Preservice Mathematics Teachers’ Understanding of and Abilities to Differentiate Proportional Relationships from Nonproportional Relationships

Arıcan, Muhammet

doi:10.1007/s10763-018-9931-x

Cited by 29 publications

(37 citation statements)

References 19 publications

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“…Among these strategies, two types of strategies are very common as building additive and multiplicative relationships (Arican, 2019). The first of the strategies is to establish a multiplicative relationship.…”

Section: Students' Cognitive Strategies In Solving Proportional Reasomentioning

confidence: 99%

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Investigation of Proportional Reasoning Problem Solving Processes of Seventh Grade Students: A Mixed Method Research

Öztürk

DEMİR

Akkan

2021

IJonSES

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This study was carried out to examine proportional reasoning problem solving processes of seventh grade students. This study was conducted with the explanatory sequential mixed method design. In this respect, firstly, quantitative data from 56 students were collected and analyzed. Then, qualitative data of the study was collected from six students selected according to their success and analyzed. The quantitative data of the study was consisted of a proportional reasoning skill test and analyzed using predictive statistics. The qualitative data of the study were collected through activity cards and the think-aloud protocol, and content analysis was applied to the collected qualitative data. The findings of the study showed that students were most successful at qualitative comparison. On the other hand, the least success was observed for quantitative comparison, and female students were found to be more successful in proportional reasoning problems.

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Section: Students' Cognitive Strategies In Solving Proportional Reasomentioning

confidence: 99%

“…Multiplication relationships include processes such as multipliply, multiplication and duplication (Lamon, 2012). Additive relationships include mathematical processes such as addition, subtraction and difference (Arican, 2019).…”

Section: Students' Cognitive Strategies In Solving Proportional Reasomentioning

confidence: 99%

Investigation of Proportional Reasoning Problem Solving Processes of Seventh Grade Students: A Mixed Method Research

Öztürk

DEMİR

Akkan

2021

IJonSES

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“…Bu çalışmayı önceki çalışmalardan ayıran başka bir önemli nokta ise çalışmanın bilişsel ve duyuşsal alanı birlikte ele almış olmasıdır. Orantısal akıl yürütme bilişsel alana ait bir beceri olup yapılan çalışmalar daha çok bilişsel olarak incelemeyi amaçlamıştır (Arican, 2019;Ayan ve Bostan, 2018;Howe, Nunes ve Bryant, 2011). Ancak matematik konularında bilişsel özellikler duyuşsal özelliklerle desteklendiğinde matematiğe yönelik becerilerin kazanılması daha kolay olabilir (Öztürk, Akkan ve Kaplan, 2019) .…”

Section: Araştırmanın Gerekçesi Ve Amacıunclassified

The Relationship between Self-Regulation and Proportional Reasoning: The Mediating Role of Reflective Thinking towards Problem Solving

Öztürk

2020

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Bu çalışma 7. sınıf öğrencilerinin problem çözmeye yönelik yansıtıcı düşünme becerilerinin öz-düzenleme düzeyleri ile orantısal akıl yürütme becerileri arasındaki aracılık etkisini incelemek amacıyla yapılmıştır. Çalışmada nicel araştırma desenlerinden ilişkisel araştırma modeli kullanılmıştır. Çalışmada önerilen tahmin modeli 279 ortaokul 7. sınıf öğrencisinden elde edilen verilerle sınanmıştır. Çalışmanın verileri "Problem çözmeye yönelik yansıtıcı düşünme becerisi ölçeği", "Algılanan özdüzenleme ölçeği" ve "Orantısal akıl yürütme becerisi testi" ile toplanmıştır. Toplanan verilere korelasyon analizi ve aracı değişken analizi yapılmıştır. Çalışmanın bulguları, problem çözmeye yönelik yansıtıcı düşünme, öz-düzenleme ve orantısal akıl yürütme becerileri arasında anlamlı düzeyde ilişki olduğuna işaret etmiştir. Aracı değişken analizi sonucu, 7. sınıf öğrencilerinin problem çözmeye yönelik yansıtıcı düşünme becerilerinin özdüzenleme düzeyleri ile orantısal akıl yürütme becerileri arasında kısmi aracı olduğunu göstermiştir. Yansıtıcı düşünme Öz-düzenleme Orantısal akıl yürütme Problem çözme

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“…One of the most reported difficulties in developing students' proportional reasoning is that traditional instruction places more attention to the rule memorization and rote computations. Hence, students usually refer to the cross-multiplication and across-multiplication strategies when solving missing-value problems (Fisher, 1988;Arican, 2018;Arican, 2019). Although these strategies are effective in obtaining correct answers, students apply them without understanding multiplicative relationships presented (Lamon, 2007;Stemn, 2008).…”

Section: Introductionmentioning

confidence: 99%

“…As explained in the previous paragraph, students usually refer to the rote computations and formulas when solving proportion problems without understanding constant ratio and constant product relationships between quantities. Moreover, they frequently attend to the simultaneous increases or decreases and rate of change when determining directly and inversely relationships which are not sufficient in distinguishing proportional relationships from nonproportional relationships (Arican, 2018;Arican, 2019). Therefore, it is essential for mathematics teachers to develop their students' meaningful understanding of ratios, directly, inversely, and nonproportional relationships.…”

Section: Introductionmentioning

confidence: 99%

A diagnostic assessment to middle school students’ proportional reasoning

Arıcan

2019

Turkish Journal of Education

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This study investigated Turkish middle school students' proportional reasoning and provided a diagnostic assessment of their strengths and weaknesses on the ratio and proportion concepts. A proportional reasoning test with 22 multiple-choice items was developed from the context of the loglinear cognitive diagnosis model. The test was developed around four core cognitive skills (attributes) that required in solving middle school ratio and proportion problems. These skills included understanding ratios, directly, inversely, and nonproportional relationships. The test was applied to 282 seventh grade students, and the collected data were analyzed using the Mplus software. The analysis showed that approximately 62% of the students were able to recognize directly proportional relationships. Whereas, roughly 48% of them were able to recognize inversely proportional relationships. Moreover, while 25% of the students did not master any of the four cognitive skills, 39.1% mastered all four of these skills. In addition, many students had difficulty distinguishing proportional relationships from nonproportional relationships. Diagnostic feedbacks on the students' strengths and weaknesses were provided based on the findings.

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Preservice Mathematics Teachers’ Understanding of and Abilities to Differentiate Proportional Relationships from Nonproportional Relationships

Cited by 29 publications

References 19 publications

Investigation of Proportional Reasoning Problem Solving Processes of Seventh Grade Students: A Mixed Method Research

Investigation of Proportional Reasoning Problem Solving Processes of Seventh Grade Students: A Mixed Method Research

The Relationship between Self-Regulation and Proportional Reasoning: The Mediating Role of Reflective Thinking towards Problem Solving

A diagnostic assessment to middle school students’ proportional reasoning

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