The following comments refer specifically to the Earlybird Kindergarten Series, Primary Mathematics Series and New Elementary Mathematics Series.

Mario Borelli - Notre Dame

Melody Hazelton - Marvin Elementary School

Leonard Zeplin - Yeshiva of Flatbush

John Hoven - Montgomery County


Prof. Mario Borelli - University of Notre Dame, Indiana - Year 2005.  On  New Elementary Mathematics

I have been involved in in-service (and a little pre-service) teacher training in Mathematics for a good many years of my professional life. I have used nationally produced materials such as SMSG, and many of the series produced by various publishers, such as the Dolciani series and others.
I had the opportunity last summer (2005) to conduct a one-month workshop for in-service math and science teachers in grades 7 and 8. A colleague in my department had alerted me to the existence of the Singapore New Elementary Math series; after having looked at two Junior High offerings, one from Wisconsin the other from Michigan, I decide to give the Singapore Math books a try.

I found them to be excellent! The US oriented version maintains a barely (and pleasantly) noticeable trace of its Asian origin (some names, some metric units), but what is truly exceptional over what is offered today in pre-college Mathematics is the fact that the student is trusted to be able to think and treated accordingly. There is enough challange to make students realize the value of correct reasoning, very little easy and boring repetition.

It seems to me that the creators of the series have the point of view that students will react to what is implicitly expected of them. Simple minded, rote and calculator-based presentations will produce students who are simple minded, learn only by rote, and cannot survive without calculators (I have a few in my University frashman classes!); Singapore Math books have outstanding collection of exercises which, while providing the necessary drill features, also constantly challange the students, make them think and explore.

The theory is presented concisely and with forceful clarity, reinforcing the notion that Mathematics is precision and inventiveness.

Of all the series of pre-college materials I have seen in my 30+ years of University teacher training activities, Singapore Math is by far the best, a very happy marriage of the old math textbooks (very high level and somewhat elitist) I used in my High School years in Italy and the more "relevancy" oriented tendencies in today's Math teaching. Anyone who cares about Math teaching should give this series very serious consideration. I recommend it enthusiastically.

Prof. Mario Borelli
Mathematics Department
116 HAYE
Notre Dame, IN 46556
Tel. 574.631.7334
Fax 574.631.6579

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Melody Hazelton - Marvin Elementary School, North Carolina - Year 2004.  On Primary Mathematics Series

Two years ago, Linda Bell, the director of AIG (Academically/Intellectually Gifted) services for Union County, gave me a copy of the fifth grade textbook and teacher's guide for the Singapore Primary Math series.  I didn't know at the time that it would be the single-most exciting and rewarding milestone in my professional development.

I was in my third year of teaching fourth and fifth grade mathematics and language arts to students in the AIG program at an elementary school in Union County.  Always enthusiastic about literature, I had no difficulty planning and teaching effectively in that content area.  However, the math curriculum used by the school was, in my opinion, mediocre at best.  The school used a fifth grade text to teach fourth grade students and a sixth grade text to teach fifth graders.  The presentation of concepts was unexciting and shallow and the problem-solving component sparse.  The difference between the fifth and sixth grade text was insignificant with little new material added from one grade level to the next.  Although I supplemented the curriculum with outside resources and used the textbook merely as a guide, I was still dissatisfied.  Looking for a curriculum that was deeper and more challenging, I picked up the Singapore materials and began to investigate them.

From the moment I opened the Singapore Primary Math book, I knew I had found something unique and exciting.  The presentation of concepts was clear and logically tiered as the lesson moved from concrete, pictorial, to abstract.  Each lesson progressed quickly from familiar material into more difficult and unfamiliar territory and challenged the students to think about math in a different way.  A poster in my classroom which quotes the famous mathematician, George Polya read, " It is better to solve one problem five different ways, than to solve five problems one way."  With multiple methods offered to explain the same concept, I knew that this adoption's philosophy was consistent with my own.  When I saw the challenging, multi-step word problems that concluded each unit, I had a sense that I was on the threshold of something great.

At the conclusion of my third year, I transferred to a newly built school in nearby Marvin.  Although it was a seemingly radical idea - adopting a math program from the island nation of Singapore - my principal agreed to purchase the Singapore Primary Math series as the sole curriculum for the AIG math students.  However, given Singapore's distinguished record in international mathematics competition, perhaps it was not such a risk-taking venture after all: In the late 1990s, the Third International Mathematics and Science Study, the most comprehensive study of student achievement ever undertaken, found United States' math students far behind those of the world leader - Singapore.

There are many articles and press releases regarding the accomplishments of Singapore's math students and the curriculum they use.  In "Looking East for Math Techniques." an article from The Washington Post, Nora Flood, director of Madison Country Day School in Wisconsin says, "I am familiar with almost every math program there is, and I really do believe in my heart of hearts it [Singapore Primary Math] is far and above any other textbook math program."  Having taught Singapore Primary Math for two years, I, too, have found it to be superior to other adoptions.  It is also a perfect fit for my gifted students.  Since each year is comprised of two books, one for each semester, Singapore Primary Math recommends that a class of average fourth grade students begins with the previous year's semester.  Starting gifted fourth graders with the 4A textbook, instead of 3B, and gifted fifth graders with 5A, instead of 4B, presents AIG students with material at an appropriate level of difficulty for them.  I find that for my fourth grade students (the grade level at which gifted services begin), and fifth graders who are new to the program, there is a definite adjustment period.  They soon find that many problems cannot be solved by applying a formula or an algorithm, but require a firm mathematical foundation and sound mathematical thinking.

Adopting the Singapore Primary Math series for Marvin's AIG program was a significant accomplishment in my growth as an educator.  Relying on research, press reports, and my own instincts, I undertook this adventure, wondering if I would succeed or fail.  Finding the teacher's guide radically different from our American adoptions, and being the first to implement it in the county, I was on my own to make it a success.  However, I found that even though I had no mentor to turn to for guidance or a teacher's guide to spell things out for me, the logical and sequential design of the program enabled each unit to unfold effortlessly.

Singapore Primary Math isn't a perfect curriculum.  The teacher's guide is not scripted, does not show a sample student page, and purposely serves only as a guide.  Tests must be teacher-made and when to test is the teacher's decision.  Some objectives required by the North Carolina Standard Course of Study are not included in the series, therefore, teachers must be aware of the NCSCOS objectives and supplement the text as needed.  However, these are small inconveniences compared with the fundamental strength and design of the program.

Incorporating fundamentally sound lessons, innovative activities, and difficult multi-step word problems, the Singapore Primary Math series has provided my gifted students with a well-rounded and relevant curriculum.  It has challenged them to become problem-solvers and mathematical thinkers.

Melody Hazelton, 
Academically/Intellectually Gifted Teacher, Marvin Elementary School
Waxhaw, NC 28173

Ms Hazelton is selected as Union County's Academically/Intellectually Gifted Teacher of the Year 2004.  She was also selected as a state finalist for the 2004 N.C. Outstanding Teacher of the Gifted Award.

Above published with permission from the author.

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Yeshivah of Flatbush, Brooklyn - Year 2003.   On Earlybird Kindergarten Series and Primary Mathematics Series

Singapore Math is a rigorous math curriculum that is noted for its high level of math achievement.  We have been piloting this innovative math program in the elementary school (K-5) for the past three years, and have noticed that this program is truly effective in making our students more intuitive in the math process.  Many parents have praised their children's successes using this approach.  This excellent program based on Singapore's Primary Mathematics books available in America, has been used in our school, the Yeshivah of Flatbush, in Brooklyn, New York.  It was first used in to classed on each grade from one through five.  It is now being used in kindergarten, all of first and second grade, and in two classes in each of the other grades.

We knew that our students could be more successful in their study of mathematics.  How could we get them to really love math and do well while finding it challenging, exciting and fun?  After looking into many programs, Singapore Math was our answer.

The primary focus of this program is teaching mental math.  Students solve most problems in their heads using logical steps and often do not need to use pencil and paper.  New concepts are introduced in a logical and sequential manner, simplifying the students' understanding and leading to a more conceptual thought process.

All basic skills are taught, but the methodology is very different from that of a mathematics text.  Mental math allows the children to think rather than memorize everything.  Connections are made between mathematical operations.  The students start to think logically.  Every student feels that they can be good at math.  With many solutions to one problem, many children are given the opportunity to share with other in the class.  Singapore Math enables the student to see relationships between what is being taught and mathematics already learned.  They see how to apply what they have learned to many different math problems.

The Singapore program has a concise text with many clear examples and illustrations.  The workbook has an abundance of examples, drill and problem solving.  There are other books available for review and enrichment.  The program is now available in American version which makes it even better.  This version includes customary measurement, American names, and American money.

Most of the program is taught with the use of manipulative materials.  The children love to find solutions with materials such as counters, clocks, fraction tiles, scales  and weights, place value blocks, and graphing materials.  Use of concrete materials makes learning of concepts easier and lots of fun.

In order to achieve the full benefits of this program, Singapore Math should be started as early as kindergarten.  Working with this math program, I have found that students are more capable of higher mathematical learning at a younger age than with other math programs that I have used.  Over time, my school has observed consistently higher scores on standardized tests for the students in this program.  I am confident that this program will help to build better mathematicians for our future.

 The parents and students have been impressed with the results and are enthusiastic about the mathematical maturity being achieved at such an early age.  Within a short time, it will be used in classes in grades kindergarten through five.

Leonard Zeplin
Principal - General Studies
Yeshivah of Flatbush

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John Hoven - Montgomery - Year 2002.  On Primary Mathematics Series

Important strengths of the Singapore Math textbooks are:
-- strikingly clear, simple explanations of math concepts
-- focus on important topics that prepare students for algebra and beyond
-- logical sequence of topics
-- an ingenious problem-solving strategy built into the curriculum

Clear, simple explanations (often cartoons) let students get started quickly on problems, so they have the problem-solving experience needed to acquire mastery of math skills and an understanding of the nuances of math concepts. Focus means that the books are blessedly free of low-priority "activities" like probability and the construction of bar graphs by hand. Logical sequence means that when 2nd and 3rd graders learn about money, they add and subtract numbers up to $10 (2nd grade) and $100 (3rd grade) in preparation for decimals in 4th grade.

The Singapore Math problem-solving strategy (the "model method") is a powerful device for solving 2-step problems, proportions, and problems that are so difficult a child doesn't quite know where to begin. Students who grow up with these books will waltz through the SAT math exam.

I would prefer to sacrifice some geometry in favor of more algebra in the upper elementary grades. (That's what I'm recommending for my school district, using Hands-On Equations in grades 3-5.)

The major shortcoming of Singapore Math is a universal failing of K-8 math texts: the failure to introduce the basic concepts of statistical 
inference. Fourth graders can rank numbers from largest to smallest, find the median and interquartile range, construct a box-and-whisker plot, and use that to begin to understand statistical error and hypothesis testing. Scatter plots can serve a similar purpose. With that foundation, middle schoolers can be introduced to standard deviation and 2-sigma confidence interals. These simple ideas don't have to wait for a college course in probability and statistics.

John Hoven, co-president
Gifted and Talented Association of Montgomery County, MD, Inc.
308 Penwood Road, Silver Spring, MD 20901
H301-593-1702 W202-307-5740

Above published with permission from the author.

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