*The following guest post is from Barry Garelick, co-founder of the U.S. Coalition for World Class Math**, an education advocacy organization that addresses mathematics education in U.S. schools.*

The New York Times ran a story on September 30 about Singapore Math being used in some schools in the New York City area. Like many newspaper stories about Singapore Math, this one was no different. It described a program that strangely sounded like the math programs being promoted by reformers of math education, relying on the cherished staples of reform: manipulatives, open-ended problems, and classroom discussion of problems. The only thing the article didn’t mention was that the students worked in small groups.

Those of us familiar with Singapore Math from having used it with our children are wondering just what program the article was describing. Spending a week on the numbers 1 and 2 in Kindergarten? Spending an entire 4th grade classroom period discussing the place value ramifications of the number 82,566? Well, maybe that did happen, but not because the Singapore Math books are structured that way. In fact, the books are noticeably short on explicit narrative instruction. The books provide pictures and worked out examples and excellent problems; the topics are ordered in a logical sequence so that material mastered in the various lessons builds upon itself and is used to advance to more complex applications. But what is assumed in Singapore is that teachers know how to teach the material—the teacher’s manuals contain very little guidance. Thus, the decision to spend a week on the numbers 1 and 2 in kindergarten, or a whole class period discussing a single number is coming from the teachers, not the books.

The mistaken idea that gets repeated in many such articles is that Singapore Math differs from other programs by requiring or imparting a “deep understanding” and that such understanding comes about through a) manipulatives, b) pictures, and c) open-ended discussions. In fact, what the articles represent is what the schools are telling the reporters. What newspapers frequently do not realize when reporting on Singapore Math, is that when a school takes on such a program, it means going against what many teachers believe math education to be about; it is definitely not how they are trained in ed schools. The success of Singapore’s programs relies in many ways on more traditional approaches to math education, such as explicit instruction and giving students many problems to solve, in some ways its very success represented a slap in the face to American math reformers, many of whom have worked hard to eliminate such techniques being used.

Singapore Math does not rely heavily on manipulatives as so many articles represent. It does make use of pictures, but even that is misrepresented. Singapore makes use of a technique known as “bar modeling”. It is a very effective technique and is glommed onto as the be-all end-all of the program, when in fact, it is only a part of an entire package. People mistakenly believe that all you have to do is teach kids how to draw the right kind of pictures and they can solve problems. (In fact, there are now books written that provide explicit instruction on how to solve problems using bar modeling—meant to supplement Singapore’s books. That such books rely on a rote-like procedure is ironic considering that reforms criticize US programs as being based on rote instruction.) Pictorial representation is indeed a gateway to abstraction, but there are other pathways that Singapore uses as well. Singapore’s strength is the logical consistency of the development of mathematical concepts. And much to the chagrin of educators who may have learned differently, mastery of number facts and arithmetic procedures is part and parcel to conceptual understanding. Starting with conceptual understanding and using procedures to underscore it is an invitation to disaster—such approach is making profits for outfits like Sylvan, Huntington and Kumon.

The underlying message in articles such as the Times’ is that math education is bad in the U.S. because it is not being taught according to the ideals of reforms—and the reason it is successful in Singapore is because it is being taught that way. Never considered is the possibility that the reform minded methods and textbooks written to implement them are one of the root causes of poor math education in this country. Katharine Beals in her blog “Out in Left Field” does an excellent job describing this.

A friend of mine recently admonished me for my criticism of the article. At least schools are using Singapore Math and it is getting worthwhile publicity, he said. Fortunately, the logical structure and word problems in Singapore’s books are so good it will work in spite of the disciples of reform. My friend is right. If the education community wants to think that Singapore Math is student-centered and inquiry-based and the realization of US reforms, let them think it. For those of us who know better, it will remain our dirty little secret.

*Barry Garelick is an analyst for the U.S. EPA and plans to teach math when he retires this year. He has written articles on math education in Education Next and Educational Horizons.*

Yes, Robert. It is raining cats and dogs here in the Bay State.

This is an interesting synopsis of the widely acclaimed Singapore program. However, missing for me is any mention of the value Singapore society places on education versus the ubiquitous disdain education often encounters in this country, especially from our most at risk communities.

Comment by Paul Hoss — October 6, 2010 @ 10:37 am

In the lower grades, the Singapore Home Instructor’s Guide encourages the use of manipulatives. Manipulatives aren’t bad things- the problem comes when they become a “crutch” and students don’t move beyond using them to doing pencil & paper calculations. Singapore doesn’t allow that to happen unlike many of the “reform” curricula.

Comment by Crimson Wife — October 6, 2010 @ 11:37 am

Yesterday the NCATE released a report stating that the new Common Core standards are designed to get at the 3 domains of learning-

-social

-emotional, and

-academic/cognitive competencies.

It states that emotional and social needs have to be addressed first and that the way to meet those needs is to teach in the project based, collaborative, culturally respectful manner described in the Model Teaching Standards.

All this federal spending appears designed, based on the accompanying documents, to move the US away from academics because academic knowledge and skill is not equitably distributed among the US population.

No wonder it was so important to get states like Massachusetts to sign up.

Ed Week’s misleading headline “Education Schools Overlook Developmental Science, Panel Finds” suggests the author either did not read the actual report or is actively trying to misportray the planned emphasis on social and emotional learning first. That’s what the report actually says.

Everything coming out from the feds is moving us away from teacher instruction and an emphasis on knowledge and academic skills. Citing Singapore to mean inquiry learning is simply part of this very organized disinformation campaign.

Comment by Student of History — October 6, 2010 @ 11:47 am

Thanks to Paul Hoss for an interesting point. It is quite true that the culture in Asian countries is quite different regarding education. However, the reason why the Singapore Math program is effective is largely because of its presentation, sequence and word problems as discussed above. The disdain that Hoss describes has manifested itself in many of the ideas and fads of education which downplay the need for memorization and mastery of procedures. The idea of concept first, mastery of procedures later simply does not work. But the belief that the difference between Singapore Math and American math is just in the culture is a rationalization used to account for the success of Singapore’s program. There is an unstated belief that programs like Singapore’s and other similar programs cannot be imported because our culture won’t work to support its success–this said despite repeated successes with Singapore’s program in the U.S. Never considered is that the educational culture in those countries leads to practices held in disdain by this country. Schools in the US thus revert to the typical practices described in the Times and other articles. As I stated in my piece above, the Singapore program seems to thrive in spite of those who believe in overuse of manipulatives and reliance on open-ended problems and working in groups.

Comment by Barry Garelick — October 6, 2010 @ 1:01 pm

Having attended at least a dozen sessions by Dr. Yeap in the last few years, I believe that the trend in Singapore is heading the way of U.S. reform mathematics. I have copies of the primary materials currently in use in Singapore: My Pals Are Here and Shaping Maths, both dated 2007. The Teacher’s Guides and student textbooks are loaded with games to consolidate learning, base-10 blocks, counters, macaroni pieces, fraction strips, fraction disks, Singapore stamps, linking cubes, whatever you call them, they are all considered manipulatives. Singapore Math does rely on manipulatives as a first step in the development of mathematical concepts, but it’s the first step, with the ultimate step being the understanding and application of the abstract concept.

The Primary Mathematics materials that Barry refers to:

Those of us familiar with Singapore Math from having used it with our children are wondering just what program the article was describinghaven’t been in use in Singapore since 2001. It will be interesting to see how the changes in Singapore towards reform math affect the 2011 TIMSS scores. (http://www.iea.nl/timss2011.html)

Dr. Yeap on “Why Singapore Leads the World in Early Mathematics”

In the video, he describes spending weeks on a concept and purchasing balance scales in the U.S. at NCTM conferences.

Comment by Cassyt — October 6, 2010 @ 2:00 pm

I used Singapore Math with my children as a homeschooling parent, having first investigated its reputation for success. At the time it was still being imported from Singapore. The US distributor warned me that the great results seen in Singapore were directly attributable to after school math clubs where students were drilled in basic math facts, for speed and proficiency. That’s not something the proponents of Singapore Math seem to mention.

Comment by Janice — October 6, 2010 @ 4:53 pm

SOH,

Good points, all.

Your description above of the new direction in US teaching is the way I was conditioned to teach in the early seventies. At the time it was called the affective (social) and cognitive (academic) domains with an equal emphasis on both.

I believe this all originated back in the day from the NEA with their policy of the education of the “whole child.” It may sound sexy but I’m with you; it’s a de-emphasis on academics and that does not bode well for schools and our students. It’s also the way folks like Linda Darling-Hammond and many other P21 folks would like to see US schools operate. It’s also the reason the Stanford charter school in East Palo Alto, California was shuttered for chronically under performing since 2001.

And BTW, I’m still fuming about Massachusetts giving in to the new Common Core Standards to replace our best in the nation standards as well as ditching our MCAS tests. Not happy about this at all. How about; if ain’t broke don’t fix it. Anyone ever hear that one? Our clown governor and his campaign financing teacher union apparently have not.

We need a Singapore math summary here from Erin Johnson. She’s a big fan of the program and very knowledgeable about it as well. Just reading her revues on SM makes me wish it was around when I was still teaching. I would have used it.

Janice’s comment from above appears to substantiate my belief that at least some of SM’s success stems from the country’s value on education.

Comment by Paul Hoss — October 6, 2010 @ 7:13 pm

Barry raises an issue that I’ve begun to notice. It’s the co-opting or fuzzifying (?) of Singapore Math. Educational thought gobbles up everything in its path. Understanding and critical thinking? Gobbled up. Authentic education? Taken. You thought you knew Singapore Math, but just watch how it changes. Apparently, it’s now just right for the Common Core Standards. Core Knowledge better watch out. They might start talking about Common Core Knowledge Standards.

Details matter. Too often, educators talk in generalities to get people to go away. Then they can decide all of the details. Call it Singapore Math if you wish, as long as you don’t look at the details. Low expectations are low expectations, no matter what you call them. Before you start talking about the educational disdain of the US public, you better look closely at the educational disdain of US educators.

Comment by SteveH — October 6, 2010 @ 10:58 pm

Paul-

On ditching the MCAS, did you know both testing consortia have written commitments from most of their public colleges and universities agreeing that any student deemed “college and career ready” under Common Core will not be put in remedial classes.

Now if this really was a high academic threshold you wouldn’t need to get such commitments. They envision reworking math and science in college too. Everything is to be based on active learning.

I keep reading all these STEM reports and recognizing our ed spending is based on an assumption that we are moving away from a market economy to command and control where each citizen can “find rewarding work at a living wage”.

The culmination is the new science standards being drafted now. The definition of what constitutes “science” is rather ridiculous. They also talk a lot about research and you check the footnote and the cite on how students best learn science and math is to “Eyeballs in the Fridge”.

How on earth can we be planning to restructure education and schools throughout this country based on childhood memories of 76 practicing scientists and mathematicians of what prompted their interest?

Comment by Student of History — October 6, 2010 @ 11:00 pm

Also our friend LDH was on that NCATE panel. She has been very busy.

Comment by Student of History — October 6, 2010 @ 11:02 pm

Robert,

Probably doesn’t belong in this thread, but I thought you’d find this link interesting –a Russian woman compares the education she received with what her child in NYC is experiencing. She concludes that he’s working much more and learning much less, and that Russian ed is superior to American ed because of its national curriculum. She asks why we need to develop new ways of learning when the old ways worked well. Found this reading comments to a post on HuffPost praising Finland’s ed system.

http://underzodiacclock.com/2010/10/05/american-education-reform/

Comment by Ben F — October 7, 2010 @ 12:17 am

Paul, You are too kind. And if you have any free time, you might still appreciate the thoughtfulness and systematic progression embeded into the Singapore Math program. The program is fairly inexpensive and approachable.

While I would never discount the cultural support for excellence in education, Singapore Math (compared to either conventional or reform math) reshapes what we were all taught as mathematics into a conceptually integrated program that embraces the idealistic (but never obtained) notions of fuzzy math (TERC, Everyday Math, et al.) while explaining and providing the foundational support needed to understand every traditional algorithm that we were taught in school. Truly the best of both worlds.

In one sense, Singapore Math does for math what Prof. Hirsch did for reading comprehension; defined the fundamentals of learning into a comprehensible, understandable framework that is consistent and applicable with all children.

Anecdotally, my experience with Singapore Math is that it provides a seamless transition for students of all abilities from arithmetic (concrete calculations) to Algebra (abstract and generalized arthimetic) in ways that are unlike anything that I have seen with conventional or reform US mathematics. Considering that Algebra is considered a “gateway” course for students, that seamless transition would be something that we should all aspire our students to have.

Comment by Erin Johnson — October 7, 2010 @ 1:48 am

One issue that percolates through many of the comments is the following: Many factors contribute to student success besides the textbook — e.g., manipulatives, teaching, student effort, state accountability standards, social culture, etc. So how do we sort out the effect of the Singapore Math textbooks themselves?

As a first cut, let’s take all the rest of it as a given. Assume whatever you like about the other factors, and then consider the choice of Singapore Math rather than some other textbook (or no textbook). In nearly any setting, student success will be enhanced by the distinctive features of Singapore Math – i.e., the focus on essential math skills, exceptionally simple explanations, and the bar model method of solving multi-step word problems.

Next, let’s assume that the other factors reinforce the benefits of Singapore Math — e.g., appropriate manipulatives, skilled teaching, disciplined students, sensible state standards. Will students learn more? Of course. Conversely, the Singapore Math textbooks reinforce the benefits of all of the other positive factors.

Finally, let’s assume that the other factors work against Singapore Math: frivolous manipulatives, teaching that emphasizes engaging activities rather than student learning, state standards that waste huge amounts of instructional time on fluff, undisciplined students. Will students learn less? Of course. But even in this setting, students will learn more if they have some access to a textbook that offers a focus on essential math skills, exceptionally simple explanations, and the bar model method of solving multi-step word problems.

Comment by John Hoven — October 7, 2010 @ 9:42 am

[...] This post was mentioned on Twitter by USWorldClassMath, Carrie Schneider. Carrie Schneider said: Singapore Math Is “Our Dirty Little Secret” « The Core Knowledge Blog: The New York Times ran a story on September… http://bit.ly/cImWoP [...]

Pingback by Tweets that mention Singapore Math Is “Our Dirty Little Secret” « The Core Knowledge Blog, The Core Knowledge Blog -- Topsy.com — October 7, 2010 @ 10:55 am

The cautionary tale in the New York Times story is that Singapore Math, and Common Core, get bastardized if the teachers are not trained to used them the way there were intended. The fuzzy math curricula like Everyday Math, TERC Investigations have well developed training networks – which, I am sorry to say, propagate all sorts of romantic educational ideas about group and discovery learning in place of stressing academic subject matter.

Somewhere lost in this discussion is the fact that the bar method is .01% of Singapore Math, and manipulatives are .01%. You could already tell that Singapore Math was misconstrued when it was presented by advocates in terms of its Concrete to Pictorial to Abstract approach.

The secret sauce is in Singapore Math’s careful sequencing of the material. It starts with additions and subtractions of groups of objects; then with numerical additions and subtractions. Multiplication is eased in by single digit multiplication, followed by multiplication by tens, then multiplication of a double digit number by a single number, followed by that of two double digit numbers, and so on.

Every topic is carefully augmented by exercises in increasing level of logical difficulty. Without these exercises, students can’t master the theory. The exercises themselves at level N make use of all topics learned in level N-1 and earlier.

What is very apparent is that Singapore Math was written by mathematicians that went back and studied arithmetic and pulled out its essence. I don’t have to even see who wrote Singapore Math; the names of the authors don’t appear on the book; but I am sure they are mathematicians.

For comparison, I don’t think a single US elementary math textbook exists that was written from beginning to end by a mathematician. Save for Core Knowledge, whose math portion was written in part by David Klein, if I understand right.

I have gone to school in Romania back in the end of the 1970′s, beginning of the 1980′s. Romania, wouldn’t you know, has had its share of problems in education. But it had great math curricula, and it really had a tradition of strong elementary math education. You go today in Bucharest in any book store, and you find empty shelves in the department of Sociology, of History, Cultural Studies and what not. But you find great elementary math books. There’s shelf loads of them. Compare that to the nicely colored, poorly conceived, NCTM-approved math worksheet material you find at the local Barnes and Noble.

And here’s an interesting tidbit about Singapore Math. My Romanian textbooks looked eerily similar to those of Singapore Math. The sequencing was precisely the same in arithmetic.

Of course, the writers of Singapore Math had never seen the Romanian books; they both were probably inspired by a common source, which might have been earlier French or Russian elementary math textbooks.

My geometry sequencing was different, however, than that of Singapore math, as more emphasis was put beginning in 6th and 7th grade on the concept of mathematical proof. There was a discussion of angles and segments. The postulate of Euclid was discussed, and its implications. Then there was a discussion of the three congruence cases of triangles – side-angle-side, angle-side-angle, and side-side-side. This was all leading up to the 1st theorem: a triangle has two equal sides iff it has two equal angles.

The concept of mathematical proof was thus introduced early, and build on year after year, so that in 9th grade Geometry students were ready to prove things formally in terms of axioms. The side-angle-side, angle-side-angle, and side-side-side were thus rudiments of axioms introduced from the 6th grade.

I am also sure that the Russian and the French elementary math curricula also stress demonstrative geometry more than Singapore Math. But then again things may have changed since the 1970′s. French mathematicians today bitterly complain about the dumbed down elementary math textbooks in their country.

And here’s a cautionary tale: the French education system is as centralized as there ever was one. Yet Jean-Pierre Serre, Alain Connes, Laurent Lafforgue are bitterly struggling to have a say in the elementary math taught in french schools. Singapore also has stopped using the excellent curriculum that we’re lauding on this thread.

This debasing of elementary science education is a western civilization phenomenon, a cancer growing on old societies, regardless of their politics or of how decentralized they are.

Comment by andrei radulescu-banu — October 7, 2010 @ 11:21 am

Love the thoughts of the relative newcomers here, SteveH and JohnH. They are definitely on the same page of ed reform as many of the regular contributors.

While this blog could use some differing viewpoints from that of the CK hardcore advocates, it’s certainly refreshing to see some sane people talking about a number of these important issues. Some of the battles in other places on the education blogosphere are often difficult to stomach.

Comment by Paul Hoss — October 7, 2010 @ 12:20 pm

[...] program accurately. Barry Garelick of NYC HOLD answers the question on the Core Knowledge Blog: No way. (The Times) described a program that strangely sounded like the math programs being promoted by [...]

Pingback by The secret of Singapore Math — Joanne Jacobs — October 8, 2010 @ 8:17 am

[...] program accurately. Barry Garelick of NYC HOLD answers the question on the Core Knowledge Blog: No way. (The Times) described a program that strangely sounded like the math programs being promoted by [...]

Pingback by The secret of Singapore Math — Joanne Jacobs « Parents 4 democratic Schools — October 8, 2010 @ 9:50 am

When I read Mr. Garelick’s post, this piece sticks out the most:

“…when a school takes on such a program, it means going against what many teachers believe math education to be about; it is definitely not how they are trained in ed schools. [Programs like Singapore rely] in many ways on more traditional approaches to math education, such as explicit instruction and giving students many problems to solve, [and many math reformers have] worked hard to eliminate such techniques being used.”

I haven’t yet seen ‘Waiting For Superman’. From what I’ve read, though, it doesn’t sound as if the film (or any of the attendant ed buzz it’s unleashed), when it addresses America’s Bad Teacher Problem, focuses much (at all?) on ed training programs, which have, plainly, instilled legions of teachers with ineffective principles for the past century or so.

If effective ways of doing things exist–and examples like Singapore Math, CK, etc., are proving that they do–but are rejected by the institutions that prepare wave after wave of teachers, should we be surprised when we have a dearth of effective teachers and academic results that never seem to turn around?

Anyone up for making a documentary about the real reasons America’s schools are failing?

Comment by Eric Kalenze — October 8, 2010 @ 11:02 am

Being a French teacher involved in education problems, I just want to add a precision concerning the French system (reply to Andrei Radulescu-Banu ). If our children don’t succeed now, it is mainly because inefficient methods have been used since the last 50 years. I am speaking of constructivist methods like discovery learning, problem based and so on.

It is true that our system is centralized. There is a curriculum (defined in terms of contents) for each grade: what a children aged of … is supposed to know at the end of school year. It must be applied in all public schools. This is a rather good thing, but the fact is that our school inspectors (most of them) try to influence the teachers to use constructivist methods as the only truth possible. This leads to the results we know.

The mathematicians you are mentioning (Serre, Connes, Lafforgue) are certainly brilliant in their discipline, no doubt. But this is not the guarantee that they are also brilliant in pedagogy. Laurent Lafforgue belongs to an education trend which is very traditionalist and considers that a good teaching only relies on good content. He is not interested at all in teaching methods, nor in evidence based practices.

The same thing happened with G.Charpak, who was presented as a scientifical value when he imported in France his project Main à la pâte, which in fact is nothing else than a pure copy of the project Hands on created by the American L.Lederman (Nobel price in physics too); what I want to say is that being a Nobel price in any discipline is not necessarely synonym of being a Nobel price in Pedagogy.

We now know that all methods are not equal in terms of efficiency. I am convinced that with efficient methods like Explicit Teaching, the French curriculum in mathematics, science and language, could be reached for all children, even disadvantaged.

I cant finish without sending a “bonjour” to people from Core Knowledge who welcomed us to the national Conference in Washington DC in 2007.

Comment by Françoise Appy — October 9, 2010 @ 8:33 am

Bill Jackson, mentioned in the NYT article and in this post, wrote an excellent four-part exclusive series in the Daily Riff, “Singapore Math Demystified!” in March 2010 (series links displayed on home page of the Singapore Math link provided by the Times).

http://www.thedailyriff.com/2010/10/singapore-math-demystified-why-we-should.php

In addition, Jackson is also featured with his guest post series, a multi-part “Travel Journal to Singapore” about teacher training and professional development as it relates to Singapore Math.

http://www.thedailyriff.com/2010/10/the-five-key-features-at-singapore-chinese-girls-school.php

Quite surprised The New York Times did not provide a link to these which include extensive first-hand coverage of the topic by one of the featured teachers.

Comment by CJ — October 10, 2010 @ 5:25 pm

Thanks for the link to the Daily Riff articles. Interesting that Mr. Jackson credits the success of Singapore’s programs to the ideologies of US schools of education. Mr. Jackson describes a top performing school in Singapore called the Singapore Chinese Girls School (SCGS). He states:

“The SCGS consistently scores among the top schools in Singapore on the PSLE and O-Level exams – extremely high stakes tests that students take at the end of grades 6 and 10 respectively. The school seeks to develop both academic competency and character. Education at SGCS has five key features:

1) Infusion of character development and social-emotional learning into academic subjects

2) Teaching for enduring understanding using the Understanding by Design framework

3) Meaningful real-world application to contemporary issues

4) A constructivist approach to inquiry, knowledge creation and problem-solving

5) And differentiated instruction that takes into account students’ interests, readiness and learning styles.

Given Cassy T’s comment above, I wonder how much Singapore’s educational system copies the fads and trends of the US system, and how much the success of Singapore’s students owe to the curriculum–particularly the carefully sequenced lessons in Singapore’s math program. If Singapore schools were to follow the Understanding by Design framework, then following the lessons of a textbook would be viewed as a “sin”; in the world of UbD, the textbook is a resource and not a curriculum. People who have used Singapore Math’s books might tend to disagree with this. Also, the extent to which discovery or inquiry based learning is used would be interesting to document. Discovery learning can be quite effective if done right, emplying proper scaffolding techniques. Is that what’s going on, or do they follow the model of how it’s done by the proponents of UbD and Differentiated Instruction? (See http://www.educationnews.org/commentaries/book_reviews/99791.html )

Comment by Barry Garelick — October 11, 2010 @ 2:44 pm

Barry,

Bill Jackson responded to your comment over at The Daily Riff – fyi -

http://www.thedailyriff.com/2010/10/producing-some-of-the-best-math-teachers-in-the-world.php

He also did a series on teacher professional development in Japan before his Singapore series: http://www.thedailyriff.com/2010/09/what-american-teachers-can-learn-from-japan.php

Comment by CJ — October 12, 2010 @ 2:43 pm

Home Schooling…Singapore Math Is “Our Dirty Little Secret” ” The Core … is a very well written blog post on homeschooling methods I just found….

Trackback by Home Schooling — October 14, 2010 @ 12:20 pm

As a long-time Singapore Math educator and trainer, I have to disagree with a few points in this post. Overall, the post seems to be advocating a “traditional” approach to math, the same approach that has led to poor US performance in math and science in the last few decades and an epidemic of math phobia among American adults. This “traditional” approach has also led to one of the main reasons elementary math education suffers these days: too many educators had poor math education and don’t understand the concepts themselves, so they have no idea how to teach it to the children. They are afraid of the subject, so how can they be successful in teaching their students? If they were taught algorithms with no idea of the workings behind them, they cannot pass an understanding of the workings on to their students.

When I teach my workshops, one of the things I see is when I demonstrate one of the basic four operations on whole numbers – addition, subtraction, multiplication and division – with number disks on a place value chart, many of the participants have an “Aha!” moment. So that’s how it works, they realize. And once they have this understanding and practice it, teaching it to the students – and being able to be flexible enough in their approaches to reach all students – becomes a reachable goal.

This use of place value disks is an example of the concrete stage of concrete > pictorial > abstract that Singapore Math is based upon. The textbooks are full of diagrams that show the place value chart being used in this way, but those diagrams are meant to illustrate what the students have already done with the place value charts and disks, which then builds into understanding of the algorithm and how it works. And yes, this is part of the process of learning from conceptual understanding to algorithm built into the curriculum. Manipulatives can be very powerful, and I find them necessary for most students. There are always the few who will understand no matter what, but those are not the students we need to help.

I had used the textbooks and workbooks for a few years, even with training, without understanding this pedagogy, and was somewhat successful – just because I understand math myself. But when I became equipped with the deeper understandings mentioned above, I became a much better math teacher, able to differentiate and address different learning needs.

Regarding the model-drawing books, the cynical comment about them in this post is misplaced. Some teachers may use the steps for model drawing as a rote formula, but that’s not how they are intended. If you have never learned how to do model drawing, you need some kind of instruction, and the books teach that. Then after that stage, the steps are just there to remind you until they are internalized and personalized. Singapore teachers also use steps for their students, though they may vary by teacher.

I have taught several model-drawing workshops in which participants (mostly high school teachers) have said the most valuable part of the workshop for them was the step, “Write your answer statement first.” This is a sentence with a blank for the answer, reworded from the question in the problem. It serves the purpose of refocusing the student at the end of the problem when they need to find which of the many calculations they may have worked is actually the answer to the problem. The Singapore workbook problems are set up this way, but without instruction, children may miss out on this step. I know I did!

I agree that the purely constructivist math approaches leave a lot to be desired, but the idea that Singapore Math has no constructivist elements is incorrect. I think that if it is taught well, it strikes a good balance between constructivist and elementary knowledge in such a way that children can master the math knowledge they need to succeed – and I have seen this success in my own students over the years.

Comment by Susan Midlarsky — October 18, 2010 @ 10:28 am

Susan, thank you for your extensive comment. My post was critical of the New York Times’ article and others similar to it, which paint Singapore Math in a manner that suggests it relies very heavily on manipulatives, and open ended discussions. I don’t doubt that manipulatives are used in early grades as several other commenters have pointed out, but it moves very quickly to pictorial representations. Another commenter above, Andrei Radulescu-Banu has talked about this and other aspects of the Singapore program.

There have been many accusations made, like yours, that the traditional method of teaching math has failed to teach math properly with the result that many teachers cannot teach algorithms because they don’t understand the workings behind them. There are many different definitions of what people mean by “traditional” math, but if you mean in the last 20 years, I would venture to say that much math teaching has been influenced by the National Council of Teachers of Mathematics (NCTM) and their standards. It is fine to teach multiple ways to solve a problem, but what is also happening is that algorithms for addition, subtraction, multiplication and division are also taught in multiple ways, with the thought that such methods will teach the inner workings. The result has been much confusion not to mention that the “inner workings” of why the procedures work has not conveyed very well. A look at textbooks from the 40’s, 50’s and 60’s shows that the explanations given for the various algorithms were not at all inconsistent with how Singapore’s math texts present them. Procedural fluency has always been an important part of understanding. Singapore builds on this with a very coherent and well developed sequence of topics.

I believe bar modeling is a very efficient way to learn how to solve problems and Singapore’s textbooks link the concepts they have been teaching into the bar modeling techniques. They are an important part of the program but not the only part. I am glad to hear how you instruct teachers in using this technique but I am afraid there are others who are using it in rote fashion, so I stand by my comment.

I don’t disagree that discovery plays an important role in Singapore’s math programs, just as it has in traditional math. It is a matter of terminology. Singapore’s texts provide carefully scaffolded material. The sequence of topics and the gradation of problems is such that discovery occurs during the practice of problems. There are some who might think that working problems is “drill and kill” and that true “discovery” must be rooted in a problem-based approach. So if you mean that Singapore provides good guidance and scaffolding, I do not disagree with you. I do not believe that Singapore is taught in an approach in which students are immersed in what Carol Ann Tomlinson and Jay McTighe (two proponents of reform methods of education) call “contextualized grappling with ideas and processes”. This is an approach that I call “just in time” learning in which students are given an assignment or problem which forces them to learn what they need to know in order to complete the task. The tools that students need to master are dictated by the problem itself until it is actually needed. Reformers who advocate this approach point to it as a “direct instruction” as if to say “You see? We don’t always push constructivism!” They justify such approach by claiming that it does not burden the student’s mental inventory with “mind numbing” drills for mastery of a concept or skill until it is actually needed. In fact, Singapore does NOT use this approach, and they very carefully build the procedural fluency and skills that students will need to take on more challenging problems. In that sense, Singapore uses a traditional model.

If you have been reading this and saying “Yes, that’s what I mean” then fine. We both agree.

Comment by Barry Garelick — October 18, 2010 @ 11:50 am

For examples of the sort of traditional math Barry is talking about, and a sense of how it compares with Reform Math, see some of the math problem comparisons I post on my blog:

http://oilf.blogspot.com/2010/07/math-problems-of-week-6th-grade_15.html

http://oilf.blogspot.com/2010/06/math-problem-of-week-core-plus-math-vs.html

http://oilf.blogspot.com/2010/05/math-problem-of-week-core-plus-math-vs.html

http://oilf.blogspot.com/2010/05/math-problems-of-week-middle-school.html

http://oilf.blogspot.com/2010/05/math-problems-of-week-middle-school.html

Comment by Katharine Beals — October 19, 2010 @ 10:52 am

The bigger the number of available methods, the greater choice children, parents and teaches have. Different methods complement each other. I vote for variety of different methods and free choice by teachers and parents.

My favorite examples are:

http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html

http://www.aplusclick.com/map.htm

Comment by Igor Kokcharov — October 20, 2010 @ 5:07 pm

I was sent an interesting article with tables that I posted on my blog showing the difference in number of math topics covered per year in the US vs. A+ countries (including Singapore). With the number of topics we throw at our kids per year in the US, it’s amazing that any of it ever sinks in! http://zerosumruler.wordpress.com/2010/12/06/us-vs-a-countries-breadth-vs-depth-in-math-which-is-better/

Comment by Shana Donohue — December 6, 2010 @ 7:11 pm

I have been researching Singapore Math every since my son started this program this year in his elementary school. He is starting the program as a third grader and enjoys the methodology thus far. Thanks for the great insight you and the others have provided. http://singaporeapproachtomath.com

Comment by Melissa — March 18, 2011 @ 12:06 am

This posting about Singapore Math is really a distortion of the curriculum. It does not fly in the face of “reform” math as this author suggests. In fact, it implements all the best parts of mathematics reform. Any teacher from Singapore will tell you that the difference between reform math in the US and in Singapore is that they actually DO it. They use problem solving, communication, representations through modeling, etc. In fact, this curriculum is FAR from traditional. I think the problem is that “reform” in the US has come to be understood as synonymous with programs like “Everyday Math” – one of the WORST programs ever. Before we launch on a tirade about “reform vs. traditional” let’s make sure we understand what this really means.

Comment by Sally — June 11, 2011 @ 11:22 am

Singapore Math is similar in many respects to how math was taught in schools in the 50′s and 60′s, which most people view as “traditional” and mischaracterize it as rote learning. I grew up in that era and was taught problem solving and representation through modeling, though I believe Singapore presents more challenge and I like the structure better.

The reform approach includes much “investigation” into certain problems with little to no background in the procedures and concepts behind the problems. Students are put into small groups and are supposedly facilitated by the teacher to come up with insights into whatever investigation is on the books for the day. This sometimes amounts to a “just in time” learning situation in which students are given instruction in a procedure or concept necessary to solve the problem. The thinking is that by motivating the learning of such procedure and instruction, students are given a context for learning. Singapore (and older traditional texts) do this through carefully sequenced topics and careful scaffolding.

I would agree that carefully sequenced topica and careful scaffolding are good. There are good and bad ways to elicit discovery, and many of the reform methods (not including Everyday Math and Investigations which you mentioned) are very poor. I should add that the methods used in EM and Investigations are viewed as worthwhile by schools of education and others in the education establishment–spiralling, and small groups and student-centered inquiry based learning are still very much in vogue in many elementary schools.

I stand by my statements in the article.

Comment by Barry Garelick — August 11, 2011 @ 11:47 am

They have implemented SM in my son’s “gifted” class in NYC public school (most of the students scored above the 95th percentile in whatever test it is they administer). I think they used everyday math for kindergarten, but I think the teacher used a more traditional approach, which seemed to work fine for these students.

For what it’s worth, being Brooklyn, we have a fair number of Russian parents and they are very upset with SM thus far. To simplistic, childish, too slow for 1st graders. A repeat of what we did in kindergarten. I guess they had a different approach back home.

I’m not too thrilled as it seems he is re-doing what he did in kindergarten because they decided to move to SM for 1st grade. He’s doing simple addition now when at the end of last year he was doing simple multiplication and the basics of division (4 divided by 2, that sort of thing).

I’m wondering if this is really a program that is so great for so called gifted students who probably can learn pretty well under the “old” methods (which seemed to work just fine for me in the 70′s…my problem with math came when I took differential equations in college).

Comment by JH — October 13, 2011 @ 9:51 am

It seems that the approach being implemented in my son’s school is to teach a currciulum where every child in the class will get 100% on every test, rather than challenging the kids and have a potential lack of success with some kids/some areas.

Comment by JH — October 13, 2011 @ 9:56 am

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The problem we’ve encountered with singapore is that it jumps very quickly from one concept to another. I would prefer a variety of lessons that center around the same concept so students have the opportunity to practice. Only practice, hands on activities and consistency will help little ones to internalize and generalize complex math concepts.

Comment by barbcinque — February 20, 2012 @ 8:29 pm

I will have the responsibility of teaching common core standards to 8th grade students beginning this fall. I am the only high school math teacher in my small rural public school and now I have had 8th grade added to my list of responsibilities. We will be tested by both old and new standards next spring. Additionally, I have received no training for common core other than what initiative I have taken myself, (Algebra 1 for the 21st Century; 10 days, and An Introduction to Singapore Math; 1 day). I cannot remember how I was taught precisely in my upbringing. I missed lots of recess in my initial 2 years of Catholic being confined to doing “punishment papers” of my phonics drills, but I still have trouble with those Old Testament genealogies. I have vague recollections of doing work with “sets” in 7th or 8th grade, and am sure about the proof focus of Geometry in the 9th grade. I was fortunate to be taught Integration my senior year, which carried me to the 3rd quarter of Introductory Calculus at Ohio State University in 1970 before I encountered something new/confusing/challenging, and I suspect today that this had more to do with being instructed by a math grad student than the content itself. I have always said of my Trig and Calc teacher(an emphasis on proofs continued through these classes as well) that if you couldn’t learn math from him then you couldn’t learn math. He also taught 9th grade general math. I became a math teacher 4 years ago via a non-traditional route. I swear I was taught less and learned more 45 years ago. My students virtually refuse to draw pictures in Geometry. They want all math solutions to be as simple as “see the problem, say the answer”. This is just my tirade or diatribe, as you will, but nobody plays jazz without memorizing their scales and practicing them continually. In educational parlance I guess that’s procedural fluency. Either way there’s no music without it. “Just in time” may provide motivation, but it won’t provide mastery. To quote my students, “I’ve slept since then.” In the Singapore workshop I did find the bar model method to be a powerful tool for representing a problem. I wonder though, after reading this blog, whether instituting it at the 8th grade level will have much of the benefit it potentially offers.

Comment by Tom Rabe — July 13, 2012 @ 2:11 pm

It doesn’t really matter what you decide to label it this week, whether it’s “Singapore math” or “US math” or “Toy Jeebies math”. The fact is, most students learn very little genuine mathematics in class anyway and what little they do “learn” [in quote marks because they're not really learning anything, just manipulating rules aimlessly] cannot be put to any daily practical use.

For more, read Paul Lockhart’s “a mathematician’s lament”. Although I disagree with Paul on certain aspects [he emphasises the beauty of mathematics, I would not underestimate it's functionality], on the whole he presents the argument in compelling fashion. To summarize: children are not learning any real mathematics on any of these syllabuses, what they do learn cannot be useful to them in any way, AND [most importantly] they are not even taking away the very essence of mathematics. Which is to solve problems and think logically. Which ironically [in my opinion] is robbing the subject of providing any real utility [which would be MY emphasis in the first place].

Comment by Abdak — August 27, 2012 @ 4:17 pm

Hello, this is a nice blog. I wanted share my singapore math experince with you. you can read the whole story here: http://www.teachadvice.com/2012/10/singapore-math-experience.html

Comment by Teach Advice — October 30, 2012 @ 3:35 pm

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“Many problems to solve” is not at all my experience of Singapore math. Our school switched from Saxon to Singapore this year. I’ve seen the actual Singapore workbooks. My daughter went from solving 20 problems a night to solving 5-6, but taking a much harder, longer, visual, roundabout way of solving them. This decreased her recall of math facts (there is very little DRILLING in Singapore, so she has no mastery of the facts). Presumably it’s supposed to help number sense, but she already has SENSE – what she needs is to MASTER math facts and skills, and Singapore is absolutely not doing that for her the way Saxon did. She went from loving math for three years (it was her very best subject) to crying every night when she does her Singapore homework, because she has to take a problem that, had she learned it in an old school “American way,” she could have solved in five seconds, and now spend five minutes drawing ridiculous bar graphs and number bonds to arrive at the SAME answer. So much of the curriculum puts the cart before the horse – giving them division word problems before they’ve even drilled the kids in their times tables, expecting them to do algebra before they’ve taught them to divide properly and quickly. I’m starting to supplement at home with Saxon math so she won’t fall behind in her understanding of basic math facts and so she can solve the Singapore problems easier, but there’s hardly time when the math homework takes three times as long as it did under the old curriculum. The homework takes longer, but she is learning LESS. I know, because I see what my younger child is learning – and it’s way behind what my daughter was learning at the same age with the Saxon curriculum. Now, the youngest kids are also no longer learning to tell time to the minute or basic geometry or any of the many other things they were learning with Saxon in addition to the basic math facts.

We are not Asian. We come from a culture that values efficiency because we want more leisure time. Let’s recognize that and teach to our strengths. The result, if we do, is that we put in 1 hour of time to produce 2X while Asians put in 3 hours of time to produce 3X. Yes, they produce more, but we have three times the leisure hours while still having 2/3 of the product. It won’t destroy our ability to feed our families and innovate if we don’t beat the Asians at math. This crazed desire to rival the Asians in math is going to backfire on us.

Comment by ET — February 28, 2013 @ 5:13 pm

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