Mathematical Knowledge for Teaching the Function Concept and Student Learning Outcomes

Hatısaru, Vesife; Erbaş, Ayhan Kürşat

doi:10.1007/s10763-015-9707-5

Cited by 35 publications

(40 citation statements)

References 32 publications

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“…These bases for mathematical proficiency have been variously described as the practices that students engage with and demonstrate that they can do as they learn and use the mathematical content (ACARA, 2016; National Council of Teachers of Mathematics [NCTM], 2014). With context related factors (e.g., the school, home, wider education system) in the lesson implementation in mind (Kilpatrick et al, 2001), the nature of classroom mathematics teaching impacts the development of mathematical proficiency in students (Hatisaru, 2017;Hiebert & Grouws, 2007;NCTM, 2000).…”

Section: Introductionmentioning

confidence: 99%

Exploring Evidence of Mathematical Tasks and Representations in the Drawings of Middle School Students

Hatısaru

2020

INT ELECT J MATH ED

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The drive to explore students' experiences in mathematics classrooms remains imperative for mathematics education research in order to better understand how effective teaching and learning classroom practices lead to desirable learning outcomes. As part of a larger research project exploring a group of 120 Turkish middle school students' (grades 6 to 8, aged 11 to 14) perceptions of their mathematics classroom experiences, this article presents an analysis of the nature of mathematical tasks and the forms of mathematical representations depicted in students' drawings. An analysis of the data obtained from the students' drawing task (Draw a Mathematics Classroom Test) revealed little to no variety in students' classroom experiences in relation to the types of mathematical tasks and mathematical representations. The most common mathematical tasks were found to be tasks that focus on procedural skills, while the most common way students represented the mathematics was through symbolic representations. None of the student drawings involved physical or contextual representations. Findings raise concerns about whether Turkish students are well prepared for the demands of the 21 st century.

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Section: Introductionmentioning

confidence: 99%

Exploring Evidence of Mathematical Tasks and Representations in the Drawings of Middle School Students

Hatısaru

2020

INT ELECT J MATH ED

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“…The rulebased definition was a category stated by Vinner and Dreyfus (1989) and Viirman et al (2010). Being one of the most observed definitions in both the literature and textbooks (Akkoç & Tall, 2005;Hatisaru & Erbas, 2017;Vinner & Dreyfus, 1989), using Drichlet-Bourbaki definition more than other definitions was a usual finding. As Viirman et al (2010) stated, the structural Bourbaki definition was used in upper-secondary schools (Akkoç & Tall, 2005;Hatisaru & Erbas, 2017), but in their study, Viirman et al (2010) found most of their sample (student teachers and engineering students) used rule-based definition as defined in their textbooks.…”

Section: Discussionmentioning

confidence: 95%

Examination of Pre-service Mathematics Teachers’ Mental Constructions of Function Transformation

Boz-Yaman¹,

Koyunkaya²

2019

ADN

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Learning and teaching function transformation has a significant place since it provides new opportunities for learners to use, reflect and discover knowledge related to the concept of function. This study's main goals related to the importance of learning function transformation are to examine pre-service mathematics teachers' (PMTs) mental constructions of function transformation from APOS theory perspective and identify their concept images and concept definitions of function transformations. Two frameworks, APOS theory and concept images and concept definitions, were considered in this study. The qualitative study adopted case study design. The participants were three female PMTs. Clinical interview methodology was used to collect the main data. Data were analyzed based on the APOS framework, and the descriptive analysis method was used in the process. The results of the study present PMTs' mental constructions as well as to their concept images or definitions of function transformation. In this study it is found that PMTs had limited knowledge regarding function transformation, but their mental constructions were changed throughout the process and they partially overcame their difficulties related to the families of functions and related function concept images and definitions.

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“…Por otro lado, estudios sobre el conocimiento de los profesores sobre la función (Even, 1993;Hatisaru & Erbas, 2015;Wilson, 1994) informan que la mayoría de los profesores desconocen aspectos conceptuales sobre ella, aprueban definiciones informales y las perciben como definiciones matemáticamente formales, identifican ejemplos estándar de funciones, y manifiestan dificultades para identificar fenómenos físicos que se modelan con relaciones funcionales. Del mismo modo, la naturaleza arbitraria de las funciones está ausente, y muy pocos estudiantes pueden explicar la importancia y origen del requerimiento de la univalencia.…”

Section: Magisunclassified

Significados de la función pretendidos por el currículo de matemáticas chileno

Pino-Fan

Urrea

Castro

2019

magis

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En esta investigación, analizamos la representatividad de los significados pretendidos para la función por el currículo chileno de matemáticas. Para ello, se realiza tanto la reconstrucción del significado holístico de referencia, mediante una revisión documental de estudios histórico-epistemológicos, como la determinación del significado pretendido por el currículo chileno de matemáticas, para la función, a través del análisis de sus programas de estudio y de libros de texto sugeridos. Los resultados permiten evaluar la riqueza matemática de los significados pretendidos por el currículo chileno, además de proporcionar información que los profesores deberían conocer para gestionar adecuadamente los aprendizajes de sus estudiantes.

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Mathematical Knowledge for Teaching the Function Concept and Student Learning Outcomes

Cited by 35 publications

References 32 publications

Exploring Evidence of Mathematical Tasks and Representations in the Drawings of Middle School Students

Exploring Evidence of Mathematical Tasks and Representations in the Drawings of Middle School Students

Examination of Pre-service Mathematics Teachers’ Mental Constructions of Function Transformation

Significados de la función pretendidos por el currículo de matemáticas chileno

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