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Anghileri, Julia; Beishuizen, Meindert; Putten, Kees van

doi:10.1023/a:1016273328213

Cited by 35 publications

(19 citation statements)

References 9 publications

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“…Fagginger Auer, Hickendorff, Van Putten, B eguin, & Heiser, 2016;Hickendorff, van Putten, Verhelst, & Heiser, 2010;Selter, 2001;van den Heuvel-Panhuizen et al, 2009). For multidigit division problems such as 168: 12 = , these numberbased strategies include repeated addition, repeated subtraction, partitioning, and compensation (Anghileri, Beishuizen, & van Putten, 2002;Hickendorff, 2013a;Hickendorff et al, 2010). Repeated addition proceeds by repeatedly adding (multiples of) the divisor, until the dividend is reached.…”

Section: Multidigit Division Strategies and Instructionmentioning

confidence: 99%

“…Regarding the impact of instruction on children's strategy use, Anghileri et al (2002); (see also Van Putten, van den Brom-Snijders, & Beishuizen, 2005) found that English fourth graders had more difficulties than their Dutch peers in progressing from numberbased 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, found that Dutch sixth graders' use of the written digit-based strategy was related to whether or not teachers instructed this strategy.…”

Section: Previous Studiesmentioning

confidence: 99%

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

Hickendorff

Torbeyns

Verschaffel

2017

British J of Dev Psycho

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We aimed to investigate upper elementary children's strategy use in the domain of multidigit division in two instructional settings: the Netherlands and Flanders (Belgium). A cross‐sectional sample of 119 Dutch and 122 Flemish fourth to sixth graders solved a varied set of multidigit division problems. With latent class analysis, three distinct strategy profiles were identified: children consistently using number‐based strategies, children combining the use of column‐based and number‐based strategies, and children combining the use of digit‐based and number‐based strategies. The relation between children's strategy profiles and their instructional setting (country) and grade were generally in line with instructional differences, but large individual differences remained. Furthermore, Dutch children more frequently made adaptive strategy choices and realistic solutions than their Flemish peers. These results complement and refine previous findings on children's strategy use in relation to mathematics instruction. Statement of contribution What is already known? Mathematics education reform emphasizes variety, adaptivity, and insight in arithmetic strategies.Countries have different instructional trajectories for multidigit division.Mixed results on the impact of instruction on children's strategy use in multidigit division. What does this study add? Latent class analysis identified three meaningful strategy profiles in children from grades 4–6.These strategy profiles substantially differed between children.Dutch and Flemish children's strategy use is related to their instructional trajectory.

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Section: Multidigit Division Strategies and Instructionmentioning

confidence: 99%

Section: Previous Studiesmentioning

confidence: 99%

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

Hickendorff

Torbeyns

Verschaffel

2017

British J of Dev Psycho

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“…Plunkett (1979) claimed that the algorithms should be discarded, not least because they cause "frustration, unhappiness and a deteriorating attitude to mathematics" (Plunkett, 1979, p.4). Others have criticized the teaching of traditional algorithms simply because many children fail to master them (Anghileri et al, 2002). The presence of systematic errors in students' application of algorithms is well-known (Brown & VanLehn, 1980;Fuson, 1990b;Träff & Samuelsson, 2013) and sometimes justified as a result of students relying solely on rote manipulation of symbols (Fuson, 1992).…”

Section: Discussion About Algorithms In School Mathematicsmentioning

confidence: 99%

The Effect on Students’ Arithmetic Skills of Teaching Two Differently Structured Calculation Methods

Engvall

Samuelsson

Östergren

2020

PEC

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Mastering traditional algorithms has formed mathematics teaching in primary education. Educational reforms have emphasized variation and creativity in teaching and using computational strategies. These changes have recently been criticized for lack of empirical support. This research examines the effect of teaching two differently structured written calculation methods on teaching arithmetic skills (addition) in grade 2 in Sweden with respect to students' procedural, conceptual and factual knowledge. A total of 390 students (188 females, 179 males, gender not indicated for 23) were included. The students attended 20 classes in grade 2 and were randomly assigned to one of two methods. During the intervention, students who were taught and had practiced traditional algorithms developed their arithmetic skills significantly more than students who worked with the decomposition method with respect to procedural knowledge and factual knowledge. These results provided no evidence that the development of students' conceptual knowledge would benefit more from learning the decomposition method compared to traditional algorithm.

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“…For example, Figure 5(a) shows how the chunking method is used to solve 585÷16. Literature (Anghileri, Beishuizen, & van Putten 2002;Khemani & Subramanian, 2012) suggests that partial quotients builds on students' intuitive strategies and allows for greater flexibility in the choice of chunks unlike the standard division algorithm. Although the partial quotients method is described in the textbook, and Pallavi was following the textbook closely, she had avoided introducing this method in her class in the previous years.…”

Section: Year 2: "I Don't Understand How This Methods Work Why Don'tmentioning

confidence: 99%

“…Thus, even those students who use the division algorithm correctly to solve problems may not understand the meaning of the algorithm and why it works. Anghileri, Beishuizen, & van Putten (2002) conducted a comparative study of written solutions to division problems of Grade five students from England and the Netherlands. In England, students were being taught the division algorithm from an early age.…”

Section: Teachers' Knowledge Of Arithmeticmentioning

confidence: 99%

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2018

AJTE

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Cited by 35 publications

References 9 publications

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

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

The Effect on Students’ Arithmetic Skills of Teaching Two Differently Structured Calculation Methods

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