Remember when it was enough to just come up with the right answer? While your teacher may have admonished you to “show your work,” credit was given simply based upon whether or not you got the correct answer to a given problem. An algorithm was taught in Math class, you used that algorithm to work through several problems, and it didn’t matter if you really understood what you were doing as long as you memorized the necessary steps.
Fast-forward now to “Mathematics the Posnack Way” where the standards for demonstrating proficiency in Mathematics have changed. Research has shown that as a predictor of future mathematics success, a student’s understanding of a mathematical task is equally as important as his ability to demonstrate computational skills. But how do you know when your child “understands” a concept or idea? If your child can recite his multiplication tables without hesitation, isn’t he demonstrating proficiency in a valuable skill?
The answer is a resounding “Yes”AND “No!” Yes – your child has memorized an algorithm for finding the product of two numbers. This IS a necessary skill and will greatly benefit your child as he moves forward to higher levels of math. But does this ability to recite numbers based on rote memorization demonstrate a strong number sense? No – it does not. A strong number sense is not developed from memorizing facts or algorithms, but rather when children use learned strategies and an understanding of numerical relationships to solve problems.
At Posnack, our focus is on a problem-centered Mathematics curriculum. Students are encouraged to use manipulatives, drawings, games, and graphic representations to solve a variety of word problems. By discovering not just the “how” behind problem solving, but the “why” as well, your child will not only become a mathematical thinker, but will develop a life-long love and appreciation for Mathematics.
So what will your answer be the next time your child asks the question “Why do I need to show my work?” Before answering, consider this quote from Paul Lockhart, a mathematician, teacher, and author:
“It is the story that matters, not just the ending.”