Singapore math, or just simply ‘maths’, as it is known here
in Singapore, is mathematics done based on the Singapore syllabus. This term
was first coined in America to refer to this particular type of mathematics. At
present, over 20 countries use it, including the United States, Chile and
Israel.
Before the 1980s, Singapore got most of its mathematics syllabus from other countries. It was only in 1981 where a group of teachers from the Curriculum Planning and Development Division were asked to come up with a specific math syllabus for Singapore. They did research based on other countries’, and based our current math syllabus on research done by an American psychologist, Jerome Bruner, who mentioned that people learnt best through a three approaches. They are concrete, pictorial and abstract approach.
In short, it simply means that children first involve the use of physical
objects and real life experiences, for instance stationery such as paperclips
and pencils and blocks to help them visualise questions, before moving on to
using bar models drawn on paper in place of these physical objects, and finally
using only mathematical concepts and symbols to solve questions. This method engages
students in learning, stirs them away from rote learning and memorising, and
instead instil problem solving strategies and habits of mind. Singapore math
also allows for mastery of content. This means that we choose to focus more on
depth, instead on breadth, in terms of the topics chosen to cover. Hence,
students would be given ample time and practice to allow them to fully
understand what they are learning.
So what makes
Singapore math so special?
The Trends in International Mathematics and
Science Study, or TIMSS, is a
study which assesses the ability of pupils from 63 different education systems
across the world. In the 2016 study, it was found that Singapore students in
primary 4, aged 10, and secondary 2, aged 14, emerged top in both subjects. For
the primary 4s, students in Singapore achieved the highest average score of 618
in mathematics, with Hong Kong coming in second at 615, and South Korea third
with a score of 608. For these same students in Science, they achieved the
highest average score of 590, with South Korea coming in second with a score of
589, and Japan third at 569. Students in Singapore were not only found to have
the highest average scores, they were also found to have much more positive
learning attitudes as compared to their international counterparts, as well as
having improvements in higher order thinking skills.
Not just in TIMMS, but in the Programme for International Student Assessment as well. This study, better known as PISA, is conducted once every three years by the Organisation for Economic Co-operation and Development (OECD), and tests the ability of 15 year olds around the world to use their knowledge to solve problems. In the 2015 study, a total of 72 economies took part, and the results showed that Singapore students have emerged top in all three categories, which are science, reading and mathematics. This led to Singapore’s best PISA scores yet. Other than this, Singapore students were also found to be able to apply their knowledge well in unfamiliar contexts, and that they are capable of thinking critically.
Source: Organisation
for Economic Co-operation and Development
How Singapore
math is taught
So how are
students taught using Singapore math?
The first approach
is known as concrete experiences. This approach is hands-on, and in Singapore
classrooms, items such as dice, blocks and stationery are used to teach
students about basic mathematical concepts. This approach helps students
directly visualise these concepts and mathematical problems, thus helping them
better understand and observe what they are doing. This comes as result of students
being able to directly add and remove objects, in order to simulate addition and
subtraction respectively. In Singapore classrooms, students are also given
worksheets with these objects used in the real-life demonstrations printed on
the pages, and students will be asked to colour them in, in order to simulate
the actual adding and removal of objects in real life.
The second approach is known as pictorial. Using the
pictorial approach, it is similar to the concrete approach in the sense that
both methods use visualisation and representation to help students better
understand mathematical concepts and questions. However, they differ in that
while the concrete approach uses real-life objects, the pictorial approach uses
drawings, pictures and also the ‘model method’. The model method essentially
uses bar model drawings to illustrate and represent data in the questions. The
bar model method is able and effective in teaching students not only about
addition and subtraction, but multiplication and division as well. With respect
to addition and subtraction, there may be such a question:
Tom has 100 sweets and Jerry has 70 sweets. What is the
difference in the number of sweets between the 2 boys?
Using the bar model drawing method to solve this question, a longer bar representing 100 sweets can be drawn, with a slightly shorter bar representing 70 sweets drawn below it. The difference between the lengths of the two bars can be marked with a question mark. Hence, this representation makes it clear to students as to how to solve the question. The final model should look something like this:
Source: Wikipedia
However for the slightly more difficult questions involving
multiplication and division, the model will look slightly different. Let us
consider the following question instead:
Tom and his 3 friends have 30 sweets each. How many sweets
do they have altogether?
In this question, manual addition works as well. However, let’s say we wish to use multiplication to solve it instead, in which case 4 bars of roughly equal lengths will be drawn next to each other, to represent the total number of sweets that they have altogether. Each of these bars will represent the 30 sweets that each of them have. After this has been drawn, it should be very clear to the student as to how the question should be solved. The final model should look something like this:
Source: Wikipedia
Hence, this
proves that models are effective at teaching students their basic mathematical
concepts as well as arithmetic, including multiplication and division. They can
also very easily be used to represent the larger numbers that the concrete
method is unable to do, all while using a similar approach of visualisation and
representation of numbers.
The last method
is known as the abstract method. Once students have mastered bar model drawing,
they should be able to solely rely on numbers and symbols to solve their
questions, with little to no visualisation being needed.
Benefits
There are a number
of benefits with regard to using the Singapore approach to solve and
understand mathematical concepts and questions.
The first is that Singapore uses a ‘spiral’ approach. This means that the topics in textbooks are arranged in sequence, where each subsequent topic builds on what students have learnt before in previous chapters. The second is that it was found that using the pictorial method to educate people was efficient. This came as a result of a study done by The Straits Times, Singapore’s local newspaper, in 2015, where the pictorial method was found to be useful in teaching African students, despite there being a language barrier, and the students having special needs. The third is that students are involved in the learning process in the Singapore method, as it uses physical objects to simulate mathematical concepts and questions. Hence this works better as compared to solely memorising formulas and tables. In fact, the director of SIM Global Education’s academic division, Dr Timothy Chan has even stated that ‘During my time, there was a lot of formulae and tables. Now, the subject includes more real-life and day-to-day examples…’ This proves that the approach that Singapore is taking, coupled with the results from TIMSS and PISA, is working.
Another
reason as to why Singapore math is so effective is due to the teachers who
teach them. Teachers in Singapore have to
undergo extensive training at the National Institute of Education, also known as NIE, where they
are assessed by actual teachers already working in schools. Even after they
start working they will also be given opportunities for improvement, such as through
attending workshops and seminars in order to improve their skills, as well as
keeping themselves updated on the latest syllabus. Hence, this proves that
Singapore teachers are extremely qualified.
Challenges
Despite the
benefits that comes with Singapore math, there are bound to be some challenges as
well. These challenges exist on the individual level and national level
The first
is that there are differences between other countries’ curriculum, and the
Singapore curriculum. One example of this is in Britain, which focuses more on
covering a wide range of topics, while Singapore’s curriculum aims to develop
mastery in topics, and hence chooses to focus on fewer topics. Thus, when
teachers attempt to implement Singapore math into Britain’s education system,
it is very difficult due to the difference in structure of each countries’
national curriculum, resulting in a conflict of interest.
The second challenge
is that teachers have also found it difficult to implement Singapore math as
our syllabus is more teacher-driven, in-depth and takes place at a much slower
paced, as compared to what teachers in New Jersey, America were used to. The third
challenge is that teachers require sufficient numbers of advisory board
committee members and higher-ups to be on board with this idea before Singapore
math can be implemented into the curriculum. The last challenge is that the
methods used in Singapore, such as the model drawing approach, can be used to
solve many questions, however it cannot be used to solve all types of
questions. These are just some of the difficulties faced when implementing
Singapore math on a national level.
On the
individual level, other challenges exist. Resources for learning Singapore math
is not much of a problem any longer as such textbooks are readily available
online, for instance through online bookstores such as The Book Depository,
which even offers free shipping. In some schools overseas, there is funding to
have Singapore math used in their local syllabus. Hence, this allows textbooks
such as the Inspire Math series in the United Kingdom to be developed and used in
schools. Thus, even home-schooled students are able to gain access to Singapore
math resources for learning.
However, one
of the challenges is that the students have no one to turn to should they
encounter problems when studying, as there are likely to be very few teachers
overseas who are trained in teaching Singapore math. Most people will be
educated in their local mathematics syllabus instead. Hence, this will make it
harder for students overseas without proper Singapore math educators to learn
and apply it properly.
Even if the
students are able to find teachers to teach them, they are likely to be very
expensive and not sustainable, as these teachers are not commonly found and may
be in high demand. Thus, it becomes costly for overseas students to learn
Singapore math should they not learn it from school. This is not to say
that home-schooling is not an appropriate way to study, rather a little more
effort has to be put in, especially for studying an obscure syllabus, such as Singapore
math, overseas.
Home-schooling
Now, what is home-schooling you might ask? Parents.com defines home-schooling as “a progressive movement around the country and the world, in which parents choose to educate their children at home instead of sending them to a traditional public or private school.” Parents may choose to home-school their children for a number of reasons, for instance, religious beliefs, safety, to accommodate learning disabilities or even just general dissatisfaction with the school options available locally.
Source: Ann Arbor Family
However, as with
everything, there are pros and cons to home-schooling.
Pros
Pros
include the designing of one’s own curriculum, one to one teaching, allows for
family time, flexibility of time, and protects children.
For designing of
own curriculum, parents get to choose what their children learn. Hence, they
can choose to focus on topics that best suit their child’s needs and strengths,
and slowly teach their child what they are weak at. Parents
are able to tailor their own ‘curriculum’ and timetable to suit their
children’s unique personality and needs, as compared to a traditional school,
where people who do not personally know each and every child design a
curriculum for them. These people are unlikely
to have each child’s best interest at heart. Hence based on this, home-schooling
seems a much more reasonable choice for
parents, as parents can help develop their child’s strengths, thus better
helping their child as compared to using a standardised curriculum.
Parents can also
choose to teach children subjects that may not be often taught at school, or may
not be as in-depth as parents would like, for instance subjects such as music
or theatre. Parents are also given the option to choose materials that align
with the family’s religious and personal beliefs. In the case of Singapore
math, students may learn it through home-schooling as a result of their
parents. Their parents may be dissatisfied with the local curriculum, or they
may believe that their child should use a different method when it comes to
approaching mathematics. It could also be that they already know of Singapore
mathematics however there are no schools nearby which uses it, or even if there
are they may not be affordable. Hence, parents may take it upon themselves to
teach their children this method instead.
The second pro is
one to one teaching. One to one teaching is more effective as compared to the
traditional classroom setting, as the child will get individual attention from
the teacher, and the teacher will be more able to work on and identify each
child’s strengths and weaknesses. In a classroom setting, students who need
more help may not receive it, and students who are more advanced may not be
getting the materials and lessons that they need. For Singapore math, one to
one coaching is more useful as the Singapore approach is very different from
what children are learning in traditional schools, assuming Singapore math is
already implemented in the national curriculum, or in the local schools. Hence,
more time and effort can be put in, to ensure that students fully grasp the
concept and are able to apply it effectively.
For family time,
this allows stronger bonds to be forged between siblings, and between the
children and their parents, as the children typically study and play only with
each other, and learn from their parents. Hence, most of their time is spent
interacting with their families. In some cases, parents with more children can
allow their older children to help teach their younger siblings. This further
strengthens the bond between siblings. When one of the children achieve
academic success, the entire family will also celebrate together with them, as
each member of the family would have contributed in some, albeit small, ways to
help them.
For flexibility
of time, home-schooling allows parents to plan their children’s lessons around
their own schedules. The lessons can take place at any time, and it
does not have to follow the usual traditional school hours, although some
parents may still wish to do that. If not, lessons can be taught based on when
the child is best able to focus, or whenever the child grows curious about
anything. Hence, the child’s creativity will not be hindered, and they will be
encouraged to learn and be more curious about the world around them. Families
will also be able to organise their own schedules and fit their child’s
education around their busy schedules, instead of having to work around the
traditional educational institution’s timings. This
is beneficial if the parents are typically very busy.
The final pro is
that children grow up more protected and are exposed to fewer things than they
would traditionally be exposed to in a normal school. Examples of this include
bullying, profanities, drugs and alcohol, just to name a few. Although
home-schooling is unable to fully protect children from everything as they will
still get exposure to television and the internet, parents are at least more
able to control what their children view and are influenced by at home.
Source: U.S.News
Cons
For the cons
of home-schooling, there exists a few as well.
The first is that
home-schooling is time consuming and stressful.
Parents not only
have to play the role of teachers, they also have to be responsible for
researching and printing worksheets for their children, buying assessment
books, marking and grading of papers, and even keeping track of their child’s
progress. Other than this, parents still have to be responsible for everything
that happens in the house, such as caring for the other children, cooking and
even cleaning. Hence, home-schooling can be very time consuming and it can add
even more stress on the family.
As parents have
to play the role of both parent and teacher, they will not get a break at all, especially
in the case of Singapore math, parents have to first educate themselves on this
way of learning and teaching mathematics, which is likely very different from
what the parents themselves are used to and what they learnt back in school.
The second con is
the lack of expertise that parents have.
Should the
parents have previous experience teaching students, then it would be relatively
okay for them to teach their own children. However, most parents do not have
this background knowledge, and a lot of them would not have the necessary
skills to teach the children everything that they need to know. Although this
is a problem that can be overcome, for instance parents can educate themselves
on what their children needs to know, it will take a lot of time and effort.
Parents may also
end up hindering their child’s learning process if this is not done right, as
their child may not be able to fully understand and master concepts that they
may need in later stages of their education. In the case of Singapore math for
instance, parents who do not fully understand it may only end up confusing
their child more and potentially causing their child to dislike something that could
prove to be more beneficial to them in the long run.
The final con is
that children will have limited peer interaction.
It is true that
children will have their siblings, and maybe even their neighbours to play
with. However, it is not healthy to constantly be interacting with the same
people, especially for young children, and it is likely that these children
will have known each their all their lives. This thus makes it even more
difficult for them to hone their social skills, especially when it comes to
making new friends. The friends that the children play with may also be much
older or younger, and it is important that children get to interact with others
of their own age. Social interaction is thus something that home-schooling is
unable to provide for children.
Source: IMGBIN
iMath
Now, there is a
solution to all the challenges that comes with learning Singapore Math through
home-schooling. iMath is an app providing online tuition and
tutorials on Singapore Math, making it extremely easy for students and parents
who are studying Singapore math, especially in places where there are few
tutors on this subject, to ask questions and get help. Other than tuition,
iMath also has a community wall where parents and students can post queries,
for instance regarding the mathematics curriculum, math questions, or even on
iMath itself. The community wall will be answered by tutors and other users of
the wall. What’s more, the use of the wall is completely free!
Some features of
iMath are that all lessons are recorded. Hence, students and parents can easily
review past lessons, better helping them reinforce concepts previously learnt. In
places with limited access to Singapore math, iMath also has a huge database of
answered and unanswered questions in order to help students gain more practice.
Students and
parents can choose any tutor they would like who is best suited to their learning style, and easily book them for a 1
to 1 video call based on the student or parent’s own schedule. Hence, timings
are made extremely flexible. What’s more, a reminder will be sent to the
student or parent’s phone regarding upcoming sessions. This is made possible as
iMath is available as an application, greatly adding convenience for its users.
Conclusion
Hence, home-schooling can be used to teach students about Singapore Math. However parents have to be properly educated, and have the proper resources to be able to teach their children effectively, in order to allow their children to reap the benefits of learning Singapore Math. However, should they require help, online resources such as iMath are always available to aid students and parents.
