Preservice Middle and High School Mathematics Teachers’ Strategies when Solving Proportion Problems

Arıcan, Muhammet

doi:10.1007/s10763-016-9775-1

Cited by 28 publications

(23 citation statements)

References 16 publications

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“…Moreover, students' and PSTs' overreliance on using rote computations and rules while solving proportion problems is also noted by researchers (e.g., Fisher, 1988;Harel & Behr, 1995;Orrill & Brown, 2012). Although these rules can be effective in terms of obtaining correct answers, students use them with little understanding of the multiplicative relationships presented (Arican, 2018;Izsák & Jacobson, 2017;Kaput & West, 1994).…”

Section: Introductionmentioning

confidence: 94%

“…In order to conduct this content analysis, I generated an Excel file and recorded summaries of each PST's responses in this file. I considered my research questions and related literature on PSTs' solution strategies (e.g., Fisher, 1988;Arican, 2018) and representations (e.g., Arican, 2019;Johnson, 2017;Lo, 2004) when generating these summaries. The summaries included information about the correctness of solutions and relationships identified, appropriateness of representations provided, relevance of mathematical interpretations, and strategies used in solving these problems.…”

Section: Data Collection and Analysismentioning

confidence: 99%

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Investigating Preservice Teachers’ Determination and Representation of Proportional and Nonproportional Relationships in Terms of Problem Contexts

Arıcan

2020

Necatibey Eğitim Fakültesi Elektronik Fen Ve Matematik Eğitimi Dergisi

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Özet -Bu çalışmada, 46 ortaokul matematik öğretmen adayının çözüm yöntemleri, orantısal olan ve olmayan ilişkileri belirleyebilmeleri ve temsil edebilmeleri problem içerikleri bağlamında incelenmiştir. Öğretmen adaylarına, 2017 ve 2018 güz dönemlerinde, iki adet sorudan oluşan bir kağıt-kalem testi verilmiştir. Adayların kağıt-kalem testine verdikleri cevaplar içerik analizi yöntemi kullanılarak analiz edilmiştir. Analizler sonucunda sekiz öğretmen adayı ile yarı yapılandırılmış görüşmeler gerçekleştirilmiştir. Elde edilen bulgular, öğretmen adaylarının çözüm yöntemlerinin ve orantısal olan ve olmayan ilişkileri belirleyebilmelerinin ve temsil edebilmelerinin problem içeriklerinden etkilendiğini göstermiştir. Alan yazında belirtilenin aksine, öğretmen adayları ters orantılı ilişkiyi belirleme ve temsil etme konusunda doğru orantılı ilişkiyi belirleme ve temsil etmeye göre daha başarılı olmuşlardır. Öte yandan, adaylar en çok orantısal olmayan ilişkinin belirlenmesi ve temsil edilmesinde zorlanmışlardır. Derinlemesine inceleme gerektiren problemler daha gelişmiş çözüm yöntemlerinin ortaya çıkmasını sağlayıp, öğretmen adaylarının ezbere hesaplamaları kullanmaktan kaçınmasına yardımcı olmuştur.

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Section: Introductionmentioning

confidence: 94%

Section: Data Collection and Analysismentioning

confidence: 99%

Investigating Preservice Teachers’ Determination and Representation of Proportional and Nonproportional Relationships in Terms of Problem Contexts

Arıcan

2020

Necatibey Eğitim Fakültesi Elektronik Fen Ve Matematik Eğitimi Dergisi

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“…A solution that included setting up a proportion to solve for an unknown quantity was coded as falling into this category (Arican, 2016;Cullen et al, 2017;Lo & Luo, 2012). Pictorial/direct modeling A solution that involved drawing a picture representing the problem, using a picture as a reference, or solving the problem by using direct modeling was coded as pictorial/direct modeling (Cullen et al, 2017;Kent et al, 2015;Lo & Luo, 2012).…”

Section: Setting Up a Proportionmentioning

confidence: 99%

“…Pictorial/direct modeling A solution that involved drawing a picture representing the problem, using a picture as a reference, or solving the problem by using direct modeling was coded as pictorial/direct modeling (Cullen et al, 2017;Kent et al, 2015;Lo & Luo, 2012). Algebraic A solution that included using an algebraic expression, a symbol for an unknown quantity, or a formula to denote the relationship received this code (Arican, 2016;Fisher, 1988). A solution that used an algebraic expression to set up a ratio was not included in this category if the expression was not used during solving problems.…”

Section: Setting Up a Proportionmentioning

confidence: 99%

Strategic competence for multistep fraction word problems: an overlooked aspect of mathematical knowledge for teaching

Çopur-Genctürk

Doleck

2021

Educ Stud Math

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Prior work on teachers’ mathematical knowledge has contributed to our understanding of the important role of teachers’ knowledge in teaching and learning. However, one aspect of teachers’ mathematical knowledge has received little attention: strategic competence for word problems. Adapting from one of the most comprehensive characterizations of mathematics learning (NRC, 2001), we argue that teachers’ mathematical knowledge also includes strategic competence, which consists of devising a valid solution strategy, mathematizing the problem (i.e., choosing particular strategies and presentations to translate the word problem into mathematical expressions), and arriving at a correct answer (executing a solution) for a word problem. By examining the responses of 350 fourth- and fifth-grade teachers in the USA to four multistep fraction word problems, we were able to explore manifestations of teachers’ strategic competence for word problems. Findings indicate that teachers’ strategic competence was closely related to whether they devised a valid strategy. Further, how teachers dealt with known and unknown quantities in their mathematization of word problems was an important indicator of their strategic competence. Teachers with strong strategic competence used algebraic notations or pictorial representations and dealt with unknown quantities more frequently in their solution methods than did teachers with weak strategic competence. The results of this study provide evidence for the critical nature of strategic competence as another dimension needed to understand and describe teachers’ mathematical knowledge.

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“…El tratamiento de las situaciones de pc en la investigación aparece generalmente integrado en estudios más generales centrados en la ps (Arican, 2018;Bosch, 1994;Carretero, 1989;Levain y Vergnaud, 1995;López y Figueras, 1999). Bosch (1994) estudia el tratamiento de la pc en textos antiguos e identifica técnicas de resolución (método de las proporciones, reducción a la unidad, reducción de la regla de tres compuesta a la simple y método de causas y efectos).…”

Section: Marco Teóricounclassified

Una experiencia de investigación-acción para la enseñanza de la proporcionalidad compuesta

2019

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RESUMEN • En este trabajo describimos y analizamos los resultados de una experiencia de enseñanza de la proporcionalidad compuesta llevada a cabo con alumnos de 1.º y 2.º de secundaria bajo el paradigma de la investigación-acción. La propuesta de enseñanza está elaborada a partir del análisis de los objetos didácticos y los problemas de la enseñanza tradicional. La experimentación se llevó a cabo durante cuatro cursos académicos, en los que se realizaron dos ciclos de investigación-acción. La amplia muestra de trabajo, con unos 120 alumnos involucrados en cada ciclo, y la variedad de instrumentos de recogida de información utilizados durante la fase de acción permiten la obtención de conclusiones sólidas sobre la viabilidad y los puntos fuertes, así como sobre los aspectos mejorables de la propuesta.

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Preservice Middle and High School Mathematics Teachers’ Strategies when Solving Proportion Problems

Cited by 28 publications

References 16 publications

Investigating Preservice Teachers’ Determination and Representation of Proportional and Nonproportional Relationships in Terms of Problem Contexts

Investigating Preservice Teachers’ Determination and Representation of Proportional and Nonproportional Relationships in Terms of Problem Contexts

Strategic competence for multistep fraction word problems: an overlooked aspect of mathematical knowledge for teaching

Una experiencia de investigación-acción para la enseñanza de la proporcionalidad compuesta

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