# Tag Archives: curriculum

## Comparing Singapore Math Materials: Textbooks

In Part 1, I shared some examples from the Teacher’s Guide from four sets of materials used in Singapore and the United States.

The materials are all from the third grade level:

1. Primary Mathematics U.S. Edition (2003)  from SingaporeMath.com
2. Primary Mathematics Standards Edition (2008)  from SingaporeMath.com
3. My Pals Are Here Maths (2007) obtained in Singapore from Marshall Cavendish Education
4. Shaping Maths (2007) obtained in Singapore from Marshall Cavendish Education

Following are the pages from each textbook unit on addition within 10,000  that introduces regrouping in the hundreds. As before, each thumbnail links to a full-sized file.

There are minimal differences between the U.S. and Standards editions. The Standards edition is in color and there are two additional prompts asking students to estimate their answer first, then check for reasonableness. The first example shows regrouping in the hundreds. Problems 1-5 ask students to recall addition with regrouping the ones or tens or hundreds.

U.S. Edition Textbook 3A:

Standards Edition Textbook 3A:

My Pals Are Here includes two pages of instruction, another page with directions to a game and a final page exploring regrouping in the hundreds. Problem 5b on page 29 is the only problem that demonstrates  regrouping in both the ones and hundreds places,  although students are only asked to find the missing ones value in one addend.

Note the example #2 on page 29 that spells out the concept in words  (5 hundreds + 8 hundreds). This is a great reminder of how teachers can model this concept in a classroom and is included in the Teacher’s Guide for Primary Math both U.S. and Standards editions ( 7 ones + 5 ones = 1 ten 2 ones).

My Pals Are Here Textbook 3A:

The Shaping Maths lesson is two pages of slightly more abstract description than My Pals Are Here. Place value disks are used instead of images of base-10 blocks.

Shaping Maths Coursebook 3A:

## Math Problem Comparison

Teachers often ask, “What’s the difference between (the textbook I’m using now) and Singapore Math textbooks?” While there are many answers, I’d like to direct you to a resource that has been pointing out some differences  for over a year.

Once a week, Lefty (as in left-brained) over at Out In Left Field posts assignment comparisons between either a traditional math program or Singapore Math and various reform math textbooks.

From the original post:

Math problems of the week: Reform Math vs. other math

We’ll pair up a specific assignment drawn from this set with a specific assignment drawn either from a traditional series like McGraw-Hill, or from the foreign series most popular in America: Singapore Math.
I’ll try to pick assignments that take place at approximately the same point in the school year.  For example, I might choose two assignments from the first few weeks of first grade, or from the last few weeks of second grade, or from approximately 2/3 of the way into third grade.

At the end of many posts are some thought provoking Extra Credit questions. Some examples:

• Which problem set involves more rote repetition of a given algorithm?
• Which problem set is more accessible to children with language impairments?
• Discuss how the two problem sets reflect the cultural and political differences between American and Singaporean societies.

Although many of the sample problems come from Singapore Math, there are also comparisons to traditional math books from the 1920s.

Enjoy!

## Grade 6 Word Problem Solutions

Earlier this month, I posted the following problem from a Nanyang Primary School 2007 Preliminary Examination I found at MissKoh.com:

A mixture, weighing 100 kg is made up of 2 chemicals A and B in the ratio of 7:3. When some volume of Chemical A evaporates, the content of Chemical A is reduced to 60% of the new mixture. What is the mass of the mixture now?

I thought I’d share how my son worked the problem:

He knew that if he multiplied 40% x 2.5, he’d get 100% so:

2.5 x 30 kg = 2.5 x 40%

75kg = 100%

I used a different drawing for “after” :

How did you solve the problem?

## Singapore Math Tests..from Singapore

MissKoh.com (The url is actually http://www.MissKoh.info) is a website supported by Singapore’s Straits Times. If you click on the academic year, then the grade level you are interested in, you will be brought to a page of mid-year and final semestral papers as well as a few continual assessment papers, all from top schools in Singapore. For example; select 2008 and Primary 6 and you are offered test papers for English, Chinese, Maths or Science from 5 schools. (You need to register for some of the schools)

Go back to the 2007 Academic year and find tests through the second year of Junior College. All assessments are scans from actual school papers, so expect some rough looking pdfs.

My 8th grader and I had a great time working our way through some challenging word problems on a test.  For your mathematical enjoyment, here’s one from the Nanyang Primary School 2007 Preliminary Examination:

A mixture, weighing 100 kg is made up of 2 chemicals A and B in the ratio of 7:3. When some volume of Chemical A evaporates, the content of Chemical A is reduced to 60% of the new mixture. What is the mass of the mixture now?

Misskoh.com is set up to create awareness for “The Straits Times School Pocket Money Fund” to help students from low income families who cannot even afford a proper meal during recess…

Most of the these students do not have extra revision materials to revise, so we hope you can help by sharing your printouts with them if you know of any such friends in school.

## Challenging Word Problems series discontinued

The Singapore Math series: Primary Mathematics Challenging Word Problem from EPB Pan Pacific is being discontinued. Get your copies while you still can! According to the publisher, these books are:

“Highly recommended for capable students as a source of interesting review and challenging word problems”

If you’ve ever used the books, you know what a loss this will be to future users. While the books may be relics compared to the current Singapore Syllabus, one can’t help wonder if the changes in the “Teach Less, Learn More” syllabus in Singapore haven’t contributed to the country’s ever so slight drop on the most recent TIMSS.

SingaporeMath.com may have most books in the series available through summer, although it sounds like Primary 3 is in short supply.

For your problem-solving enjoyment, here’s a sample from the end of the Primary 6 book – Challenging level:

Cindy had four times as many postcards as Annie. After Cindy gave 20% of her postcards to Jane and Annie gave 10% of her postcards to Jane, the number of Jane’s postcards increased by 75%. If Jane had 252 postcards in the end, how many postcards did Cindy have at first?

Have fun!

## Why Singapore is another model for teaching excellence

The Christian Science Monitor is running a series entitled “What Makes a Teacher Good?” that includes articles on teacher pay, teacher training, and lessons from international schools. An example of a strong international education system is highlighted in the article: Why Singapore is another model for teaching excellence that discusses the way Singapore ensures that their teachers are truly highly qualified. Three U.S. visitors to Singapore were interviewed. Steven Paine, the superintendent of West Virginia’s schools:

asked a Singapore official about the basis of their math curriculum, she cited a standards framework put out by the National Council of Teachers of Mathematics – in the United States. West Virginia’s curriculum takes guidance from the same source, Mr. Paine says. “So the question remains, why is it that they lead the world in student achievement? I think it’s because of their teacher quality,” he says.

While teacher quality is a part of the success that Singapore has experienced, curriculum is another large  part. The Singapore official may have cited the NCTM standards, however it’s clear that Singapore’s Ministry of Education has created a more refined framework document. The NCTM’s Principles and Standards for School Mathematics runs 402 pages for elementary and secondary while Singapore’s Ministry of Education can cover both primary and secondary in a concise, content-rich 82 pages.

From the NCTM online access for Principles and Standards:

From the MOE primary syllabus (Primary 1 is 1st grade):

As a teacher, which set of 1st grade standards would you prefer to follow?

## What’s the difference?

### Singapore Math U.S. v. Standards edition

When I was in Singapore two years ago, Marshall Cavendish unveiled the new primary Mathematics Standards edition materials and there were murmurs of concern throughout the room. The general consensus was that the books looked too big; they must have added so much material that the series will look just like any American curriculum. There are added pages and concepts. Schools and homeschooling families that have a choice (sorry California, no choice for you) will want to review the materials thoroughly before purchasing.

Let’s back up a bit. Why did Marshall Cavendish/SingaporeMath.com decide to create the Standards edition? From the SingaporeMath.com website:

Primary Mathematics Standards edition is an adaptation of Primary Mathematics to meet the Mathematics Contents Standards for California Public Schools, adopted by the California State Board of Education in 1997 for grades 1-5 as one of the approved textbooks. It is similar to the US edition but has some rearrangement of topics and some added units, primarily in probability and data analysis, negative number, and coordinate graphing.

A side-by-side comparison of the scope and sequence of the two curricula appears on the SingaporeMath.com website. Of note, there are Extra Practice books for both series as well as Teacher Guides. Home Instructor Guides are available for the U.S. edition and the following Standards edition levels: 1A, 1B, 2A, 2B, 3A and 3B. 4A will be available in the summer of 2009. The Standards edition has comprehensive tests books for each level. Although the distributors state that materials are not interchangeable between the editions, anyone willing to do a bit of work will find that the test books can be adapted to the U.S. materials. If you enjoy this overview and  would like to see one for another grade level, feel free to email me.

Prompted by a comment by Ali in VA, I took a look, book-by-book, at the 1st grade materials and found a few differences. Please do not make your decision on edition based on just the 1st grade materials. The curriculum is sequential, and spirals with mastery.  I would not, therefore, advise jumping between the two different editions.

Minor changes to the series include the numbering of units in the textbook and exercises in the workbook. I believe that it organizes the materials better for teachers. Added to each of  the textbooks are a glossary and index. Added to each workbook are 33 pages of Math at Home activities. Pictures have been used occasionally in place of clip art, a few names have been changed, color added, number bonds are now circles, not squares, etc. Starting with the unit Numbers to 40, the colors on the place value strips have been standardized. Ten strips are always pink, ones are blue. (You can purchase Place Value Strips or make your own from sentence strips.)

More important changes include the addition of concepts. The following concepts were added in the first grade textbooks with complementary additions for practice in the workbook exercises and reviews.

1A Units:

1. Position & Direction -lesson has been added to the unit on Ordinal Numbers.
2. Shapes –lesson has been added that focuses on vocabulary: flat, stack, roll, slide, corners, sides.
3. Capacity – three lessons on comparing and measuring in non-standard units.

1B Units:

1. Graphs – Lesson on tally charts and bar diagrams has been added.
2. Numbers to 40 – lesson on counting by 2’s.
3. Time – two lessons: Before & After & Estimating Time.
4. Numbers to 100 – one lesson on addition with the vertical algorithm, one with subtraction (without renaming).

Now, having gone though through all four books, literally page-by-page, I could ONLY find one page in the U.S. edition that was omitted from the Standards edition.

Additions and eliminations duly noted, here are a couple of quirky difference between the editions.

Two pages from the same exercise – U.S. edition on the left, Standards on the right.

And two pages from the textbook. U.S. edition on the left, Standards on the right.

Finally, it looks like school starts 2 hours later in the Standards edition. Again U.S. edition on the left, Standards on the right.