Solution strategies and adaptivity in multidigit division in a choice/no-choice experiment: Student and instructional factors

Grade‐related differences in strategy use in multidigit division in two instructional settings

“…(); (see also Van Putten, van den Brom‐Snijders, & Beishuizen, ) found that English fourth graders had more difficulties than their Dutch peers in progressing from number‐based to digit‐based strategies, reflecting the instructional differences: a gradual transition in the Dutch curriculum based on RME's principles of progressive schematization versus a discontinuous transition in the English curriculum. Fagginger Auer, Hickendorff, & van Putten () found that Dutch sixth graders’ use of the written digit‐based strategy was related to whether or not teachers instructed this strategy. So, the few studies that have examined the relation between strategy instruction and children's strategy competence in division suggest that instruction impacts strategy use, in particular the use of the digit‐based strategy.…”

“…First, the digit‐based strategy involved the long‐division algorithm (see Figures A and B). Second, in the column‐based strategy (Figures C and D), multiples of the divisor are repeatedly subtracted from the dividend, using a structured vertical notation (Fagginger Auer, Hickendorff, & van Putten, ; Treffers, ). Note that the number of steps made can differ between solutions.…”

“…Compared to the other three computational operations, multidigit division has received limited research attention. Recent Dutch studies showed that in the period 1997 to 2011, sixth graders in national assessments had an increasing tendency to solve multidigit division problems mentally without making written notes – most likely with a number‐based strategy; that mental strategies were less accurate but faster than written ones; that a substantial number of children did not adaptively choose between written or mental strategies; that the format of the problem (contextual vs. symbolic) did not affect children's strategy use; that children with lower mathematical abilities were more likely to use mental strategies than their higher achieving peers; and that girls were more inclined to use a written strategy than boys (Fagginger Auer, Hickendorff, & van Putten, ; Fagginger Auer, Hickendorff, van Putten, Béguin, et al. ; Hickendorff, ; Hickendorff, Heiser, Van Putten, & Verhelst, ; Hickendorff et al ., ).…”

Dutch sixth graders’ use of shortcut strategies in solving multidigit arithmetic problems

“…The studies of Fagginger Auer et al (2016a) with Dutch sixth graders showed that in multidigit division, shortcut strategies were used rather frequently but still in a minority of solutions, and more often when students calculated mentally (in the head) than when they wrote their solution steps down. However, since the factors that were identified to affect shortcut strategy use in addition and subtraction were not studied systematically in the studies addressing multiplication and division, it is yet unknown whether these factors' effects generalize beyond the additive domain.…”

“…Because the dependent variables were dichotomous (shortcut strategy used yes or no in research questions 1 to 3, and answer correct or incorrect in research question 4), we used binary logistic random effect models, or equivalently multilevel logistic regression models, (Jaeger 2008; see also applications by Fagginger Auer et al 2016aAuer et al , 2016b. We specified these models with random intercepts for students, schools, and items (De Boeck 2008).…”