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
Why can’t math questions on high-stakes tests be direct, clear and to the point like in the good old days?! Some of the math questions on high-stakes annual tests seem vague and apparently written by people with questionable grammar skills. To many parents it just seems unfair that some questions are not only vague and unclear but to add insult to injury, some seem like they have nothing to do with math.
While in Singapore this past autumn, I witnessed some parental uproar about a particular question on the current national test that all students in Primary 6 (12 year olds) had to answer. The question was:
How heavy are eight $1 Singapore coins?
A) 6 grams
Was this a fair math question for a 12 year old? Or was this more of a MENSA type question trying to find out the IQ of student?
Steven, a colleague of mine in Singapore, has a 12 year old who took the test and had to answer this very item. I asked Steven what his son thought of the question and how he answered it. His son thought the question was weird and was pretty certain that this type of question was not “covered” in math class. While in the middle of trying to figure out what to do he remembered having been in the supermarket with his parents and holding certain fruit and how much that weighed. He connected that experience with this problem and determined that eight $1 Singapore coins would be about 61g as the other choices made no sense. Was Steven’s son just lucky to get the correct answer or did he do exactly what the Ministry of Education in Singapore was hoping that all students would do with this item?
All students in grade 6 have to take the high-stakes test called the Primary School Leaving Examination (PSLE). Every year the PSLE contains items that upset parents like the coin problem. A similar situation occurs with some of the math questions on the Common Core tests from both the Partnership for Assessment of Readiness for College and Careers (PARCC) and the Smarter Balanced Assessment Consortium (SBAC) which seem confusing, unfair and seemingly not related to math. Parents here also get upset by these items.
Perhaps the goal of teaching and learning math in the past was to learn a subject that would help us learn higher level subjects. Today’s standards like the Common Core propose different goals. Today’s goal of teaching and learning mathematics is to help students become problem solvers in the real world where students make connections to real world experiences and apply what they have learned. An additional goal is to help students use prior knowledge to learn new knowledge so that they can become better problem solvers. Ultimately, learning how to become problem solvers through math will help to enable students to become college and career ready.
In the U.S. it is now officially the beginning of the first phase of the high-stakes testing season as many, not all, administrators and teachers across the country make plans and implement strategies and programs to help students prepare for testing. The reality is that the stakes are high not only for students but also for teachers and administrators. Parents can certainly help.
As educators, we can help more parents adapt and understand the evolving role that mathematics education plays in the lives of their children. As adults in the real world we are often faced with problems whose solutions can be found in seemingly unrelated past experiences. Everyday real life experiences like taking their children to a sporting event or to the mall can be an opportunity to make connections and apply what is being taught in school. And who knows, perhaps such a mundane thing as a trip to the supermarket may just help a student answer what some say is an unrelated math question on a high-stakes test.
What do you think? We’d love to get a conversation started on this topic. Be sure to leave a comment back at the LinkedIn blog area.
by Hoover Herrera
Singapore Math® expert
by Hoover Herrera
Singapore Math® expert
There are some pretty tough math problems out there. Math problems come in many forms. There are math problems that can make students feel like they need a superhero to conquer them. Some math problems come disguised as one-step problems when in reality they are multi-step. Some word problems use words that no other English speaking person seems to use or the verbs and adjectives in the problem are in the wrong place. Some problems involve those intimidating fractions and sometimes even their ugly cousins, the mixed numbers. The worst are those problems that seem innocent when in fact they are not! And whose idea was it to include fractions, decimals and ratios all in one math problem?!
Students don’t need a superhero to fight their battles for them because they can be their own heroes of problem solving. Recently, the CEO of Marshall Cavendish Education, the Director of Marshall Cavendish Education US and I had the privilege of visiting a third grade class using Math In Focus® Singapore Math® at the Ridge Road School of the North Haven Public Schools and we saw not one, but many superheroes of problem solving in action. Led by superhero teacher Ms. JoAnn McLane and donned in her powerful blue cape, students without fear confronted some fierce looking problems. Armed with strategies and creativity, students devised plans, used those plans to solve and then checked to see if their mission had been accomplished. Then they went on confidently creating their own fierce looking problems.
All students believe and have confidence that their teachers can solve all of the math problems but it is quite another thing when a teacher convinces her students that they too have the power to solve problems, even big scary ones. “Who thinks they can be the superhero of problem solving today?” asked Ms. McLane. We witnessed every little hand lift up high to the sky not because they had to but because they were confident and fearless. That’s quite an impressive attitude and confidence considering the math problems students are confronted with each day. A quote from a website I often frequent stated “For some, it may be that their confidence has been severely dented by someone who taught them maths [sic] in a forceful or unsympathetic manner, so that they came to believe that they were ‘no good at math’” (Fewings, 2011)1.” Thank goodness for hero teachers like Ms. McLane who is developing confident heroes of problem solving everyday.
As educators, we can certainly teach students math content, help them to develop skills, how to use strategies, and even how to think, AND we should continue to do so, but helping students to become their own heroes of problem solving full of confidence to confront tough math problems is one of our strongest superpowers that we need to continue developing as educators.
We’d love to hear about your experiences in the classroom. Be sure to leave a comment back at our LinkedIn Singapore Math community. Who are the hero teachers in your school? Share with us the amazing powers your students have demonstrated. Tell us a story about your own confident superheroes of problem solving.
By Hoover Herrera
Singapore Math® expert
I confess, I taught math for my first eight years of teaching in the same way I was taught math when I was a young student in elementary school. I’m pretty sure my math teachers taught me in the same way they were taught when they were students… and what’s wrong with that?!…a lot it appears…
He wasn’t impressed by any of his math teachers until he was in college. Why? He never had a math teacher “with common sense, who (could) write some lines to make you see maths as something human at the reach of anyone.” Recently, because of the internet he has found some who fit the bill. Are you a math teacher or know of one who fits the bill?
“I never ever enjoyed maths, because all the teachers I had were “math-Daltonics” which means that they know the stuff, but they do not feel it, they do not transmit the essence, the beauty of concepts. Are you a math teacher or know of one who transmits the essence of concepts?
The reason students don’t like or struggle with math has nothing to do with the content but “Its people… a subject is completely ruined by a teacher, (or) completely enhanced by (an)other.” How many of your math teachers “enhanced” your math education?
The math hasn’t changed since we were all young students but the expectations have. Whether it be because of Common Core or the Economy, or both, the way we teach mathematics to young learners needs to be “something human at the reach of anyone”, not about how much teachers know but about transmitting the “beauty of concepts” and about teachers “enhancing” the learning experience. If so, we would certainly have fewer math-phobic adults walking around these fifty great states.
Perhaps you were taught by a brilliant math teacher who knew everything there is to know about elementary math by delivering a perfect model lesson. Perhaps they broke down a concept into ten easy to follow steps that you could replicate. I had many students that I awed with my skills having never transferred that ability to them. I became the grand magician on the stage with my model lessons and some even noted that in their yearbooks.
There is a better way to teach mathematics to youngsters today. We don’t have to be the sages on the stage. Students aren’t blank slates (even if they claim amnesia of prior knowledge). We need to leverage that possession of prior knowledge to add new knowledge and skills. No need for model lessons. Those take a lot of work but it only means that teachers are working very hard and students are hardly working. Students need to work just as hard, or even harder than teachers. Anchor Tasks provides a better way. This model makes math “at the reach of anyone” in the classroom. Anchor Tasks transmit the “essence” and “beauty of concepts”. Anchor Tasks is the better way to “enhance” not just teaching mathematics but also learning mathematics. Engaging students in the problem solving process is at the heart of an Anchor Task. It takes no less work to plan and prepare an Anchor Task but students will work just as hard or even harder than the teacher who planned it. A recent teacher who participated in one of our Anchor Task professional development workshops said “I used your suggestion of how to structure the initial lesson on multiplication, and the lesson went beautifully.”
Singapore textbooks are written with the main learning task being an Anchor Task. An Anchor task is the single task used over a prolonged period of instructional time. It embodies the idea of “Teach Less, Learn More”, a philosophy of the Singapore education system.
Marshall Cavendish Educationwill be offering a FREE webinar this coming December 9th that will provide more information about Anchor Tasks. Our professional development experts Chris Coyne and Ellen Lauterbach will be presenting and sharing more details. I encourage you to register by clicking on the link below.
Make sure to head back to our Singapore Math® LinkedIn community and leave a comment. We’d love to hear back from you and get the conversation started.
Have you used Anchor Tasks? Share with us the math teacher who “impressed” you not with their math skills but with the way they made math reachable, taught you the beauty of concepts and enhanced your learning experience.
Can you go back in your mind to when you were seven? Imagine seeing this question:
59 people buy tickets to a show. 46 of them buy tickets to grandstand seats. 37 of them buy tickets to bleacher seats. How many people buy tickets for both grandstand seats and bleacher seats?
If I remember correctly, if I had seen this at seven years old, I would have just taken those three numbers in the problem and added them up, then subtracted them, in other words, I would have done a series of operations with those numbers in the hopes that one of my answers matched the correct solution. I called it my “doing anything is better than doing nothing method”. My childhood friend Marlon would probably had not gotten past the word “grandstand”. What would you have done as a seven year old? What do we expect our current seven year olds to do this school year with such a problem? Common Core expects second graders to represent and solve problems involving addition and subtraction. (CCSS.MATH.CONTENT.2.OA.A.1) Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (wow!)
How important are Bar Model drawings or the use of a Tape Diagram as Common Core calls it? I didn’t have Bar Models when I was seven and somehow I survived. However, the problems our current young students are expected to solve these days sure do look a lot harder than the ones we used to get.