## Abstract

The purpose of this study was to investigate eight preservice middle and high school mathematics teachers’ solution strategies when solving single and multiple proportion problems. Real-world missing-value word problems were used in an interview setting to collect information about preservice teachers’ (PSTs) reasoning about proportional relationships. An explanatory case study methodology with multiple cases was used to make comparisons within and across cases. Analysis of the semi-structured interviews with each PST revealed that using practical problems, in which plastic gears and a mini balance system were provided, and multiple proportion problems facilitated the PSTs’ recognition of the proportional relationships in their solutions. Therefore, they avoided using cross-multiplication and erroneous strategies in those problems. Among the strategies that the PSTs used in solving single and multiple proportion problems, the ratio table strategy was the most frequent and effective strategy. The ratio table strategy enabled the PSTs to recognize the constant ratio and product relationships more than the other strategies. The results of this study illuminate how PSTs reason about proportional relationships when they cannot rely on computation methods like cross-multiplication.

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### 28 November 2018

This correction stands to correct Acknowledgments in the original article.

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## Acknowledgments

Parts of this study were presented at the 2016 annual meeting of the American Educational Research Association Conference, Washington, DC, USA.

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Arican, M. Preservice Middle and High School Mathematics Teachers’ Strategies when Solving Proportion Problems.
*Int J of Sci and Math Educ* **16, **315–335 (2018). https://doi.org/10.1007/s10763-016-9775-1

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### Keywords

- Proportions
- Proportional reasoning
- Proportional relationships
- Ratios