scholarly journals Differences in Norwegian and Swedish student teachers’ explanations of solutions of linear equations

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Niclas Larson ◽  
Kerstin Larsson

This study draws on data from 146 Norwegian and 161 Swedish student teachers. They were given a correct but short and unannotated solution to the linear equation x + 5 = 4x – 1. The student teachers were invited to explain the solution provided for a fictive friend, who was absent when the teacher introduced this topic. An accurate solution of this equation contains two additive and one multiplicative operation. There are two main strategies for solving a linear equation, ‘swap sides swap signs’ (SSSS) and ‘do the same to both sides’ (DSBS). Of the Norwegian student teachers, 2/3 explained the additive steps in the solution by SSSS, while only 1/3 of the Swedish student teachers applied SSSS. Consequently, DSBS was more frequent among the Swedish student teachers regarding the additive steps. However, in the final, multiplicative step, 3/4 of the Norwegian student teachers chose to explain by DSBS. On the contrary, among the Swedish student teachers the proportion applying DSBS for the multiplicative step of the solution decreased, and almost as many provided a deficient explanation of the final operation. We discuss possible reasons for differences between the nations. We also suggest how teacher educators in both countries can use the results of this study to improve student teachers’ explanations of how to solve linear equations.

Author(s):  
Darshana Sharma

Teaching Practice is widely recognised as the sine-qua-non of any teacher education programme. It is a component in the teacher preparation programme where prospective teachers are provided with an opportunity to put their theoretical studies into practice, get feedback, reflect on practice and consequently further improve their teaching skills. As teaching practice is an important component of a teacher education programme, considerable attention must be given to make it more effective and fruitful. This paper is based on a research study conducted to know pre-service teachers' experiences of the quality of teaching practice and the common concerns they have during teaching practice. On the basis of focussed group discussion a total of five themes were identified, these are (1) usefulness of teaching practice (2) experiences/concerns with pupils' behaviour (3) experiences/concerns with own behaviour (4) experiences/concerns with supervisors' behaviour (5) experiences/concerns with institutional and personal adjustments. The outcome of the focussed group discussion was used to prepare a structured questionnaire. Among other things, the study recommended rigorous practical training in lesson planning, demonstration lessons by teacher educators, simulated teaching before the commencement of practice teaching, school orientation programmes, a separate internship of two weeks and writing a journal by student teachers during teaching practice.


Author(s):  
Sunanta Klibthong ◽  
Joseph Agbenyega

This paper gives an account of a teacher preparation program in which a problem based learning approach was used to enact inclusive learning among student teachers. Taking a postmodernist perspective, the student teachers' experiences of participation in group activities on a problem-based scenario in an Australian university was documented through chat-rooms, online postings and reflective journal writings. Knowledge about peer interaction and communities of learning relationship, reflective practice and opportunity to manage difference and question the status quo are areas that were highlighted by the students. We concluded that problem-based learning is transformative and that whatever teacher educators expect their student teachers to do in their teaching contexts when they graduate, they need to give them the opportunity to practise these in their learning during training.


Author(s):  
Chein-Shan Liu ◽  
Essam R. El-Zahar ◽  
Chih-Wen Chang

Abstract In the paper, we develop two novel iterative methods to determine the solution of a second-order nonlinear boundary value problem (BVP), which precisely satisfies the specified non-separable boundary conditions by taking advantage of the property of the corresponding boundary shape function (BSF). The first method based on the BSF can exactly transform the BVP to an initial value problem for the new variable with two given initial values, while two unknown terminal values are determined iteratively. By using the BSF in the second method, we derive the fractional powers exponential functions as the bases, which automatically satisfy the boundary conditions. A new splitting and linearizing technique is used to transform the nonlinear BVP into linear equations at each iteration step, which are solved to determine the expansion coefficients and then the solution is available. Upon adopting those two novel methods very accurate solution for the nonlinear BVP with non-separable boundary conditions can be found quickly. Several numerical examples are solved to assess the efficiency and accuracy of the proposed iterative algorithms, which are compared to the shooting method.


2019 ◽  
Vol 6 (1) ◽  
pp. 69-84
Author(s):  
K. Ayu Dwi Indrawati ◽  
Ahmad Muzaki ◽  
Baiq Rika Ayu Febrilia

This research aimed to describe the thinking process of students in solving the system of linear equations based on Polya stages. This study was a descriptive qualitative research involving six Year 10 students who are selected based on the teacher's advice and the initial mathematical ability categories, namely: (1) Students with low initial mathematics ability, (2) Students with moderate initial mathematics ability, and ( 3) students with high initial mathematics ability categories. The results indicated that students with low initial mathematical ability category were only able to solve the two-variable linear equation system problems. Students in the medium category of initial mathematics ability and students in the category of high initial mathematics ability were able to solve the problem in the form of a system of linear equations of two variables and a system of three-variable linear equations. However, students found it challenging to solve problems with complicated or unusual words or languages.


2020 ◽  
Vol 4 (2) ◽  
pp. 113
Author(s):  
Nafiye Cigdem Aktekin ◽  
Hatice Celebi

In this study, we direct our focus to identity construction in an English language teaching (ELT) teacher education program. We explore the teacher roles in which student teachers are struggling to position themselves comfortably and the teacher expertise domains (subject matter, didactics, and pedagogy) that they are dedicating themselves to improving. To address our research focus, we have collected reflections and survey responses from 18 student teachers in an ELT education department. Our findings indicate that ELT student teachers find it difficult to position themselves as experts in and about the English language and that they feel a need to be equipped with expertise first and foremost in the subject matter, and then in didactics, followed by pedagogy. These results imply that in ELT teacher education, certain language ideologies are still prevalent and need to be dealt with by teacher educators for transformative outcomes in education.


Author(s):  
Jane Abbiss ◽  
Eline Vanassche

A review of the field of practice-focused research in Initial Teacher Education (ITE) reveals four broad genres of qualitative research: case studies of teacher education programs and developments; research into student teacher experience and learning; inquiry into teacher educators’ own learning, identity, and beliefs; and conceptual or theory-building research. This is an eclectic field that is defined by variation in methodologies rather than by a few clearly identifiable research approaches. What practice-focused research in ITE has in common, though, is a desire on the behalf of teacher educator researchers to understand the complexity of teacher education and contribute to shifts in practice, for the benefit of student teachers and, ultimately, for learners in schools and early childhood education. In this endeavor, teacher educator researchers are presented with a challenge to achieve a balance between goals of local relevance and making a theoretical contribution to the broader field. This is a persistent tension. Notwithstanding the capacity for practice-focused research to achieve a stronger balance and greater relevance beyond the local, key contributions of practice-focused research in ITE include: highlighting the importance of context, questioning what might be understood by “improvement” in teacher education and schooling, and pushing back against research power structures that undervalue practice-focused research. Drawing on a painting metaphor, each genre represents a collection of sketches of practice-focused research in ITE that together provide the viewer with an overview of the field. However, these genres are not mutually exclusive categories as any particular research study (or sketch) might be placed within one or more groupings; for example, inquiry into teacher educators’ own learning often also includes attention to student teachers’ experiences and case studies of teacher education initiatives inevitably draw on theory to frame the research and make sense of findings. Also, overviewing the field and identifying relevant research is not as simple as it might first appear, given challenges in identifying research undertaken by teacher educators, differences in the positioning of teacher educators within different educational systems, and privileging of American (US) views of teacher education in published research, which was counteracted in a small way in this review by explicitly including voices located outside this dominant setting. Examples of different types of qualitative research projects illustrate issues in teacher education that matter to teacher educator researchers globally and locally and how they have sought to use a variety of methodologies to understand them. The examples also show how teacher educators themselves define what is important in teacher education research, often through small-scale studies of context-specific teacher education problems and practices, and how there is value in “smaller story” research that supports understanding of both universals and particularities along with the grand narratives of teacher education.


2018 ◽  
Vol 12 (2) ◽  
pp. 6
Author(s):  
Juliet Hilary Munden

AbstractExperiencing literature is part of the English as a foreign language (EFL) subject in Norway. It is both challenging and possible to educate competent reading teachers who can foster this experience. The present article is a thematic exploration of some of these challenges and possibilities. The challenges are discussed under four headings: the profession of the teacher educator; the complaint that student teachers do not read enough; the role of national tests in forming how reading in English is taught in school; and the challenge of making sense of the concept of reading strategies. The second part of the article considers possibilities. These are grounded in the principle that teacher educators should not primarily lecture. Instead, they should alternate systematically between enactment and metacognition. The article describes scenarios in which students try out a sequence of pre-, during- and post-reading activities related to the short story “The Demon Lover” by Elizabeth Bowen. After engaging with each activity, the students take part in a reflection led by the teacher educator on their experience as readers, the learning potential of the activity, and questions related to its adaptation and organisation in a diverse school classroom. This operationalisation of a pedagogy of enactment (Grossman et al., 2009) allows student teachers to gain experience of and reflect on core practices. In the present case, the core practice is the planning and teaching of coherent and motivating learning sequences that promote increased reading motivation and proficiency in the English language classroom.Keywords: teacher education, subject English, reading strategies, learning sequence, metacognitionUtfordringer og muligheter i utdanningen av leselærere i engelskfagetSammendragLitteraturopplevelser hører til i engelskfaget i norsk skole. Det er både ut-fordrende og mulig å utdanne kompetente leselærere som kan fremme slike opplevelser. Denne artikkelen er en tematisk utforskning av noen av disse utfordringene og mulighetene. Utfordringene diskuteres under fire overskrifter: lærerutdanneren som profesjonsutøver; misnøyen med at studenter ikke leser nok; betydningen av nasjonale prøver for hvordan lesing i engelsk er undervist i skolen; og utfordringen med å forstå lesestrategier som konsept. Den andre delen av artikkelen tar for seg mulighetene som ligger i prinsippet om at lærer-utdannere ikke primært skal forelese. Isteden bør de veksle systematisk mellom utøvelse og metakognisjon. Artikkelen beskriver en sekvens hvor studenter prøver ut før-, under- og etter-lesningsaktiviteter tilknyttet Elizabeth Bowens novelle “The Demon Lover”. Etter å ha engasjert seg i hver aktivitet, deltar studentene i en refleksjon ledet av lærerutdanneren, hvor de drøfter sine opplevelser som lesere, aktivitetens læringspotensial, og spørsmål om tilpasning og organisering av aktiviteten i et mangfoldig klasserom. Denne operasjonaliseringen av en enactment-pedagogikk (Grossman et al., 2009) gir lærerstudenter anledning til å skaffe seg erfaring med og reflektere over kjerne-praksiser. I dette tilfellet er kjernepraksisen det å planlegge koherente og moti-verende læringssekvenser som fører til økt lesemotivasjon og kompetanse i det engelske klasserommet.Nøkkelord: lærerutdanning, engelskfaget, lesestrategier, læringsøkt, metakogni¬sjon


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