Exemplifying definitions: a case of a square

Zazkis, Rina; Лейкин, Роза

doi:10.1007/s10649-008-9131-7

Cited by 117 publications

(77 citation statements)

References 9 publications

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“…Van Dormolen & Zaslavsky, 2003), students' beliefs about them (Zaslavsky & Shir, 2005), and students' guided collaborative development of definitions in contexts new to them (Larsen & Zandieh, 2008;Zandieh & Rasmussen, 2010). Studies have suggested that students who spontaneously generate examples in response to new definitions later perform better on tasks involving the defined concepts (Dahlberg & Housman, 1997), and there has been much recent discussion of the way in which example generation tasks might help students to modify their example spaces so that these more closely coincide with the extensions of the defined concepts (Mason, 2002;Watson & Mason, 2005;Zazkis, Liljedahl & Chernoff, 2008;Zazkis & Leikin, 2008). Definitions are also discussed in the extensive literature on proof, which focuses on the role of definitions as a deductive base in arguments about whole classes of objects.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Classification and Concept Consistency

Alcock

Simpson

2011

Canadian Journal of Science, Mathematics and Technology Educati

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This paper investigates the extent to which undergraduates consistently use a single mechanism as a basis for classifying mathematical objects. We argue that the concept image/concept definition distinction focuses on whether students use an accepted definition, but does not necessarily capture the more basic notion that there should be a fixed basis for classification. We examine students' classification of real sequences before and after exposure to definitions of 'increasing' and 'decreasing'; we develop an abductive 'plausible explanations' method to estimate the consistency within the participants' responses and suggest that this provides evidence that many students may lack what we call 'concept consistency'.Running head: Classification and Concept Consistency

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Section: Theoretical Backgroundmentioning

confidence: 99%

Classification and Concept Consistency

Alcock

Simpson

2011

Canadian Journal of Science, Mathematics and Technology Educati

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“…A special issue of this journal was recently dedicated to the role of examples in students' learning, and several articles in that issue discussed example generation (e.g., Watson and Shipman, 2008;Goldenberg and Mason, 2008;Zazkis and Leikin, 2008). Research in this area includes investigations into the richness and structure of students' example spaces (Goldenberg and Mason, 2008), the role of examples as pedagogical tools (Weber et al, 2008) and the pedagogical benefits of asking learners to generate their own examples of mathematical concepts (Watson and Mason, 2005).…”

Section: Introductionmentioning

confidence: 99%

Does generating examples aid proof production?

et al. 2011

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract. Many mathematics education researchers have suggested that asking learners to generate examples of mathematical concepts is an effective way of learning about novel concepts. To date, however, this suggestion has limited empirical support. We asked undergraduate students to study a novel concept by either tackling example generation tasks, or reading worked solutions to these tasks. Contrary to suggestions in the literature, we found no advantage for the example generation group on subsequent proof production tasks. From a second study we found that undergraduate students overwhelmingly adopt a Trial and Error approach to example generation, and suggest that different example generation strategies may result in different learning gains. We conclude by arguing that the teaching strategy of example generation is not yet understood well enough to be a viable pedagogical recommendation.

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“…The research data was analyzed by content analysis. The researchers considered the framework specified by Zazkis and Leiken (2008) and then expanded by Gokkurt (2014) in the identification process under categories and encodes of the data obtained defining derivatives, giving examples to derivatives, visualizing the definition of derivative and explaining the relationship between derivatives and continuity.…”

Section: Method(s)mentioning

confidence: 99%

Lise Matematik Öğretmenlerinin Türevin Tanımına ve Türev-Süreklilik İlişkisine Yönelik Pedagojik Alan Bilgileri

Duran¹,

Kaplan²

2016

EEF DERGI

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ÖzetBu araştırmanın amacı lise matematik öğretmenlerinin türevin tanımına, türevin tanımının görselleştirilmesine ve türev-süreklilik ilişkisine yönelik pedagojik alan bilgilerini konu alanı bilgisi bağlamında incelemektir. Öğretmenlerin konu alanı bilgileri; türevi tanımlama ve örneklendirme, türevin tanımını görselleştirme ve türev-süreklilik arasındaki ilişkiyi açıklama şeklinde üç başlık altında incelenmiştir. Nitel araştırma modellerinden özel durum çalışmasına göre desenlenen bu araştırma 2015-2016 öğretim yılı güz döneminde Karadeniz Bölgesi'ndeki bir şehirde gerçekleştirilmiştir. Araştırmanın katılımcıları ikisi fen edebiyat fakültesi mezunu, diğer ikisi ise eğitim fakültesi mezunu olmak üzere dört lise matematik öğretmenidir. Araştırmanın veri toplama aracı araştırmacılar tarafından geliştirilmiş yarı yapılandırılmış görüşme formudur. Araştırmanın verileri içerik analizi tekniğiyle incelenmiştir. Araştırmadan elde edilen sonuçlara göre lise matematik öğretmenlerinin türevin tanımına yönelik gerekli ancak yetersiz tanım yaptıkları belirlenmiştir. Öğretmenlerin türev kavramına verdikleri örneklerin anlık değişim, değişim hızı ve değişim oranı gibi prototip örneklerle sınırlandığı görülmüştür. Öğretmenlerden ikisinin türev-süreklilik ilişkisine yönelik yeterli açıklamalarda bulundukları tespit edilirken diğer ikisinin bu ilişkiyi gerekli ancak yetersiz şekilde açıkladıkları sonucuna varılmıştır.Anahtar Sözcük: Türev, Pedagojik Alan Bilgisi, Konu Alanı Bilgisi Abstract The purpose of this research is to investigate high school mathematics teachers' pedagogical content knowledge in the context of subject matter knowledge * Bu araştrıma birinci yazarın doktora tezi pilot çalışmasında kullanılan verilerin bir bölümünden üretilmiştir. Araştırmada katkısı olan Dr. Muhammet DORUK'a teşekkür ederiz.

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Exemplifying definitions: a case of a square

Cited by 117 publications

References 9 publications

Classification and Concept Consistency

Classification and Concept Consistency

Does generating examples aid proof production?

Lise Matematik Öğretmenlerinin Türevin Tanımına ve Türev-Süreklilik İlişkisine Yönelik Pedagojik Alan Bilgileri

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