NCTM Takeaways

The National Council of Teachers of Mathematics Annual Meeting and Exposition (NCTM) has ended and I wanted to share a few quick items regarding Singapore Math.

First off, Houghton Mifflin’s division Great Source premiered their new Singapore math series. Called Math in Focus, the textbooks are hardbound (and are heavy!) and the Teacher’s Editions appear quite comprehensive. This series looks like an American textbook series. I chatted with Patsy Kanter, one of the authors, as well as Shar Hammet, the head of the mathematics division for Houghton Mifflin, and they feel that they’ve kept the true essence of the curriculum while adding value to a classroom teacher.  I hope to procure a grade level to review and share. At each grade level, the series includes:

• Student Book A and Student Book B
• Workbook A and Workbook B
• Teacher’s Edition
• Extra Practice (Blackline Masters)
• Assessment (Blackline Masters)
• Reteach (Blackline Masters)
• Enrichment (Blackline Masters)
• Manipulatives

You can download a sample lesson from the first grade.

Next:

The Singapore Model Method for Learning Mathematics was available from the Marshall Cavendish booth and will be available next month from Singaporemath.com. Written by the Ministry of Education, this book ( or monograph, as they refer to the publication) is designed to serve as a resource book on the Model Method:

The main purpose is to make explicit how the Model Method is used to develop students’ understanding of fundamental mathematics concepts and proficiency in solving basic mathematics word problems.

Although I’ve just begun reading the book, it appears to be a comprehensive overview of the Model Method and provides examples for both basic and quite challenging word problems.

The table of contents (click to enlarge):

And a sample page 77 from Appendix A:

Finally, there were 4 presentations on Singapore Math at the NCTM:

• Singapore Math Sixth Graders Solve Harder Problems than the Eighth-Grade NAEP by John Hoven
  
• Every Child Counts, and Every Child Can Count! Strategies from Singapore Classrooms by Ban Har Yeap
• Taking the Problem out of Word Problems with Singapore’s Model-Drawing Approach by Char Forsten
• What’s so Good About Singapore Math – An exhibitor workshop by SingaporeMath.com

ALL four Singapore Math sessions were oversubscribed, with disappointed attendees listening outside at the door. Dr. Yeap’s session saw people lining up 40 minutes beforehand to get a seat!

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!

(Cross-posted at Kitchen Table Math – The Sequel)

Grade 4 Word Problem

An interesting word problem was recently posted at the SingaporeMath Yahoo group. The original poster wrote for help solving it without algebra and mentioned that it was from the Primary 4 books. This seems a little advanced compared to the problems in the text and workbooks. I believe the problem could be from the Challenging Word problems series, which provides answers only.

There are 285 teachers and students in the hall. 5/6 of the students and 1/3 of the teachers went out of the hall. There is an equal number of students and teachers left in the hall. How many teachers were there in the hall at first?

If 5/6 of the students and 1/3 of the teachers went out, there would be 1/6 of the students and 2/3 of the teachers left in the hall.

Begin with the end result:

2/3 of the amount of teachers is equal to 1/6 of the amount of students. For every unit of students, there are 2 units of teachers.

Then let’s work back to how many there were at first:

There are 285 people divided into 15 units.
285 ÷ 15 = 19 people per unit.

There were 3 units of 19, or 57 teachers in the hall at first.

Then, to check out work, let’s find out how many students there were at first.
12 units x 19 people in each = 228 students

228 students + 57 teachers = 285 teachers and students were in the hall at first.

How can you extend the problem?

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?

Singapore: Crossroads of the East

A break from Singapore math for…Singapore history:

This 1938 documentary comes from The Travel Film Archive (via  IZ Reloaded). The video…

…gives us a tour of the British colony of Singapore in 1938. It was filmed by Andre de la Varre who in the early 1930’s, went out on his own as “The Screen Traveler” and made theatrical shorts for independent release as well as for many of the major Hollywood Studios.

I originally found the video from a tweet by mySingapore which bills itself as “your one stop community site for everything Singapore.” If you are interested in developing a Professional Learning Network, Twitter is a great place to start – you never know what you’ll learn.

Enjoy!

You can follow me: Cassyt.

(Cross-posted at Math in Singapore 2009)

April is Math Awareness Month

Sponsored by the American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics, the theme for April’s Math Awareness Month is Mathematics and Climate.  From the press release:

One of the most important challenges of our time is modeling global climate. Some of the fundamental questions researchers are currently addressing are:

• How long will the summer Arctic sea ice pack survive?
• Are hurricanes and other severe weather events getting stronger?
• How much will sea level rise as ice sheets melt?
• How do human activities affect climate change?
• How is global climate monitored?

You can write to the AMS for a free copy of the poster below or download it direct from their site. Looking for inspiration for the classroom? The site also has a list of activities and events happening around the country as well as a place for you to submit your own.

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 1^st 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.

Personal Whiteboards

In the post about Number Strings, I referred to a student’s “personal whiteboard”.  I use whiteboards throughout the day as a way of informally assessing students.

Instead of a store bought whiteboard, I prefer to provide students with a customized version.

1. Start with a glossy page protector, a box of which which can be purchased inexpensively on eBay or at Sam’s Club or Costco.
2. Insert a brightly colored sheet of card stock. Card stock makes the whiteboard a little sturdier and by using color on one side, I can instantly tell when the entire group of students is ready.
3. Add appropriate pages. In the first grade, I might have a pre-made number bond page ready to go. When I’m teaching a lesson on adding or subtracting, I’ll insert a place value chart.

By keeping a classroom set of these on the shelf with the student textbooks, they would last an entire school year. Here are some printables to get you started:

• Number Bond
  
• Ones/Tens Place Value Chart
• Ones/Tens/Hundres Place Value Chart
• Isometric dot paper
• 1 or 4 Quadrant Graph Paper

You can find information on Alexandria Jones’ Pharaoh’s Treasure in the picture at Let’s Play Math.

These are also great for games and learning centers…

Sudoku, Kenken, Contig or

The Hex game:

Or any of the international logic games on the handouts page of this site.

Pi Day Songs

Only 3 more shopping days until Pi day.

In case you were seeking some music for your celebration:

Happy Pi Day

Happy Pi day to you,
Happy Pi day to you,
Happy Pi day everybody,
Happy Pi day to you.

(to the tune of “Happy Birthday”)

And there are more at this Pi day website. Be sure to check out all the mathematics and science songs at Greg Crowther’s site.

You missed the shipping date this year, but who says there’s a “season” for Pi shirts and aprons?

(Image via flickr user myklroventine)

Number Strings as a Math Warm-Up…

…or cool down, or any time a teacher wants to get students working mental math.

Number strings are short mental math activities designed so that students work several calculations in their head then provide the answer in chorus, either verbally, with whiteboards, fingers or pencil and paper. Have students write their answer on their personal whiteboard and place it upside down on their desks. (To avoid excessive drawing, remind students that you want to hear their marker “click”.)

When directed, students will show their answer to the teacher, who immediately checks for comprehension and enthusiastically provides an answer to each student (“I challenge your answer” or “Yes!”).

In addition to providing a teacher with instant formative assessment, number strings offer the opportunity to integrate mathematics throughout the curriculum. Use the following samples or write your own!

First Grade:

Begin with the number of legs on a cat. (4)
Add the number of wheels on a bicycle (4 + 2 = 6)
Subtract the number of teachers in the classroom right now (6 – ?)

When I say: “Show me the answer”, I want you to raise the same number of fingers in the air as your answer.

“Are you ready?  Show me the answer!”

Second Grade:

Start with the number of halves in a whole. (2)
Triple that number. (2 x 3 = 6)
Add the number of sides on a rectangle (6 + 4 = 10)

Write your answer on your whiteboard and flip it upside down. Hold it high over your head when I say: “Show me the answer!”

Third Grade:

Begin with the number of legs on an ant. (6)
Multiply by the number of legs on a spider. (6 x 8 = 48)
Divide by the number of legs on a human. (48 ÷ 2 = 24)
Subtract the number of legs on a horse. (24 – 4 = 20)

Sixth Grade:

Begin with the number of days in a leap year. (366)
Subtract the number of months in a year. (366 – 12 = 354)
Subtract the number of days in May. (354 – 30 = 324)
Add the number of days in a week. (324 + 7 = 331)