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Thoughts from NCTM session on Singapore Math + Technology

May 3, 2012 by 1 Comment

Last week I presented with Lauri Susi at the National Council of Teachers of Mathematics (NCTM) 2012 Annual Conference in Philadelphia.  Here was our session description:

470 – Technology + Singapore Strategies = Number Sense
Lead Speaker: Cassandra Turner
Co-Speaker: Lauri Susi

Visual reasoning is a powerful tool for making sense of mathematics. Learn successful visual strategies and instructional methods from Singapore that allow students to develop a deeper understanding of number concepts using hands-on manipulatives and software. Walk away with strategies for guiding students’ learning that you can use tomorrow.

We displayed the above image of lions on the screen while discussing the Concrete-Pictorial-Abstract progression of understanding. A teacher raised her hand and said something along the lines of:

I don’t like that picture. There are male lions and female lions, they aren’t the same. I can’t add them together and students get confused in upper grades when they think that these can be added.

Which is such a great comment. Why? Because this illustrates one of those interesting points that isn’t always in a student textbook and as the teacher you have to be aware of it : labels matter. Yet it isn’t so obvious at a kindergarten level.

2 male lions and 3 female lions make 5 lions altogether.

Well, they’re all lions and we’re looking at a part-whole understanding of addition. Here’s another image from the kindergarten book:

2 boys and 3 girls make 5 children.

2 daisies and 2 tulips make 4 flowers.

So how does this apply to later, more advanced concepts? Consider:

  • 2 ones and 3 ones make 5 ones.
  • 2 tens and 3 tens make 5 tens.
  • 2 tens and 3 ones make 23 ones.
  • 2 dimes and 3 pennies make 5 coins and they also make 23 cents.
  • 2/5 and 3/5 make 5/5
  • 2/5 and 3/4 make…hmmm, we need some common terminology here.

Thanks kindergarten and first grade teachers for laying this foundation!

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Quick thought from NCTM conference

May 1, 2012 by Leave a Comment

 

Tweet from the National Council of Teachers of Mathematics conference regarding a discussion of number lines.

Archived twitter conversations from last week’s conference can be found by searching #NCTM12 or #NCTM2012.

 

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NCTM 2012 Conference Singapore Math Sessions

March 29, 2012 by 1 Comment

If you’re like me, you’re already excitedly paging through the NCTM Conference program book, choosing which workshops and sessions to attend.  With over 700 sessions this year, planning your days can be quite a challenge.  If you’re  looking to check out some Singapore Math sessions, there’s good news and bad.

Good news? There are 11 sessions on Singapore Math this year and they are much more diverse than in the past. (Though the number of choices is down from the 14 offered last year)

Bad news? Anything listed below in pink is an overlapping session.  Below are my thoughts on which session to choose, if you have a conflict.

The best news! I’m presenting a  session on Friday, April 27 at 11 AM with Lauri Susi entitled, “Technology + Singapore Strategies = Number Sense.” (More on this below)

FYI – Four of the eleven sessions are Exhibitor’s Workshops:

Exhibitor Workshops (60 minutes) are set theatre style for at least 115 people. Exhibitors showcase their products and services away from the Exhibit Hall.

Thursday, April 26: 8:30 AM-9:30 AM – No conflict

EW – Differentiating Singapore Math Lessons with Yeap Ban Har
Exhibitor Workshop: Marshall Cavendish International

 Understand how Singapore Math is designed to provide learners, especially struggling ones, with adequate scaffold. Suitable for educators teaching Grades 2-7.

Thursday, April 26: 9:30 AM-10:30 AM – No conflict (but you’ll need to hustle from the Convention Center to the Marriott)

79 – Let’s Mix Drinks: Ratio in Japanese and Singapore Textbooks
Lead Speaker: William Jackson

The Common Core State Standards have students learn about unit rate and equivalent ratios in grade 6. See how to bring to these ideas to life using Asian textbooks, bar models, and lesson study.

Thursday, April 26 12:30 PM – 01:30 PM

166 – Using Primary School Classroom Computer Gaming for Number Sense
Lead Speaker: Ashish Amresh
Co-Speaker: Tricia Salerno

Enhancing classroom math using video games develops number sense. Involving gaming keeps students’ engagement and motivation high. The speakers created the games from Singapore Math, because of its alignment to the Common Core State Standards. They will demonstrate social media that promote students’ success further motivation. Designed for teachers working with grades preK – 2.

Thursday, April 26 1:00 PM – 02:30 PM

207 – Model Drawing for Challenging Word Problems, the Singapore Way
Lead Speaker: Anni Elizabeth Stipek

Come on a tour of how to successfully solve challenging word problems using model drawing. This revolutionary tool will help students understand word problems by first drawing a picture and eventually move to the equation. Designed for teachers working with grades 6 – 8.

196 – Singapore Math Strategies You Can Count On!
Lead Speaker: Char Forsten

 Come see specific Singapore Math strategies that will deepen and improve students’ number sense and problem solving skills. Learn practical, technology-friendly strategies that align with and support the Common Core Standards. Designed for teachers working with grades 3 – 5.

The first session will spotlight Rocket Solvers, a number sense app based on Singapore Math.  Both Anni Stipek and Char Forsten work for Staff Development for Educators. All three are knowledgeable presenters, so you won’t make a mistake if you  head to the grade strand that you teach.

Recommendations:

-> Need preK – 2 Number Sense ideas? Head to the first session.
-> If you’re  looking for grades 6 – 8 content, head to Model Drawing.
-> Seeking grades 3 – 5 CCSS aligned material? Head to Char’s session
*Personally, I’ll be attending this one: Using Students’ Misunderstanding to Deepen Teachers’ Understanding

Friday, April 27 11:00 AM – 012:00 PM No conflict – Woohoo! -This is a session I’m presenting with Lauri Susi.

470 – Technology + Singapore Strategies = Number Sense
Lead Speaker: Cassandra Turner
Co-Speaker: Lauri Susi

Visual reasoning is a powerful tool for making sense of mathematics. Learn successful visual strategies and instructional methods from Singapore that allow students to develop a deeper understanding of number concepts using hands-on manipulatives and software. Walk away with strategies for guiding students’ learning that you can use tomorrow.

Friday, April 27 1:00 PM – 02:00 PM

EW – Math Buddies – The Singapore Online Math Program for CCSS
Exhibitor Workshop: Marshall Cavendish International

Math Buddies adopts the same pedagogical principles of our Singapore mathematics textbooks and combines multimedia technologies and instructional strategies to make teaching and learning Math easier. Gain insight into its various components and how these can help you transition to CCSS and an effective online teaching and learning environment.

Friday, April 27 1:00 PM – 02:30 PM

509 – Singapore Math: Building Blocks to Learning Volume
Lead Speaker: Katherine de la Garza

Learn how to bring hands-on Singapore Math to life in your classroom. Use blocks to build solids, share your strategies, and then watch classroom footage of students to understand how this concrete-pictorial-abstract approach can deepen students’ understanding of volume and encourage inquiry. Hands-on session designed for teachers working with grades 3 – 5.

The first session is an Exhibitor Workshop, meaning that you can find more information about their company on the exhibit floor.

Recommendation:
-> Interested in Singapore Math in an online environment, go to the first session.
-> Looking for “use it tomorrow” ideas? Head to the volume session.
-> Leave early to get to the next session with Dr. Yeap. This one will fill up fast!

Friday, April 27 2:30 PM – 03:30 PM – No conflict

EW – Intervention Strategies with Singapore Math with Yeap Ban Har
Exhibitor Workshop: Marshall Cavendish International

How does Singapore schools deal with middle school students who struggle with mathematics? This session includes a discussion on how curriculum design and teaching strategies can help such students recover enough to be able to cope with mathematics at the secondary level. Suitable for educators teaching Grades 5 – 8

Friday, April 27 4:00 PM – 05:00 PM – No conflict

EW – Singapore Math Is for Middle School Too!
Exhibitor Workshop: SingaporeMath.com

The international success of Singaporean students has led many elementary schools to use Singapore Math® textbooks. But Singapore’s students also perform at the top of the world in middle school. Come see how new Singaporean textbooks, aligned to the Common Core State Standards,can help students learn mathematics in powerful and meaningful ways.

Saturday, April 28: 11:00 AM-12:00 PM – No conflict

688 – Intriguing Lessons about Teaching and Assessing Math around the World
Lead Speaker: Steven J. Leinwand

It’s really not an accident that countries like Singapore and Hong Kong significantly outperform the United States. Take a look at some of the features, instructional approaches, and assessment items that can guide our own efforts to improve U.S mathematics teaching and learning.

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Making math masters: A brief overview of Singapore Math®

March 16, 2012 by 10 Comments

My students love math class. In fact, many will tell you math is their favorite subject. Why? They’ll tell you it’s because Singapore math is fun. I’d say it’s because once they understand how math works, they become confident in their abilities. So what exactly is Singapore math?

Wait, math from Singapore? Isn’t that some little island in Asia?

Primary Mathematics is based on a program of study introduced by the Ministry of Education in Singapore in 1981, a time when Singapore’s students were middling in math. Fifteen years after the adoption of its new Primary Mathematics Syllabus, Singapore students led the world in global Math achievement tests (Singapore topped international rankings first in 1995, and again in 1999, 2003 and 2007).

The Singapore math success story—from mediocre to world-class in a generation—is no secret. The curriculum provides students with a solid foundation in mathematics by focusing on visual understanding, connections, number sense, mastery, and word problems.

Concepts in Singapore Math® are taught in a concrete – pictorial – abstract sequence

Hands-on manipulatives or real life objects are used to demonstrate the concept, then students use and create pictorial representations. This interim visual step is typically missing from many curricula used in the U.S. It provides a transition from the words to an abstract algorithm. The goal is always to use the concrete and visual components  to get to a standard algorithm.

To gain number sense, students are taught to make connections between topics. While first graders will still work on “fact families”, Singapore math also uses a pictorial representation called a “Number Bond” to help students see the connections between addition and subtraction.

Fact Families:                  Number Bonds:

Understanding numbers and operations is critical to mathematics

Singapore materials focus on place value to provide a deep knowledge of numbers. As students work with and manipulate numbers, they work towards fluency by learning and using mental math strategies.

For example:

“If I know that 7 and 3 make 10, I could solve the problem of 47 + 8 by breaking the number 8 apart into 3 and 5. Adding the 3 to 47 gives me 50, then I can easily add on 5.”

These mental math skills show flexible thinking and provide a “check” students use when the algorithm is learned. I was in a first-grade classroom last week where the teacher was talking about addition and subtraction strategies with her students. They were working with numbers like 9 + 5 and the teacher had asked the students how they got their answers:

“I counted on from 9”
“I took 5 apart to 1 and 4 and made a ten first”
“I used automaticity!”

To get to mastery, students work on focused concepts and skills. U.S. curricula are typically criticized for being “A mile wide and an inch deep”. Topics continually spiral and “It’s ok if kids don’t have their multiplication facts memorized this year, we’ll reteach them again next year.”

And next year and next year…

Not so with schools using Singapore Math®. In first grade, students will learn multiplication of twos and threes within 40. In second grade, they’ll master multiplication and division by 2,3,4,5 and 10. Each year builds on the prior foundation and extends student understanding. By the end of third-grade students will have mastered all of their multiplication tables as well as multiplying and dividing by a single digit. Yep, they will even become proficient with the dreaded “long division algorithm”.

Understanding problem solving

Another component of mastery is the ability to take what you already know and apply it in a new context. Remember being tortured in school with story problems? The heart of the Singapore curriculum is an emphasis on problem-solving — and that means word problems. They are incorporated throughout the materials to provide context to each topic as it’s taught. The key to solving these begins with a bar model or pictorial representation of the word problem. For instance:

1)  Ginny has 40 cherry and grape gumballs in all. She has 24 cherry gumballs. How many grape gumballs does she have?

gumballs (1)

 

2)  Ginny has 24 gumballs. She has 3 times as many gumballs as Paul does. How many gumballs does Paul have?

paul_and_ginny

3) 2/5 of the students in a class are boys and the rest are girls. There are 35 students in the class. How many boys are in the class?

students

4)  The ratio of the number of boys to girls in a class is 2:3. After 6 boys join the class, the ratio becomes 5:6. How many boys were in the class at first?

Students 2

 

This is a sixth-grade problem from a unit on changing ratios. Can you see the answer? Note that the number of girls doesn’t change.

1 unit = 6 boys

4 units = 24 boys

Mastering Math Makes Math Fun!

Singapore Math® is a great foundation for elementary math success. Working with teachers in their classrooms, I see the impact the materials have on students every day. Singapore math can help make every child in every classroom a competent and confident mathematics student.

 

Answers to Word Problems

1) Ginny has 16 grape gumballs

2) Paul has 8 gumballs

3) There are 14 boys in the class

4) There were 24 boys in the class at first

 

Bar Models generated from ThinkingBlocks.com

 

 

 

 

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In the news: Schools rave about Singapore math

March 15, 2012 by Leave a Comment

 

Some recent schools in the news:

Mansfield Township woman learns Singapore Math overseas

Director of the Lower School at Gill St. Bernard’s School in Peapack-Gladstone, New Jersey heads to Singapore to learn about Singapore Math.

*A word of caution for Ms. Campbell-Rush…after teaching Singapore math in an elementary classroom for several years, I visited Singapore in 2007 to learn about it from the source.  That experience rocked my career trajectory. I returned even more excited by the curriculum and embarked on a new career: championing Singapore Math and working with schools and teachers to adopt it effectively.

At Marymount of Santa Barbara, Math Is No Problem: Students excel with an engaging method that raises the bar on achievement

Marymount School finds the curriculum has a…

…profound impact on the mathematical abilities of its students.

Bland Elementary using Singapore math

Singapore Math is …

“…a strategy that helps kids break down multi-step word problems and makes it easier for them to do,” explained Diana Tibbs, Bland Elementary School principal. “I was skeptical at first, but now I’m very impressed.”

Madison’s New School Superintendent On Going To The Next Level And Why Less Is Sometimes More

Weston school piloting Singapore Math finds…

“Our biggest takeaway is the ‘less is more’ approach. The program goes to a level of depth so students understand they are not just plugging in numbers

What’s The Big Deal about Singapore Math?

Taking a look into what differentiates Singapore Math from other methods, and why parents are raving about it in the Philippines.

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