Number Sense and Nonsense: Building Math Creativity and Confidence Through Number Play
no definite answers Many of the activities are easy for you to check you will decide whether they are correct See page 123 126 for the answers to some of the activities although you probably won't need to refer to the answer pages very often It's much more satisfying to work out the solutions yourself even if it takes time Some activities are harder than others and may be too difficult for you to complete at present Try them anyhow Discuss them with your friends or a grown up Your number sense will grow as you work on them even if you don't get the final answer correct And you will feel so proud when you do work out a hard problem But if you can't finish some of the activities now come back to them next year or the year after next You probably already know about odd and even num bers But did you know that an odd number might be even and an even number might be odd Chapter 1 is all about odds and evens Chapter 2 introduces other relationships among numbers You will have a chance to work on an idea called a conjecture about even numbers that no one has been able to prove either true or false although mathematicians have worked on it for over 200 years In Chapter 3 you will learn why zero is a very spe cial number For example we cannot divide a non zero number by zero When I try to divide six by zero
on my calculator the display shows the word error Zero is special in other ways too Chapter 4 deals with money and decimal points and measures You will learn how the United States lost hundreds of millions of dollars because of a mix up in units of measurement Riddles and puzzles are the subject of Chapter 5 although you will also find some riddles and puzzles in other chapters You will learn clever tricks with numbers that will make people think you are a genius How did numbers begin How have people used numbers in the past That's what Chapter 6 is all about You will read about finger counting number words in several languages signs for numbers and ways of calculating that have been used in different parts of the world over thousands of years You may wonder what about the calculator Why bother learning about numbers when the calculator can do all the work Not true The calculator has no number sense It takes a human being to tell the calcu lator what to do The same is true of the computer But the calculator can be very useful as you will find out in Chapter 7 You will learn about negative num bers repeating and terminating decimal fractions and a lot more Chapter 8 is about big numbers Would you like your allowance to take the form of one cent on the first day of the month two cents on the second
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
