Questions? Call 800-624-6242

| Items in cart [0]

PAPERBACK
price:\$34.95

## Adding It Up: Helping Children Learn Mathematics (2001) Center for Education (CFE)

### Citation Manager

. "6 Developing Proficiency with Whole Numbers." Adding It Up: Helping Children Learn Mathematics. Washington, DC: The National Academies Press, 2001.

 Page 195

The following HTML text is provided to enhance online readability. Many aspects of typography translate only awkwardly to HTML. Please use the page image as the authoritative form to ensure accuracy.

Adding + It Up: Helping Children Learn Mathematics

development, many of the linkages among strands result from children’s natural inclination to make sense of things and to engage in actions that they understand. Children begin with conceptual understanding of number and the meanings of the operations. They develop increasingly sophisticated representations of the operations such as counting-on or counting-up procedures as they gain greater fluency. They also lean heavily on reasoning to use known answers such as doubles to generate unknown answers. Even in the early grades, students choose adaptively among different procedures and methods depending on the numbers involved or the context.45 As long as the focus in the classroom is on sense making, they rarely make nonsensical errors, such as adding to find the answer when they should subtract. Proficiency comes from making progress within each strand and building connections among the strands. A productive disposition is generated by and supports this kind of learning because students recognize their competence at making sense of quantitative situations and solving arithmetic problems.

### Multidigit Whole Number Calculations

Step-by-step procedures for adding, subtracting, multiplying, or dividing numbers are called algorithms. For example, the first step in one algorithm for multiplying a three-digit number by a two-digit number is to write the three-digit number above the two-digit number and to begin by multiplying the one’s digit in the top number by the one’s digit in the bottom number (see Box 6–5).

In the past, algorithms different from those taught today for addition, subtraction, multiplication, and division have been taught in U.S. schools. Also, algorithms different from those taught in the United States today are currently being taught in other countries.46 Each algorithm has advantages

 Box 6–5 Beginning a multiplication algorithm
 Page 195
 Front Matter (R1-R20) Executive Summary (1-14) 1 Looking at Mathematics and Learning (15-30) 2 The State of School Mathematics in the United States (31-70) 3 Number: What Is There to Know? (71-114) 4 The Strands of Mathematical Proficiency (115-156) 5 The Mathematical Knowledge Children Bring to School (157-180) 6 Developing Proficiency with Whole Numbers (181-230) 7 Developing Proficiency with Other Numbers (231-254) 8 Developing Mathematical Proficiency Beyond Number (255-312) 9 Teaching for Mathematical Proficiency (313-368) 10 Developing Proficiency in Teaching Mathematics (369-406) 11 Conclusions and Recommendations (407-432) Biographical Sketches (433-440) Index (441-454)