Number Sense and Nonsense: Building Math Creativity and Confidence Through Number Play
four cents on the third day eight cents on the fourth day and double the amount every day until the end of the month Guess how much money you would receive In the final section are lists of books for children and adults Reading some of these books will help your number sense grow Happy reading thinking and talking about math A Note to Parents and Teacher This book introduces groups of children having a wonderful time discussing reflecting on and arguing about mathematical ideas These children discover that some ideas make good number sense while other ideas do not make sense they are just plain nonsense Math is for everyone Research has shown that every child can learn math When experienced through challenging activities math can be a source of great joy and satisfaction to children and to adults No longer can parents excuse their children by say ing I was poor in math so I am not surprised that Jennifer has trouble learning the subject No longer can teachers justify their students failure with the excuse Those kids can't learn We now know a great deal about how children learn The British neuropsychologist Brian Butter worth believes that the brain has specialized circuits that he calls the Number Module In his fascinating and comprehensive book What Counts How Every
Brain Is Hardwired for Math he writes There is noth ing intrinsically dull or hateful about mathematics It will be and can be fun as long as children under stand what they are doing and feel pride of owner ship in mathematical ideas page 320 see the bibliography on page 127 of this book He advises teachers to use group discussions encourage differ ent solution strategies acknowledge pupils own intuitions and knowledge to stimulate inventiveness page 298 Of course this advice is equally relevant for parents According to the Principles and Standards for School Mathematics published in 2000 by the National Coun cil of Teachers of Mathematics NCTM Students learn more and better when they can take control of their learning When challenged with appropriately chosen tasks students become confident in their ability to tackle difficult problems eager to figure things out on their own flexible in exploring mathe matical ideas and trying alternative solution paths and willing to persevere page 21 In other words children must learn mathematics with understand ing Unfortunately much school instruction in mathe matics has been based on rote memorization of facts and procedures rather than on understanding Mem orized procedures are easily forgotten or confused but the ability to reconstruct methods and arrive at solutions on the basis of mastering the underlying
concepts remains with a person over the years As I write these words educators and the public are caught in a dilemma On one side are parents who feel that their children are being shortchanged because many of the current math programs do not call for extensive drill on multiplication tables and addition facts the so called basics On the other side are those who object to the kind of rote learning advanced by the older math programs still used in many schools and by teachers who teach as they have been taught using drill and kill methods With the increasing emphasis on standardized test scores teachers are pressured to spend a great deal of time drilling for tests in spite of the fact that research shows that when children learn the basics in the course of doing challenging math work they are far better prepared to cope with new ideas than if they had learned by rote memorization methods This book focuses on numbers their characteris tics and relationships applications of numbers in society and the history of number systems As rec ommended in the NCTM Standards 2000 readers also make connections to geometry and other branches of mathematics they develop skills in esti mation and problem solving they generalize about patterns of numbers and they are encouraged to engage in discussions with peers and adults see pages 139 140 This book provides a model for cre ativity and independence in the learning of mathe
matics and for the development of a positive attitude toward the subject The book is addressed to children in grades three to six and encompasses a wide range of mathemati cal knowledge I prefer not to specify a grade level or a level of difficulty for each activity Children should be encouraged to try as many activities as possible They should not be afraid to make mistakes or to fol low a wrong path Mathematicians do that all the
