Mehmet Ozmantar
University of Gaziantep, Mathematics Education, Faculty Member
Sınıf içi uygulamaların temel amaçlarından biri uygun ve etkili bir öğretim sağlamaktır. Bu çalışmada etkili matematik öğretimine ilişkin kavramsal bir çerçeve önerisinin ortaya konulması amaçlanmıştır. Bu amacı gerçekleştirmek için son... more
Sınıf içi uygulamaların temel amaçlarından biri uygun ve etkili bir öğretim sağlamaktır. Bu çalışmada etkili matematik öğretimine ilişkin kavramsal bir çerçeve önerisinin ortaya konulması amaçlanmıştır. Bu amacı gerçekleştirmek için son yıllarda üretilen ve öğretim uygulamalarının etkililiğini değerlendirmek için geliştirilen çerçeveler üzerine odaklanılmıştır. Eleştirel ve sistematik alanyazın incelemesi sonucunda 12 farklı öğretim değerlendirme çerçevesi belirlenmiştir. Bu çerçeveler çeşitlilik ve kapsamlılık bağlamında karşılaştırmalı olarak içerik analizine tabi tutulmuştur. Analizler sonucunda etkili matematik öğretimine ilişkin oluşturulacak çerçevenin yedi farklı boyut üzerinden yapılandırılabileceği belirlenmiştir: bağlam değişkenleri, planlama ve hazırlık, sınıf ortamı, sınıf içi uygulamalar, değerlendirme, ürün değişkenleri ve mesleki sorumluk. Belirlenen boyutlar arasındaki ilişkiler, bütüncül bir bakış açısı ortaya koymak amacıyla modellenmiş ve buna dayalı olarak da kav...
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Bu calismada ogretmenlerin etkinlik uygulama sirasinda ustlendikleri ve ogrencileri icin belirledikleri roller ile bu rollerin etkinlik uygulamasina olan etkilerinin incelenmesi amaclanmistir. Bu calismada nitel arastirma yontemlerinden... more
Bu calismada ogretmenlerin etkinlik uygulama sirasinda ustlendikleri ve ogrencileri icin belirledikleri roller ile bu rollerin etkinlik uygulamasina olan etkilerinin incelenmesi amaclanmistir. Bu calismada nitel arastirma yontemlerinden coklu durum calismasi kullanilmistir. Bu baglamda bir matematik ve bir sinif ogretmeninin uyguladiklari etkinliklerin video kayitlari ve planlarinin yazili dokumanlari incelenmistir. Incelemede ogretmen ve ogrencilerin ortaya cikan rolleri belirlenmistir. Yapilan analizler sonucunda etkinlik uygulama surecinde ogretmen ve ogrenci rollerinin sekillendiren bir takim dinamikler belirlenmistir. Bunlar arasinda, ogretmen oryantasyonu, etkinlik icin secilen gorevin ozelligi, materyal kullanimi, uygulama icin ayrilan sure ve bu surenin kullanim sekli konulari one cikmistir. Bu dinamikler ile birlikte ortaya cikan roller arasindaki etkilesimin de uygulamaya olan etkisi tartisilmistir.
Research Interests: Art and Social Science
Bu calismada uzunluk olcme ve farkli uzunluklarin karsilastirilmasina iliskin ogrenci dusunusleri incelenmistir. Arastirmanin orneklemini 4, 5 ve 6. siniflardan 68’er ogrenci olmak uzere toplam 204 ogrenci olusturmaktadir. Veri toplama... more
Bu calismada uzunluk olcme ve farkli uzunluklarin karsilastirilmasina iliskin ogrenci dusunusleri incelenmistir. Arastirmanin orneklemini 4, 5 ve 6. siniflardan 68’er ogrenci olmak uzere toplam 204 ogrenci olusturmaktadir. Veri toplama araci olarak uzunluk kavramina dair acik uclu sorularin bulundugu bir form kullanilmistir. Formda bulunan bazi sorularda verilen sekillerin uzunluklarinin bulunmasi istenmis, bazi sorularda ise verilen iki seklin uzunluklarinin kiyaslanmasi istenmistir. Veriler nitel olarak analiz edilmistir. Analizlerden elde edilen bulgularda ogrencilerin cogunlukla uzunluk olcerken birim kullanarak olcme yapmalarina karsin uzunluklari kiyaslarken gorunuse gore karar verdikleri gorulmustur. Arastirmadan elde edilen bulgulara gore olcmeye dayali cevaplar kategorisinde katilimcilarin frekanslarinin dusuk oldugu gorulmektedir. Bu da katilimcilarin daha cok gorsel-butunsel degerlendirme yaptiklarini, birim yinelemeyi ve sekillerin parcalarini ayri ayri karsilastirmayi v...
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This paper is a by-product of a research that aimed to explore primary teachers" preparedness of the implementation of the new curriculum with particular regard to their pedagogical content knowledge. The study is carried out with... more
This paper is a by-product of a research that aimed to explore primary teachers" preparedness of the implementation of the new curriculum with particular regard to their pedagogical content knowledge. The study is carried out with 216 primary teachers working in 104 different schools in a large province in Turkey. Teachers were applied a questionnaire that included open-ended questions on different mathematical concepts covered in the primary mathematics curriculum. We report only on the questionnaire item on fraction in this paper. The findings obtained from this item show that almost a quarter of teachers have serious mathematical difficulties and misconceptions with regard to fractions. We discuss the concerns that these findings raise in terms of the implementation of the new curriculum and the issue of teachers" professional development
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The aim of this study is to designate the mathematics teachers' needs, evaluations and expectations of inservice training programs that constitute an important dimension of teacher professional development. This is a descriptive study... more
The aim of this study is to designate the mathematics teachers' needs, evaluations and expectations of inservice training programs that constitute an important dimension of teacher professional development. This is a descriptive study and adopts a survey method. Participants of the study were 214 mathematics teachers employed in state schools. Of them, 104 were working in high schools and 110 in middle schools. Data were collected via a questionnaire with openended items. The written responses of the participants were subject to content analysis. Through the analysis, the topics that participants received training as well as stated needs within and outside of their field (i.e. mathematics education) were determined; their evaluations and expectations of the training programs were put forth; and the favoured personal and professional qualities of the trainers were ascertained. The findings regarding each one of these issues are discussed with regard to the features of effective p...
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Özet İlköğretim seviyesinde, 2005 yılında yenilenen öğretim programları, öğrencilerin bazı beceriler (eleştirel düşünme ve araştırma-sorgulama becerileri gibi) kazanmasını hedeflemiştir. Bu çalışmada, söz konusu becerilerin öğrencilere... more
Özet İlköğretim seviyesinde, 2005 yılında yenilenen öğretim programları, öğrencilerin bazı beceriler (eleştirel düşünme ve araştırma-sorgulama becerileri gibi) kazanmasını hedeflemiştir. Bu çalışmada, söz konusu becerilerin öğrencilere kazandırılmasına yönelik olarak, Milli Eğitim Bakanlığı tarafından hazırlanan öğretim programları incelenerek sınıf içinde oluşturulması gereken bir takım normlar belirlenmiştir. Belirlenen "sınıf içi normlar" ile programların hedeflediği her bir beceri arasındaki ilişki sınıf ortamında elde edilmiş veriler üzerinden örneklendirilmiştir. Son olarak, sınıf içinde oluşturulması gereken normların, öğrencilerin bahsedilen becerileri kazanabilmelerine nasıl katkıda bulunacağı tartışılmıştır. Anahtar Kelimeler: Öğretim programları, sınıf içi normlar, temel beceriler 1 Bu çalışma TÜBİTAK tarafından desteklenen bir proje sonucu ortaya çıkmıştır (proje numarası: 108K330).
What is involved in consolidating a new mathematical abstraction? This paper examines the work of one student who was working on a task designed to consolidate two recently constructed absolute function abstractions. The study adopts an... more
What is involved in consolidating a new mathematical abstraction? This paper examines the work of one student who was working on a task designed to consolidate two recently constructed absolute function abstractions. The study adopts an activity-theoretic model of ‘abstraction in context’. Selected protocol data are presented. The initial state of the abstractions and changes that were observed during the consolidation process are discussed. Features of consolidation noted are: reconstruction of the abstractions, increased resistance to challenges, developing a language for the abstractions and greater flexibility. ABSTRACTION AND CONSOLIDATION Abstraction and consolidation are important issues in mathematics education but there are differing interpretations as to what these constructs are and involve. An empiricist view of abstraction is that it involves generalisations arising from the recognition of commonalities isolated in a large number of specific instances (see Ohlsson & Leh...
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This paper reports on the relation between the construction of mathematical knowledge and scaffolded discourse. We work within an operational model of ‘abstraction in context ’ which views abstraction as a vertical reorganisation of... more
This paper reports on the relation between the construction of mathematical knowledge and scaffolded discourse. We work within an operational model of ‘abstraction in context ’ which views abstraction as a vertical reorganisation of previously constructed knowledge into new knowledge. We extend this model by considering human mediation, the functions of scaffolding interventions and emergent goals. We exemplify our arguments by considering verbal data from two students engaged in tasks concerned with the graphs of the absolute value of linear functions and discuss interrelations between human mediation, scaffolding interventions and emergent goals.
This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both... more
This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both accounts. Then it outlines a recent model which takes a dialectical materialist approach to abstraction in context. This model constitutes the basis of the second section where we describe an empirical study designed to investigate mathematical abstraction in socially rich (e.g., peer-interacted and tutor-assisted) environments. We then present data on two students working with the help of a tutor on tasks concerned with graphs of absolute value functions. On the basis of these data, we discuss four particular themes which are relevant to the purpose of this special issue and are important in the discussion of mathematical abstraction: human and artefact mediation, tutor interventions in assisting the formation of mathematical abstractions, implica...
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This study aims to document and examine mathematics teacher educators’ (MTEs) knowledge sources in teacher education practices. The study adopts a mixed-method, embedded research design. Data were collected via a questionnaire with... more
This study aims to document and examine mathematics teacher educators’ (MTEs) knowledge sources in teacher education practices. The study adopts a mixed-method, embedded research design. Data were collected via a questionnaire with elicitations about MTEs’ descriptive features as well as with open-ended items. Target population was all MTEs working in mathematics education departments across Turkish universities. The questionnaire was emailed to all MTEs, and 281 out of 522 returned with their answers. MTEs’ written statements were examined via inductive thematic analysis. A post hoc quantitative analysis was also conducted to explore the relationships between knowledge sources and four variables: gender, self-identification, teaching experience and academic ranking. The analysis allowed the determination of a variety of knowledge sources in teacher education practices and established certain relationships. The findings are discussed with regard to MTEs’ professional development, co...
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Bu calismada, mesleki gelisimin onemli bir boyutunu teskil eden hizmetici egitim programlarina iliskin matematik ogretmenlerinin ihtiyac, degerlendirme ve beklentilerinin belirlenmesi amaclanmistir. Bu amaca donuk olarak tasarlanan... more
Bu calismada, mesleki gelisimin onemli bir boyutunu teskil eden hizmetici egitim programlarina iliskin matematik ogretmenlerinin ihtiyac, degerlendirme ve beklentilerinin belirlenmesi amaclanmistir. Bu amaca donuk olarak tasarlanan calisma, tarama modelinde betimsel bir arastirma olarak desenlenmistir. Calismanin orneklemi, Milli Egitim Bakanligi bunyesinde resmi egitim kurumlarinda gorev yapan 104’u lise ve 110’u ortaokul olmak uzere toplam 214 matematik ogretmeninden olusmustur. Veriler acik uclu sorulardan olusan bir anket araciligiyla toplanmistir. Katilimcilarin yazili olarak verdikleri cevaplar icerik analizi yontemiyle cozumlenmistir. Analizler sonucunda katilimcilarin kendi alanlari (matematik egitimi) ve alanlari disinda aldiklari ve ihtiyac duyduklari egitim konulari belirlenmis, hizmetici egitim programlarinin verimliligine iliskin degerlendirmeleri ortaya konulmus ve hizmetici egitim programlarinda gorev alacak egitmenlerde aradiklari mesleki ve kisisel ozellikler tespit...
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In the classical Aristotelian empiricist view, abstraction is associated with an ascending developmental process from the concrete to the abstract. In this paper, however, I argue that the development coming about in the formation of... more
In the classical Aristotelian empiricist view, abstraction is associated with an ascending developmental process from the concrete to the abstract. In this paper, however, I argue that the development coming about in the formation of mathematical abstraction can be best portrayed as a dialectical development to and fro between the concrete and abstract. This argument is exemplified on the basis of the verbal protocols of two students working together on a task connected to sketching the graphs of absolute value linear functions. Abstraction is a term often linked with an empiricist philosophy tracing from the writings of, for example, Aristotle to Locke to Russell. In this tradition abstraction is considered as higher-order knowledge which consists of 'classifications' (Dienes, 1963) and 'generalisations' (Dreyfus, 1991) arising from the recognition of commonalities isolated in a large number of specific instances (see Ohlsson and Lehtinen (1997) for a critique). Thi...
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ion is a difficult activity that can sometimes be beyond students’ unassisted efforts, in which case supportive intervention of a scaffolder through several means of assistance is observed to help the students achieve the abstraction. The... more
ion is a difficult activity that can sometimes be beyond students’ unassisted efforts, in which case supportive intervention of a scaffolder through several means of assistance is observed to help the students achieve the abstraction. The issue of abstraction has attracted the attention of many educators (Dienes, 1963; Piaget, 1970; Skemp, 1986). Purely cognitive views see abstraction as ascending from ‘concrete’ to ‘abstract’, e.g. “the extraction of what is common to a number of different situations” (Dienes, 1963, p.57). Criticism of this view of abstraction comes from an epistemological point of view which recognises that contextual and social factors are crucial to knowledge acquisition (see van Oers, 2001). Empirical studies of abstraction in context are a relatively recent phenomenon and include Noss and Hoyles’ (1996) concept of situated abstraction and Hershkowitz, Schwarz and Dreyfus’ (2001) activity-theoretic model of abstraction. This paper works within the Hershkowitz e...
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Bu calismada, Turkiye’de 1926’dan gunumuze Cumhuriyet donemi ilkokul matematik dersi ogretim programlarinda matematik okuryazarligi icin yapilan duzenlemelerin karsilastirmali olarak incelenmesi amaclanmistir. Arastirma, nitel bir calisma... more
Bu calismada, Turkiye’de 1926’dan gunumuze Cumhuriyet donemi ilkokul matematik dersi ogretim programlarinda matematik okuryazarligi icin yapilan duzenlemelerin karsilastirmali olarak incelenmesi amaclanmistir. Arastirma, nitel bir calisma olup dokuman incelemesi yontemi kullanilmistir. Cumhuriyet tarihi boyunca uygulamaya konulan 10 ogretim programinin yazili metinleri arastirmanin veri setini olusturmustur. Matematik okuryazarligi baglaminda alanyazindaki tanimlarin incelenmesiyle bu kavrami sekillendiren yedi tema belirlenmistir. Matematik ogretim programlarinin yazili metinleri belirlenen her bir tema kapsaminda icerik analizine tabi tutulmustur. Analizler sonucunda, programlarda matematik okuryazarliginin temalara gore kullanim amaci, yontemi ve yonlendirmelere iliskin degisiklikler yapildigi belirlenmistir. Ayrica Bilgi ve Iletisim Teknolojileri Kullanimi temasi disindaki diger tum temalarin Cumhuriyetin ilanindan gunumuze kadar tum programlarda, degisen vurgulamalar ve cesitli...
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This study investigates the development of prospective mathematics teachers’ use of multiple representations during teaching in technologyrich environments. Forty prospective teachers took part in a teacher preparation programme which... more
This study investigates the development of prospective mathematics teachers’ use of multiple representations during teaching in technologyrich environments. Forty prospective teachers took part in a teacher preparation programme which aims to develop technological pedagogical content knowledge (TPCK). As part of this programme, prospective teachers participated in workshops during which the TPCK framework was introduced focusing on function and derivative concepts. Various components of TPCK were considered. This study investigates one particular component of TPCK: knowledge of using multiple representations of a particular topic with technology. The content we focus on in this paper is the “concept of radian measure”. Two out of forty prospective teachers introduced the concept of radian measure as part of their micro-teaching activities. The data obtained from semi-structured interviews, videos of prospective teachers' lessons, their lessons plans and teaching notes was analys...
This study examines the role of scaffolding in the achievement of a mathematical abstraction by focusing on emergent goals. An activity-theoretic approach to abstraction in context is taken. The examination is carried out with regard to... more
This study examines the role of scaffolding in the achievement of a mathematical abstraction by focusing on emergent goals. An activity-theoretic approach to abstraction in context is taken. The examination is carried out with regard to the verbal protocols of two 17-year-old students working on a task related to the graphs of y=f(|x|). This examination suggests that abstraction is likely to be achieved through satisfaction of several emergent goals. These goals are observed to be contingent upon four parameters: the scaffolder's interventions, students, tasks, and prior emergent goals. Dynamic and dialectical interrelationships amongst these parameters are discussed with regard to the students' verbal protocols.
A structured assessment tool on the quality of mathematics instruction is considered to be important. It is believed that such a tool could play an important role in providing feedbacks to the preservice teachers during their trainings as... more
A structured assessment tool on the quality of mathematics instruction is considered to be important. It is believed that such a tool could play an important role in providing feedbacks to the preservice teachers during their trainings as well as in evaluating the quality of in-service teachers’ practices. From this point of view, firstly, it has been performed a comprehensive examination of the relevant frameworks developed to evaluate the quality of mathematics instruction. As a result, it was observed that the Mathematical Quality of Instruction (MQI) framework differed from the others with respect to both functional and structural features. Within the scope of this study, the adaptation of the MQI framework to Turkish language has been realized. In this study, the characteristics, usage, components and theoretical background of the MQI framework are shared with the reader. In addition, the adapted version of MQI framework was shared and the performance indicators to help potenti...
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Bu calismada, matematik ogretmenlerinin ders kitabi disinda kaynak kullanim durumlarinin belirlenmesi ve ogretmenleri kaynak kitap kullanimina iten nedenlerin incelenmesi amaclanmistir. Bu amac kapsaminda sekillenen calisma tarama... more
Bu calismada, matematik ogretmenlerinin ders kitabi disinda kaynak kullanim durumlarinin belirlenmesi ve ogretmenleri kaynak kitap kullanimina iten nedenlerin incelenmesi amaclanmistir. Bu amac kapsaminda sekillenen calisma tarama modelinde betimsel bir arastirma olarak desenlenmistir. Calismaya 100 ortaokul matematik ogretmeni katilmistir. Katilimcilara acik uclu sorulardan olusan bir anket uygulanmistir. Anketten elde edilen veriler icerik analizine tabi tutularak cozumlenmistir. Yapilan analizler sonucunda katilimcilarin %80 gibi buyuk bir cogunlugunun ucretsiz olarak dagitilan ders kitabi disinda kaynak kitap kullandiklari belirlenmistir. Milli Egitim Bakanliginin kaynak kitap kullanilmamasi yonundeki duzenlemeleri, en azindan calismamiza katilan ogretmenler ozelinde, ders kitabi disinda kaynak kullanimini engelleyemedigi tespit edilmistir. Katilimci ogretmenler kendilerini ekstra kaynak kullanmaya iten sebepler bulundugunu; ders kitaplarinin hem soru bakimindan, hem konu anlatimi hem de ogrenci ozelligine uygunluk bakimindan beklentilerini karsilamadigini belirtmektedirler. Elde edilen bulgular ve ulasilan sonuclar, ders kitaplarinin hazirlanmasi ve secimi, ucretsiz dagitimi, kitaplarin kullanimi ve surecte ogretmenlerin ihtiyac duyacagi destek ve kitaplarin kullanimiyla birlikte ortaya cikan degisimin yonetimi konulari ekseninde tartisilmis ve bir takim onerilerde bulunulmustur.
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... Sınıf Öğretmenleri ve Matematiksel Zorlukları Primary Teachers and Their Mathematical Difficulties Mehmet Fatih Özmantar* ve Erhan Bingölbali Gaziantep Üniversitesi, Eğitim Fakültesi, İlköğretim Bölümü ... Hata yoktur. ▪ Doğru ▪ Bence... more
... Sınıf Öğretmenleri ve Matematiksel Zorlukları Primary Teachers and Their Mathematical Difficulties Mehmet Fatih Özmantar* ve Erhan Bingölbali Gaziantep Üniversitesi, Eğitim Fakültesi, İlköğretim Bölümü ... Hata yoktur. ▪ Doğru ▪ Bence en güzel çözüm bu. ...
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Abstraction is an important issue in mathematics education but there is no agreement upon a definition amongst educators (see Ohlsson and Regan, 2001; van Oers, 2001). This paper adopts an activity-theoretic model of abstraction... more
Abstraction is an important issue in mathematics education but there is no agreement upon a definition amongst educators (see Ohlsson and Regan, 2001; van Oers, 2001). This paper adopts an activity-theoretic model of abstraction (Hershkowitz, Schwarz and Dreyfus 2001), ...
This paper reports on the relation between the construction of mathematical knowledge and scaffolded discourse. We work within an operational model of 'abstraction in context' which views abstraction as a vertical reorganisation... more
This paper reports on the relation between the construction of mathematical knowledge and scaffolded discourse. We work within an operational model of 'abstraction in context' which views abstraction as a vertical reorganisation of previously constructed knowledge into new knowledge. We extend this model by considering human mediation, the functions of scaffolding interventions and emergent goals. We exemplify our arguments by considering verbal data from two students engaged in tasks concerned with the graphs of the absolute value of linear functions and discuss interrelations between human mediation, scaffolding interventions and emergent goals.
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This paper examines the views of pre-service and in-service teachers with regard to the sources of students‟ mathematical difficulties. A group of 40 pre-service mathematics, 15 in-service mathematics and 15 in-service elementary teachers... more
This paper examines the views of pre-service and in-service teachers with regard to the sources of students‟ mathematical difficulties. A group of 40 pre-service mathematics, 15 in-service mathematics and 15 in-service elementary teachers participated in this study. Questionnaires are used ...
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In this article we focus on university lecturers’ approaches to the service teaching and factors that influence their approaches. We present data obtained from the interviews with 19 mathematics and three physics lecturers along with the... more
In this article we focus on university lecturers’ approaches to the service teaching and factors that influence their approaches. We present data obtained from the interviews with 19 mathematics and three physics lecturers along with the observations of two mathematics lecturers’ calculus courses. The findings show that lecturers’ approaches to teaching the same topic vary across departments; that is, they consciously privilege different aspects of mathematics, set different questions on examinations and follow different textbooks while teaching in different departments. We discuss factors influencing lecturers’ decision of what (mathematics) to teach in different departments and offer educational implications for service mathematics teaching in terms of students’ mathematical needs and the role of mathematics for client students.
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In this chapter we address the question: are mathematical abstractions situated? We first consider empiricist accounts of abstraction which see abstraction as a development process from the concrete to the abstract achieved through the... more
In this chapter we address the question: are mathematical abstractions situated? We first consider empiricist accounts of abstraction which see abstraction as a development process from the concrete to the abstract achieved through the recognition of commonalties isolated in a large number of instances. We discuss difficulties involved in empiricist accounts and propose an alternative approach which we call a dialectical account of abstraction. In this approach, an undeveloped initial idea develops through the use of mediational means and social interaction. This development is not from the concrete to the abstract but, rather, a dialectical to and fro between the concrete and the abstract. Unlike empiricist views, our approach regards context, in the formation of mathematical abstractions, as paramount. Although the construct ‘context’ is difficult to delineate precisely, we focus on the importance of students’ personal mathematical histories, the tools and knowledge artefacts they work with, the people they work with and the tasks they work on. We exemplify the importance of these contextual factors through a study where two teenage girls worked collaboratively, with an interviewer assisting them, in completing tasks designed to generate abstractions in the field of graphs of linear absolute value functions.
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This paper reports on the relation between the construction of mathematical knowledge and scaffolded discourse. We work within an operational model of 'abstraction in context'which views abstraction as a vertical reorganisation... more
This paper reports on the relation between the construction of mathematical knowledge and scaffolded discourse. We work within an operational model of 'abstraction in context'which views abstraction as a vertical reorganisation of previously constructed knowledge into ...
Abstraction is an important issue in mathematics education but there is no agreement upon a definition amongst educators (see Ohlsson and Regan, 2001; van Oers, 2001). This paper adopts an activity-theoretic model of abstraction... more
Abstraction is an important issue in mathematics education but there is no agreement upon a definition amongst educators (see Ohlsson and Regan, 2001; van Oers, 2001). This paper adopts an activity-theoretic model of abstraction (Hershkowitz, Schwarz and Dreyfus 2001), ...