Delaware School District Succeeds Using Singapore Math

Saturday, March 12th, 2011


A Delaware school district has successfully implemented Singapore Math, raising enjoyment, understanding, and test scores. This article describes their success. Here is one example:

Mount Pleasant Elementary Principal Joyce Skrobot did not need to be convinced to add Singapore math to the curriculum. Her school piloted the program over the past four years in some second-grade classes, and, on state tests, they outperformed the classes that did not use the math, she said.

“It really establishes a strong foundation of math skills with a lot of repetition,” she said. “It’s a very concrete approach to teaching.”

The district plans to offer parent workshops to explain the differences in the Singapore approach, a key component of long-term success.

Core Knowledge vs. Singapore Math

Monday, October 18th, 2010


About two weeks ago, a post titled “Singapore Math Is ‘Our Dirty Little Secret’” appeared on the Core Knowledge blog. It criticized the New York Times article about Singapore Math that appeared on October 1. Apparently, the author believes that the poor state of math education in the US is due to what he calls “reform math.” This ignores an entire generation of math-phobic adults who learned math through “traditional” methods, and most likely instigated the reform movement due to their dissatisfaction with those methods.

While the curricula based purely on constructivist approaches have their limitations, the idea that Singapore Math is a traditional approach is mistaken. It’s better than traditional approaches.

Below are the comments I wrote on the blog:

As a long-time Singapore Math educator and trainer, I have to disagree with a few points in this post. Overall, it 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. Then after that, the steps are just there to remind you until they are internalized and personalized.

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.

The Daily Riff: Singapore Math Articles

Wednesday, October 13th, 2010


Bill Jackson, the Scarsdale Singapore Math coach who is making waves nationwide, wrote an interesting series for The Daily Riff. The first article lays out how he got interested in Singapore Math. Here is a quote from his experience working with Japanese math teachers:

When I began working with the Japanese teachers, I soon realized three important reasons why they were such good math teachers:

(1) They had a high level of math content knowledge. In fact, I felt that their first grade teachers knew more about math than I did as an 8th grade teacher!

(2) They used thin, lightweight paperback textbooks that were much more focused and coherent than our heavy hard cover books.

(3) They continually worked to improve their teaching throughout their careers by conducting lesson study.

The next article describes a lesson that uses problem solving and model drawing to bridge children’s thinking from concrete to pictorial to abstract. I really like the way he describes the differences in approach between Singaporean lessons and traditional American textbooks:

Problem solving and mathematical thinking are two big ideas behind Singapore math. To understand this better, let’s look at an example that many American elementary students struggle with, long division. As noted in part one of this blog, word problems are often the last thing on the page in U.S. mathematics textbooks. Often times teachers never even get to these problems or if they do, usually only the advanced students have the opportunity to tackle them while struggling students continue to practice procedures. The third grade Primary Mathematics textbook, however, introduces long division with a word problem. The description below is one way how the concept of long division might be introduced in Singapore math.

After a brief warm up with multiplication and division flash cards, the teacher introduces a problem by saying, “Our friend Meihua has some toy soldiers. She wants to put them equally in some tents.” (Note that no numbers are mentioned and there is no question asked yet.) The teacher then asks the students to try to imagine the situation and discuss what it means to put the soldiers in tents equally. Students share examples such as, “If she has 15 soldiers and 3 tents, she could put 5 soldiers in each tent,” and “If there were 10 soldiers and 5 tents she could put 2 soldiers in each tent.”

I highly recommend a visit to these articles; he has much of value to say about teaching math.

Comment: A Slower Approach to Math

Friday, October 8th, 2010


Following on from last Friday’s New York Times article, the NY Times blogs ran a brief follow-up article titled, “A Slower Approach to Math,” with the opportunity to add your own comments to it. There were some pretty interesting thoughts there, which inspired me to add the following comment:

As a teacher experienced in teaching Singapore Math and training other teachers to use it, I am constantly learning about the state of education around our country, especially in math.

I see Singapore Math has many strengths as a curriculum and approach, and more of these are being adopted into our schools, as well as into other curricula. The model drawing approach to problem solving, for example, is a powerful tool that is obvious when you know it, but takes a while to understand and apply.

Without adequate training and development, however, Singapore Math cannot be a panacea for schools that are failing to teach math well. Much more needs to happen there, from teaching the methods to making more time for math in the classroom, as others have noted.

But we are dealing with a double deficit: a generation of teachers who have been impacted by poor math teaching when they were growing up, so they feel inadequate in that area. Not everyone, of course, but those who are confident and able in math tend to be in the minority. How do we solve this problem?

In addition, I too had trouble recognizing the curriculum in the beginning of this article about Singapore Math. Maybe what the writer was referring to, in terms of “slowness,” was the time the curriculum spends on mastering the number bonds for each number. That is, knowing all the different numbers that can be used to make seven (5+2, 3+4, 6+1, 7+0) becomes a powerful tool later to be able to compose and decompose numbers at will, allowing strong mastery of math facts and the basis for number sense.

Finally, @Learningcoach, forgive me, but I found your video difficult to take. First of all, the ability to recall multiplication facts is a useful skill and should be practiced, but to make that a priority in first grade may do more harm than good. The boy in the video seemed stressed to me. To ensure success for everyone, even those who find memorizing math facts difficult, we need to take the stress out, or why will they even want to continue to learn math? Enough challenge to keep them at the edge of their comfort zone is important for learning, but not outright stress. And from what I understand, they do drills like that in Asian countries anyway, so I doubt we will get ahead of Singapore that way.

What will help us to rise up in the ranks is to combine the mathematical skills other countries have achieved with the unique assets of our country, the creative and independent thinking and innovation we prize so highly.

Math and Baseball

Friday, October 8th, 2010


Are you looking for ideas about how to engage students in math, or show them how it applies to the real world? Here is a fun one for sports lovers. John Roach at recently published an article called “The Math and Science of Baseball.” It outlines various ways in which math and science have been applied to the sport.

We all know about batting averages, but did you know scientists have analyzed everything from how likely it is that the best team will win with the current number of games vs. the ideal number of games per season, that mathematical models judging fielding ability have been created, and that statisticians have studied managerial style in relation to different types of teams?

Also, do you know which is faster, a head-first or a feet-first slide into base? Check out the article to find out – and maybe include some of these fascinating facts in your next math class!

NY Times on Singapore Math

Monday, October 4th, 2010


Last Friday, this New York times article about Singapore Math appeared. The premise of the beginning of the article is that by studying one number at a time slowly, students learn more thoroughly and therefore build a better mathematical foundation. This is true, even if it is an oversimplification of the curriculum.

Here is a quote from the article:

Principals and teachers say that slowing down the learning process gives students a solid math foundation upon which to build increasingly complex skills, and makes it less likely that they will forget and have to be retaught the same thing in later years.And with Singapore math, the pace can accelerate by fourth and fifth grades, putting children as much as a year ahead of students in other math programs as they grasp complex problems more quickly.

This is true, from what I have seen and heard from different teachers. Not only that, but the mental flexibility for problem solving can be much greater with Singapore Math, if it is taught correctly.

And here is one of the main reasons I recommend this program:

Singapore math’s added appeal is that it has largely skirted the math wars of recent decades over whether to teach traditional math or reform math. Indeed, Singapore math has often been described by educators and parents as a more balanced approach between the two, melding old-fashioned algorithms with visual representations and critical thinking.

So you don’t have to sacrifice any of the important aspects of teaching math if you adopt this method. It does require some training and/or learning in order to implement it well, though, because the curriculum books on their own don’t offer a thorough grounding in the theory and practice.

What are your thoughts about the article?

Pluses and Minuses of Singapore Math

Wednesday, September 29th, 2010


This homeschooling website has an article about Singapore Math that is short but informative. It tells a brief history of Singapore Math in the US, then goes into why it may or may not be the best choice for a homeschooling curriculum. Here is an extract from the article:

The curriculum uses a true spiral approach, a method that is used less successfully in the United States. In the spiral approach, the curriculum assumes prior mastery of the subject in the previous grade and so does not review basic processes but moves on to a higher level in each subject. If single digit addition is learned in grade one, then it will not be reviewed in grade two. Instead, double digit addition will be introduced and taught.In the United States, the student generally has a review of basic concepts each year before moving on to the next level of learning.

I think the article’s points are good, with the exception of the idea that all of the curriculum is consumable. With the textbooks, it is possible to reuse them (though as paperbacks, they can take a beating) and have the students copy their answers into math journals or separate pieces of paper.

Measuring Teacher Quality: Classroom Management vs. Content

Monday, September 27th, 2010


A New York Times Magazine article titled Building a Better Teacher appeared last March. It’s an excellent contribution to the debate about what makes a good teacher. As the article describes, it’s not enough to care a lot; there are many caring teachers who can’t get their students’ attention to teach them anything. Being a good teacher is not strongly correlated with the graduate schools they attend, their teacher test scores, or particular personality characteristics. None of these predicts teacher effectiveness well. Merit pay and high pay incentives, haven’t worked to improve teacher quality (or test scores) either.

In fact, it is so difficult to quantify what makes a good teacher that the latest strategy is to throw out all the “bad” ones and keep all the “good” ones. That comes from the notion that there is some sort of magic that can’t be taught that makes a good teacher.

But the article describes two major issues regarding teacher education. One is the lack of explicit classroom management instruction, something every teacher I have met bemoans about their teacher training program. Doug Lemov, who helped found Uncommon Schools, traveled around the country to observe and record the techniques master teachers would use to manage their classrooms. Rather than some kind of “magic” or innate genius, these were techniques the teachers were often conscious of implementing, but they were so good at them that they looked like magic. He compiled them into a taxonomy and implemented them in the Uncommon Schools training program. After going through this training, apparently even first year teachers demonstrated classroom management mastery.

I can testify to the importance of explicit teaching in this area. Unlike many teachers, it seems, I had the benefit of excellent mentorship by Charles Fischer, among others, at a private school at which I made special arrangements to do my student teaching. It was such a valuable experience, and I took away many new arts and skills to help survive even very difficult teaching environments.

The second major issue is to do with content area teaching. The article focuses on math, which doesn’t surprise me. A teacher can have excellent management skills and not have a strong grasp of the content areas he or she is teaching, and teacher tests aren’t enough to assess that. Deborah Loewenberg Ball started a research project to look at the specialized skills in teaching even elementary math, which include not only understanding how math works, but why certain misconceptions would lead to children’s mistakes.

She also developed a test for Mathematic Knowledge for Teachers, or M.K.T. Scores on this test did translate into predictions of effective teaching. However, the question of how to teach teachers so they do score well on this test remains. In my experience, this kind of critical thinking is an essential part of teaching and learning Singapore Math, and strong training in teaching this program can really help a teacher with the understanding they need to be an effective math teacher.

What are your thoughts?

Yet Another Private School Adopts Singapore Math

Sunday, September 26th, 2010


It’s a measure of what a difficult situation our US schools are in when the math program a school adopts makes the news. But that is exactly what is happening often now that our nation is recognizing how far behind we have fallen in math and science.

This article outlines the reasons this Chester, PA private school is adopting Singapore Math for their lower school. I have included it here in PDF form so I don’t lose the link when it is archived. The reasons are pretty solid reasons as to why any school should at least consider this program when looking to improve their math education.

Professional Development: What Do Teachers Really Need?

Monday, September 20th, 2010


My friend and esteemed colleague, Charles Fischer, brought to my attention the frightening lack of time and resources spent on professional development for teachers. His blog post relates a report from the National Staff Development Council and the Stanford Center for Opportunity Policy in Education to his own experience with professional development. Here is a quote from the report that I found pertinent:

Analysis of a broad range of studies indicates that the kind of sustained professional development that increases student learning requires between 49 and 100 hours of contact on a single professional development focus. However, the report notes that in most areas, teachers were receiving less than 8 hours of training on a given topic, and the average reported number of hours of professional development in the United States was only about 44 hours combined across all six topic areas.

Compare this to Singapore, where teachers receive a broad, consistent education to start, and each year receive about 100 hours of continuing professional development. Now one reason why they are succeeding where others are struggling becomes obvious.

I travel to different parts of the country to offer professional development to teachers. I have heard from many how much they enjoy learning what I have to offer, but they bemoan the lack of time they are given to absorb the new material in order to implement it. A rare few have enough time, immersion and follow-up, for instance if they are able to attend professional seminars over several days, to catch fire with new and better methods and use them in their teaching. But this requires money, often out of the teacher’s own pocket, and this is simply out of reach for the vast majority of teachers.

In his blog, Charles lists a number of short workshops he has attended that have had little or no impact on his teaching, while longer ones transformed his teaching for the better. I’m sure many teachers could come up with similar lists.

If we really do want education to improve in this country, then we need to invest more time and resources in educating not just the students, but the teachers as well.

Read Charles Fischer’s excellent blog post here.


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