Ben's consolidation of knowledge structures about infinite sets

Dreyfus, Tommy; Tsamir, Pessia

doi:10.1016/j.jmathb.2004.06.002

Cited by 57 publications

(71 citation statements)

References 15 publications

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“…Students become aware of construct and they decide to use it immediately (Anabousy & Tabach;. Dreyfus and Tsamir (2004) showed that consolidation can be identified in terms of psychological and cognitive characteristics of selfevidence, confidence, immediacy, flexibility and awareness. Tsamir and Dreyfus (2005) explained the characteristics of consolidation as follows:…”

Section: Abstraction In Context (Rbc+c Model)mentioning

confidence: 99%

“…Most of the researchers carried out researches on abstraction in context "Recognizing", "Building-with" and "Constructing" as epistemic actions, (Altun & Kayapınar, 2011;Kidron & Dreyfus, 2010), while several researchers emphasized the consolidation process (Dreyfus & Tsamir, 2004;Tabach, Hershkowitz & Schwarz, 2006;Monaghan & Ozmantar, 2006;Dreyfus, Hadas, Hershkowitz & Schwarz, 2006) and characteristics of consolidation (Dreyfus & Tsamir, 2004, Tsamir & Dreyfus, 2005Anabousy & Tabach, 2015). Dreyfus and Tsamir (2004) carried out a study which revealed the characteristics of consolidation that emerges from a sequence of interviews about the comparison of infinite sets with a talented student.…”

Section: Abstraction In Context (Rbc+c Model)mentioning

confidence: 99%

“…Dreyfus and Tsamir (2004) carried out a study which revealed the characteristics of consolidation that emerges from a sequence of interviews about the comparison of infinite sets with a talented student. They stated the mentioned characteristics as self-evidence, confidence, immediacy, flexibility and awareness which are the psychological and cognitive components.…”

Section: Abstraction In Context (Rbc+c Model)mentioning

confidence: 99%

“…In order to construct the mentioned length some theorems and rules should be known and consolidated as Pythagorean and Euclidean Theorem and similarity. Consolidation is an epistemic action which has a place in abstraction in context; RBC+C model (Dreyfus & Tsamir, 2004). In addition, Wiles (2013) stated that levels of MHM can be observable by paper folding and by this way thinking way of the person can be explained.…”

Section: Introductionmentioning

confidence: 99%

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Construction Process of the Length of 3√2 by Paper Folding

Güler

Gürbüz

2018

International Journal of Research in Education and Science

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The main purpose of this study is to investigate mathematics teachers" mathematical thinking process while they are constructing the length of √ by paper folding. To carry out this aim, two teachers -who are PhD. students-were interviewed one by one. During the construction, it was possible to observe the consolidation process of Pythagorean and Thales Theorem. All interviews were videotaped and analyzed through descriptive methods, according to abstraction in context, characteristics of consolidation and mathematical habits of mind. It was found that both two teachers constructed the knowledge of Pythagorean and Thales Theorems before the study and also these knowledges were consolidated. In addition, it was determined that these two approaches (abstraction in context and mathematical habits of mind) were close and corroborated each other. Moreover, consolidation process corroborated mathematical habits of mind.

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Section: Abstraction In Context (Rbc+c Model)mentioning

confidence: 99%

Section: Abstraction In Context (Rbc+c Model)mentioning

confidence: 99%

Section: Abstraction In Context (Rbc+c Model)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Construction Process of the Length of 3√2 by Paper Folding

Güler

Gürbüz

2018

International Journal of Research in Education and Science

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“…Burada öğrenciler önceki bilgilerinden yararlanarak fonksiyon kavramını oluşturma uğraşı içine girmeleri beklenir. Ayrıca fonksiyonun temel elemanları olan tanım, değer kümesi ve kuralı kavramları burada ele alınmaktadır.2) Öğrenilen kavramların pekiştirilmesi amacıyla tasarlanan etkinlikler (Dreyfus & Tsamir, 2004) Etkinlik: Aşağıdaki grafiklerin fonksiyon olup-olmadığını araştırınız. Fonksiyon ise tanım ve değer kümelerini belirtiniz.…”

unclassified

Matemati̇ksel Öğrenme Etki̇nli̇ği̇ Türleri̇ne Yöneli̇k Kuramsal Bi̇r Çalişma: Fonksi̇yon Kavrami Örneklemesi̇

Özgen¹

2017

Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi

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ÖZETMatematik eğitiminde öğrenen merkezli eğitimin önemli unsurlarından birisi etkinlik temelli öğrenmedir. Bu doğrultuda etkinlikler matematiği öğrenme-öğretme sürecinin temel yapıtaşları olarak görülebilir. Etkili öğrenme etkinliklerinin özellikleri, yapısı ve hangi amaçla tasarlandığı önemli konular arasında yer almaktadır. Ayrıca etkinlik türlerinin ve sınıflandırmasının neler olduğunun bilinmesi önemli görülmektedir. İlgili alan yazında etkinlik türleri ve sınıflandırılmaları farklı kuramsal yaklaşımlar ve çerçeveler açısından ele alındığı belirlenmiştir. Ancak özellikle matematiksel etkinliklere yönelik yapılan çerçeve ve sınıflandırmalarda amaç, bilişsel süreçler, matematiksel yeterlikler ve becerilerin odak noktada olduğu söylenebilir. Bu çalışmada matematiksel öğrenme etkinliklerine yönelik önemli konulardan biri olan etkinliklerin türleri ve sınıflandırılması üzerinde durulacaktır. Çünkü matematik öğretmenlerinin etkinlik türleri arasındaki farklılıkları anlamaları ve özellikle öğretim amaçları ile öğrencileri için daha uygun etkinlikleri seçebilmeleri önemlidir. Bu doğrultuda, bu çalışmada etkinlik türleri; amaç, bilişsel süreçler, matematiksel yeterlik ve beceriler açısından incelenecektir. Bu farklı türlerdeki matematik öğrenme etkinliklerini somutlaştırmak amacıyla fonksiyon kavramına yönelik örneklemeler yapılacaktır. Anahtar Kelimeler: Etkinlik türleri, fonksiyon kavramı, matematik dersi A THEORETICAL STUDY ON MATHEMATICAL LEARNING ACTIVITIES: A CASE OF FUNCTION CONCEPT ABSTRACTOne of the important elements of student-centered education in mathematics education is activitybased learning. In this sense, activities can be seen as the capstone of the mathematics learningteaching process. The characteristics, structure, and purpose of effective learning activities are among the most important topics. It is also important to know what kinds of activities and their classification are. In the related literature, it was determined that the types of activities and classifications were considered in terms of different theoretical approaches and frameworks. However, it can be said that the purpose, cognitive processes, mathematical competencies, and skills are the focus points in the frameworks and classifications, especially for mathematical activities. This study will focus on the types and classification of activities that are important topics for mathematical learning activities. It is important for mathematics teachers to understand the differences between the types of activities, and to be able to choose more appropriate activities for their students, especially for teaching purposes. In this respect, the types of activities in this study will be examined in terms of purpose, cognitive processes, mathematical competencies, and skills. To embody mathematical learning activities in these different types samples for function concept should be shown. 1.GİRİŞÖğrencilerin etkinliklerle matematik öğrenmesi, öğrenme sürecinin temel yapıtaşı olarak görülebilir. Çünkü öğrencilerin öğrenme etkinlikleri ile öğre...

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