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Research Article 
EEO. 2016; 15(1): 186-203


Two Distinct Perspectives on Ratios: Additive and Multiplicative Relationships between Quantities

İbrahim Burak Ölmez.

Abstract
The purpose of this study is to investigate how pre-service teachers’ formation of additive and multiplicative relationships support and constrain their understandings of ratios and proportional relationships in terms of quantities. Six pre-service teachers were selected purposefully based on their performances in a previous course. An explanatory case study with multiple cases was used to make comparisons within and across cases. A semi-structured interview was conducted with pairs of pre-service teachers. The results revealed that pre-service teachers’ heavy reliance on additive or multiplicative relationships critically shaped their reasoning about ratios from the two perspectives. Pre-service teachers who only attended to multiplicative relationships were found to have a robust understanding of proportional relationships. Pre-service teachers, who did attend to additive relationships, even if they used multiplicative relationships, struggled to form appropriate proportional relationships from the two perspectives.

Key words: Ratio and Proportion, Addition and Multiplication, Pre-service Teachers


 
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Pubmed Style

İbrahim Burak Olmez. Two Distinct Perspectives on Ratios: Additive and Multiplicative Relationships between Quantities. EEO. 2016; 15(1): 186-203.


Web Style

İbrahim Burak Olmez. Two Distinct Perspectives on Ratios: Additive and Multiplicative Relationships between Quantities. https://ilkogretim-online.org/?mno=124051 [Access: April 07, 2022].


AMA (American Medical Association) Style

İbrahim Burak Olmez. Two Distinct Perspectives on Ratios: Additive and Multiplicative Relationships between Quantities. EEO. 2016; 15(1): 186-203.



Vancouver/ICMJE Style

İbrahim Burak Olmez. Two Distinct Perspectives on Ratios: Additive and Multiplicative Relationships between Quantities. EEO. (2016), [cited April 07, 2022]; 15(1): 186-203.



Harvard Style

İbrahim Burak Olmez (2016) Two Distinct Perspectives on Ratios: Additive and Multiplicative Relationships between Quantities. EEO, 15 (1), 186-203.



Turabian Style

İbrahim Burak Olmez. 2016. Two Distinct Perspectives on Ratios: Additive and Multiplicative Relationships between Quantities. Elementary Education Online, 15 (1), 186-203.



Chicago Style

İbrahim Burak Olmez. "Two Distinct Perspectives on Ratios: Additive and Multiplicative Relationships between Quantities." Elementary Education Online 15 (2016), 186-203.



MLA (The Modern Language Association) Style

İbrahim Burak Olmez. "Two Distinct Perspectives on Ratios: Additive and Multiplicative Relationships between Quantities." Elementary Education Online 15.1 (2016), 186-203. Print.



APA (American Psychological Association) Style

İbrahim Burak Olmez (2016) Two Distinct Perspectives on Ratios: Additive and Multiplicative Relationships between Quantities. Elementary Education Online, 15 (1), 186-203.








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