Course Guide - USAID Teacher Education Project

• It is also important that students recognize that zero is neither positive nornegative.a. Finally, although this section has been on integers, eventually students will needto realize that in order for our number system to be consistent, there will benumbers (fractions such as – 1/2½, decimals such as –0.3, and later irrationalnumbers) that lie between negative integers.17. How children think about these conceptsa. When youngsters begin to work with integers, they need to deal with multipleconcepts and integrate them. This is because they are being exposed to a newkind of number in our number system, a type of number that differs from wholeor natural numbers.Recall that dealing with and integrating concepts happened when children firstlearned about fractions. In order to develop “fraction sense,” they needed toconnect new terminology (“fourths” rather than “four”), a new symbol fornotation (the fraction bar), a new relationship between two numbers (a/b), andseveral new visual models to help them understand this new concept. And all ofthis needed to be done before they could meaningfully compute with fractions,decimals, and percents.Similarly, this same long list of tasks relates to integers as youngsters begin todevelop “integer sense.” This integrating is a complex procedure that means,just as with fractions, students will need both multiple models for integers aswell as time and relevant activities to make sense of this new type of number.b. Just as children often use whole number thinking when considering the numberof digits in decimals (thinking incorrectly 3.0001 must be greater than 3.1), theytend to apply whole number thinking to integers. A common misconception isthat a number like -14 must be greater than 3 because -14 has more digits.Children need to work extensively with number lines in order to realize that anynumber to the right is greater than any number to its left, and that any positivenumber (even 1) is always greater in value than any negative number (even -100).c. Giving youngsters rules for integer operations before they understand integerconcepts is almost always ineffectual. Not only do children not comprehend themeaning of what they are doing, but the various rules simply become a list tomemorize—and often forget. If students continually need to refer to a referencesheet when doing operations with integers, it is a sign that they have not yetinternalized basic concepts about integers.d. As mentioned above, youngsters often become confused by the subtledistinction in notation of the dash (indicating a negative integer) and the minussign (indicating the operation of subtraction). And as such, students needreminders to call -3 “negative 3,” not “minus 3.”