# Csíkos (2016)

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

## Abstract

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.

## Summary

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 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.

## Corrolary

APA
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
BibTeX
@article{Csikos2016,
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}},