Showing papers on "Number sense published in 1992"

A Proposed Framework for Examining Basic Number Sense.

Abstract: A boy in a classroom was being observed by a visitor. After writing the problem 37 + 25 in vertical form, and drawing a horizontal line, he recorded the answer of 62. \"Fine,\" said the visitor, \"tell me how you did that.\" \"All right\" answered the boy hesitantly, \"but don't tell my teacher I said 37 and 20 is 57 and 5 makes 62.\" nThat's a very good way,\" commented the visitm \"Why can't I tell your teacher?\" \"Because I wouldn't get a mark then. I can't understand the way she tells us to do it on paper, so I do it this way in my head and then write down the answer and I get a mark.\" A clerk was serving in a newsagent's shop in England A customer wanted to purchase two identical diaries, each originally costing 2.50 pounds, but now, in February, marked \"half marked price .. \" The customer picked up the two diaries and took them to the counter \"How much please?\" asked the customer. The clerk picked up the first diary and a pencil, wrote the original price, divided by two using the standard written algorithm for long division, and obtained the new price 1.25 pounds. She then picked up the second identical diary, wrote the original price, used the standard written algorithm again, and obtained the new price 125 pounds She then wrote 1.25, underneath it wrote I 25, added them correctly using the standard written algorithm, turned to the customer and, without a shadow of a smile, said, ''That will be two pounds fifty, please.\" The boy could not follow the formal written algorithm but understood enough about numbers to invent his own efficient mental method The clerk showed impeccable performance in the formal written algorithm and yet revealed an alarming lack of awareness of fundamental arithmetic relationships. One might say that the boy, but not the clerk, exhibited number sense

Making Sense of Numbers in School Mathematics

Abstract: In this chapter, the author explores four curricular topics that are closely related to number sense: numeration, number magnitude, mental computation, and computational estimation. She also examines some other areas of learning that should be addressed when considering the role of instruction in developing number sense. A disposition toward making sense of numbers is discussed. An understanding of the many aspects and uses of numbers, particularly those related to cardinal and ordinal meanings and to the notion of place value, is fundamental to the acquisition of number sense. The foundations for the development of whole number sense were discussed in this chapter. The analysis of the foundations for rational number sense focuses on how fractions and decimal numbers are introduced, that is, how the texts attempt to link meaning to symbols, and then how numbers are compared and ordered.

What Is Left to Teach If Students Can Use Calculators

Abstract: Let us begin at the beginning, say, first grade. We give every student a simple calculator that does all the basic arithmetic opera tions, including square roots and operations with fractions. We teach every student to use the calcu lator, that is, to find the answer to problems like 2 + 5, 3 7, -4 + 9 (-8), 32.97 485.47, 2/3 + 3/4, and so on. Students do not have to memorize any thing except how to use the calculator to find the value of an arithmetic expression. Of course, they have to know how to read and write the numbers and know which keys denote plus, minus, and so on, so as to be able to communicate verbally with the teacher or someone else, so some learning is necessary besides pressing keys. But then what? First, the students have to have some number sense. We want them to have a "feeling" for what the numbers mean and what the arithmetic opera tions mean. When do we add? When do we multi ply? Does it make sense that 2 plus 5 equals 7? Does it make sense that 1 330 065 divided by 495 equals 2 687? Or that V77841 equals 279? What do these equivalents mean and where might they be used? Why might a calculator show 54.394999 as the square root of 54.395 times itself? So that stu dents can become comfortable with these ideas, we teach number sense instead of drilling students on such memorized facts as the addition and multipli cation tables. We start with the meaning of whole numbers and have our students count objects, combine groups of objects, and count objects in the com bined set; measure lengths of objects; and so on. Then we have them guess the number of objects on a table and in combined groups, and we teach them to estimate the lengths of objects. In particular, we teach about 0 and 1?that 0 results when a num