Csíkos (2016)

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Strategies and Performance in Elementary Students' Three-Digit Mental Addition


The focus of this study is the relationship between students' performance in mental calculation and the strategies they use when solving three-digit mental addition problems. The sample comprises 78 4th grade students (40 boys and 38 girls). Their mean age was 10 years and 4 months. The main novelties of the current research include (1) exploration of the relationship between strategy use and response time, (2) revealing the uniformity of the strategies used throughout the series of tasks, and (3) pointing out between-school differences in strategy use, but not in success rate or response time. Although connections between strategy use and success have been demonstrated, about half of the students insisted on one given strategy throughout the series of eight tasks. The results indicate that teachers developed their students' mental calculation skills in a way such that some strategies became preferred and others ignored. In the discussion a comparison to previous research results and educational implications are provided.


Csíkos summarizes some of the different names used for various strategies with this table:

Example Fuson et al. (1997) Selter (2001) Heinze, Marschick, & Lipowsky (2009)
123+456=123+400+50+6 "begin-with-one-number" stepwise stepwise
123+456=(100+400)+(20+50)+(3+6) decompose hundreds-tens-ones htu (hundreds, tens, ones) split
527+398=527+400-2 change-both-numbers auxillary (simplifying) compensation (simplifying)
701-698=the number which must be added to 698 to get 701 unknown addend adding up indirect addition

Csíkos used 8 tasks with the students: the first four (342+235, 143+426, 702+105, 284+202) were designed to encourage students to use a stepwise or split strategy. Student success rates on the first four tasks were strong (>94%) with response times less than 14 seconds. About 25-30% of students used a stepwise strategy and 40-50% of students used a split strategy, with about a quarter of students using a mental version of a pencil-and-paper "standard algorithm" strategy. Tasks 5 and 6 (527+398, 498+256) should have elicited a simplifying strategy. About 70% of students were successful on Tasks 5 and 6, with response time around 23 seconds. About 30% used a stepwise strategy, 36% used a split strategy, and 27% used a mental version of the written algorithm. On Task 6 only, 2.7% of students used a simplifying strategy. Tasks 7 and 8 (701-694, 646-583) should have encouraged an indirect addition strategy. Csíkos saw only about a 50% success rate on these tasks, which took 24-28 seconds to answer. About 37% used a stepwise strategy, 17-21% used a split strategy, and 25% used a mental version of the written algorithm. Just 9.3% of students used indirect addition on Task 7, and only 6.7% used that strategy on Task 8. Forty-seven percent of students applied the same strategy on all eight tasks. Analysis of common student errors showed that "early over-automatization of the written computation strategy" (p. 135) led to a number of student errors.

The choice of strategy had a medium effect on response time for Tasks 1-6, but a large effect on Tasks 7-8. Students using indirect addition (N=6) had the fastest response at about 12 seconds, while students mentally performing the written algorithm (N=6) had the slowest response at about 39 seconds. Both students using stepwise (N=15) and split (N=5) had response times of about 28 seconds. Students who used different strategies for the eight tasks were, in general, no faster or slower than students who only used one strategy. There was also no significant connection between success on each task and the strategy used, although when all 8 tasks were considered together students using the same strategy had slightly more success. Digging further into the data, Csíkos found that the preferred strategy used by students depended on which of the two schools in the study they attended.

Csíkos acknowledges some limitations of this study. There may have been too few tasks to gauge students' mental calculation abilities, and students' use of a mental version of the written algorithm is likely influenced by the recency most would have learned it as part of the school curriculum. Csíkos also speculated that textbook choice may be a factor, as only one 45-minute lesson in the Grade 4 text focused on mental addition and subtraction, or, more likely, that teachers' beliefs about arithmetic influenced students' choice of strategies or whether they used multiple strategies.


Csíkos, C. (2016). Strategies and performance in elementary students’ three-digit mental addition. Educational Studies in Mathematics, 91(1), 123–139. http://doi.org/10.1007/s10649-015-9658-3
author = {Cs{\'{\i}}kos, Csaba},
doi = {10.1007/s10649-015-9658-3},
journal = {Educational Studies in Mathematics},
number = {1},
pages = {123--139},
title = {{Strategies and performance in elementary students' three-digit mental addition}},
url = {http://link.springer.com/article/10.1007/s10649-015-9658-3},
volume = {91},
year = {2016}