and collaborative learning methods
.

2. CANADA
BASIC TEACHING STRATEGIES
1. Repetition
A simple strategy teachers can use to improve math skills is repetition. By repeating and
reviewing previous formulas, lessons and information, students are better able to comprehend concepts
at a faster rate.
2. Timed testing
Taking a short test and then grading the test in class will help teachers assess student
understanding. When the test shows that students are answering more questions correctly within the
time period, teachers are able to determine that students have mastered the basic skills.
3. Pair work
Group work is a simple strategy that allows students to work and problem solve with a buddy.
When a teacher has provided the basic instruction, it’s helpful to split the class into pairs or groups to
work on problems.
4. Manipulation tools
Manipulation tools make it easier for students to learn and understand basic skills. These are
ideal when students learn best through hands-on experience and building rather than traditional lessons
and repetition.
5. Math games
Reinforcing the information learned in class is not always the easiest task for teachers, but
math games provide the opportunity to make the lesson interesting and encourage students to
remember the concepts.

3. DENMARK
1.Short introduction to new content/tasks
The capable students are quick to catch the point and may on that Account sooner than
the rest continue their individually work.
2. Grouping by academic criteria
This is when the capable students are put together in more permanent groups, where
they challenge each other.
3. Amount of content/time
Let students solve the same tasks at different levels – or differentiate in time. The more
capable students can handle more tasks or the same tasks in shorter time.
4. Different tasks
Working within a content area, you may present tasks in various degrees of difficulty,
which the student elects/gets handed.
 Exposition by the teacher (of new content or homework).
Discussions between the teacher and the students and among students themselves.
Appropriate practical work.
Consolidation and practice of fundamental skills and routines
Problem solving, including the application of mathematics to everyday situations
Investigations and experiments.

4. TAIWAN
1. Spontaneity refers to individual children’s self-learning ability, ability to think
systematically to solve problems, to plan and execute, and to innovate and
improvise when faced with ever changing situations.
2. Interaction refers to the ability to communicate and express so that the each
individual self, namely the learner, is aware of the world outside of self, such as
other people, the environment, or school cultures.
3. Common good or symbiosis refers to the idea that learning is not for just
oneself. Variety is not only valuable, but necessary, and students should be
enabled to care about the health of society and the world, not only themselves
and their immediate circles.

IV-BEST APPROACHES CAN BE APPLY IN PHILIPPINES
In each country have its own strategies used in teaching mathematic but some of its have a
common like in Philippines. The strategies like pair work, manipulation tools, math games and
repetition. As a whole, even we are not same in races, economic stability and ways but we have
common goals towards the success of the learning area, the mathematics and to the students.
V-CONCLUSION
Teaching strategies is one tool to determine the appropriate and efficient appropriate and
efficient it has to be in relation with the characteristic of the learner and the type of learning it is
supposed to bring about. As a teacher, I should have a different strategies can apply in teaching
mathematics because mathematics is one of the hardest subject for the students. I should to teach
them how to love and enjoy mathematics. Mathematics is not only to comply or to pass it but it is
necessary to understand to them how mathematics is important to our daily lives.
One of the desires of my heart is to teach my students how education important is. I would
like to change their negative ways of thinking in math. I want to love them that math is
adventurous and enjoyable. Because I believe that the success of the students is the success also of
the administration in education, schools and teachers.

“ Effective schools are only
‘effective’ to the extent
that they are have
‘effective’ teachers”

REFERENCES
• https://www.reddit.com/r/MapPorn/comments/7ypeh3/pisa_worldwide_ranking_average_score_of_math/?st=jhhkd8fl&sh=737bb62e
• http://studyindenmark.dk/study-options/the-danish-way-of-teaching-1
• https://ustraliancurriculum.edu.au
• http://www.curriculum.edu.au/verve/_resources/National_Declaration_on_the_Educational_Goals_for_Young_Australians.pdf
• http://www.edu.gov.on.ca/eng/about/excellent.html
• https://estudandoeducacao.files.wordpress.com/2011/05/dinamarca.pdf
• https://scholarworks.umt.edu/cgi/viewcontent.cgi?article=1213&context=tme
• http://www.austms.org.au/M2+-+Models+of+maths+learning
• http://www.austms.org.au/M6+-+Assessing+students+in+classes
• https://education.cu-portland.edu/blog/classroom-resources/basic-math-teaching-strategies/
• http://www.tdsb.on.ca/Portals/research/docs/reports/Teaching%20and%20Learning%20Math%20Research%20Series%202.pdf
• http://www.oecd.org/education/school/programmeforinternationalstudentassessmentpisa/46052236
• http://www.math.chalmers.se/Math/Grundutb/CTH/mve375/1112/docs/KOMkompetenser.pdf
• Read more: Denmark - Primary Preprimary Education - Schools, School, Children, and Compulsory - StateUniversity.com
http://education.stateuniversity.com/pages/371/Denmark-PRIMARY-PREPRIMARY-EDUCATION.html#ixzz5EzrZADxY
• Dewey, J. (1938). Experience and Education. NY, New York: Kappa Delta Pi.

Thank You
Ma’am Erlinda for
everything
you shared to us!!!
GOD Bless us all!!!

Different teaching strategies in mathematics by Rutchel T. Regarido

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