EXAMINING PROSPECTIVE TEACHERS’ BELIEF AND PEDAGOGICAL CONTENT KNOWLEDGE TOWARDS TEACHING PRACTICE IN MATHEMATICS CLASS: A CASE STUDY

Grounded in scholarship on multilingualism, this multimodal case study aims to identify factors related to ideologies of language and culture in an English language classroom in a public lower secondary school in Sweden for an enhanced understanding of learning conditions for multilingual students. Using a triangulation of methods, participant observation, materials analysis, and interviews, the study examines teaching practice, materiality, language use and teachers’ perspectives on multilingualism and their own teaching practices in the multilingual classroom. The study finds a predominance of factors rooted ideologies of monolingualism and monoculturalism. Teaching practice was marked by the traditional approach to teaching English with a focus on Britain/the U.K. as a homogenous monocultural and monolingual nation and a Swedishness norm dominated teaching practice and classroom interaction: extensive usage of the Swedish language, examples of teaching strategies related to a contrastive Swedish-English grammar approach and a study of target language culture from a national Swedish perspective. An application of Nancy Hornberger’s model of the continua of biliteracy to the data identifies teaching practice in the classroom as close to the privileged ends. The analysis of interviews suggests that the traditional approach was normalized and that teachers had limited awareness of pedagogical strategies for the inclusion of multilingual students.

As indicated by the Warnock Report, even forty years ago, the necessity of responding to different student abilities and needs in school and thus the importance of adequate adaption of a regular curriculum regarding differentiation and personalization had already been described. Due to changes in policy and legislative frameworks, more and more students with special educational needs (SEN) attend regular education. However, placing the students with SEN within mainstream classrooms does not automatically lead to changes in teaching practices in these classrooms. In line with this, it would be interesting to know the way in which and to what extent students in inclusive classes perceive established inclusive practices, such as differentiation and personalization. Therefore, data from 47 inclusive classes from North Rhine-Westphalia (Germany) were collected. In total, 872 primary school students (grade 4; ages 9–11 years) were asked to rate how frequently their class teachers used inclusive instructional practices (personalization and differentiation) using the Inclusive Classroom Practices Scale (ITPS). In addition to students, teachers were also asked to rate their own teaching practices in general and then in addition for each student separately. As differentiated instruction and multifaceted teaching practices are considered to be measures for meeting the needs of children with different educational needs, results that show a high use of these approaches were expected. Descriptive results indicate a consistent homogeneous understanding of prevailing inclusive teaching practices, which could be characterized by existing, but not intensive implementation, of inclusive practices. Differences regarding students’ gender, migrant background, or SEN were not found for the students’ ratings of teachers’ inclusive practices or the teachers’ self-ratings group. Moreover, the teachers’ student-specific ratings indicate that teachers did not strongly differentiate or personalize with a focus on students’ characteristics. A small overlap between teachers’ general ratings of their own inclusive teaching practices and students’ individual ratings was found. The results of the current study provide insights into actual inclusive teaching practices in German inclusive classrooms and make it possible to address the need for action and inclusive interventions.

Prospective teachers' beliefs have a beneficial effect on their knowledge and actions. Furthermore, teachers' pedagogical content knowledge is an essential contributor to teachers' impact on students' academic outcomes. However, examining how prospective teachers' beliefs influence their pedagogical content knowledge is still unclear. The current study investigates prospective mathematics teachers' beliefs and pedagogical content knowledge. We recruited three undergraduate students in the mathematics department consisting of one male and two female participants in this study. By assigning two interviews, a test, and observation, we examined three prospective mathematics teachers' pedagogical content knowledge and their beliefs about the nature of mathematics, mathematics learning, and mathematics teaching. Prospective mathematics teachers' test, interview, and observation results were analyzed in three stages: data condensation, presentation, and conclusion drawing and verification. The findings point out that traditional beliefs (instrumentalist and platonist views) are more dominant in prospective teachers' beliefs about the nature of mathematics. Moreover, the more sophisticated prospective teachers' beliefs about the nature of mathematics, mathematics learning, and mathematics teaching are, the higher one's content knowledge and pedagogical content knowledge levels are. Implications of this study, mathematics teacher educators should assist and foster prospective teachers in developing constructivist or problem-solving beliefs.

الملخص: هدفت هذه الدراسة إلى بحث أثر استخدام استراتيجيات التدريس التأملي على تطوير الأداء الصفي للطالبات المعلمات، تخصص اللغة الانجليزية. ولقد تبنت الدراسة المنهج شبه التجريبي. وتكونت عينة الدراسة من(٣٢) طالبة مقيدة بالمستوى الرابع في تخصص اللغة الانجليزية واساليب تدريسها بكلية التربية في جامعة الاقصى بغزة، وتم تقسيمهن عشوائيا إلى مجموعتين (ضابطة وتجريبية). اعتمدت المجموعة الضابطة على الطريقة المعتادة في أدائها، وهي تعليقات المشرفين فقط، بينما استخدمت المجموعة التجريبية استراتيجيات التدريس التأملي في فترة التربية العملية (2) حيث تم تدريب المجموعة التجريبية على استخدام استراتيجيتين للتدريس التأملي وهي: المذكرات اليومية، وملاحظة الزملاء أو الرفاق. ولقد تمت الاستعانة في هذا البحث بوسائل جمع البيانات وهي: قائمة ملاحظة بممارسات وأداء التدريس الصفي، ومقياس (متدرج) لتحليل وتقدير استراتيجيات التدريس التأملي. تم تحليل البيانات كميا وكيفيا. واستخدمت الدراسة الإحصاء الوصفي (المتوسطات، والانحرافات المعيارية، والتكرارات، والرتب، والنسب المئوية واختبار ت في تحليل البيانات. ولمعرفة حجم التأثير الناتج عن استخدام استراتيجيات التدريس التأملي (المتغير المستقل) على الأداء الصفي للطالبات المعلمات (المتغير التابع) تم الاستعانة بمربع إيتا. أظهرت نتائج الدراسة اهم ممارسات الأداء الصفي التي تحتاجها الطالبات المعلمات داخل الغرفة الصفية. كما اوضحت النتائج تحسنا ملحوظا في الأداء الصفي للمجموعة التجريبية. وعلاوة على ذلك، اظهرت نتائج الدراسة أن فروق ذات دلالة إحصائية عند مستوى 0.01) ) بين متوسطي درجات المجموعتين (التجريبية والضابطة) في التطبيق البعدي لقائمة معايير الأداء الصفي ككل وفي كل محور من المحاور الستة (توجيه التعليمات، استخدام تقنيات طرح الأسئلة المحفزة، استخدام التقنيات المناسبة لتصحيح الأخطاء، تعزيز الإجابات الصحيحة، الاستخدام المنظم للسبورة، واستخدام مصادر المعلومات والوسائل المتوفرة) لصالح المجموعة التجريبية. كذلك وتوصلت الدراسة إلى وجود فروق ذات دلالة إحصائية عند المستوى بين متوسط درجات المجموعة التجريبية في التطبيق القبلي والبعدي لقائمة معايير الأداء الصفي ككل وفي 0.01) ) كل محور من المحاور الستة السابق ذكرها وذلك لصالح التطبيق البعدي. وخلصت الدراسة إلى فعالية استخدام استراتيجيات التدريس التأملي خلال التربية العملية في تحسين الأداء الصفي للطالبات المعلمات تخصص اللغة الانجليزية واساليب تدريسها. وفي ضوء النتائج التي تم التوصل إليها، جاءت بعض التوصيات ومنها: وجوب دمج استراتيجيات التدريس التأملي في برامج إعداد معلمة اللغة الانجليزية، وفي مقررات طرق تدريس اللغة الانجليزية خاصة. وأنه من الضروري أن تتعرف الطالبة المعلمة على أساليب وطرق مختلفة ومتعددة للتأمل ٠ وقد أوصت الدراسة بإمكانية تطوير أداء المعلمات أثناء الخدمة باستخدام التدريس التأملي وأنشطته، بالإضافة إلى وجوب تدريب الطالبات المعلمات على استخدام الأدوات التي تدعم التفكير التأملي. الكلمات الدلالية: التدريس التأملي، الأداء الصفي ، الطالبات المعلمات، اللغة الإنجليزية كلغة اجنبية

The COVID 19 pandemic promotes several new technological products to facilitate learning process. However, there are still few studies on the integration of Augmented Reality (AR) technology into Blended Learning (BL), particularly on the education of prospective mathematics teachers. This research examines the effect of using augmented reality blended learning during the COVID 19 epidemic on 3D geometry, as well as the learning motivation and attitudes. 15 prospective teachers, including 4 males and 11 females, at one of Indonesia's private universities were engaged in to determine how 3D geometry is understood. Data on learning motivation and attitudes were collected through questionnaires and interviews and analyzed using descriptive statistics and paired-samples t-test. The results show that during the COVID-19 pandemic, augmented reality blended learning facilitates the comprehension of 3D geometry knowledge by prospective teacher applicants and promotes learning motivation and attitudes. Therefore, the use of new technology is significant to prospective teachers' needs, especially during the COVID 19 pandemic, to facilitate their teaching practice in real classrooms.

The aim of this study was to examine prospective science teachers’ pedagogical content knowledge in terms of their approach to error. For this purpose, a data collection tool consisting of 5 questions for conceptual understanding of electrical circuits and steps containing correct and incorrect explanations for each question was prepared and applied to prospective science teachers. This study was carried out using case study method, one of the qualitative research approaches. The participants consisted of 30 prospective science teachers studying in 4th Grade in a state university. The data were analyzed using descriptive analysis method. The findings showed that the rate of prospective teachers who provided correct explanations in the solution of the questions about electrical circuits was high. In addition, the rate of detecting the solution steps given incorrectly was at a moderate level. It was revealed that very few participants who identified the wrong solution steps were able to make correct explanations for the solution of the question. Majority of the participants had some misconceptions such as “Generators are constant current sources”, “Local reasoning” and “Regardless of how the generator and light bulbs are connected in the circuit, if the number of generators increases, the brightness of the bulb increases”. These misconceptions were evaluated as an indication that prospective teachers’ pedagogical content knowledge was not at a level that could be considered sufficient in terms of understanding the student. In this context, error-based activities can be included in teaching in order to prevent the formation of misconceptions, incomplete and/or incorrect information in students or prospective teachers, and to correct existing misconceptions. The effects of error-based activities on individuals’ learning can be investigated in future studies.

Objective: The current study intended to identify successful teaching strategies and practices in EFL virtual classrooms and to build a proposed model for designing teaching strategies and successful practices in virtual classrooms. Theoretical Framework: The research concerns itself with studies that concentrate on applications of artificial intelligence, adaptive learning, teaching methods, communication, and interaction in EFL virtual classrooms. Method: the study adopted the qualitative documentary method as the paradigm of qualitative research through extensive qualitative analyses of the contents of several previous studies. Results and Discussion: The study obtained results that comprised several successful teaching strategies in EFL virtual classrooms and a proposed model for designing teaching strategies in virtual classrooms. Research Implications: In addition to these results,this study presents numerous teaching strategies and successful practices in EFL virtual classrooms that help teaching faculty, teaching cadres in a virtual classroom environment. It also gives a proposed model for successful teaching strategies and practices in EFL virtual classrooms that aids e-learning designers in designing teaching strategies in a virtual classroom environment. Originality/Value: This study is amongst the first to investigate successful teaching strategies and practices in EFL virtual classrooms especially in the context of arabian countries .

As teacher training plays a major role in the development of (prospective) teachers’ knowledge, differences between the professional knowledge of prospective teachers at Austrian and German universities were examined in the current study. The teacher training systems of business and economic education in both countries differ substantially regarding structure and content. The German system consists of two consecutive phases with different foci (university education with an emphasis on theories and domain-specific knowledge, followed by school-based practical training with the objective of acquiring practical experience). Thus, in Germany, opportunities to learn (OTL) mainly cover domain-specific knowledge with less focus on didactics and teaching experience. In contrast, Austrian universities offer an integrated approach that combines the two phases (i.e., theoretical input and practical teaching experiences are closely linked) at the university level. A paper-and-pencil test was used to measure content knowledge (CK) and pedagogical content knowledge (PCK) in the domain of accounting of prospective teachers in Germany and Austria. The total sample consists of n = 1,401 prospective teachers from German and Austrian universities. Taking the structural differences in teacher education into account, differences in CK and PCK between German and Austrian prospective teachers were expected. Accordingly, the results show that the Austrian sample outperformed the German one. In addition, for both the German and the Austrian sample, university-based OTL in accounting had a crucial impact on the CK score. Concerning PCK, however, the situation is different: none of the university-based OTL had an impact on Austrian prospective teachers’ PCK, and only small effects were found for the German sample. Possible reasons for the unexpected findings are discussed.

In this paper, we explore how teaching practices in classrooms influence students’ civic knowledge achievement in three Scandinavian countries: Denmark, Norway, and Sweden. Using data from the 2009 International Civic and Citizenship Education Study (ICCS), our investigation focuses on the measures of “open classroom climate”, which include seven items that ask students how often they experience each of the seven teaching practices during regular lessons. From the students’ perspective of teaching practices in the classroom, we hypothesize and assume that there should be a balanced combination of classroom practices where each method/activity carries a different weight or level of importance. Applying logistic regression analysis, we assess the effect of each of the practices on the probability with which a student becomes a high achiever of civic knowledge (as represented by odds ratios). Our results show both similarities and differences in the combinations of classroom practices that have contributed to students’ high civic knowledge achievement in the three Scandinavian countries. Our findings provide useful messages to teachers in the classroom, and they also have implications for teacher education and research.

PurposeTo understand how lesson study (LS) can promote the development of pedagogical content knowledge (PCK) of prospective primary teachers. More specifically, to know what PCK prospective primary teachers develop during LS and how this development occurs.Design/methodology/approachFollowing a qualitative approach, this study took place in a teacher education institution where a LS was carried out during the last semester of the academic year with the participation of two prospective teachers, a teacher educator, a cooperating teacher and a researcher.FindingsThe results suggest that prospective teachers may develop PCK when they participate in LS, regarding lesson planning (goals and lesson plan), task design, students' difficulties and solving strategies, whole-class discussions and observation of student learning. This development occurs through the engagement in LS activities that allow prospective teachers to deepen their knowledge.Originality/valueThis study investigates how the development of prospective teachers' PCK occurs during LS, providing knowledge about how different activities of the LS help develop different aspects of PCK.

IntroductionElementary teachers need a solid understanding of so that they can teach it as a coherent, reasoned activity and communicate its elegance and power (Conference Board of Mathematical Sciences [CBMS], 2001, p. xi}. However, research studies on prospective teachers' knowledge have shown that many possess a limited knowledge of in key content areas as number (e.g.. Ball, 1990a; Thanheiser, 2009; Tobias, 2013}. This is particularly true in case of which, along with ratio and proportion, Lamon (2007} calls, the most protracted in terms of development, most difficult to teach, most mathematically complex, most cognitively challenging, most essential to success in higher and science, and one of most compelling research sites (p. 629}.The National Mathematics Advisory Panel (2008} affirmed that with fractions is a major goal for K-8 education because such proficiency is foundational for algebra and, at present time, seems to be severely underdeveloped (p. xvii}. Therefore, developing proficiency in prospective elementary teachers (PTs} is a critical task for educators. As authors of Mathematical Education of Teachers, Part 1 suggest, The key to turning even poorly prepared prospective elementary teachers into mathematical thinkers is to work from what they do know (CBMS, 2001, p. 17}. Thus, in order to design courses for prospective teachers that will help them to develop solid understanding of mathematics called for by Conference Board of Mathematical Sciences (2001}, including a deep understanding of and with fractions, we must begin by determining what it is that PTs know. In this paper, we discuss main findings from a research summary of existing studies on prospective elementary teachers' fraction knowledge to identify directions for future research.Theoretical FrameworkIn looking at teacher knowledge, we begin by examining work of Shulman (1986], who proposed three categories of content knowledge for teachers: (a] subject matter content knowledge, (b] pedagogical content knowledge, and (c] curricular knowledge. For Shulman, subject matter content knowledge includes knowing a variety of ways in which the basic concepts and principles of discipline are organized to incorporate its facts and truth or falsehood, validity or invalidity, are established (p. 9]. Pedagogical content knowledge refers to knowledge of useful forms of representations (e.g., analogies, illustrations, explanations] of subject-matter ideas that make it understandable to others, as well as an understanding of conceptions and preconceptions students bring to learning processes. third type of knowledge, curricular knowledge, includes knowledge of a full range of programs designed for teaching of particular subjects and topics at a given level, variety of instructional materials available in relation to those programs, and set of characteristics that serve as both indications and contraindications for use of particular curriculum or program materials in particular circumstances (p. 10].Shulman's ideas on pedagogical content knowledge sparked a huge interest in knowledge for teaching, eliciting over a thousand studies (Ball, Thames, & Phelps, 2008] throughout a number of content areas, with a large number of these studies focusing on teachers' knowledge of (e.g., Ball et al., 2008; Davis & Simmt, 2006; Hiebert, 1986; Ma, 1999]. Deborah Ball and her colleagues introduced term mathematical knowledge for teaching (MKT) (e.g., Ball & Bass, 2002), which focused on work that teachers do when teaching mathematics.Building on Shulman's (1986) categories of knowledge, Ball, Thames, and Phelps (2008) introduced a framework for mathematical knowledge for teaching. …

In this keynote, the development of pedagogical content knowledge (PCK) within (prospective) science teachers is explored and discussed. First of all, the meaning of the term ‘pedagogical content knowledge’ is examined and some core elements of this concept are described. Secondly, several methods and techniques to explore PCK are reported. Thirdly, important sources for the development of PCK are described. Finally, a naturalistic case study of the development of PCK within a group of prospective science teachers (all M. Sc.) is presented. The group has taken a post-graduate course module, incl. some teaching practice, on a central issue in science education: teaching models. The results indicate that the prospective teachers’ knowledge of students’ conceptions of models was promoted. Besides, the prospective teachers became aware of their own limited knowledge of appropriate models, and ways to teach this issue. This absence of this knowledge can have caused the observed discrepancy between their teaching intentions (models as constructs) and their teaching practice (models as facts). Implications for (prospective) science teacher courses are discussed.

The purpose of the current study was to contribute to a better understanding of Zambian prospective mathematics secondary teachers’ pedagogical content knowledge of mathematics (M-PCK) as part of a larger project aimed at characterising their subject matter and pedagogical content knowledge (PCK) related to the function concept. K-means Cluster analysis was used to derive profiles based on M-PCK perceptions. Three profiles related to M-PCK perceptions of prospective teachers emerged from the clustering process namely (i) self-doubting (cluster 1), (ii) anti-M-PCK (cluster 2) and (iii) confident and enthusiastic (cluster 3). A One-way ANOVA test was performed to determine the existence of differences in prospective teachers’ perceptions between Clusters based on the five M-PCK sub-factors. The test revealed significant differences between Clusters of prospective teachers’ perception of all sub-factors. Prospective teachers in Clusters 1 and 2 showed low confidence in their M-PCK perceptions while those in Cluster 3 generally showed moderate confidence.

The study determined the extent of leadership styles of school heads and the extent of classroom practices of public secondary school teachers. This study employed a non-experimental quantitative research design utilizing the descriptive-correlation method. Validated questionnaires and a Universal sampling procedure were utilized considering the minimal number of teachers in the research locale. Two hundred fifty (250) public secondary school teachers were the respondents of the study. Using mean, pearson-r, and regression analysis, the findings revealed that the extent of leadership styles of school heads was extensive while the extent of classroom practices of public secondary school teachers was very extensive. Moreover, the overall results revealed that indicators for leadership styles of school heads have a strong positive relationship to the classroom practices of public secondary school teachers. Further, results from the regression analysis revealed the following have a strong influence on leadership styles of school heads on classroom practices of public secondary school teachers: Supportive, Participative, Achievement-Oriented, and Directive. It was recommended that school heads should manage change and develop a mechanism to improve the schools system through creative support of its manpower of teachers, staff, learners, and community. Education can be effective in an environment that is not conducive to teaching and learning. School heads conduct seminars and workshops on Different Leadership Styles to sustain high performance in managing and leading the school. KEYWORDS: Leadership style of school heads, classroom practices

The present study was undertaken through a qualitative research model in order to examine which sub-categories of Pedagogical Content Knowledge (PCK) emerged during the practicum process of four novice English teachers enrolled in a teaching certificate (formation) program at a public university. The teaching sessions of four prospective teachers (PTs) were recorded and follow-up interviews were conducted with the prospective teachers. Stimulated recall technique was used in the interviews. Each prospective teacher was observed for four times and the lessons conducted by prospective teachers were recorded. The PCK categorization suggested by Moradkhani et al. (2013) was utilized. They categorized PCK in 8 macro categories with accompanying micro strategies. The study was conducted throughout one semester in which the novice teachers were supposed to complete their practicum. The results indicated that knowledge of students is extremely important in the language teaching process, which is followed by knowledge of transferring knowledge and knowledge of teaching techniques. Further, findings also indicate that PTs need development in knowledge of language, knowledge of language teaching methods, and knowledge of linguistics. PTs must develop insight into how to provide effective input.