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.