Singapore math is a term coined by the United States to describe the mathematics syllabus that is used by the city-state, Singapore. However, it is more commonly known as just ‘maths’ here in Singapore. After Singapore gained independence, we initially adopted the math syllabus of other countries and it was not until 1981 that the Curriculum Planning and Development Division in Singapore began planning its own mathematics syllabus. Singapore math has been adopted not just in Singapore but in many other countries, including the United States, Africa and Chile.
What makes Singapore math so unique that it requires its own special term? In the 2016 Trends in International Mathematics and Science Study (TIMSS), which ranks Primary 4 , aged 10, and Secondary 2, aged 14, students in Singapore against those of 63 other education systems, Singapore emerged top in both subjects. At the primary 4 level, Singapore students were found to have the highest average score of 618 in mathematics, with Hong Kong coming in second at 615, and South Korea coming in third with 608. These same students achieved the highest average score 590 for science, followed by South Korea with 589, and Japan with 569. Singapore students are also found to have much more positive learning attitudes as compared to their international counterparts.
Not just in TIMSS, but Singapore has also topped the scores in the Programme for International Student Assessment, better known as PISA, in 2016. This study is conducted once every 3 years by the Organisation for Economic Co-operation and Development, OECD, and it measures the ability of 15 year olds around the world to use their knowledge to solve problems. Singapore has ranked first in all three categories, Mathematics, Science, and reading, which resulted in Singapore’s best ever PISA scores.
So how does Singapore Math work? Singapore math focuses on getting students to have a mastery of selected topics. This means that Singapore math focuses more on depth, instead of breadth, in terms of the topics that they choose to cover. It uses a specific learning approach developed by Jerome Bruner, an American psychologist, who suggested that people learn better through a three step approach, which are concrete, pictorial and abstract. In short, it means that students are taught to use real-life objects to illustrate mathematical concepts, before applying drawings such as the ‘model’ method , and lastly using solely mathematical concepts and symbols to solve questions. This method was chosen in an attempt to divert away from rote learning and memorizing and instead, teach students how to solve problems.
Using the concrete method, students use physical objects to simulate questions. For instance, in Singapore classrooms, dice, blocks and even stationery are used to teach students how basic mathematics work. Hence, the students are able to use a ‘hands-on’ approach to help them observe and better understand what they are doing, as they are able to physically remove and place the blocks back, helping them reinforce what subtraction and addition is respectively. In fact, even in assessment books and worksheets given out in schools, kindergarteners and Primary 1 students are given diagrams of these stationaries and blocks used in their real-life demonstrations. They are then asked to colour the appropriate number of items in in order to symbolize ‘addition’ and ‘subtraction’.
The second method is known as pictorial. Through this, students are taught how to use the ‘model’ method in order to help them better understand questions. These involve the use of bar models in order to help students visualize the questions. This is similar to the pictorial approach, in the sense that they both use representation to help students. The bar model is able to help students learn not only basic addition and subtraction, but multiplication and division as well. With respect to basic addition and subtraction, there may be such a question:
Tom has 70 books, while Mary has 30 books. How many books do they have altogether?
In order to solve this question, students would draw a model that will look something like this:
A longer bar will be drawn to represent the larger number, 70, and a shorter bar will be drawn to represent the smaller number, 30. Hence, this makes it extremely clear to the students how the question ought to be answered. For subtraction, something similar will be drawn as well.
However, for the harder questions involving multiplication and division, the model will look slightly different. Let’s consider this question:
Tom and his 3 friends have 30 sweets each. How many sweets do they have in total?
The addition approach will work here as well, but let’s say we wish to use multiplication to solve it instead. In that case, the model will look something like this:
Hence, each bar will be of a certain length , and it will represent 30. 3 other bars of the same length will then be drawn side by side in order to represent the number of sweets that the three friends have altogether. Once again, this will make it very clear to the student as to how to solve the question should they already understand multiplication.
This proves that models are effective at helping students better understand their mathematical problems, as well as teaching them basic arithmetic, including multiplication and division.
The last approach is abstract, which is used once students have mastered the bar model. Using this approach, students will solve mathematical problems using solely numbers and symbols, with little to no visualisation steps.
There are a number of benefits in regards to using the Singapore approach to solve mathematical problems. The first is that textbooks are designed in what is known as a ‘spiral’, which is that chapters are arranged in sequential order and builds on what students have learnt in previous chapters. The second is that according to a study conducted by The Straits Times in 2015, it shows that Singapore’s pictorial methods is effective as it was successfully used to teach students in South Africa who have special needs and a language barrier. Lastly, students are required to use physical objects and a ‘hands on’ approach to help them learn mathematical concepts, which is a lot more effective as compared to solely rote memorising tables and formulas. In fact, even the director of SIM Global Education’s academic division, Dr Timothy Chan has 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 this approach that Singapore is taking, coupled with the results from TIMSS and PISA, is working.
One of the other main reasons as to why Singapore Math is so effective is due to the teachers in Singapore. Singapore teachers have to undergo training at the National Institute of Education, or NIE, before they are allowed to begin teaching at schools, where even then they will have extensive help from mentors, and given many opportunities for collaboration. Hence this proves that Singapore teachers are indeed extremely qualified.
However, despite these benefits of using Singapore maths, there still exists many challenges faced by students, parents and teachers who are not in Singapore and want to use, learn and implement Singapore Math. Challenges exist on the individual and national level.
On the individual level, for international students and parents who have taken an interest in Singapore math, one of the main challenges in adopting Singapore math is that although they have the resources such as the textbooks, they may not have anyone qualified enough to teach the students. Textbooks teaching Singapore math are relatively accessible now, especially on websites such as The Book Depository, with free online shipping. Schools overseas are also funding the use of Singapore math, hence allowing textbooks such as The Inspire Math series in the United Kingdom to be developed and used for teaching in schools. However, for home-schooled students, or for students who are not in these schools which uses the Singapore syllabus and want to learn by themselves, it may be a bit more difficult. Even though they have the materials, they lack trained educators who are able to guide them should they encounter any difficulties. This is due to there being very few people who are educated in the Singapore approach as it is still not commonly found, and most people are likely to only be educated in their local method. Hence, this may make it harder for students with a lack of access to trained educators to learn and apply Singapore math effectively. Even if the students are able to find such educators, they may also be expensive due to the low number of educators who are able to teach it, thus making it costly for these home-schooled students to continue learning Singapore math.
On the national level, there exists some challenges as well. Firstly, the Singapore math approach and syllabus may not be in line with those of other countries. One example would be Britain. In Britain, they have a much stronger emphasis on covering a broad range of topics. However, the Singapore method focuses on depth, hence covering fewer topics, and emphasises on building a strong foundation on basic mathematical concepts. Hence, there will be a conflict of interest between Britain’s syllabus and the approach that Singapore is taking. Secondly, teachers in America have stated that it is difficult for them to implement Singapore Math as Singapore’s approach is more teacher driven and takes place at a much slower paced as compared to what students and teacher in New Jersey are used to. Thirdly, teachers also need to have the professional training that comes with teaching students Singapore maths, and there must be sufficient advisory board committee members and leaders who are willing to support this idea, in order for there to be a smooth transition to the Singapore syllabus. Lastly, the ‘model’ method, while useful and is applicable to a number of questions, is not applicable to every question. These are just some of the challenges faced when trying to implement Singapore math overseas on a national level.
Hence, in order to facilitate student learning, a new approach in order to fix the lack of skilled and affordable tutors has been proposed, which is learning through video conferencing. Instead of students having to find their own tutors and educators with regards to Singapore math, they can use applications, or online resources to aid them instead.
Firstly, what is video conferencing? Video conferencing allows people to communicate without having to meet face to face. Video conferencing can also include other materials such as presentation slides, whiteboards and flipcharts, just to name a few. This is particularly useful and convenient as people need not have to meet at a particular location to have their business conducted, or lessons taught for instance, especially if the location is very far for them. Video conferencing works through software and web cameras that can be used to establish high quality videos and clear sound, allowing the conference to continue without a hitch. However, the stability and consistency of the video and sound quality itself also depends on the internet connection, and not solely on the quality of equipment used.
What are the benefits of video conferencing then you might ask? Well the first as mentioned above is that it allows for long-distance communication. Video conferencing enables group collaboration with overseas partners, and makes it seem as though they are seated in the same setting, sharing ideas, despite the time zone and locational differences. Video conferencing can be used to overcome such hurdles. Communicating through video calls can also help strengthen bonds, and enables the individual to pick up on visual cues from their overseas counterparts that can easily be missed in a standard audio call. This allows for better insights and understanding of the topic at hand. As a video conference call can be joined from practically anywhere in the world, this helps to drastically reduce costs involved, and also makes it much more convenient for everyone, especially in the case of students looking for teachers trained in Singapore maths as mentioned above.
Some other benefits of video conferencing is that it helps to save time and money as it allows the teacher and student to meet online. This is because, for these students, even if they manage to find a qualified teacher, they would still have to travel to meet the teacher. This can then incur even more costs for the students in addition to the high costs of hiring the teacher, especially if the location is out of place. Another benefit would be that video conferencing allows for there to be flexible timings as it is very easy to access video calls in our current day and age.
Communicating online is also much safer as there need not be physical contact and face to face meetings between the student and teacher, such as in a traditional classroom setting. This can thus help to allay the fears of parents especially if their child is very young and still requires some form of parental supervision. This is especially so as the student will be learning in a potentially more dangerous environment, due to these lessons not being held in a school environment. In some cases and in some websites, the online video lessons can also be recorded for future reference.
This helps the students as they are able to review the material to aid them in their learning, in order for them to fully master the content. Hence, the students will be able to play back the videos again in their own time to help them revise. Parents can also benefit from this as they will be able to watch the recording to help their child determine if the teacher is the right fit, good enough and whether they are getting their money’s worth. This is an added benefit as compared to the use of a physical classroom where parents are absent and it is up to the student to decide if the teacher is suitable for them.
Of course, there are disadvantages to using video conferences. For instance, a large amount of money will have to be invested at first in order to purchase all the equipment needed. The video and audio quality is also subjected to strong Wi-Fi connections which can pose a problem should the Wi-Fi be down that day. However, the benefits of using video conferences still outweighs the costs involved, as it is more convenient, and students get to save time and money on commuting regularly for their lessons.
Another potential use for the video conferencing would be to have online consultation sessions instead, for students who may not be able to afford or have no need for consistent lessons. Hence, students will consolidate questions that they have beforehand , or ask them during the consultation sessions. Students will then have them all addressed at once. This is a more efficient system, and is more cost effective as students will be helped on a needs basis, and not a regular basis, which is the more traditional method. Students will still be able to opt for the traditional, regular method, however, video conferencing allows for this other option to be made available as well, coupled with all the benefits that already comes with video conferencing.
Hence, with the growing interest in Singapore Maths, as a result of Singapore students topping the ranks in both TIMSS and PISA, video conferences prove to be a more useful, efficient and cost saving method, as compared to using the traditional method of physically meeting up with teachers, for students overseas and students who are unable to gain access to trained teachers to learn Singapore Math. Now imath has done the hard work of curating qualified tutors and offering them at a fraction of the price. Download the app and try it out now.