How do you make sure that all high school graduates can solve complex problems of work and family life before they enter work and family life? Help elementary school students develop number sense and learn problem solving strategies. In a word: numeracy! Number sense is the knowledge of how numbers relate to each other and how to use that knowledge to solve problems. Instead of relying on traditional rote memorization and repetitive exercises, teachers need to focus on building deep understanding of how numbers work. In addition, they need to focus on developing a variety of strategies for solving problems, such as working backwards or looking for a pattern or solving a simpler version of a problem or drawing a picture.
Larry Martinek, cofounder of Mathnasium, says at Mathnasium, “we teach children to work with numbers beyond written exercises, which helps them to access number sense -- an important step before they can apply their understanding on paper.” An example Martinek likes to use in his demonstrations is the solution to the problem 99 + 99 + 99 = ? Most teachers show students how to solve this problem by vertically adding the ones column, carrying the number of groups of ten to the tens column, leaving the leftover ones in the ones column, and adding the groups of tens in the tens column. Martinek directs students to look at the 99s and look for a number that is close to 99 and easy to add: 100. Since 100 is one more than 99, add one to all three 99s to round them to 100. Add the three 100s. You get 300. Now subtract the three ones you added to the three 99s. You get 297. No calculator or vertical addition needed!
The key to solving this problem mentally was the awareness that 99 is close to 100 and that you can round 99 to 100, add 100s, then take away the extra you added. The dirty little secret is all mathematically literate people solve problems this way. Contrary to popular belief, they were not born with a math gene and they do not have calculators in their brains. They employ one or more problem solving strategies to break a big problem into small problems that can be solved then combined to solve the big problem. Like we do in real life!