Connecting with the horizon: developing teachers’ appreciation of mathematical structure

Vale, Colleen; McAndrew, Alasdair; Krishnan, Siva

doi:10.1007/s10857-010-9162-8

Cited by 18 publications

(24 citation statements)

References 12 publications

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“…Matematiğin sembolik, grafik, numerik temsilleri arasında ilişkilendirme yapmanın matematiği öğrenme ve öğretme sürecinde temel unsurlar olduğunu belirtilir (Vale, McAndrew & Krishnan, 2011 (Marchi, 2012). Ayrıca trigonometrik fonksiyonlar sadece cebirsel formüller ile açıklanmayan işlemlerdir ve öğrencilerin bu işlemleri fonksiyon olarak görmeleri gereken muhakemeye sahip olmaları gerekir (Breidenbach, Dubinsky, Hawks & Nichols, 1992).…”

Section: Resultsunclassified

Lise Öğrencilerinin Trigonometrik Fonksiyonlarda Grafik Çizme Becerileri

Özgen¹,

Aygün²,

Hanazay³

2017

Necatibey Eğitim Fakültesi Elektronik Fen Ve Matematik Eğitimi Dergisi

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-The aim of this study is to identify skills of high school 10 th grade students' in graphing trigonometric functions. In this study, case study method which was descriptive method was used. A testconsisting of five open-ended questions including graphing trigonometric functions was prepared. Data collection tools were applied to 48 randomly selected students who were educated in Anatolian high school.Descriptive analysis was used in the analysis of the data. According to the findings, it was determined that most of the students who participated in study succeeded in drawing graphs of basic trigonometric functions such as sinx and cosx functions. However, some students draw the graph of the function of such as sin3x, arctanx and cosecx which are derivated from sinx and cosx functions, were found to be unsuccessful. In addition, students' skills of connection with graphical representation were to be low level. The students were not successful in drawing graphs of different functions other than the basic trigonometric functions such as sinx and cosx. It was determined that students couldn't use enough graphical connection skills in drawing graphs of trigonometric functions. Teachers should give more importance to graphical connection in trigonometric function.

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Section: Resultsunclassified

Lise Öğrencilerinin Trigonometrik Fonksiyonlarda Grafik Çizme Becerileri

Özgen¹,

Aygün²,

Hanazay³

2017

Necatibey Eğitim Fakültesi Elektronik Fen Ve Matematik Eğitimi Dergisi

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“…To achieve this objective, students must be provided with basic mathematical skills such as understanding and interpreting mathematical concepts and relationships between them, using them in their lives, and connecting mathematics with different fields and disciplines (Ball, 1990;Kinach, 2002;Vale, McAndrew & Krishnan, 2011;NCTM, 2000;Skemp, 1978;Van de Walle, 2013). In this regard, current mathematics curricula or standards documents evidently highlight connection as one of the most important skills of the processes of learning and doing mathematics (Chapman, 2012;MEB, 2013).…”

Section: A Theoretical Examination Of the Mathematical Connection Skimentioning

confidence: 99%

A Theoretical Examination of the Mathematical Connection Skill: The Case of the Concept of Derivative

Mumcu¹

2018

Turkish Journal of Computer and Mathematics Education (TURCOMAT)

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Öz: Bu çalışmanın amacı öğretmen adaylarının matematiksel ilişkilendirme becerilerinin türev kavramı bağlamında ele alınarak yorumlanmasıdır. Bu kapsamda öncelikle matematiksel ilişkilendirme becerisi kuramsal olarak analiz edilerek bu becerinin değerlendirilmesinde kullanılabilecek bir kuramsal yapı oluşturulmaya çalışılmıştır. Daha sonra ise bir devlet üniversitesinin eğitim fakültesi son sınıf öğrencilerinden seçilen ve 51 kişiden oluşan matematik öğretmen adaylarına araştırmacı tarafından geliştirilmiş olan İlişkilendirme Beceri Testi (İBT) uygulanmıştır. İlişkilendirme Beceri Testi'nin temel bileşenleri farklı gösterimler arası ilişkilendirme, kavramlar arası ilişkilendirme, gerçek yaşamla ilişkilendirme ve farklı disiplinlerle ilişkilendirme olarak ifade edilebilir. Çalışma sonucunda öğretmen adaylarının genel olarak türev kavramına yönelik ders kitaplarında yer alan ezberi bir takım bilgilere sahip oldukları fakat bu bilgileri birbiri ile ilişkili olarak anlamlandırmakta ve kullanmakta güçlük çektikleri gözlenmiştir. Matematiğin daha anlamlı ve ilişkisel olarak öğrenilmesi anlamında, matematik eğitimcilerinin sınıflarında, kavramsal anlamaya odaklanmaları ve kavramların anlamlı öğrenilmesini ve gerçek yaşamla ilişkilendirilebilmesini sağlayacak etkinlik ve uygulamalara yer vermeleri önerilmiştir.

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“…We do not know the level of detail that is needed for horizon knowledge to be useful (Ball and Bass, 2009, p. 11). Recently, some researchers (e.g., Figueiras et al, 2011;Foster, 2011;Vale et al, 2011;Zazkis and Momolo, 2011) have proposed their own meanings of HCK, and these meanings helped us deepen our understanding about HCK. However, we thought that their discourse and instantiation did not correspond to an important aspect that …”

Section: Hck-an Unsolved Problemmentioning

confidence: 99%

“…Here, we thought there might be some differences between this subcategory of SMK and the subcategory KCC of PCK. Vale et al (2011) provided a professional learning program for teachers of junior secondary mathematics with regard to the content and pedagogy of senior secondary mathematics. They analyzed teachers' reflections on their learning to explore teachers' understanding of mathematical connections and their awareness of mathematical structure, and verified that this kind of connections in mathematical structure was unquestioningly beyond connections in curriculum.…”

Section: Hck-awareness or Understandingmentioning

confidence: 99%

Complementing Mathematics Teachers’ Horizon Content Knowledge with an Elementary-on-Advanced Aspect

Cho

Tee

2018

Pedagogical Research

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Although Ball and her colleagues provided empirical evidence to support the existence of the six subdomains in mathematical knowledge for teaching (MKT) and further explained or defined the majority of these sub-domains, there were few explanations of what horizon content knowledge (HCK) embedded in MKT meant and they merely provided ideas about HCK. Many researchers attempted to provide some teaching incidents and exemplification to interpret the construct of HCK. Moreover, they thought teachers' studies of tertiary mathematics are useful for classroom teaching practice. Their discourse and instantiation of HCK was correspondent with a higher perspective on elementary mathematics mentioned by Felix Klein (1924), but was not entirely coincide with a kind of elementary perspective on advanced knowledge introduced by . This study lasted 1 years, and data collection included in-depth interviews, classroom observation and video analysis. We provide a shared classroom teaching incidence and illustrations to explain and to describe the construct of HCK. HCK not only is a kind of elementary perspective on advanced mathematical knowledge, but also complements to a higher perspective on elementary mathematics. Furthermore, HCK could be seen as a reciprocal pathway between the elementary and advanced mathematical knowledge.

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Connecting with the horizon: developing teachers’ appreciation of mathematical structure

Cited by 18 publications

References 12 publications

Lise Öğrencilerinin Trigonometrik Fonksiyonlarda Grafik Çizme Becerileri

Lise Öğrencilerinin Trigonometrik Fonksiyonlarda Grafik Çizme Becerileri

A Theoretical Examination of the Mathematical Connection Skill: The Case of the Concept of Derivative

Complementing Mathematics Teachers’ Horizon Content Knowledge with an Elementary-on-Advanced Aspect

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