An Experimental Research on Error Patterns in Written Subtraction

Fiori, Carla; Zuccheri, Luciana

doi:10.1007/s10649-005-7530-6

Cited by 25 publications

(18 citation statements)

References 4 publications

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“…Various studies (e.g., Beishuizen, Van Putten, & Van Mulken, 1997;Fiori & Zuccheri, 2005;Kraemer et al, 2009) have shown that SE students experience many difficulties in solving subtraction problems up to 100 that require crossing the ten, i.e., problems in which the ones digit of the subtrahend is larger than that of the minuend (e.g., 62 − 58). These problems can be solved in different ways that clearly have a different success rate.…”

Section: Solving Subtraction Problems With Crossing the Tenmentioning

confidence: 99%

Special education students’ use of indirect addition in solving subtraction problems up to 100—A proof of the didactical potential of an ignored procedure

Peltenburg

Heuvel–Panhuizen

Robitzsch³

2011

Educ Stud Math

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In this study, we examined special education students' use of indirect addition (subtraction by adding on) for solving two-digit subtraction problems. Fifty-six students (8-to 12-year-olds), with a mathematical level of end grade 2, participated in the study. They were given a computer-based test on subtraction with different types of problems. Although most students had not been taught indirect addition for solving subtraction problems, they frequently applied this procedure spontaneously. The item characteristics were the main prompt for using indirect addition. Context problems that reflect an addingon situation and problems that have a small difference between the minuend and subtrahend most strongly elicited the use of the indirect addition procedure. Moreover, indirect addition was identified as a highly successful procedure for special education students, and the best predictor of a correct answer was found in combination with a stringing strategy.

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Section: Solving Subtraction Problems With Crossing the Tenmentioning

confidence: 99%

Special education students’ use of indirect addition in solving subtraction problems up to 100—A proof of the didactical potential of an ignored procedure

Peltenburg

Heuvel–Panhuizen

Robitzsch³

2011

Educ Stud Math

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show abstract

“…The study by Fiori and Zuccheri (2005) does not lead to a clear decision as well, as it is mainly focused on error patterns and, in addition, did not use the equal addition method as such (see above).…”

Section: Different Subtraction Algorithmsmentioning

confidence: 99%

Taking away and determining the difference—a longitudinal perspective on two models of subtraction and the inverse relation to addition

et al. 2011

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Subtraction can be understood by two basic models-taking away (ta) and determining the difference (dd)-and by its inverse relation to addition. Epistemological analyses and empirical examples show that the two models are not relevant only in single-digit arithmetic. As curricula should be developed in a longitudinal perspective on mathematics learning processes, the article highlights some exemplary steps in which the inverse relation is discussed in light of the two models, namely mental subtraction, the standard algorithms for subtraction, negative numbers and manipulations for solving algebraic equations. For each step, the article presents educational considerations for fostering a flexible use of the two models as well as of the inverse relation between subtraction and addition. In each section, a mathedidactical analysis is conducted, empirical results from literature as well as from our own case studies are presented and consequences for teaching are sketched. Two models of subtractionMany adults as well as school children understand subtraction solely as taking away. In this paper, we shall show the importance of the second model of subtraction (determining the difference) and the relevance of the inverse relation between addition and subtraction by adopting a longitudinal perspective. 1 Beforehand, some remarks are necessary with respect to the notions that we use. 1 Note that we do not present an empirical longitudinal study where we followed a set of students or a programme over a longer period of time. We adopt a longitudinal perspective for conducting a mathedidactical analysis (van den Heuvel-Panhuizen and Treffers, 2009).C. Selter (*) : S. Prediger : M. Nührenbörger : S. Hußmann

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“…However, most of these studies did not address learning from errors per se. Going deeper into this issue, a line of research has investigated students' error patterns from a diagnostic perspective (for mathematics : Clements, 1980;Fiori & Zuccheri, 2005;Resnick, 1984) and has elaborated on error-types and taxonomies (e.g. Frese & Zapf, 1994).…”

Section: Current State Of Researchmentioning

confidence: 99%