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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer and James Hiebert

Although often asked tactfully, a frequent question posed to authors by JRME reviewers is “So what?” Through this simple and well-known question, reviewers are asking: What difference do your findings make? How do your results advance the field? “So what?” is the most basic of questions, often perceived by novice researchers as the most difficult question to answer. Indeed, addressing the “so what” question continues to challenge even experienced researchers. All researchers wrestle with articulating a convincing argument about the importance of their own work. When we try to shape this argument, it can be easy to fall into the trap of making claims about the implications of our findings that reach beyond the data.

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Karen C. Fuson, Diana Wearne, James C. Hiebert, Hanlie G. Murray, Pieter G. Human, Alwyn I. Olivier, Thomas P. Carpenter and Elizabeth Fennema

Researchers from 4 projects with a problem-solving approach to teaching and learning multidigit number concepts and operations describe (a) a common framework of conceptual structures children construct for multidigit numbers and (b) categories of methods children devise for multidigit addition and subtraction. For each of the quantitative conceptual structures for 2-digit numbers, a somewhat different triad of relations is established between the number words, written 2-digit marks, and quantities. The conceptions are unitary, decade and ones, sequence-tens and ones, separate-tens and ones, and integrated sequence-separate conceptions. Conceptual supports used within each of the 4 projects are described and linked to multidigit addition and subtraction methods used by project children. Typical errors that may arise with each method are identified. We identify as crucial across all projects sustained opportunities for children to (a) construct triad conceptual structures that relate ten-structured quantities to number words and written 2-digit numerals and (b) use these triads in solving multidigit addition and subtraction situations.