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

email jnd@math.umd.edu

The only really good K-6 math
textbooks in English are the Singapore Math textbooks, available at the
new website

http://www.singaporemath.com/Mathematics_s/1.htm

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."

(http://www.singaporemath.com/Essential_Parent_s_Guide_for_Primary_Math_p/pgpm.htm)

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

(http://ingenuityproject.org/comp_awards/press05152000.htm):

"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.