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## 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.

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 Page 190

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Adding + It Up: Helping Children Learn Mathematics

support and justification for different procedures. Rather, the research provides evidence that, at any one time, most children use a small number of procedures and that teachers can learn to identify them and help children learn procedures that are conceptually more efficient (such as counting on from the larger addend rather than counting all).22

Mathematical proficiency with respect to single-digit addition encompasses not only the fluent performance of the operation but also conceptual understanding and the ability to identify and accurately represent situations in which addition is required. Providing word problems as contexts for adding and discussing the advantages and disadvantages of different addition procedures are ways of facilitating students’ adaptive reasoning and improving their understanding of addition processes.

#### Single-Digit Subtraction

Subtraction follows a progression that generally parallels that for addition (see Box 6–3). Some U.S. children also invent counting-down methods that model the taking away of numbers by counting back from the total. But counting down and counting backward are difficult for many children.23

 Box 6–3 Learning Progression for Single-Digit Subtraction
 Page 190
 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)