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.

## Giving Thanks – Reflecting on An Outstanding 2015

I don’t know about you, but 2015 has come and gone in a flash. Exciting things are happening here in 2016 as this company grows and adds some fabulous training and coaching consultants. But you’ll have to wait to hear about 2016…

First, it’s important to take stock and reflect on the past year, both personally and professionally. (Past Giving Thanks reflections are here: 20142013, 2012 and 2011)

As I enter my ninth year as a Singapore Math® trainer, consultant, and coach, I am still humbled by the wonderful opportunities that continue to come my way.

I say this every year, but it continues to be true: I am so grateful to champion elementary math education and spend time in classrooms with teachers and students.  I extend my heartfelt thanks to everyone who has played a part in making the year so special.

2015 has been my year busiest ever. I’ve spent more than 35 weeks traveling across North American (and to England!) to work with schools and present seminars. I love to travel, especially when the end result is helping teachers making more competent and confident math students. (I could do without the bedbugs, though.)

#### 2015 Highlights

Again this year, more schools were repeat and long-term clients where my role was that of an advisor and instructional coach.  That said, I really loved visiting and working with teachers at 20 schools for the first time. Best of all: schools I’m working with are achieving remarkable results, even on the new Common Core-aligned testing.

Highlights from 2015 include:

Meeting my personal “continuing education” goals by attending:

#### Special Thanks

My sincere thanks to administrators, teachers and support staff at all of the schools I worked with in 2015. I so appreciate your trust and confidence. My sincere thanks, too, to several other long-time partners and supporters:

#### Singapore Math Source

Now in its eighth year, SingaporeMathSource.com continues to be an authoritative resource for those seeking information about the curriculum. This year, we added many printable games and activities for teachers to use in the classroom. Bookmark the page: Favorite Printable Math Resources as we’re adding materials all the time.

Maybe not the best photo of me, but mom looks good!

#### Personal

2015 has been personally gratifying as:

• We spent two weeks visiting my mother, who lives in Diani Beach, Kenya.
• I once again surpassed my goal of reading 50 books in the year, by reading 62 books!
• I continue to serve on the Board of the Middle School Math Institute, a non-profit dedicated to helping students succeed at algebra.

2016 promises to be even more busy and exciting. I’m looking forward to:

Once again, my sincerest thanks to clients, colleagues, and partners for making 2015 such a wonderful year. If I may be of service at any time, don’t hesitate to get in touch with me.

As passionate as ever about Singapore Mathematics.

-Cassy

## 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

## Our Journey to Singapore: A Singapore Math Adoption Success Story

Beth Curran

For some time, I’ve wanted to share stories of schools that have successfully implemented a Singapore Math curriculum.

To present the first such case study, I asked my colleague Beth Curran to summarize the adoption process at St. Anne’s-Belfield School, an independent Pre-K to 12 school in Charlottesville, Virginia.

#### Our Journey to Singapore

by Beth Curran
Preschool – 6th Grade Math Department Chair, St. Anne’s-Belfield School
Singapore Math Teacher and Trainer

It all began with a strategic plan.  In 2011, St. Anne’s-Belfield School released its 2011-2016 Strategic Plan.  The first of six goals focused on teaching and learning in the 21st century.  Key elements to this goal included teaching with depth rather than breadth, teaching critical thinking and problem-solving skills, improving the quality of our computation, and ensuring that our pedagogy reflects researched based best practices.  The Action Plan that followed gave direct mention to Singapore Math as a curriculum to explore.

While teachers felt strongly that the students were leaving our Lower School (grades Kindergarten through four) very well prepared for Middle School (grades five through eight), we had to ask a tough question; could we be doing better?

#### Why Singapore Math?

As the Lower School Math Coordinator at the time, I was charged with taking a critical look at the Lower School’s current math curriculum and learning all I could about Singapore Math.  The more I learned, the more I was convinced that Singapore Math would be a great match for us.  It was almost as if the Strategic Plan was written with Singapore Math in mind.  The curriculum teaches concepts to mastery, focusing on depth rather than breadth.  Critical thinking and problem-solving are embedded within the curriculum, not taught as a stand-alone unit.  Concepts are introduced, practiced, and applied immediately to solve problems.  Computation and numeracy are also a major focus.  Check, check, and check!

Learning Village at St. Anne’s-Belfield School

Not all of the homeroom teachers were as enthusiastic as I was.  It was a daunting task convincing them that learning a new math curriculum, on the tails of learning a new writing curriculum, was a good thing.  St. Anne’s-Belfield’s Head of School, being the visionary that he is, saw an opportunity to not only implement a new math curriculum, but to change the way math instruction is delivered at the Lower School level.  If we were going to ask our teachers to become Singapore Math specialists, why not hire and train dedicated math teachers?  And that’s just what he did.  Four math teachers were hired to deliver math instruction and these dedicated math specialists would co-teach math with the homeroom teacher taking on a supporting role.  This had an added benefit of cutting our student to teacher ratio in half during math class.

With the faculty in place and the Primary Mathematics materials ordered, we set out to train our dedicated math teachers in Kindergarten through sixth grade.  We contracted with Cassy Turner, Singapore Math Specialist and Trainer to work with our math teachers for an intensive one-week boot camp.  We learned the ins and outs of mental math and the bar model.  We asked questions, practiced, collaborated, practiced, designed an implementation schedule, and practiced.  Cassy’s enthusiasm and extensive knowledge left us feeling confident to tackle the upcoming year.  We knew professional development was crucial to a successful implementation and with that in mind we continued our relationship with Cassy throughout the year.  She made three more trips to the school, observing and teaching lessons and providing her guidance to keep us on track.

#### Successes and Challenges

Fast forward to today.  We are now a year and a half into our implementation. Our students are stronger problem-solvers than ever before.  Their computational skills have shown marked improvement.  Their overall sense of number and place value has increased.  Our students are confident and persevere through challenging problems.

We have done a lot of things really well.  We understood and placed value on professional development.  This is not a curriculum that can be picked up and taught from the Teacher’s Guides.  Most teachers did not learn math the way that a Singapore Math curriculum is taught.  Training is key.  If not trained, teachers will revert to teaching math the way they learned it.  Having a successful plan for ongoing professional development is critical to a successful implementation.

We put value on mathematics instruction at the Lower School level.  We saw the need for math specialists and took a huge financial risk to improve our instruction.

We implemented the curriculum in Kindergarten through sixth grade.  We felt so strongly about the benefits of the curriculum that we knew that even one or two years of exposure would be better than none.  This has been one of the most challenging hurdles of our implementation.  We worked with Cassy to anticipate and develop a plan for “back-teaching” missing skills.   In grades three through six, this plan guided us through our first year and fortunately, Kindergarteners through second grade students benefited from needing very minimal “back-teaching.”  Developing a relationship with a knowledgeable Singapore Math consultant is crucial.

If there was an area for improvement, it was parent communication and education.  We hosted a parent night early into the school year to give parents an overview of the curriculum and a brief introduction to some of the components that are unique to Singapore Math.  That wasn’t enough.  Parents didn’t learn math the way their children were now learning it. The focus of Singapore Math is to develop conceptual understanding before learning the mathematical steps or procedures.  Parents need to understand and support the school in teaching math this way.  Parent education is not an option; it is a requirement of a successful implementation.  In our second year, we designed a plan for parent chats spread throughout the year with topics including fact practice, mental math strategies, and bar modeling as a tool for problem-solving.  Your professional development provider or consultant can assist you in designing a parent education program that meets the needs of your school.

Our journey continues and our students are stronger math students as a result.  The first year was clearly the most challenging.  Our commitment to professional development, perseverance, and acceptance of this unfamiliar approach to teaching math has guided us and we are confident that each passing year will continue to confirm the benefits of teaching a Singapore Math curriculum.

## Giving Thanks — Looking Back on 2014

I’ve just returned from my tenth consecutive week of travel and welcome the arrival of Thanksgiving. A brief break from out-of-town training and coaching jobs affords the opportunity to once again take stock and reflect on the past year, both personally and professionally. (Past Giving Thanks posts are here: 2013, 2012 and 2011)

As I enter my eight year as a Singapore Math® trainer, consultant and coach, I continue to be amazed by the wonderful opportunities that continue to come my way.

I say this every year, but it continues to be true: I am so grateful to be able to champion elementary math education and GET PAID to spend time in classrooms with teachers and students.  I extend my heartfelt thanks to everyone who has played a part in making the year so special.

2014 has been my busiest year ever. I’ve spent more than 30 weeks traveling across North American (and Germany for a week) to work with schools and present seminars. I’ve been to Denver International Airport so much that Google recognizes it as my office. Don’t get me wrong: I love to travel, especially when the end result is helping teachers hone their skills to make students more competent and confident math learners.

#### Changing Role and 2014 Highlights

This year, more than half of the schools I visited were repeat and long-term clients where my role often was that of an instructional coach. I still love to present introductory workshops and lead implementation trainings (the Ah Ha! moments are truly priceless), but it’s been especially rewarding to spend time with teachers working at a deeper level.  At these schools, I’ve also hosted lots of parent education events, including hands-on bootcamps, to help ensure that Singaporean methods are reinforced at home. Best of all schools are achieving remarkable results (more on that to come).

There are many highlights from 2014, including:

• Working with 28 school clients in 9 states and Germany, where I had the opportunity to work with teachers at the International School of Hamburg!
• Acceptance of proposals to present at the 2015 Annual Conferences at Annual Conferences of both the National Council of Teachers of Mathematics (NCTM, for the second time!) and NCSM (for the first time). Lauri Susi of Conceptua Math is my co-presenter;
• Presenting Singapore Math Workshops for the Bureau of Education of Research (for the sixth consecutive year!);
• Presenting  at the Tennessee Conference on Singapore Math Strategies hosted by SDE.
• Meeting my personal “continuing education” goals by attending:
• Annual conferences of NCTM and NCSM (for the 6th consecutive year);
• The National Charter Schools Conference (for the first time);
• SDE’s National Conference on Singapore Math Strategies (for the second consecutive year); and
• Earning A-list Preferred status on Southwest Airlines (didn’t I say I love to travel!).

Cassy (2nd from L) with teachers and staff at the International School of Hamburg

#### 2014 by the Numbers

2
Continents visited (I’ve now conducted trainings on four continents; c’mon South America and Asia…I’d love to visit there, too)
9
States visited to work with school clients
19
States visited to conduct Singapore Math seminars or trainings
20+
Singapore Math presentations conducted for parents
25
Seminars presented for BER
97+
Days working directly with teachers
Hundreds
of inquiries from teachers, administrators and parents with questions about Singapore Math curriculum responded to
103,448 and counting
Miles flown

#### Special Thanks

My sincere thanks to all the administrators, teachers and support staff I worked with in 2014. ( You know who you are!) I so appreciate your dedication to students and your trust and confidence in me!  A hearty thank you as well to my other long-time partners and supporters:

• Singapore Math Inc.
• Bureau of Education of Research (BER)
• EAI Education
• Staff Development for Educators (SDE)

One of my favorite evaluations from 2014

#### Singapore Math Source

Now in its seventh year, SingaporeMathSource.com continues to be an authoritative resource for those seeking information about the curriculum. This year, I completed a long-planned, thorough comparison of the two leading Singapore Math® curricula available in the US: Primary Mathematics and Math in Focus. (Quite a few of my school clients are using Math in Focus). I also updated my popular page on Singapore math iPad apps.

#### Personal

2014 has been personally gratifying as:

• We celebrated our youngest son’s high school graduation. It’s hard to believe we have two students at Colorado State University. It’s not hard to believe one is a math major!
• I once again reached my goal of reading 50 books in the year. As of this date, I am at 89!
• I continue to serve on the Board of the Middle School Math Institute, a non-profit dedicated to helping students succeed at algebra.
• I continue to serve on the District Accountability Committee for the Poudre School District.

2015 promises to be just as busy and exciting. I’m really looking forward to:

• Continuing to work with many schools that have retained me on a long-term basis;
• Visiting teachers, administrators and parents at schools that hire me for the first time (believe it or not, my fall 2015 schedule is starting to fill up);
• Presenting at the 2015 Annual Conferences of NCTM and NCSM in Boston (and hopefully other events);
• Presenting BER workshops for a seventh consecutive year;
• Sharing news about the successes some of the schools I work with are achieving — please let me know if you want to be a part of this series; and
• Other opportunities that are, as yet, unknown. I can’t wait to see what is ahead!

Once again, my sincerest thanks to my clients, colleagues and partners for making 2014 such a wonderful year. If I may be of service at any time, don’t hesitate to get in touch with me.

As passionate as ever about Singapore Mathematics!

-Cassy