There are many places of employment that promise a new start with New Year’s Day or the start of a new fiscal year but more often than not that new start is fleeting and the same old ruts soon reemerge.
Education is unique in that we truly start anew with each school year. It is full of opportunity to get to know another group of students, reacquaint ourselves with colleagues and administrators – or perhaps get to know new ones. It is also a chance to revisit our classroom management procedures and implement new best practices in our classrooms. It is our time to shine with each new teachable moment. As teachers, we know that it is the procedures and practices along with appropriate responsibility and consequences that aid in our sanity throughout the new year, and we need to begin with them from day one.
When it comes to Singapore Math®, the research is clear – the use of manipulatives is non-negotiable. With a new school year, we need to establish the structure for their use with our new group of students. Manipulatives need to be readily available in your classroom. If we ask students to “hold that thought” so we can go look for manipulatives, we have lost a teachable moment. As educators, we need to consider how we will create the opportunity for students of all levels – those who may be struggling with a particular topic, those who are moving towards mastery with a particular topic and those who could benefit from enrichment with a particular topic – to make use of manipulatives to see and explain math.
Another teaching approach which should be established at the start of the school year is the use of productive struggle to help students build confidence and learning persistence. Singapore Math® offers ample opportunity for students to discuss, justify and analyze their answers and strategies – as well as those of their peers – through the use of problem-solving. The Singapore Math® lesson gives students an opportunity to discover the process needed to solve a given problem through discourse, exploration, and revision. As teachers, we must allow wait time as we encourage student participation, ask students to provide additional methods and probe student thinking as they productively struggle through problems. Sometimes this wait time can be difficult but as educators, we must be willing to let students think and work through math problems before swooping in to help guide them.
Setting the procedures and the expectations from day one sets us up for a positive year and sets our students up for success in math.
National Education Consultant
National Education Consultant
There is much written about differentiation in the math classroom. But at the core of it all, there seems to be a central idea: a student-centered classroom managed by a teacher who knows the varying learning needs of his or her students and addresses those needs appropriately.
Easy, right? Well, as Mark Twain said, “If talking were teaching, we would all be smarter than we could stand.”
We kept this in mind when developing Singapore Math®, which uses a problem-solving approach and incorporates opportunities for multiple representations—both of which provide the context for differentiation. Let’s consider this adding with regrouping problem:
Can you find one way? Can you find more than one way? How many ways are there, and why? Think about this problem with your students. Which students would you ask for one way? More than one way? How many ways?
With Singapore Math®, differentiation often becomes about what questions to ask students rather than developing different tasks. Perhaps your struggling students find one way, while your on-level students find more than one way, and the higher-achievers for this lesson find how many ways and why. Students must learn how to break concepts down and, just as important, how to build them up. Differentiation is as important for advanced learners as it is for struggling learners.
An opportunity for multiple representations helps students conceptualize the math while also helping to develop number sense. Let’s consider subtraction. If students are simply taught to put the “larger number on top and the lower number on the bottom” to subtract, it will likely lead to subsequent issues. Students may end up incorrectly subtracting decimals (not to mention integers) like this—after all, the larger number is on top:
Through the use of multiple representations—including concrete manipulatives, pictorial representations, and abstract symbols—students can begin to visualize the math (in this subtraction problem, place value) and develop strategies which lead to them developing number sense, persistence, and confidence in math class.
Interested in learning more about Singapore Math®, which aims to facilitate differentiation in the math classroom?Register herefor our webinar, “Differentiating and Small Group Instruction in Singapore Math®,” presented by Terry Goldfischer and Christopher Coyne on Sept. 19 at 4 to 5 p.m. ET.
Should U.S. students live in a Smart Nation? Currently, Singapore is on their way to becoming the first nation in the world to be a “Smart Nation”.
Singapore likes to be first and rank first. For more than 20 years now, Singapore has consistently ranked first (or near first) in mathematics and science. While waiting at the airport last week, my CNN app sent me an alert that Singapore is now first on the list of the World’s 10 Most Expensive Cities To Live In1. Being first or being in first place seems to be part of their DNA.
Singapore’s government, through their office of The Infocomm Development Authority (IDA), wants to make the country the world’s first true Smart Nation2. Their slogan is “E3A”: Everyone, Everything, Everywhere, All the time. What makes a nation “Smart”? – Technology.
Like most developed countries, Singapore has big problems. Transportation problems, population problems, security problems, healthcare problems and many others and they are convinced that technology is the pathway that will enable them to develop and grow infrastructures and technology capabilities to help its citizens, businesses, and government solve their nation’s problems.
How is math class related to all this? Well, a Smart Nation needs Smart Students. We need to make a distinction, “Smart” is not the same as “smart”. Carol Dweck, author of Mindset, might argue that students can always grow “smarter”3. In this context, a “Smart” student is a student who is able to use technology to innovate and solve problems. A Smart Student uses logic and thinking skills through technology. A Smart student surely gets smarter.
Those familiar with Singapore Math textbooks in the U.S. are also familiar with the Singapore Math’s Framework Pentagon that specifically has problem solving as the focus of mathematics instruction. These students, with their teachers’ help are becoming smarter students and better problem solvers. Incorporating technology to the math class can further develop these skills.
Recently in the news in Singapore, I read an article about young students signing up for coding workshops and classes offered by various companies4. The goal is not to develop programmers but to train them in logic and clear thinking. Becoming a programmer is not such a bad idea either and according to the App Economy (apparently a real term) more than 627,000 jobs5 have already been created and growing rapidly here in the U.S. Parents in Singapore are sending their children in droves to these types of “enrichment” coding classes because they are recognizing two things: 1) technology is the present and future for their children and 2) developing logic and thinking skills directly benefits their current schoolwork.
Another important component in achieving a Smart Nation is the need for Smart Schools. Learning in the 21st century demands technology. School districts everywhere are planning and implementing these plans on improving and developing their technology infrastructures. However, having high-tech alone is not enough. Schools everywhere are reimagining teaching by using technology. One such impressive initiative can be found in New York State’s “NY Smart Schools Commission Report”6 The Keys to Success for Achieving a Smart School is very helpful and critical is key number 5: Provide high-quality, continuous professional development to teachers, principals, and staff to ensure successful integration of technology into the teaching and learning experience. Is your school a Smart School?
U.S. schools across the country have made significant infrastructure upgrades. It was rare only a few years ago to see schools that had more than just a few computer workstations in the classrooms. Soon after that, carts of iPads or Chromebooks became normal. Now students bring their own mobile devices. However, in many places there is a sense that students are and have been ready for Smart Schools for a while now and we are the ones trying to catch up. For example, I recently visited a school in Texas that was using Math Buddies (a Marshall Cavendish Education digital program) and I was blown away by how fluid they were in their ability to multitask between talking and helping each other, using paper and pencil to do scratch work, dragging and dropping on screen, typing and giving each other high-fives because they solved a problem correctly. A Kindergarten teacher confessed that one surprising challenge had nothing to do with the program but with their hardware as her students had to be taught how to use a computer mouse because instinctively, her students wanted to just touch and swipe the screen to get the program to do what they wanted it to do. In some cases, it is us, the adults who have to do the catching up. Young students have been ready to be part of Smart Schools for a long while.
Personally, my own 13 year old son has recently shown interest in being part of a Hackathon. Suspecting it might be some nefarious “-athon” I looked it up and realized that a hackathon is a marathon computer-programming competition. Again, as an adult, I am the one needing to catch up.
The more Smart Students we have in our Smart Schools the closer we too are to becoming a Smart Nation.
Do you teach Smart Students? Is your school a Smart School? Do you teach in a Smart Math Class? We’d love to hear about your experiences in the classroom with technology. Be sure to leave a comment back at the LinkedIn blog area. Share with us the amazing logic and thinking skills your students have demonstrated using tech. Tell us a story about the Smart Students you work with.
Share your thoughts on this article or any other Singapore Math topic by joining our LinkedIn community.
By Hoover Herrera
Singapore Math® expert
Marshall Cavendish Education is headed to The Lone Star State for a three-day road trip on Singapore Math®: Anchor Tasks & Problem Solving! We’ll be visiting Dallas, San Antonio, and Houston. These dynamic, one-day interactive workshops will benefit all K-5th grade educators – those already using Math in Focus®, Primary Mathematics, or Math Buddies, as well as newcomers drawn to the Singapore Math® Approach because of its results in high student achievement in math.
Why should you attend?
See the pedagogy of Singapore Math® in action.
Learn how to plan and teach an Anchor Task.
Understand the operations of fractions and how to problem solve using bar modeling.
Understand how bar modeling supports the Concrete-Pictorial-Abstract approach.
Engage in hands-on activities and learn how to transfer them to your classroom.
Covering three important topics –Anchor Tasks, Teaching of Fractions and Bar Modeling–presenters Hoover Herrera and Chris Coyne will demonstrate how Singapore Math® Anchor Tasks are developed and taught, how Fractions are taught using the Singapore approach and present and solve a series of word problems of varying degree of difficulty using the bar model method. Educators will learn proven and practical strategies that will boost student confidence, engage pupils, and impart life-long, real-world problem-solving skills.
Each workshop will begin at 8:00 AM and conclude at 3:30 PM. Also, coffee and lunch are included! Click the links below to view the program schedule and speakers for each event!
I suppose the precursor question should be “Should we teach students how to be innovators?” In a recent edition of “Today”, one of Singapore’s most widely read newspapers, there was an article titled “Schools Too Bogged Down For Push Towards Innovativeness”. The article was pro-innovation but pointed out the biggest obstacles schools are faced with when trying to make room for teaching innovation in the classroom. We’ll get back to the article in a minute, but first we should answer the first question which is “Should we teach students how to be innovators?” Well, whether or not you are a fan/supporter of Common Core, those set of standards propose to prepare students “to enter a world in which colleges and businesses are demanding more than ever before. To ensure all students are prepared for success after graduation.”1 The world Common Core is describing needs innovators to solve existing real world problems. Some of those existing real problems such as our global energy problems need immediate attention so much so that Bill Gates is funneling 2 billion dollars to fund new ideas that will develop a global carbon-free source of energy and he believes that the only way to accomplish this “is to drive innovation at an unnaturally high pace.”2 So not only should we help students become innovators, but they will in some cases have to use that skill with a sense of urgency once they join the workforce.
The White House published a 76 page document called “A STRATEGY FOR AMERICAN INNOVATION: Securing Our Economic Growth and Prosperity” where President Obama calls innovation “the foundation of American economic growth and national competitiveness”3 while in a Wired magazine, there was an article about innovation that suggested that “we need Americans to think and act as innovators”4. I took all that to mean that innovation is in the best interest of the nation our students live in.
I think one can make a strong case in favor of teaching innovation in the classroom because of a student’s personal career needs, national needs and global needs. I also think weaving innovation into a math class makes a nice fit which brings us back to the “Today” article. The Acting Education Minister in Singapore, Ng Chee Meng, has stated that “Students must be innovators for Singapore to succeed”.5 In Singapore they are wrestling with how to best implement programs that promote innovation that support schools, parents and students. They are working on how to embed innovation into their national curriculum, and most of all how to do it without adding more burden to an already packed curriculum full of demands such as high-stakes testing.
Marshall Cavendish Education proposes that through Singapore math and pedagogy an educator can teach students how to be innovators by allowing students to be creative in their approach to problem solving. The title of this blog article is “Is There Time to Teach Innovation in Math Class?” Perhaps the trick here is not to find time or make time to teach innovation but to make better use of the time already allotted for math. In fact, I have met many teachers in many states who leverage their students’ natural instincts for creativity and imagination to solve math problems. I have heard countless stories of teachers using Math In Focus where students derive their own strategies based on their own ideas. Yesterday I was working with a group of third and fourth grade teachers and one of them shared that in her class students attach student names to the strategies developed by students so now they have the
“Joshua strategy” and the “Darci strategy”, etc. Students like these not only are thinking like innovators but they are also acting like innovators.
The Partnership for 21st Century Learning has provided us with an excellent framework and one of its main areas of focus is Learning and Innovation skills which they describe as “increasingly being recognized as those that separate students who are prepared for a more and more complex life and work environments in the 21st century, and those who are not.”6 In their framework, creativity and innovation are described under two categories:
Use a wide range of idea creation techniques (such as brainstorming)
Create new and worthwhile ideas (both incremental and radical concepts)
Elaborate, refine, analyze and evaluate their own ideas in order to improve and maximize creative efforts
Work Creatively with Others
Develop, implement and communicate new ideas to others effectively
Be open and responsive to new and diverse perspectives; incorporate group input and feedback into the work
Demonstrate originality and inventiveness in work and understand the real world limits to adopting new ideas
View failure as an opportunity to learn; understand that creativity and innovation is a long-term, cyclical process of small successes and frequent mistakes Implement Innovations
What kind of creative thoughts, ideas, methods and strategies have you witnessed from students in math class? We’d like for you to share a story or experience that will encourage other teachers to continue looking for ways to help students develop their innovation skills during math class. Be sure to leave a comment our LinkedIn Singapore Math® Community. What’s your opinion? Is there time to teach innovation in math class?
by Hoover Herrera
Singapore Math® expert