Solving subtraction problems flexibly by means of indirect addition

Background. Subtraction problems of the type a2 b 1⁄4 ? can be flexibly solved by various strategies, including the indirect addition (IA) strategy ‘howmuch do I have to add to b to get a?’ Although rational task analyses indicate that IA is highly efficient especially on subtractions with small differences between the integers, little research has been done on the frequency and efficiency of this strategy on different types of subtractions.

[1]  Lieven Verschaffel,et al.  Whole number concepts and operations , 2007 .

[2]  Lieven Verschaffel,et al.  Do nonsemantic factors also influence the solution process of addition and subtraction word problems , 1990 .

[3]  Jeffrey Bisanz,et al.  On “Understanding” Children's Developing Use of Inversion , 2009 .

[4]  A. Demetriou.  Cognitive Developmental Change: Mind, intelligence and development: a cognitive, differential and developmental theory of intelligence , 2005 .

[5]  R. Brissiaud,et al.  Teaching and development: Solving “missing addend” problems using subtraction , 1994 .

[6]  Lieven Verschaffel,et al.  Efficiency and flexibility of indirect addition in the domain of multi-digit subtraction , 2009 .

[7]  Marja van den Heuvel-Panhuizen,et al.  Mathe-Didactical Reflections on Young Children's Understanding and Application of Subtraction-Related Principles , 2009 .

[8]  A. W. Blöte,et al.  Students' flexibility in solving two-digit addition and subtraction problems : Instruction effects , 2001 .

[9]  Lieven Verschaffel,et al.  Frequency, efficiency and flexibility of indirect addition in two learning environments , 2010 .

[10]  K. Fuson,et al.  SUBTRACTING BY COUNTING UP: MORE EVIDENCE , 1988 .

[11]  J. Flavell.  On cognitive development. , 1982 .

[12]  Jeff Shrager,et al.  SCADS: A Model of Children's Strategy Choices and Strategy Discoveries , 1998 .

[13]  Richard Cowan,et al.  Does it all add up? Changes in children's knowledge of addition combinations, strategies, and principles , 2003 .

[14]  A. W. Blöte,et al.  Mental computation and conceptual understanding , 2000 .

[15]  K. Fuson,et al.  Instruction Supporting Children's Counting on for Addition and Counting up for Subtraction. , 1992 .

[16]  A. Treffers,et al.  The empty number line in Dutch second grades: Realistic versus gradual program design , 1998 .

[17]  R. Siegler,et al.  Older and younger adults' strategy choices in multiplication: testing predictions of ASCM using the choice/no-choice method. , 1997, Journal of experimental psychology. General.

[18]  C. Thornton.  Solution strategies: Subtraction number facts , 1990 .

[19]  Lieven Verschaffel,et al.  Young Children's Understanding and Application of Subtraction-Related Principles , 2009 .

[20]  R. Siegler,et al.  The rebirth of children's learning. , 2000, Child development.