By Bill Jackson, Special to CNN
Editor's note: Bill Jackson was a Paterson, New Jersey math teacher and a district-wide math teacher trainer in Scarsdale, New York. He also provides consulting and teacher training on Singapore or Japanese approaches to mathematics teaching and professional development, and regularly speaks at national and international mathematics conferences.
Singapore math is getting a lot of attention as more and more schools in the United States are using Singapore-based methods and materials to improve the teaching and learning of mathematics. Many parents and teachers are wondering if a change is really necessary. The answer is yes.
I’ve seen firsthand the difference the Singapore math approach can make. I began using Primary Mathematics textbooks from Singapore’s Marshall Cavendish Education in 2000 when I was a classroom teacher. I have used Singapore math with both low-income inner-city students and affluent suburban students, and found that, when taught in the right way, it makes learning mathematics fun and engaging, allows students to understand mathematics deeply, and helps them become proficient at solving very complex math problems.
So what exactly is different about Singapore math? Singapore mathematics lessons begin by engaging students in hands-on learning experiences followed by pictorial representations, which help them form a mental image of mathematical concepts. This is followed by an abstract stage, where they solve problems using numbers and symbols. This approach makes the learning of mathematics fun and meaningful, and helps students develop positive attitudes about math.
Typical U.S. math textbooks are thick and heavy and they cover many topics superficially and usually in an incoherent way. In contrast, Singapore textbooks focus on fewer topics, taught in-depth for mastery, carefully building mathematical understanding in a systematic way.
In addition to these resources, there is also an interactive online program, Math Buddies, which is enhanced with animated lessons and practice questions for the digital learners.
Singapore math emphasizes conceptual understanding: the “why” not just the “how.” As it is not enough for students to just get a correct answer, multiple solution methods are encouraged and evaluated as to their advantages and disadvantages. Students need to be able to explain their thinking and understand and explain the thinking of their peers.
Singapore first drew national attention back in 1995 with the release of the results from the Trends in International Math and Science Study, where Singapore and a handful of other developed East Asian nations scored at the top of the world in mathematics. Meanwhile, scores in the United States that year and in subsequent years were less than stellar. Looking for improvement, educators in the United States decided the Singapore approach was worth exploration. Ironically, it was an American, psychologist Jerome Bruner, who developed the methodology that led to Singapore’s math curriculum.
Recently, in the process of creating the Common Core State Standards for mathematics (to develop similar goals and criteria for math instruction across America), educators took an even closer look at the Singapore math program and realized that it had a lot of what they were seeking.
The main goal of Singapore math is to foster problem-solving abilities in students, which helps in all subject areas.
One important aspect of this is the model drawing method in which students solve complex word problems by drawing pictorial “bar models” to illustrate problem situations.
Take the following problem from the fifth grade Singapore math textbook as an example:
“Ryan and Juan shared $410 between them. Ryan received $100 more than Juan. How much money did Juan receive?” We can represent the problem situation by drawing the bar model seen in the figure.
Figure: Ryan and Juan shared $410 between them. Ryan received $100 more than Juan. How much money did Juan receive?
Ryan’s and Juan’s amounts are represented by the rectangular bars. The known information is indicated with brackets. The unknown quantity, which is what we are trying to find out, is indicated by a question mark. From the diagram, it is easy to see that we first need to subtract the extra $100 that Ryan has and then divide the remaining amount by 2 to find the answer.
The bar model is really a form of pictorial algebra. (If you think of Juan’s bar as x then Ryan’s bar becomes x + 100 and you get the equation x + x + 100 = 410.) The bar model converts the abstract words of the problem into an easy to understand pictorial diagram that helps students solve algebraic problems without using formal algebra. In later grades the question mark in the model above can be replaced by a variable, making the transition to formal algebra easy.
This new way of looking at math might take some getting used to. It’s a matter of seeing things in a new way. For example, in first grade, students learn to add and subtract by decomposing numbers: to add 9 + 4, students will split 4 into 1 and 3, and do 9 + 1 + 3. To subtract 12 – 4, they split 12 into 10 and 2 and do 10 – 4 + 2.
Although Singapore math may be different from the way previous generations learned math, today’s children are using it to gain number sense and to learn to solve problems mentally, and to internalize important mathematical properties and the rules of algebra informally. Many more American students could benefit from this novel approach, as Singapore's students have already.
The opinions expressed in this commentary are solely those of Bill Jackson.
I 100% agree that understanding not only how, but why. Also, important is to show the application of math problems being used in the real world. This goes back to the question:"What do you want to be when you grow up?". Come up with math problem that are related to the student's career aspirations. They will see the importance and relevance of the concepts.
I personally still have trouble understanding the importance of reading Shakespeare. The only things I can come up with is the art of interpreting 15th century slang or if you plan on making a career out of acting in Shakespearean plays. Or...perhaps to torture high school and junior college students.. The English were, historically, good at that.
I have a degree in Physics and have had technical and computer jobs my whole career. My ex-girl friend was getting her elementary teaching credentials in the USA so I was helping her with her math teaching class homework.
The book and the exercises were almost incomprehensible and mainly involved set theory and other abstract concepts. I told her in the 25 years since college I have never seen nor used any of the concepts or problems shown in her text book while having multiple businesses and consulting technically.
I don't know what they are teaching and why in the math classes but my one exposure seems to show why there is so little useful math instruction. Of course, if I couldn't understand these books, she had no hope and she was supposed to teach it. Good luck students.
Having trained math teachers in Singapore for 11 years and I go back every year to train teachers I find much of what is being said has no basis in the reality of the Singapore Schools. They certainly do well. The textbooks are very good. But Singapore Math is not a series of textbooks. It is based on textbooks, high motivation, well qualified and paid teachers, a genuine non-political education environment (decisions being made on what is believed is best, not what is popular or will get you elected), education being valued by all levels of society, a real meritocracy, etc.. I do not disagree that Singapore textbooks could be effective, but unless the USA fundamentally changes the debate and culture associated with education you can only have a limited impact.
singapore follows indian method
I wonder where did you get your facts?
Even though I do have a huge admiration of 'Vedic Mathematics' which originated from ancient indiafor more than 5000 years ago, where sages were able to multiple an 18 digits number with another 18 digits number witnin a few seconds mentally, it is completely incorrect to say that the Singapore system is based on the Indian system.
The Singapore Education System is unique in the world and it is a proven system which is being adopted by many other nations, including in some states in India itself.
155 and 255.
the "why" is very important, it would have made more interested in algebra.
The main problem is not the method we adopt in the United States in teaching math, but the main reason is that kids are not motivated at all. Most of them do not like math at their early ages. I remember when I was in elementary school and Highschool , I used to work in math and I did it with my friends everyday. My advice is to reinforce math in elementary school more and help these students appreciate it. Although I am from a poor country, but I was motivated to do math. As a simple citizen, my voice may not be heard, but I do believe this can help us somewhat in finding a solution.
I love the Singapore method of teaching math. If you look at the books and compare them to our traditional textbooks you will see the difference immediately. We take simple concepts and make them very difficult. Singapore Math takes difficult concepts and make them so easy to understand that it just seems natural to 'get it'. The books are small (less pages) compared to ours, but so easy to understand, so developmentally appropriate. I wish I could use this curriculum in my classroom (I teach second grade) but I can only use it as a supplement. Also, the price is very reasonable. When I used Singapore Math in my classroom all of my students, including those with learning differences, scored at the highest level on our end of the year common assessment. Even better, they loved math and considered themselves mathematicians!
I think this method might be a good idea, but i don't think i could change the way I learn.
You'd be surprised! Try it!
How can U.S. math texts be "incoherent"? Aren't they written by the finest of mathematicians and education specialists? We have the greatest scientists in the world. It makes no sense that we can figure out how to land on the moon but we can't figure out how to write a math text.
That's like asking why someone who one a Nobel prize in literature can't write a good children's book. Just because someone knows math doesn't mean they can lay it out it a interesting and coherent manner for children (also see: smart teachers who can't teach at all).
math textbooks are incoherent because they are written by the same morons who think they know math. most are highschool or community college teachers with the bare minimum of understanding. They know how to do most of the simple mechanics but have little idea behind the language of math. I refuse to use textbooks in my classes as there are few that are technically correct. the dumbing down by the author is bad enough, but then an editor makes changes not knowing how the changes affect a language not understood by many to begin with.
as to Singapore math, I think it is more of the same bs. Fundamentals (or lack of) are the real problem. students can't do even the most basic fundamentals without aids and refuse to learn the necessary vocabulary. Most of this is teachers fault.
Democrats support affirmative action programs in employment and college programs. Think before you vote.
I support Obama and Biden!!
No need to teach them math, affirmative action will help them
Difficulty with understanding mathematics is not solely an issue with minority students. Students of all races in America have faced such troubles.
Malaysia Mathematics approaches is better than Singapore.
May be you should see how inefficient the Malaysian system is and how corruption is rampant in every sphere of life there in Malaysia?
If Malaysia was governed by our Singapore PAP Government, Malaysia (with its tremenduous natural resources, minigs, palm oils, huge space, etc) would have become one of the most successful nation in the whole world.
Hong Kong does something similar and their PISA scores are second only to Singapore.
At my international school, students learn to add and multiply using partial sums, partial differences, partial products, and partial quotients methods. The reason is that those methods can be easily represented with pictures. The change becomes controversial because parents and tutors do not know how to help the children with their homework using the new methods.
But, when students power through and learn the different methods, their conceptual understanding of numbers greatly improves. Change is never easy :).
Janet | expateducator.com
Teaching the alternative algorithms confuses more than enlightens. What kind of conceptual understanding do you want from 6th graders? Singapore's students have a very good conceptual and procedural understanding; they can solve many different types of problems. The Everyday Math approach you describe here may work for you as an adult, but for most students it is a disaster–unless they get outside help from parents, tutors, Kumon, Sylvan, Huntington and the like.
Agreed. We have modified the Everyday Math curriculum so that they only learn the partials algorithms. The reason is that the partial algorithms can be demonstrated using pictures better than the others.
The conceptual understanding we want is that the process of multiplication/division is the same as making arrays.
Partial sums/differences keeps students thinking of the value of a number in relation to place value rather than a digit in a memorized algorithm.
As a special education teacher and tutor, I agree that Everyday Math is a disaster. It is still a top down method of teaching. Presenting multiple ways to solve a problem before the student intuitively understands the concept just makes things worse.
It used to be how math was taught in the US as well.
This is very interesting, but as someone who has taught for many years and been in a principal in Australia (as well as a principal in the USA more recently) I have to say that the "Singapore'" method has been the mainstream way of teaching math in Australia for years.
Beginning with concrete objects, learning to manipulate them and relate them to a developed sense of number, children would express mathematical concepts in elaborated day to day language and represent the concepts with physical objects. The concept of addition, for example, would always begin with real objects being combined and the language gradually incorporating mathematical terms with phrases such as 'and another two' being replaced with 'plus two'.
The first level of abstraction would come when actual objects gave way to non linguistic representations – drawings of objects and later perhaps diagrams.
Finally the mathematical symbols would be introduced and by this time the elaborated language has given way to the more restricted code of mathematics.
This same methodology can be applied to most levels of mathematics, moving from the concrete with concepts expressed in an elaborated code, to the use of abstract symbolism and the more restricted code of mathematical terminology.
What Singapore has done is to codify this approach.
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