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.
When was the last time you sounded out the word “and?” or “dog?” or, for that matter, any other word in this paragraph? We take for granted that we are able to read words without having to process them. As literate individuals, we know the words and can easily read them, put them in context and glean understanding.
The same concept applies to math. The ability to know that 1 + 1 = 2, without counting your fingers or drawing a diagram, is analogous to learning sight vocabulary.
This is called mental math, and we actually use it every day. Adding 20 percent to your restaurant bill for a tip? Figuring out the lowest cost for produce at the grocery store, you’re doing some quick math in your head. That’s mental math.
Despite its practical, everyday use, mental math skills are woefully neglected in U.S. classrooms and underappreciated in a digital age where every smartphone comes loaded with a calculator. We all should be able to “read” a basic math problem, such as 1/2 off a $30 sweater without pencil and paper or a calculator.
In Singapore, students learn how to do many calculations by mental math. They start in kindergarten with number bonds, so that they easily understand the links and associations between numbers. The first year Singapore Math® was implemented in my school, I saw that the power of basic number bonds was misunderstood and underutilized.
By Chris Coyne, Senior Education Consultant, Marshall Cavendish Education
Today’s global economy requires critical thinkers, people who can work in teams and those who can solve problems and adapt to a changing landscape. As a former math teacher, I know that these skills are in the very DNA of mathematics. And, those skills are being more finely honed in math classes across America as math lessons start to look a bit more like an art class with drawing, discussion and building techniques used to teach challenging math concepts.
As any good educator knows, students have different ways of grasping content. And, creative teachers have always found a way to teach to individual differences.
A visual approach is certainly validated by well-established research: From Howard Gardner’s research on the multiple intelligences to Jerome Bruner’s studies that show students learn to a greater degree of mastery and retention when using the Concrete-Pictorial-Abstract (CPA) approach.