Diagnosing conflict factors in calculus through students' writings

Aspinwall, Leslie; Miller, L. Diane

doi:10.1016/s0732-3123(01)00063-3

Cited by 14 publications

(8 citation statements)

References 2 publications

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“…Bu durum türevin farklı tanımları ve gösterimlerini anlamaya engel olmaktadır (Kula, 2013). Hâlbuki öğrenciler analizdeki nümeriksel, grafiksel ve analitiksel gösterimler arasında ilişki kurabildikleri oranda anlamaları daha da gelişmektedir (Aspinwall & Miller, 2001).İkinci ve dördüncü sınıf öğrencilerinin çalışmadaki performansları göz önüne alındığında bazı bariz farklılıklar dikkati çekmiştir. Öğrencilerin türev tanımı yorumları incelendiğinde ikinci sınıf öğrencileri türev tanımını daha çok oran ve oranının limiti kavramları terimlerini kullanarak açıklama yapmaya çalışmışlardır.…”

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Li̇sans Öğrenci̇leri̇ni̇n Türev Tanimiyla İlgi̇li̇ Yorumlari Ve Türeve Yükledi̇kleri̇ Anlamlar

Doruk¹,

Duran²,

Kaplan³

2018

Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi

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ÖZETBu çalışmanın amacı ilköğretim matematik öğretmenliği bölümü öğrencilerinin türev tanımını yorumlama becerilerini ve türev kavramına yönelik yükledikleri anlamları ortaya çıkarmaktır. Nitel araştırma desenlerinden durum çalışmasına göre planlanan bu çalışma, 2014-2015 öğretim yılı bahar döneminin başında gerçekleştirilmiştir. Çalışmanın katılımcıları, Doğu Anadolu Bölgesi'ndeki bir devlet üniversitesinin ilköğretim matematik öğretmenliği bölümünde öğrenim gören ikinci (n=31) ve dördüncü (n=29) sınıf öğrencileridir (n=60). Çalışmanın veri toplama aracı, araştırmacılar tarafından geliştirilen Türev Anlayış Formudur (TAF). Çalışma sonucunda öğrencilerin türevin formel tanımını yorumlamakta güçlük yaşadıkları tespit edilmiştir. Bir noktada türevli fonksiyon kavramına yönelik çoğunlukla ilgili fonksiyonun o noktada tanımlı, limitli, sürekli olması ve fonksiyon kuralının türevinin işlemsel olarak alınabilmesi anlamlarını yükledikleri ortaya çıkmıştır.Anahtar Kelimeler: Türev, türev tanımı, matematik eğitimi INTERPREDATIONS RELATED TO THE DEFINITION OF DERIVATIVE AND ASCRIBED MEANINGS TO DERIVATIVE OF UNDERGRADUATE STUDENTS ABSTRACTThe purpose of this study was to reveal undergraduate students' interpretation skills related to the definition of derivative and ascribed meanings to derivative by the students. This study planned according to the case study of qualitative research designs was carried out at the beginning of spring semester of 2014-2015 academic terms. The participants of the study were second grade (n=31) and fourth grade (n=29) students studying in the department of primary mathematics teacher training in a state university in the province of Eastern Anatolia Region of Turkey (n=60). Data collection tool of the study was Derivative Understanding Form (DUF) developed by the researchers. Results of the study showed that the students had difficulty in interpreting the formal definition of derivative. It had been seen that ascribed meanings to differentiable function at a point by the students mostly defined as "the function was defined, limited, continuous at that point" and "operational differentiation of the function rule". Key Words:Derivative, the definition of derivative, mathematics education (Fırat Üniversitesi, 12-14 Mayıs 2016, Elazığ, Türkiye). ** Dr. Öğr. Üyesi, Hakkari Üniversitesi, Eğitim Fakültesi, mdoruk20@gmail.com *** Dr., Matematik Öğretmeni, MEB, Amasya Plevne Ortaokulu, denizyildizi2805@hotmail.com **** Prof. Dr., Atatürk Üniversitesi, Kazım Karabekir Eğitim Fakültesi, akaplan@atauni.edu.tr Muhammet DORUK, Murat DURAN, Abdullah KAPLAN 835 * Bu çalışmanın bir bölümü Uluslararası Matematik ve Matematik Eğitimi Konferansında sözlü bildiri olarak sunulmuştur 1.GİRİŞMatematikteki temel öğrenme alanlarından biri olan analizin en büyük hedeflerinden birisi değişen nicelikleri ve olguları anlamak, bunları yorumlamak ve geleceğe yönelik tahminlerde bulunmaktır (Çetinkaya, Erbaş ve Alacacı, 2013). Değişim oranı ve hareket gibi kavramları anlamlandırmasının yanında bu kavramları sembollerle ...

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Li̇sans Öğrenci̇leri̇ni̇n Türev Tanimiyla İlgi̇li̇ Yorumlari Ve Türeve Yükledi̇kleri̇ Anlamlar

Doruk¹,

Duran²,

Kaplan³

2018

Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi

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“…Berikut ini adalah berbagai kesulitan yang merupakan masalah umum dalam pembelajaran kalkulus; (1) konsep bilangan tak hingga (Tall, 2001), (2) menggambar grafik (Pichat & Ricco, 2001), (3) manipulasi aljabar (Aspinwall & Miller, 2001), (4) konsep limit fungsi (Tall & Vinner, 1981;Williams, 1991;Cornu, 1991;Szydlik, 2000;Juter, 2005;Naidoo & Naidoo;2007;Susilo, 2011;Syaripuddin, 2011;Denbel, 2014), (5) konsep limit dan kekontinuan fungsi (Bezuidenhout, 2001;Karatas et al, 2011), (6) memahami konsep turunan fungsi (Tarmizi, 2010;Tall, 2010;2012;Pepper et al, 2012;Hashemi et al ;, dan (7) konsep integral fungsi (Orton, 1983;Tall, 1993;Kiat, 2005;Metaxas, 2007;Yee & Lam, 2008;Mahir, 2009;Rubio & Gomez-Chacon, 2011;Usman, 2012;Salazar, 2014;Zakaria & Salleh, 2015;Serhan, 2015;Yudianto, 2015;Ferrer, 2016). Berbagai jenis kesulitan yang dialami oleh para mahasiswa ini akan berdampak pada hasil belajar dan juga pada kemampuan mahasiswa untuk berpikir secara logis, analitis, sistematis, kritis, dan kreatif.…”

Section: Unnes Journalsunclassified

Kesulitan Belajar Mahasiswa pada Materi Aplikasi Integral untuk Luas Daerah dalam Perspektif Disposisi Matematis

Susilo

Darhim

Prabawanto

2019

Kreano

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Penelitian ini bertujuan untuk mendeskripsikan kesulitan belajar yang dialami mahasiswa pada materi aplikasi integral untuk luas daerah dalam perspektif disposisi matematis. Penelitian ini menggunakan metode deskriptif eksploratif dengan instrumen skala, tes, dokumentasi, dan catatan lapangan. Data diambil dari 80 mahasiswa dari program studi S1 pendidikan matematika di sebuah universitas di Jawa Tengah. Hasil penelitian menunjukkan bahwa mahasiswa dengan disposisi matematis positif sedang dan tinggi memiliki jenis kesulitan yang sama yaitu (1) kesulitan dalam menggambar grafik, (2) kesulitan dalam menentukan daerah yang dicari luasnya, (3) kesulitan dalam menentukan batas integral, (4) kesulitan dalam menggunakan rumus integral, dan (5) kesulitan dalam memahami integral. Mahasiswa dengan disposisi matematis positif rendah selain mengalami kelima kesulitan tersebut, juga mengalami kesulitan dalam menghitung integral. Terdapat tren atau kecenderungan peningkatan persentase pada 2 jenis kesulitan, dan penurunan persentase pada 1 jenis kesulitan, sedangkan pada 3 jenis kesulitan yang lain bersifat fluktuatif.The purpose of this research was to described the learning difficulties experienced by students in integral application material for the area in the perspective of mathematical dispositions. This research used descriptive exploratory methods with scale, tests, documentation, and field notes instruments. Data was taken from 80 undergraduate students from the mathematics education study program at a university in Central Java. The results showed that students with moderate and high positive mathematical dispositions had the same types of difficulties, namely (1) difficulties in drawing graphics, (2) difficulties in determining the area to be searched for, (3) difficulties in determining integral boundaries, (4) difficulties in using integral formulas, and (5) difficulties in understanding integrals. Students with low positive mathematical dispositions in addition to experienced these five difficulties, also experienced difficulties in calculating integrals. There is a trend or tendency to increase percentage in 2 types of difficulties, and a decrease in percentage in 1 type of difficulty, while in 3 other types fluctuating.

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“… the modes of representation,  the relationship to the slope of a tangent,  the relationship to the concept of rate of change,  the relationship to the derivative of a function at a point,  the global view of the derived function, and  the relationship between the first and second derivative of a function (Artigue, 1991;Aspinwall & Miller, 2001;Orton, 1983;Sánchez-Matamoros, García & Llinares, 2006, 2008. It has also been reported that students encounter problems connecting the relationship between a function and a derived function to the relationship between the first and second derivative of a function (Baker, Cooley, & Trigueros, 2000;García, Llinares, & Sánchez-Matamoros, 2011).…”

Section: Introductionmentioning

confidence: 99%

How do pre-service mathematics teachers respond to students unexpected questions related to the second derivative

Ünver

2020

JPR

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The aim of this study was to determine the how pre-service mathematics teachers respond to unexpected questions from students about the second derivative. A qualitative research method was used for this purpose, applying a case study framed as an in-depth analysis of how pre-service mathematics teachers respond to students' ideas. The participants were 39 pre-service mathematics teachers who were in their final year of their mathematics teacher education program. The pre-service teachers, who participated voluntarily, were asked to respond to open-ended questions relating to a scenario that included a teacher, as well as her 12th-grade students. The written responses that the participants provided constitute the data of this study. The results revealed that most of the participants could not effectively answer an unexpected question from students. Nearly half of the participants stated that they could not answer the question. Others ignored it, while some acknowledged the question and attempted to give an answer. Moreover, a small number of the participants made an effort to explain and demonstrate the concept of concavity by drawing the graphs of the function and relating them to the first derivative.

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Diagnosing conflict factors in calculus through students' writings

Cited by 14 publications

References 2 publications

Li̇sans Öğrenci̇leri̇ni̇n Türev Tanimiyla İlgi̇li̇ Yorumlari Ve Türeve Yükledi̇kleri̇ Anlamlar

Li̇sans Öğrenci̇leri̇ni̇n Türev Tanimiyla İlgi̇li̇ Yorumlari Ve Türeve Yükledi̇kleri̇ Anlamlar

Kesulitan Belajar Mahasiswa pada Materi Aplikasi Integral untuk Luas Daerah dalam Perspektif Disposisi Matematis

How do pre-service mathematics teachers respond to students unexpected questions related to the second derivative

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