The World's a Stage@@@Structure and Insight: A Theory of Mathematics Education

Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research

Teachers' content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary school teachers

The purpose of this study was to assess 81 kindergarten teachers’ pedagogical content knowledge of mathematics on six subcategory areas such as number sense, pattern, ordering, shapes, spatial sense, and comparison. The data showed participants possessed a higher level of pedagogical content knowledge of “number sense” (M = 89.12) compared to other mathematics pedagogical content areas. The second highest scores among six subcategories of pedagogical content knowledge of mathematics was for the pedagogical content area of “pattern” (M = 82.33). The lowest scores among those six subcategories of kindergarten teachers’ pedagogical content knowledge were obtained from the subcategory of “spatial sense” (M = 44.23), which involved the means to introduce children to spatial relationships. The second lowest score was obtained for the subcategory of “comparison” (M = 50.40) which involved the means to introduce the concept of graphing and the use of a balance scale for measurement.

Exploring Kindergarten Teachers’ Pedagogical Content Knowledge of Mathematics

Over the past 25 years, PCK has become widely accepted as a useful construct in understanding the unique nature and development of teachers’ knowledge, and PCK research in the field of teacher education has rapidly accumulated. Yet while there is consensus in the literature about the importance of the construct in bringing together specific types of knowledge that teachers require to support effective student learning of particular subject matter, questions still remain about how PCK can be understood, developed and organised in the context of initial teacher education. The development of PCK has been the subject of studies in different programme formats of teacher education, at different levels (primary, secondary), in different subjects, and in various countries. From these studies, it is apparent that whatever the organizational format of the programme, the development of PCK should be related to pre-service teachers’ subject matter knowledge on the one hand, and their teaching experiences, notably during practicum, on the other. Equally, developing PCK requires pre-service teachers’ ability and willingness to view subject matter from a learners’ perspective. Depending on the level of subject matter knowledge of pre-service teachers at the start of their programme, the development of PCK may benefit from a design which integrates institute based activities with authentic classroom teaching of subject matter.

Pedagogical Content Knowledge in Teacher Education

The purpose of this research was to determine the pre-service primary mathematics teachers’ competency of pedagogical content knowledge in mathematics. The data were collected by means of four open ended problems from the participation of 45 primary mathematics teacher candidates. Teacher candidates’ responses were analyzed based on pre-determined criteria. According to findings it was found that having a deep understanding of mathematical knowledge was necessary but not sufficient to teach mathematics. This finding pointed out the connection between knowledge of mathematics and knowledge of mathematics teaching. It is suggested that primary mathematics teacher candidates should be educated both from “mathematics knowledge” and “pedagogical content knowledge” aspects.

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The pedagogical content knowledge in mathematics: pre- service primary mathematics teachers' perspectives in turkey

The object of this study was to show how prospective elementary mathematics teachers define and classify the quadrilaterals and to find out their images. This research was a qualitative study. It was conducted with 36 prospective elementary mathematics teachers studying at 3rd and 4th years in an educational faculty. The data were collected by semi-structured interview. The collected data were analyzed by inductive content analysis. It was determined that prospective teachers made personal definitions for quadrilaterals and based on these definitions it was seen that there were inaccuracies in their perceptions. Some prospective teachers' images in rhombus caused problem on indicating the differences between rhombus and square. It was revealed that the prospective teachers drew defectively, especially rhombus and trapezoid figures. Furthermore, the prospective teachers did not prefer inclusion relations for the classifying quadrilaterals and made partition classifications, in general.Key WordsPerception of Quadrilateral, Image of Quadrilateral, Classification of Quadrilateral, Prospective Primary Mathematics Teachers.Teaching geometry is as many researchers stated (Baykul, 1999; Duatepe, 2000; Fujita & Jones, 2007) not only means of comprehending information and relations about point, line, figures, space but also important in the sense of improving spatial thinking and visual skills.In the education of many subject in mathematics, people form an image in their mind about the concepts. This concept image changes and takes shape in time. Tall and Vinner (1981) defined concept image as the cognitive structure which includes mental image, features and processes about the concept. There are 3 different cases in geometrical concepts. These are the image, definition and properties of the geometric concept (De Villiers, 1998; Fujita, 2012).According to Tall and Vinner (1981), whether definitions of concepts are directly taught or students construct these definitions; individuals filter these definitions in their minds. These personal definitions may differ from formal definitions. These personal definitions of concepts may cause people to create their own concept images. Even according to Heinze and Ossietzky (2002), the academic definition of the concept is forgotten while solving problems and personally created concept image comes into prominence.In addition to this, visual image of every geometric concept may be in the forefront rather than the concept. In this sense typical (prototype) examples are the key factor. These prototype shapes always have an effect in concept image (Fischbein, 1993; Hershkowitz, 1990). As a result of many studies, Fujita (2002) have stated that definition of the geometric figure and characteristics of family relation which include this figure generally cause contradiction. This contradiction results in wrong perception and generalizations with the conceptual perception of prototype figure (Fujita; Fujita & Jones, 2006; Hershkowitz).There are various studies nearly for every age group about how the geometric figures are perceived, how the figurative display and conceptual relation of the figures are imprinted in one's mind. In this sense, this study aims to present how the elementary prospective teachers define and classify quadrilaterals and what the images related with quadrilaterals are.When the literature is analyzed, there are studies in which people are expected to name drawn quadrilaterals or mark the quadrilaterals whose names are given (Clements, Swaminathan, Hanibal, & Sarama, 1999; Fujita, 2012; Fujita & Jones, 2007; Monaghan, 2000; Okazaki & Fujita, 2007). However, as the case is so in the study of Okazaki and Fujita, it was stated that there is a problem in defining figures drawn in different ways rather than typical drawings. In a younger age group, similar images about quadrilaterals were observed which resembles to the study of Okazaki and Fujita. …

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Investigation of Prospective Primary Mathematics Teachers' Perceptions and Images for Quadrilaterals.

Bu arastirma ilkogretim matematik ogretmen adaylarinin elestirel dusunme egilim ve becerilerini belirlemeyi amaclamaktadir. Bir elestirel dusunme olcegi ve matematiksel elestirel dusunme problemleri veri toplama araclari olarak kullanilmistir. Calisma grubu Turkiye’nin batisinda yer alan bir buyuk universiteden secilmistir. 227 matematik ogretmen adayi bu calismaya katilmistir. Verilerin analizleri sonucunda, ogretmen adaylarinin elestirel dusunme egilimleri pozitif yonde fakat yeterince yuksek cikmamistir. Ayrica elestirel dusunme egilim olcegi sonuclari ve matematiksel elestirel dusunme problemleri sonuclari bir uyum gostermistir. Elde edilen bu sonuclar dikkate alinarak, ogretmen adaylarinin guclu ve zayif yanlari ortaya cikarilmistir

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Türkiye'den Bir Profil: 11-13 Yaş Gurubu Matematik Öğretmen Adaylarının Eleştirel Düşünme Eğilim ve Becerileri

Mathematical proof, which has internationally accepted rules and methods, is one of the fundamental processes of mathematics. In this study, teacher candidates’ views on proof are searched. These views on proof could supply information to reveal teacher candidates’ possible problems concerning proofs and to overcome these difficulties. Data is gathered by a scale. Results showed that majority of the teacher candidates either having no specific opinions on doing of mathematical proofs or their opinions were less than satisfactory.

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Matematik Öğretmen Adaylarının İspat Yapmaya Yönelik Görüşleri

Pedagogical content knowledge is consisted of two components: student knowledge and teaching strategies. Student knowledge was defined to sub-categories as connecting prior knowledge to new knowledge, noticing students’ mistakes, identifying students’ difficulties of understanding. The aim of this study is to examine middle school mathematics teachers’ pedagogical content knowledge in terms of student knowledge regarding quadrilaterals. Interview method was used for data acquisition. 30 middle school mathematics teachers working at 12 different schools in Turkey participated in this study. The questions asked the teachers during interviews were prepared by researchers in accordance with student knowledge component of the pedagogical content knowledge. Content analysis was used to analyze the data acquired in this study. The study results show that teachers pointed out that they teach lessons taking into consideration their students’ previous knowledge and  new knowledge they do by “reminding quadrilaterals students previously learnt” or “making association between similar quadrilaterals. Based on the data, the teachers pointed out the students’ mistakes about quadrilaterals were group under three headings. These are, mistakes regarding defining quadrilaterals, mistakes regarding visual property and, classification of quadrilaterals and family relation within quadrilaterals.  The students’ difficulties inferred from teachers’ responses are summarized in two groups: difficulties identified related with trapezoid and difficulties identified related with other quadrilaterals. Key words: Pedagogical Content Knowledge, Student Knowledge, Quadrilaterals

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Papers

The pedagogical content knowledge in mathematics: pre- service primary mathematics teachers' perspectives in turkey

Investigation of Prospective Primary Mathematics Teachers' Perceptions and Images for Quadrilaterals.

Türkiye'den Bir Profil: 11-13 Yaş Gurubu Matematik Öğretmen Adaylarının Eleştirel Düşünme Eğilim ve Becerileri

Matematik Öğretmen Adaylarının İspat Yapmaya Yönelik Görüşleri

Middle School Mathematics Teachers’ Pedagogical Content Knowledge Regarding Student Knowledge about Quadrilaterals