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What is Singapore Math?
History of Math Education in Singapore
Singapore was not always known for being world class in Mathematics education. But as with all stories, its beginnings are always never told. In this article, we try to unravel the journey of Singapore Math or Singapore Maths and then try to convince you as to why Singapore Math may be a superior way to teach students and children. In fact, the terms “Singapore Math” was not coined by Singaporean teachers or the Ministry of Education in Singapore. It was coined by Americans who were exposed to the teaching methodology and saw the efficacy of such methods when it came to teaching students mathematical concepts and more.
The education of Mathematics in schools has evolved over time since Singapore gained its independence in 1965. From the outset, the government recognised that its citizens had to be more nationally cohesive. Education served as a stepping stone for the young growing nation. From 1946 to 1965, this marked the first phase of educational awareness Singapore had as a nation with the overarching aim to improve the economic welfare of its citizens. The emphasis was largely on technical subjects, Mathematics and Science.
Today, the Singapore education system consists of 6 years in primary school (equivalent to Grades 1 to 6), 4 years in secondary school (equivalent to Grades 7,8,9,10) and 2 years of pre-university (equivalent to Grades 11 and 12)
From Primary 1 to primary 4, students in Singapore follow a common syllabus. For primary 5 and 6, students either take Foundation Mathematics or the Standard Mathematics Syllabus. While the Standard Mathematics syllabus builds on what was learnt in Primary 1 to 4, the Foundation Mathematics Syllabu revisits what was taught from Primary 1 to 4.
In Primary 6, after 6 grueling years in primary school, students sit for the PSLE or Primary School Leaving Examination where their results determine their future pathway to a secondary school. By now, students in Singapore would have been exposed to a wide variety of metacognition and thinking skills, equipping them for solving mathematical problems.
In SingaporeMathGuru, we have a question bank consisting of Primary 1 to 3 math drills and skills and exercises. This is equivalent to Grades 1 to 3. They are free to attempt and progress tracking and scoring tools are available upon sign up.
We also have higher order problem solving problem sums or word problems for Primary 4, 5 & 6 with attached video explanations to these questions that are viewable by parents, teachers and students, free of charge.
|Primary 1/Grade 1 Math||Primary 2/ Grade 2||Primary 3/ Grade 3|
|Drills,Skills, Exercises, Worksheets||Drills,Skills, Exercises, Worksheets||Drills,Skills, Exercises, Worksheets|
|Primary 4 Problem Sums||Primary 5 Problem Sums||Primary 6 Problem Sums(PSLE)|
Emphasis on Problem Solving
In 1988, the curriculum development division of the Ministry of Education established a Mathematics Review Committee. By this time, the Ministry of Education felt that the syllabus needed a revamp in the school curriculum and syllabus. The Mathematics Review Committee felt that the framework should be angled towards ‘Mathematical Problem Solving’, also in line with the needs of the times. The new framework contained a balance of skills, attitudes, processes and metacognition.
The new framework was fully implemented in 1990 in both the primary schools and secondary schools in Singapore where the emphasis was on problem solving. With the emphasis on problem solving, teachers and educators had to be trained on the heuristics approach and this often required a pictorial approach towards problem solving. This is known today as modeling or bar models as popularised by certain Singapore educators in other countries. It is also known as the “model drawing” approach to solving math problems.
Over time, the Mathematics education has been refined with directives from the Ministry of Education and what we have today is a system of sorts to help students become better mathematicians. We are not talking about a handful of students here. Students exposed to Singapore Math or Singapore Maths tend to do better amongst their international peers. But more on that later. Practically, a whole generation of students’ mathematical scores were lifted.
Singapore Mathematics Framework
Source : Ministry of Education Singapore
The table above details the Singapore Mathematics Framework. Within the framework, the Ministry of Education has detailed the concepts, the skills, attitudes, metacognition and processes needed for problem solving. From the period 2013 and beyond, thinking skills, heuristics, applications and reasoning are a large part of the “Processes” component. Combined with skills, attitudes and metacognition, a student groomed by the “Singapore Math Framework” will do relatively well compared to other students in other countries.
Mathematics In Primary School ( Grades 1 to 6)
I suppose this is the part that gets interesting for me as a writer/author of this blog because SingaporeMathGuru specialises in Primary School Mathematics. What makes Math interesting in Singapore at the Primary Schools level is because they follow a concrete-pictorial-abstract approach, inspired by American Psychologist Jerome Bruner, towards solving Mathematics questions. Together with activity-based learning, the student is able to grasp hold of mathematical concepts more easily.
Source : Wikipedia
Jerome Bruner, the man you see above is the man who cognitive psychology and learning. He has made many contributions to the fields of educational psychology. So little is spoken about him but he may be the man who inspired the whole Singapore Math movement, rather indirectly. He believed that people generally learn in 3 stages. You will see these stages described below.
In “Concrete” of the Concrete-Pictorial-Abstract approach, in conjunction with activity-based learning , students are given place value charts, cubes, clips, objects, 2 dimensional shapes to work with to enhance their learning experience. The image below shows a place value chart.
Source : Pinterest
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The images above is an example of a place value charts where students are taught to identify the thousands, hundreds, tens and ones.
In the “Pictorial” approach towards solving math problems, students learn to represent mathematical information in the form of a diagram or a drawing of a model. We will discuss this in more detail later. But on the whole, this approach is really a pre-algebra approach and it enhances a students understanding in solving mathematical questions. This really is the Singapore Math Method. The pictorial approach really is the essence of the Singapore Math approach, incorporating visuals and models towards solving mathematical questions.
And then, you have the abstract approach where learning mathematical concepts are done at a symbolic level with numbers, symbols and more.
Since the 1980’s, the Ministry of Education has developed and refined the model method which is essentially a visual tool to help students with mathematical thinking and this has remained a core part of solving mathematical problems at the primary school level.
Source : Singapore Math Guru
Example of models in worked solutions that we have on the site itself. This is actually a problem sum or word problem, involving a statement that says that an object is 20 more than the other with a given total. We have more than 10,000 questions with fully worked, step-by-step solutions for students, teachers and parents.
Bar Modeling or Models
As mentioned above, bar modeling really is a huge part of the “Pictorial” approach to solving mathematical questions. It is a way of representing all the pertinent parts of a math question into a visual form, essentially helping the student to eventually understand the abstract parts of Mathematics.
Let us look at an example.
John has 200 marbles.
Mary has 80 marbles.
How many more marbles does John have than Mary?
In this simple question involving an object having more than the other, by drawing the model above, students understand quite quickly and decide the operation to use, subtraction. 80 must be subtracted from 200 to find the space or the gap. That resultant value is 120 and hence, John has 120 more marbles than Mary. Very quickly, by drawing the model, students use the pictorial and gradually transitions to the abstract with real numbers.
These bar models resemble rectangles and the lengths of these rectangles gives students the ability to tell at once which object is greater in value. In this very example, John has more than Mary.
Models can also be used to represent fractions. Let us look at an example.
John has ¼ of all the sweets in a bag. Mary has the rest. If Mary has 20 more sweets that John, how many sweets do they have altogether.
John has 1 out of 4 units. Mary must have the other 3 units. 3 - 1 = 2 2 units = 20 1 unit = 20/2 = 10 10 X 4 = 40 They have 40 sweets altogether. This is an example where a fraction can be represented as a model. First draw 4 boxes and allocate those boxes accordingly. If John takes up 1 box or 1 unit, then logically, the other boxes must belong to Mary. So can you see that while each question is different, drawing bar models or doing models in general helps with the thinking process? It sure does.
Here, the models are show that 35 + 65 must equal to the rectangle above consisting of the question mark, the unknown. Therefore, the answer must be 100. So, bar models of modeling can help bring about the answer. Again, we move from pictorial to abstract.
Here in this bar model, we can see that 4 equal units has a value of 100. So, to find the value of 1 unit, 100 must be divided by 4. The resultant answer will thus be 25. In this case, the models tell one to perform the division operation.
Here, in the above bar models or Singapore Math models, 4 sets of 10 is equal to the value of the rectangle below. Hence, in this model, to find the unknown or the value of the question mark, we would have to multiply by 4.
Singapore math models or bar models can also be used on tougher questions as you will see below.
There are 100 black and white marbles in a bag.
If there are 20 more black marbles than white marbles, how many white marbles are there?
The larger rectangle represents the black marbles and the smaller rectangle represents the white marbles.
Since there are 100 black and white marbles:
100 - 20 = 80
80 ➗ 2 = 40
There are 40 white marbles.
Singapore Math models and the pictorial bar model approach is very versatile as you can see. You can use on it complex questions or even simple 1 to 2 step word problems. Really, it is up to your imagination. You can use it however you wish. In many of our questions in our exercises on www.singaporemathguru.com , we use these Singapore Math models or just models(we Singaporeans call them models. We don’t use the terms “Singapore Math” actually!)
How Teachers Implementing Singapore Math Should Inculcate Bar Models
As you have seen, Singapore Math bar models are really a versatile tool in solving math questions. The idea behind it is that the visuals bring about clarity and helps a child to move from pictorial to abstract.
The use of bar models should be used with 1 step word problems first. Students exposed to Singapore Math bar models should be able to use bar models for addition and subtraction in the first year or grade 1.
Eventually, with confidence, students will be able to use bar models or Singapore Math models on 2 step word problems.
Remember that it is all about practice. The more a student uses it, the better he or she becomes with Singapore Math.
Singapore Math To USA
Singapore Math textbooks have been in use in the United States since 1988.
By 2007, the Department of Education California approved the Primary Mathematics(Standard Edition) series for use in Kindergarten and elementary schools. Oregon followed suit in 2008. Many parents who homeschool their children also receive tuition in Singapore Math methods.
If you are a teacher, parent or students who are interested in Singapore math, please create an account and sign up with us. We have a ready database of questions that you can attempt on the site and many of them have video explanations to these questions.
Recognition & Accolades of Singapore Math or Singapore Mathematics
Singapore students participated in the Trends in International Maths & Science Study and Singapore students consistently rank amongst the top performing students in the world. Singapore’s 4th and 8th grade students scored 1st in Mathematics in the years 1995, 1999, 2003, 2015. This is an accomplishment recognised the world over.
In another study PISA ( Programme for International Student assessment), found that amongst 15 year old students, Singapore ranked 1st in 2015 and 2nd in 2009 and 2012. This study assessed the scholastic performance of mathematics, science and reading.
These results are notable in itself and is a testament to the efficacy if Singapore Math.
Countries That Use Singapore Math
The Singapore Math methods consisting of modeling and such methods described above has spread far and wide. Countries using the Singapore Math methods include South Africa, Saudi Arabia, Philippines, Panama, France, Pakistan, Indonesia and more. It is reported by some websites that 25 countries use Singapore Math to teach their students. We are not entirely sure if that is accurate but we do know that Singapore Mah has spread far and wide.
That is also the reason why visitors to www.singaporemathguru.com include Russia, Sweden, UK, USA and more. They are from some distant lands and from the looks of it, they are spending quite some time on our website.
And of course. Not to mention, Singaporeans spend a lot of time attempting the questions on our website as well. We trust that we have been useful to many teachers, parents and students.