## 4,000 Teachers, 100,000 Students: Celebrating 7 Years with BER

In 2008, I left teaching in the classroom to champion Singapore Mathematics and expand its reach to elementary schools and children everywhere. The following year, the Bureau of Education and Research (BER) gave me an amazing opportunity to pursue this goal by presenting Singapore Math workshops throughout North America.

Some attendees at my BER seminars came with prior knowledge about the Singapore curriculum, but a bigger number were being introduced to Math from Singapore for the first time.

At a Seattle workshop earlier this year, BER’s Mark Ita surprised me (and other attendees) by presenting me with a handsome plaque, which read, in part:

In Recognition of Your Distinguished Teaching and Your Outstanding Contribution to the Education Profession

#### 4,000 Teachers, 100,000 Students

The stats scribbled on a Post-It Note on the back of the plaque included some tangible data to support this statement:

• 165 Seminars
• 4,000 Teachers
• Over 100,000 Students

Cassy with BER’s Mark Ita

It is highly satisfying to know that I have impacted this number of teachers and students through my BER presentations. On the other hand, the National Center for Education Statistics reports that there are about 35.2 million Pre-K to Grade 8 students in the United States. Clearly, there is much more work to be done!

I am very grateful to BER for giving me the opportunity to present Singapore Math workshops on their behalf over the past seven years. Sincere thanks to Rich, Boyce, Mark, Nargis, Lisa and the entire travel logistics team, and the dozens of project managers who have provided encouragement and support along the way. Thank you so much!

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## Bar Model Solutions – by Students

After the post on Assessing Bar Model Solutions went up, Beth Curran sent a message: “We just did that problem!” She agreed to share some student work:

And when the students didn’t draw a model:

I see this as a comparison problem:

5 units -> 125 students
1 unit -> 125 ÷ 5 = 25
7 units for boys -> 7 x 25 = 175 boys in all

(That’s the Thinking Blocks Model Drawing tool that allows you to insert your own word problems and solve – or you can use the pre-made questions!)

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With performance-based standards and 21st-century skill sets teachers are asked to teach mathematics with an emphasis on problems solving and inquiry learning, but how?  The answer is simple, with anchor tasks, of course, BUT HOW?

I have attended several seminars and sessions that have done a great job of explaining what an anchor task is and how using anchor tasks can transform my instruction while meeting the needs of all learners. Few, however, have explained how to implement them into my daily lessons.  I have been told anchor tasks are right there in the materials, but I have yet to come across a section labeled, “Anchor Task.”

In a recent seminar, hosted by Dr. Yeap Ban Har, I finally got the explanation I had been searching for… I had been looking in the wrong place!  Anchor tasks are not found in the Primary Mathematics Teacher’s Guides, but rather in the textbooks.

Dr. Yeap described the evolution of the term on his Facebook page:

Basically, an Anchor Task is the concrete component of any lesson!

### How do I find an Anchor Task?

In Primary Mathematics 4A, Lesson 3.6c (Standards Edition) students will learn to interpret the fraction of a set as a whole number times a fraction.  The Teacher’s Guide leads teachers through an effective lesson where the teacher demonstrates how to find 1/3  of 24 using a couple of different methods.

I’ve included links to this same lesson in:

#### To approach this lesson with more of an emphasis on inquiry learning, look to the textbook.

To create an anchor task, I took the example at the top of the page, find 1/4 of 20, and rewrote it as a word problem.  Students worked in partner groups to solve the following: There are 20 M&Ms in a bag. Three friends each eat  1/4 of the bag of M&Ms.  How many M&Ms did they eat altogether? Students were asked to find multiple ways of solving the problem and were given 20 chips to use if needed. Because our school has several Math Teachers that teach multiple grades, we devised a lesson planning document. (<-Click for a copy if you’d like to use it to plan your lessons)

As students worked, I circulated around the room and quickly determined which students had mastered how to find  1/4 of 20, which students still needed support with this concept and which students were able to apply that concept to find  3/4 of 20.  Were they in the concrete, representational or abstract phase?

After about five minutes, I gathered the students to share their methods of solving the problem.   This is where my direct instruction came in.  As students shared their strategies, I organized their independent learning into three methods.

I anticipated their strategies in my planning document and during my direct instruction I was sure to include any methods not discovered by my students on their own.

Students were then given the task of applying their newly discovered knowledge to solve the problems from the textbook, with my support, if needed.
The lesson ended with a journal prompt that was closely related to the concept learned.

#### A well-designed anchor task will engage students in the concrete and representational phases of learning a new concept.

Students will make connections with prior knowledge, reason and think logically to apply what they know to solve a problem with a partner or small group.  All students will be given time to work in the concrete phase to develop and hone their conceptual understanding.   As students are ready, they will naturally explore the representational or abstract phases of learning and discover strategies, or methods, for solving the given problem.  Sharing methods also allows students to communicate mathematically to explain and defend their thinking and consolidate their learning.

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## New Resources, New Workshops

Over the last ten years, I’ve collected a lot of materials that I love to use in the classroom. Teachers are always asking for new ideas and games so I’ve created a new page: Favorite Printable Math Resources. Feel free to email your favorites to be included on this page!

2016 dates for my BER seminar, “How to Use the Best Strategies from Singapore Mathematics to Strengthen your Math Instruction” have just been released. Updated with March dates on 10/14/2015!

This overview of Singapore Math® strategies will put your students on the road to success with number sense, computation and problem solving. (Plus you a get a comprehensive resource handbook to take back to your classroom!)

Want to see Cassy, but a city near you is not on this list? If so, complete the form on the Bring Cassy to my School/Area page or send her an email.

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## On the Topic of Math Sprints and Anxiety

Reflecting on my time at the two national math educator’s meetings, one interesting dichotomy appeared over timed fact tests. On the one side was Jo Boaler stating that timed tests are the root of math anxiety. Pushback came from others, most notably Greg Tang and Scott Baldridge pointing out that kids are timed in real life. They are put under pressure in real life. Students should learn from these experiences, not freak out over them.

It’s a powerful discussion: How do we get kids from fluency (I can use strategies to solve 7 x 8) to automaticity (I just know 7 x 8)? Do we need to get them to automaticity? Do timed tests create math anxiety? Is there spelling test anxiety? Should the key anxiety word be “test”, not “math”?

This conversation appeared recently on twitter after someone posted the “How to Give a Math Sprint” pdf from this site:

Yep, I’d be worried if kids who couldn’t make connections were timed, too.

I’m a proponent of Math Sprints; thoughtfully structured timed tests designed to practice one skill. Sprints are not your typical timed test. Students compete against themselves to improve the number of problems completed in one minute. Then the sprints are thrown away, not recorded in a grade book. They are practice. Period. And just one way to practice math facts.

#### Do Sprints harm students or cause math anxiety?

Not when administered correctly. I work with a school for students with ADHD and learning disabilities. Initially, teachers there said things like, “I can’t time my kids, they are slow processors”. It turns out that students at this school LOVE sprints. They can always improve by at least one problem on the second sprint. With all the content flying at them, practicing facts is one thing they can do and feel successful with.

Allison Coates runs the non-profit Math Walk Institute that works with schools and students to build a bridge to Algebra.

In every school we’ve ever worked, nearly all students enjoy sprints. They don’t see them as tests if the teacher doesn’t present them as tests. They see them as another fun game they can play against themselves (or against the teacher). Practice makes permanent their knowledge, and students love knowing they have knowledge. Knowledge is power.

#### Are Sprints from Singapore?

Nope. Sprints were created by Dr. Yoram Sagher as a fluency program to work with any curriculum. I’ve considered them a way to compensate for differences between Singapore and the U.S. In Singapore, parents drill fact fluency while schools teach the conceptual understanding. It’s not unusual for a first grader in Singapore to know all their math facts. It’s the school’s job to then get the understanding of multiplication into such a student. Contrast that with the U.S., where it is less likely that parents practice math facts at home with their child. Few American programs include a fluency component, often farming it out to the web or an iPad app.

Scott Baldridge has a great blog post on sprints: Fluency without Equivocation. I suggest you read it now.

My favorite Sprint books are Differentiated Math Sprints as they offer two difficulty levels with the same answers.

Eureka Math Sprints are aligned to Eureka Math (referenced in Scott Baldridge’s post above).

Wondering about the emphasis on math facts? Read: Why Mental Arithmetic Counts: Brain Activation during Single Digit Arithmetic Predicts High School Math Scores

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