Try Singapore Math Textbooks
Your students will learn Math
By Jerome Dancis, Ph.D. (math)
Associate Professor Emeritus
Math Dept, Univ of Maryland
College Park, MD 20742-4015
Math Education Website: www.math.umd.edu\~jnd
301 345 2973 (c) 301 448 8132
The only really good K-6 math textbooks in English are the Singapore Math textbooks, available at the new website
Warning, Grade 5 Singapore Math is comparable, but better than Grade 6 here.
Also it builds on Grade 4 Singapore Math, which builds on grade 3 Singapore Math.
Just noticed on the website, there are "Elementary Mathematics for Teachers" books, for use in conjunction with the Singapore Grades 3-6 Math Books, first half of each year only. (http://www.singaporemath.com/Elementary_Math_for_Teachers_Complete_Package_p/emftcp.htm) A Math professor friend taught a college class for future elementary school teachers from these books, last fall, and really liked them.
Just noticed on the website, there is "The Essential Parents' Guide to Primary Maths", written primarily for parents. "Parents can use this guide to learn and master various strategies to help their children solve challenging and non-routine mathematical problems encountered at the upper primary level."
Many Math professors, who have looked at the Singapore K-6 Math Books, are strong advocates of them because these books
1. Do an especially good job in training students in Basic Skills and
2. Do an especially good job in providing students with Conceptual Understanding and
3. Provide an especially good background in Arithmetic and Arithmetic word problems, for the learning of Algebraic calculations and for learning how to solve Algebraic word problems.
4. Do an especially good job in training students in non-trivial Arithmetic word problems; while American texts largely avoid non-trivial Arithmetic word problems.
Grade 5 or 6 students, trained in the Singapore math model-drawing approach to problems, will consider the following Tart and Triple Ratio Problems to be child's play.
Tart Problem. (From a 5th grade Singapore math textbook) "Mrs. Chen made some tarts. She sold 3/5 of them in the morning and 1/4 of the remainder in the afternoon. If she sold 200 more tarts in the morning than in the afternoon, how many tarts did she make?" [From http://www.cbmsweb.org/NationalSummit/Plenary_Speakers/ma.htm]
Triple Ratio Problem. Three boys, Juan, Seth and Jared shared a number of stamps in the ratio 3 : 5 : 7. If Seth received 45 stamps, how many more stamps did Jared receive than Juan?
[From page 25 of the U. S. Edition of the Singapore Primary Mathematics Workbook 5B (second term of Grade 5)]
Challenge: Try the Tart and Triple Ratio Problems on Grade 7 or 8 students.
5. The main guideline for American textbooks, is "the two-page spread"; each lesson is restricted to two pages, whether it is understandable or not, often it is not. The main guideline for Singapore Math Books is that they be understandable by students; there is no two page restriction.
6. American math textbooks have so many math errors, that the 1999 California Framework and Standards introduced a unique requirement: K-6 Math textbooks be free of math errors. This applies only to the California editions. Singapore math textbooks have few if any Math errors.
7. Being able to do Tart and Ratio Problem type problems is important for doing organized logical analysis in science and economics. Greatly increasing the percentage of Grade 5 students who can do this type of problem would be a worthy goal/challenge. And, it would enable middle school science teachers to considerably raise the level of arithmetic-based science lessons.
The Tart Problem, above is quite similar to the following Geese Problem. This Geese Problem was an SAT Math test problem; one that the SAT rated at the highest level of difficulty. [It was Question #25 of Section 4 of the May 2000 Math SAT; the SAT rated it as Level #5 on its scale of 1 to 5.] Students, trained on The Tart Problem in Grade 5, will consider This Geese Problem to be child's (Grade 5 level) play.
Geese Problem. (SAT Level 5) "A flock of geese on a pond were being observed continuously.
At 1:00 P.M., 1/5 of the geese flew away.
At 2:00 P.M., 1/8 of the geese that remained flew away.
At 3:00 P.M., 3 times as many geese as had flown away at 1:00 P.M. flew away,
leaving 28 geese on the pond.
At no other time did any geese arrive or fly away or die. How many geese were in the original flock?"
Singapore math textbooks provide teachers with a ready made coherent course/curriculum; it's one less important thing for a teacher to worry about.
The Singapore textbooks were written in English for Singapore children, for whom English is a second language.
John Hoven is a local expert on Singapore Math. He is giving presentations at MD schools.
John Hoven was co-president, Gifted and Talented Association of Montgomery County, MD
Three drawbacks of Singapore math textbooks:
(*) Currently, fully certified K-8 teachers, even those with "endorsements" as a "highly qualified" middle school math teacher, may not be required to know how to do the Tart and Triple Ratio Problems, above.
(^) This is ameliorated by the complete explanations in the textbooks themselves. The textbooks are written to be understandable by students, so they should also be understandable by teachers. (In contrast, in American textbooks, the not-always-complete explanations are split between the text and the teachers' manual). It is still wise to have serious staff development for the teachers.
(^) There is a college textbook, "Elementary Mathematics for Teachers", by Math professors Thomas Parker and Scott Baldridge, which is based on and provides instruction for teachers on the methods of Singapore math books. (Scott Baldridge is a friend of J. Dancis)
(^) There are "Elementary Mathematics for Teachers" books, for use in conjunction with the Singapore Grades 3-6 Math Books, first half of year only.
(*) There are no answer books. When Singapore books were handed to the teachers at one school, the first question was: Where are the answer books? When informed, that there were none, the teaches rolled their eyes, which was interpreted as "Then why are we even considering using these books?" Two years later, these teachers were all in favor of the books.
(*) Singapore math textbooks omit the superficial data analysis and probability required for MD state exams. Supplementary material for test prep could by written and provided to teachers.
Middle school math teachers are not required to know how to do (never mind how to teach) the Triple Ratio Problem, above. The No Child Left Behind Act (NCLB) requires that middle school math teachers be "highly qualified" in math. The Maryland State Department of Education chose the Praxis II middle school math content exam, as a criteria for its official "endorsement" as a "highly qualified" middle school math teacher.
Two of the twelve sample multiple-choice items, for the Praxis II "middle school math" content exam for teachers [on the Web at ftp://ftp.ets.org/pub/tandl/0069.pdf)] are ratio questions; both are simple ratio questions. Neither of these two sample questions requires calculations as sophisticated as required by the Triple Ratio Problem, above.
Excerpts from an Associated Press article, Date: Sun, 14 May 2000
"The curriculum believes in the students' abilities," [Professor of Mathematics, Yoram] Sagher said of books approved by Singapore's Ministry of Education. "One of the effects of these books on all teachers is that they are much more courageous about giving harder problems to students."
Singapore's eighth-graders ranked No. 1 in math among 41 nations tested by the Third International Mathematics and Science Study, released in 1996. American eighth-graders came in 28th.
The Singaporean textbooks - written in English, the language of instruction there - are lightweight paperbacks filled with sample problems and step-by-step explanations that help students understand not only how to use a formula, but why.
Felicity Ross, a math teacher at Baltimore's Robert Poole Middle School, said U.S. textbooks tend to jump from topic to topic without helping students understand the basic concepts that connect all math problems.
The Singaporean texts, with their multistep word problems and emphasis on logic, develop skills that help children solve all types of problems - even those they've never tried, she said. "They're more confident problem-solvers in general," she said. "I definitely think the textbooks have something to do with it."
From my friend, retired community college math professor Herb Gross:
This year I taught in-service math courses to over 80 kindergarten and prekindergarten teachers in New Bedford, MA. As part of the course each of the teachers was given a copy of the Singapore math books for first grade and kindergarten. I wanted the teachers to have these books because they came the closest to teaching basic arithmetic in a way that was similar to what I was teaching. The teachers were under no obligation to use the books nor were they required to examine and evaluate them. The books were simply a gift. Unsolicited, over 50 teachers sent me messages telling me how much they liked the books and how helpful they were. Several wanted permission to make copies and use them in place of the books the school district was using.
These were teachers who, for the most part, had been previously intimidated by math. Their average score on the pretest was 36% [the teachers were not well versed in mathematics]. Their posttest average was 70%. In fact, that's one reason they were in the course and why Mass Insight Education offers the program. The point is that most elementary school teachers are not comfortable with mathematics and as a result they tend to teach math in the same mechanical way in which they were taught (One of the teachers commented that prior to our course all of her mathematical knowledge was faith based).
The Singapore model drawings make it almost impossible for students not to grasp what a fraction means and how to understand the arithmetic of fractions.
When the material is not being presented well by the teacher, the Singapore texts lend themselves better to self-study than most other textbook series I've been shown.
End Herb Gross's comments.