Applications and modelling in mathematics teaching

The aim of this paper is a comprehensive presentation of some important basic and general aspects of the topic applications and modelling, with emphasis on the secondary school level. Owing to the review character of this paper, some overlap with the survey paper Blum and Niss (1989) for ICME-6 in Budapest is inevitable. The paper will consist of three parts. In part 1, I shall try to clarify some basic concepts and remind the reader of a few application and modelling examples suitable for teaching. In part 2, I shall formulate some general aims for mathematics instruction and, on that basis, summarise the most important arguments for and against applications and modelling in mathematics teaching. Finally, in part 3, I shall discuss some relevant instructional aspects resulting from the considerations in part 2.

Questioning in the secondary school.

Explica los diferentes tipos y modelos de preguntas que los profesores de escuelas secundarias pueden requerir en el aula. La capacidad de preguntar a los alumnos, la búsqueda inteligente de preguntas y su uso para diferentes propósitos, así como, saber qué hacer con la respuesta es crucial para los profesores de todas las materias. Esta es una de las habilidades esenciales en la enseñanza que indican una buena práctica y pueden ayudar en el aprendizaje de los alumnos. También, facilita las distintas formas en que los profesores puedan evaluar la eficacia de sus preguntas en el aula.

Teaching reading Shakespeare.

Plantea los problemas que presenta la lectura de Shakespeare, en la actualidad, a los jóvenes lectores y ayuda a los profesores de secundaria a hacer frente a las dificultades lingüísticas de estas obras como el uso de palabras antiguas, la gramática, la retórica y la metáfora. La enseñanza de los textos de Shakespeare se realiza en el marco contextual, interpretativo y lingüístico exigido para el título del General Certificate Secondary Education (GCSE) y del A-level.

The Construction of grammar concepts at secondary school

In this study we make a general research question [1] and two specific ones [2] i [3]: [1] How can we establish a new model for teaching and learning grammar? [2] How metalinguistic knowledge is built within this model? [3] How can we elaborate an analysis model for exploring grammar knowledge?

Moving on: the challenges for foreign language learning on transition from primary to secondary school

Europe's commitment to language learning has resulted in higher percentages of pupils studying foreign languages during primary education. In England, recent policy decisions to expand foreign language learning at primary level by 2010 create major implications for transition to secondary. This paper presents findings on transition issues from case studies of a DfES-funded project evaluating 19 local authority Pathfinders piloting the introduction of foreign language learning at primary level. Research on transition in other countries sets these findings in context. Finally, it investigates the challenges England faces for transition in the light of this expansion and discusses future implications.

In-service and pre-service teachers' opinion on the use of models in teaching chemistry

The presented study examined the opinion of in-service and prospective chemistry teachers about the importance of usage of molecular and crystal models in secondary-level school practice, and investigated some of the reasons for their (non-) usage. The majority of participants stated that the use of models plays an important role in chemistry education and that they would use them more often if the circumstances were more favourable. Many teachers claimed that three-dimensional (3d) models are still not available in sufficient number at their schools; they also pointed to the lack of available computer facilities during chemistry lessons. The research revealed that, besides the inadequate material circumstances, less than one third of participants are able to use simple (freeware) computer programs for drawing molecular structures and their presentation in virtual space; however both groups of teachers expressed the willingness to improve their knowledge in the subject area. The investigation points to several actions which could be undertaken to improve the current situation.

Boundaries and Bridges: the influence of James Cooksey Culwick on the development of the teaching and learning of music in nineteenth century Ireland

James Cooksey Culwick (1845-1907) was born in England. Trained as chorister and organist in Lichfield Cathedral, he moved to Ireland at twenty- one and remained until his death in 1907. Although his reputation as scholar, musician and teacher was acknowledged widely during his lifetime - he received an honorary doctorate from University of Dublin (1893) - little is known about the contribution he made to music education. This paper addresses this gap in the literature and argues that it was Culwick's singular achievement to pay attention to music pedagogy at secondary level, by recognizing that music could be seen as a serious career option for girls, and by providing resources for teachers which emphasised the development of an 'art-feeling' in pupils of all abilities. In addition, he considered Irish music as an art which had significance as music first, and Irish music second, and advocated a 'laudable tolerance' for opposing views on matters of cultural identity to Ireland at the end of the nineteenth century.

Teacher stance as reflected in feedback on student writing: An empirical study of secondary school teachers in five countries

This study examines the feedback practices of 110 EFL teachers from five different countries (Cyprus, France, Korea, Spain, and Thailand), working in secondary school contexts. All provided feedback on the same student essay. The coding scheme developed to analyse the feedback operates on two axes: the stance the teachers assumed when providing feedback, and the focus of their feedback. Most teachers reacted as language teachers, rather than as readers of communication. The teachers overwhelmingly focused on grammar in their feedback and assumed what we called a Provider role, providing the correct forms for the student. A second role, Initiator, was also present, in which teachers indicate errors or issues to the learner but expect the learner to pick this up and work on it. This role was associated with a more even spread of feedback focus, where teachers also provided feedback on other areas, such as lexis, style and discourse.

Teaching English as an additional language: a MESHGuide

This guide has been co-authored by Naomi Flynn, an Associate Professor at The University of Reading, working with Chris Pim and Sarah Coles who are specialist advisory teachers with Hampshire’s Ethnic Minority and Traveller Achievement Service (EMTAS). It was constructed with the support of teachers in primary and secondary schools in Hampshire, selected for their existing expertise in teaching EAL learners, who used the guidance for action research during the spring and summer of 2015. The guide is written principally to support teachers and learning support assistants working with EAL learners in any educational setting and who are at any stage of fluency in the learning of English. It will also support senior leaders in their strategic response to the EAL learners in their schools. As with all MESH guides it seeks to share knowledge with professionals in order to support the growth of evidence informed practice that works in promoting the best in pupil outcomes

Motivational trajectories for early language learning across the primary-secondary school transition

The transition from primary to secondary school is an area of concern across a range of curriculum subjects, and this is no less so for foreign language learning. Indeed problems with transition have been identified in England as an important barrier to the introduction of language learning to the primary school curriculum, with implications for learners’ longer-term motivation for the subject. This longitudinal study investigated, through a questionnaire, the development of 233 learners’ motivation for learning French in England, during the transition from primary to secondary schooling. It also explored whether levels and patterns of motivation differed according to the type of language teaching experienced, comparing a largely oracy-focused approach with one with greater emphasis on literacy activities. Learners showed high and increasing levels of motivation across transition, placing particular value on learning French for travel. Being taught through an oracy or a literacy-focused approach had less impact on learners’ motivation than broader classroom experiences, with the development of a sense of progress and feeling that instruction met their learning needs being especially important. A growing disjuncture emerged between valuing the learning of French for travel/communication and learners’ low levels of self-efficacy for communication with native speakers, together with a desire for more communication-based activities. By the end of the first year of secondary school less positive attitudes towards learning French and less optimism about the possibility of future progress were beginning to emerge. The paper concludes by outlining the implications of the study for classroom practice in language learning.

Innovation and change in English teaching in the western provinces of China: the impact of overseas training

In this article we explore issues around the impact of continuing professional development (CPD) for secondary teachers of English offered by an overseas provider through the lens of participants from the Western provinces of China who completed courses at a UK university between 2003 and 2012. We start by offering an overview of English teaching in China. We then report two complementary studies of the same programme. The first aimed for breadth of understanding and involved the collection and analysis of interviews and focus groups discussions with former participants, their teaching colleagues and senior management, as well as classroom observation. The second aimed for depth and drew on data collected from a cohort of 38 teachers on one of the courses, using pre- and post-course surveys; focus group discussions at the end of the course with the whole cohort; and interviews with five of the participants both before they left the UK and again six months later. Evidence is presented for changes in teachers’ philosophies of education directly attributable to participation in the courses; for improved teacher competencies (linguistic, cultural and pedagogical) in the classroom; and for the ways in which returnees are undertaking new roles and responsibilities that exploit their new understandings. Finally, we discuss the implications of these findings for both providers and sponsors of CPD for English language teachers.

English-medium instruction in Sweden : Perspectives and practices in two upper secondary schools

This thesis presents English-medium instruction (EMI) in the Swedish context, focusing on perspectives and practices in two schools. The research question is as follows: How and why is EMI offered, chosen, and practiced in the Swedish upper secondary school today? The aim is to explore the status of the educational option, the reasons for offering EMI to stakeholders, the stakeholders’ beliefs about and goals of EMI, and the implementation of EMI in the classroom. A survey of all upper secondary schools in Sweden was conducted to ascertain the spread of content teaching through a foreign language. The educational context was studied from an ecological perspective using methods based in linguistic ethnography. Language alternation, academic language, and language hierarchy were all considered. Interviews were analysed for content; and classroom language use was analysed for language choice and function. The concepts of affordance and scaffolding together with translanguaging were key. The de facto policies of the micro contexts of the schools were examined in light of the declared national policy of the macro context of Sweden. The results indicate that the option in Swedish schools has not increased, and also tends to only be EMI—not Content and Language Integrated Learning (CLIL) or instruction through other languages. EMI is offered for prestige, an international profile, marketing potential and personal interest. EMI students are academically motivated and confident, and see the option as “fun”. 100% EMI in the lessons is not the goal or the practice. Translanguaging is abundant, but how language alternation is perceived as an affordance or not differs in the two schools. One focuses on how the languages are used while the other focuses on how much each language is used. In conclusion, the analysis suggests that a development of definitions and practices of EMI in Sweden is needed, especially in relation to language policy and language hierarchy.

An Empirical Study on Teachers’ Choice of Extensive Literature in the Swedish Upper Secondary EFL Classroom

The importance of extensive literature reading in the English as a Foreign Language (EFL) context has been given increasing attention in recent research. Literature reading is also a required part of the national syllabi of the (EFL) courses offered to both adolescents and adults at Upper Secondary level in Sweden. This thesis aims to investigate the teachers’ process of making literature choices for extensive reading in upper secondary EFL courses in Sweden. Eight teachers of three different student groups took part in the study, representing adolescent university preparatory programs and vocational programs, as well as programs for adult students. Questionnaires were used and the data was analyzed for patterns revealing three main factors affecting teachers’ literature choice: language proficiency, reading experience and contextual factors. These three factors were fitted into the theoretical framework of psycholinguistic and sociolinguistic reading models, with the addition of a perspective of motivational research. The results of this survey underline the importance of extensive reading, according to teachers, and that motivation for literature choice can be primarily related to factors associated with psycholinguistic reading models. The survey also points to the need for further investigating of teachers’ own experiences of literature reading, searching for deeper motivational factors which influence teaching choices. Another future field of research is the choice of reading activities assigned together with the chosen literature, which probably also influence teachers’ choices in the Swedish EFL classroom.

L1 Use in the EFL-classroom : A Literature Review on Teachers’ Use of the L1 in the EFL-classroom on Upper Secondary Level

Even though English should mainly be used in the EFL-classroom according to the Swedish national curriculum, some recent scholars have argued that a judicious use of the students’ L1 by the teachers in some particular situations may benefit the learning environment there. From this context, this thesis examines what research says about in what particular situations the L1 is used by teachers in upper secondary EFL-classrooms as well as the teachers’ and the students’ attitudes towards this practice. The method used was a systematic literature review, where seven articles from all across the globe were analyzed, compared and synthesized. The results show that the L1 was mainly used by the teachers when managing discipline, when explaining grammar and when teaching vocabulary. However, the articles did not conclude how the L1 could be used strategically by the teachers. Concerning the teachers’ and students’ attitudes, the majority of these were positive towards L1 use by the teacher in the above mentioned situations. However, the teachers were not aware of how the L1 could be used by them in a judicious and a strategic way. Lastly, it can be concluded that more research is needed on how the L1 can be used more strategically by the teachers as well as on the students’ perspective on this.

Teachers’ Views on ICT as a Tool in English Teaching for Students with Dyslexia : An interview study with English teachers in grades 7-9

Information and communications technology (ICT) is a broad concept, which is often discussed in relation to the development of education. More specially, ICT can be seen as a tool to help teachers individualize students’ education. Students who have literacy difficulties, such as dyslexia, are in constant need of new techniques to help them learn and new tools to make their educational development easier. The aim of this thesis is to show what views teachers have regarding using ICT in English teaching at a sample of schools in the south of Sweden. A secondary part of the aim is to see what ICT tools, or other non ICT related methods, these teachers use to improve literacy skills for students with dyslexia.This empirical study is based on interviews with six participants. Previous research within the area is presented and different aspects of ICT within the National Agency for Education in Sweden, and the English syllabus, are also discussed. The results of this thesis show that ICT is seen as a helpful tool to make education easier for both students and teachers. Tools such as ViTal, Spell Right and Legimus are being used and the participants of the study also use iPads and Chromebooks in their teaching. According to the interviews, ICT can tribute to a fun way of learning and a more individualized education. Other non ICT related methods are also used to help students with dyslexia and these are often in terms of pictures in connection to words. These findings are based on a limited number of participants in a small area of south of Sweden. Therefore, further research is needed to see if the findings can be verified with more participants, in different parts of the country.