Towards New Teaching in Mathematics How to Realize Inquiry Based and Problem Oriented Mathematics Lessons?

Дагмар Рааб Математиката е вълнуваща и забавна. Можем ли да убедим учениците, че това може да стане действителност. Задачите са най-важните инструменти за учителите по математика, когато планират уроците си. Планът трябва да съдържа идеи как да се очертае и как да се жалонира пътят, по който учениците ще стигнат до решението на дадена задача. Учителите не трябва да очакват от учениците си просто да кажат кой е отговорът на задачата, а да ги увлекат в процеса на решаване с подходящи въпроси. Ролята на учителя е да помогне на учениците • да бъдат активни и резултатни при решаването на задачи; • самите те да поставят задачи; • да модифицират задачи; • да откриват закономерности; • да изготвят стратегии за решаване на задачи; • да откриват и изследват различни начини за решаване на задачи; • да намират смислена връзка между математическите си знания и проблеми от ежедневието. В доклада са представени избрани и вече експериментирани примери за това как учители и ученици могат да намерят подходящ път към нов тип преживявания в преподаването и изучаването на училищната математика.

Readiness for school: A study of parent, teacher, and preschool provider perspectives

A possible gap exists between what parents and preschool providers know concerning children's readiness for school and what they should know when compared to teacher expectations. Students are experiencing difficulty in early schooling as a result of this gap in perspectives. This study's purpose was to describe, explain, and analyze the perspectives of parents, teachers, and preschool providers concerning school readiness. The qualitative strategy of interviewing was used with six parents, six teachers, and two preschool provider participants. Interview transcripts, field notes, member checking, and document analysis were used to interpret data and support findings. Categorization and coding organized data and aided in theory development. ^ Major findings of the study include: (a) All participant groups stress social skills, communication skills, and enthusiasm as most valuable for school readiness; (b) All participant groups agree parents have primary responsibility for readiness preparation; (c) Many participants suggest variables concerning family, economics, and home life contribute to a lack of readiness; (d) Parents place greater value on academic skills than teachers or preschool providers; (e) Preschool programs are identified as having the potential to significantly influence readiness; (f) Communicating, providing positive learning experiences, and providing preschool experience are valuable ways to prepare students for school, yet, differences were found in the types of experiences noted; (g) Participant perspectives indicate that informing parents of readiness expectations is of major importance, and they offer suggestions to accomplish this goal such as using public libraries and pediatrician offices as houses for written information and having kindergarten teachers make presentations at preschools. ^ This study concludes that parents and preschool providers do have knowledge concerning readiness for school. They may not, however, be in a position to carry out their responsibilities due to the intervening variables that inhibit the amount of time, interaction, and communication they have with the children in their care. This study discloses the beliefs of parents and preschool providers that children are ready for school, while teachers conclude that many children are not ready. Suggestions for readiness preparation and information dissemination are significant findings that offer implications for practice and future study. ^

The impact of standards -based practices in mathematics on the achievement of low -performing students

This study examined standards-based mathematics reform initiatives to determine if they would improve student achievement on the part of low-performing students. New curricula, the Carnegie Learning Cognitive Tutor®, were provided for algebra and geometry students. The new instructional strategy relied on both the teacher-led instruction and the use of computers to differentiate instruction for individual students. Mathematics teachers received ongoing professional development to help them implement the new curricula. In addition, teachers were provided with ongoing support to assist them with the transformation of the learning environments for students using standards-based practices. This quasi-experimental (nonrandomized) study involved teachers in two matched urban high schools. Analyses (ANCOVAs) revealed that the experimental group with an appropriately implemented program had significantly higher learning gains than the comparison group as determined by the students' 2007 mathematics Developmental Scale Score (DSS). In addition, the experimental group's adjusted mean for the second interim mathematics assessment was significantly higher than the comparison group's mean. The findings support the idea that if the traditional curriculum is replaced with standards-based curriculum, and the curriculum is implemented as intended, low-performing students may make significant learning gains. With respect to the teaching practices as observed with the Classroom Observation Protocol (COP), t-tests were conducted on four constructs. The results for both the algebra and geometry teachers on the constructs were not significant. The COP indicated that teachers in both the experimental and comparison groups used traditional instruction strategies in their classrooms. The analyses of covariance (ANCOVA) on the use of technology revealed no significant main effects for computer use.

The impact of standards-based practices in mathematics on the achievement of low-performing students

This study examined standards-based mathematics reform initiatives to determine if they would improve student achievement on the part of low-performing students. New curricula, the Carnegie Learning Cognitive Tutor®, were provided for algebra and geometry students. The new instructional strategy relied on both the teacher-led instruction and the use of computers to differentiate instruction for individual students. Mathematics teachers received ongoing professional development to help them implement the new curricula. In addition, teachers were provided with ongoing support to assist them with the transformation of the learning environments for students using standards-based practices. This quasi-experimental (nonrandomized) study involved teachers in two matched urban high schools. Analyses (ANCOVAs) revealed that the experimental group with an appropriately implemented program had significantly higher learning gains than the comparison group as determined by the students' 2007 mathematics Developmental Scale Score (DSS). In addition, the experimental group's adjusted mean for the second interim mathematics assessment was significantly higher than the comparison group's mean. The findings support the idea that if the traditional curriculum is replaced with standards-based curriculum, and the curriculum is implemented as intended, low-performing students may make significant learning gains. With respect to the teaching practices as observed with the Classroom Observation Protocol (COP), t-tests were conducted on four constructs. The results for both the algebra and geometry teachers on the constructs were not significant. The COP indicated that teachers in both the experimental and comparison groups used traditional instruction strategies in their classrooms. The analyses of covariance (ANCOVA) on the use of technology revealed no significant main effects for computer use.

Formação docente e conhecimento profissional: desafios para o ensino da matemática na EJA

As for the Education for Youth and Adult (EYA), the challenge of training these teachers is to provide tools to understand and act on the teaching of mathematics. It is realized just how special education in this modality and as such teaching is lacking in an adequate and solid training in the area of knowledge. One of the major problems affecting this type of education is the high dropout and failure rates, and lack of motivation among students. Thus the need to provide differentiated profile with a professional to teach youth and adults students, so that they are able to mobilize didactic-pedagogic knowledge, methodologies and theoretical frameworks that serve as a basis for school-developed teaching practice. This thesis aims to investigate how the math teacher, who acts in adult education from elementary school, has developed its didactic and pedagogical action, and that professional knowledge has been mobilized to teach? It has highlighted the importance of initial and continuing training and professionalization of teachers dedicated to this specific type of education, when teachers should be the protagonists of their professional development. The methodological approach was begun with a literature review, then the research was anchored mainly on the ideas by Gauthier, Nuñez and Ramalho (2004); Imbernon (2011), Garcia (2006); Perrenoud (2000); Tardif (2007 ); Haddad, Di Pierro (2000), D'Ambrosio (2002), Mendes (2006, 2009), Freire (1996, 2011), and other theorists and official documents of field of adult education here and abroad. That work leads us to the understanding of the present moment from a foray into historical and conceptual aspects, as well as educational policies of EYA, as well as training, professionalism, knowledge and skills necessary for professional practice. Then, the subjects and the locus of research and the instrument for data collection were set up and led by the object of study. To consolidate the study was selected a sample of 27 mathematics teachers, working in municipal EYA Network Teaching of Natal. This research is in an investigative nature, within the quantitative and qualitative approaches focused on the responses of study subjects from the content analysis by Bardin (1977). Results from the analyzes have revealed that the initial training of mathematics teachers of adult education needs to be reconfigured in order to formalize the knowledge base of professionals (the mathematical content, didactics and professional knowledge). Thus the study suggests that this base knowledge is embedded in the pedagogical practice of these teachers, so that there is a completion of the teaching and learning process for young people and adults. The study also has pointed out that there is a need for teachers to participate in a continuing education plan that prioritizes learning situations of mathematical content considering the previous knowledge of the students. The final analyses thus indicate that knowledge of mathematics and the didactic and pedagogical strategies to be mobilized by teachers must be able to motivate the students in such a way that they feel need to incorporate in their knowledge, mathematical knowledge capable of making them more likely to have access to social, economic and labor market

'Lines of flight': digital musical instruments, inclusive music bands, meaningful engagement in music-making and learning

In this study I examine the development of three inclusive music bands in Cork city. Derived from Jellison’s research on inclusive music education, inclusive music bands involve students with disabilities coming together with typically developing peers to make and learn music that is meaningful (Jellison, 2012). As part of this study, I established three inclusive music bands to address the lack of inclusive music making and learning experiences in Cork city. Each of these bands evolved and adapted in order to be socio-culturally relevant within formal and informal settings: Circles (community education band), Till 4 (secondary school band) and Mish Mash (third level and community band). I integrated Digital Musical Instruments into the three bands, in order to ensure access to music making and learning for band members with profound physical disabilities. Digital Musical Instruments are electronic music devices that facilitate active music making with minimal movement. This is the first study in Ireland to examine the experiences of inclusive music making and learning using Digital Musical Instruments. I propose that the integration of Digital Musical Instruments into inclusive music bands has the potential to further the equality and social justice agenda in music education in Ireland. In this study, I employed qualitative research methodology, incorporating participatory action research methodology and case study design. In this thesis I reveal the experiences of being involved in an inclusive music band in Cork city. I particularly focus on examining whether the use of this technology enhances meaningful music making and learning experiences for members with disabilities within inclusive environments. To both inform and understand the person centered and adaptable nature of these inclusive bands, I draw theoretical insights from Sen’s Capabilities Approach and Deleuze and Guatarri’s Rhizome Theory. Supported by descriptive narrative from research participants and an indepth examination of literature, I discover the optimum conditions and associated challenges of inclusive music practice in Cork city.

Motivation and Vocabulary Breadth in CLIL and EFL Contexts. Different age, Same Time of Exposure

Numerous studies have found a positive connection between learners’ motivation towards foreign language and foreign language achievement. The present study examines the role of motivation in receptive vocabulary breadth (size) of two groups of Spanish learners of different ages, but all with 734 hours of instruction in English as a Foreign Language (EFL): a CLIL (Content and Language Integrated Learning) group in primary education and a non-CLIL (or EFL) group in secondary education. Most students in both groups were found to be highly motivated. The primary CLIL group slightly overcame the secondary non-CLIL group with respect to the mean general motivation but this is a non-significant difference. The secondary group surpass significantly the primary group in receptive vocabulary size. No relationship between the receptive vocabulary knowledge and general motivation is found in the primary CLIL group. On the other hand, a positive significant connection, although a very small one, is identified for the secondary non-CLIL group. We will discuss on the type of test, the age of students and the type of instruction as variables that could be influencing the results.

Improving Science literacy through interdisciplinary collaboration using media reported science.

The capability to respond critically to science in the news is recognised as one aspect of science literacy. Consequently, science-related news reports are an essential resource for science teachers wishing to promote critical reading as the foundation of a critical response to media reported science. Consequently Science education in schools should prepare students to engage with informal sources of science, including news media, in the world beyond formal science education. An interest in science news media is not limited to the science specialist. Science news provides an authentic context for teachers of science and English to collaborate in promoting interdisciplinary learning. The challenges of using science related news, as a context for cross-curricular collaboration, highlight the professional development needs of both science and English teachers working in this context. This qualitative study with over 150 pupils involved secondary school science and English teachers working collaboratively using media reported science resources and collated data from interviews, pre and post intervention tasks, pupils’ classwork and teacher notes. The outcomes of the project showed pupil engagement and greater capacity to carry knowledge and skills across traditional subject boundaries. Teachers reported increased understanding of the pedagogy of the alternative subject specialist and increased confidence to move outside their subject in order to facilitate pupil learning. This study would suggest that adopting an interdisciplinary approach could enhance learning for pupils and increase the confidence and capability of teachers. Additionally teachers’ engagement in professional conversations focusing on pupil progress was noteworthy.

Matematik Öğretmeni Adaylarının Dörtgenleri Sınıflandırma Becerilerinin İncelenmesi

This study aimed to explore prospective teachers’ performance on recognizing quadrilaterals with their special cases and constructing a hierarchical classification of them. The participants consisted of 44 freshmen studying at a public university’s elementary school mathematics education department. Data was collected with a question form containing two questions at the first day of the geometry course taught in the second term of the first year. For quantifying the data of the first question, while students who identify the prototypes of quadrilaterals and their special cases were given 1 and 2 points for each correct answer respectively, -1 point was given for each incorrect answer. The similarity index was employed to quantify students’ concept maps. We investigated that students could detect the prototypes of the quadrilaterals but not their special cases. Additionally, the similarity index between majority of freshmen’ concept maps and the referent map was found as low or moderate.

Teaching EFL to Newly Arrived Adolescents : A Literature Review on EFL Teaching in Multilingual Classrooms

The Swedish curriculums point out that language is crucial to social interactions, learning and individual development as well as essential to uphold a democratic and multicultural country. However, a recent report from the Swedish National Agency for Education depicts the language introduction programs for immigrant adolescents in Sweden as a school form in great need of development (Skolverket, 2016a). This systematic literature review, which draws on sociocultural theory, contributes to the field of how to teach English to newly arrived adolescents in Sweden. The main findings, gathered from six studies from around the world, suggest several different areas for improvement concerning EFL teaching. A specific pedagogy for EFL learners is suggested as well as targeted professional development for EFL teachers. Additionally, the results point out challenges faced by EFL teachers in multilingual classrooms. Further research could investigate how EFL teachers deal with these challenges. Furthermore, further research could investigate EFL textbooks for multilingual students at upper secondary school in terms of language, culture, identity texts and difficulty level.

"It’s just very natural" – interpersonal knowledge as a didactical device in guided classroom conversations in religious education

This article investigates how teachers in religious education (RE) think and act as professionals while working with differences in religious and philosophy of life experiences and beliefs in class and trying to do this in respectful and inclusive ways. It analyses data from two research projects that were carried out in lower secondary school in Norway. The main research question is: What is the relationship between teachers’ contextual knowledge and knowledge of the child and how do these two dimensions of professional knowledge interact when religious education teachers try to strike a good balance between inclusion and productive learning in their teaching practice? The data analysed were drawn from three different data sets featuring three Norwegian religious education-teachers. The research was part of the EU-funded "REDCo"-project and the "Religious education and diversity" - project ["ROM"] funded by the Norwegian Research Council. The interviewees emphasized the potential of the religious education subject to contribute to a wider tolerance for difference and to support individual students in their identity management. The analysis shows, however, that considerable contextual awareness - of the classroom and of the local community - is needed to realize this potential. It also shows the importance of interpersonal knowledge between the teacher and each student if contextual awareness is to be effective in terms of inclusion, participation, wellbeing and good learning outcomes for all students.

Drama – viktig resurs eller hämmare för undervisningen i samhällskunskap?

The aim of this article is to discuss and problematize how teachers in civics in upper secondary school construct drama, and how it relates to teaching, and students’ knowledge formation in civics. A study like this is important as the aesthetic subjects are becoming more prominent in young people’s everyday life at the same time as school by recent reformations is increasing the adjustment to efficiency and measurability. The theoretical framework is built on discursive psychology, which emanates from social constructionist and poststructuralist theory. Data consists of interviews with four upper secondary teachers in civics. Findings show that drama can be a valuable resource for teaching and learning civics, but also a problem when it comes to assessment. The position of the student as an object, teaching as entertainment and the domination of text is also discussed and problematized. Findings are considered as problematic as drama in civics, in relation to assessment, rather enhances a text-focused three-subject school than offering an alternative challenge

Review of The young language learner: Research-based insights into teaching and learning

Introduction For a long time, language learning research focusing on young learners was a neglected field of research. Most empirical studies within the broad area of second/foreign language acquisition were instead carried out among adults in tertiary education and it was not until in the 1990s that the scope of research broadened to include also young learners, then loosely defined as children in primary and/or secondary education (see, for example, Hasselgreen & Drew, 2012; McKay, 2006; Nikolov, 2009a). In fact, some agreement upon how to define ‘young learners’ was not properly discussed until in 2013, when Gail Ellis (2013) provided some useful clarifications as regards how to label learners within the broad age-span that encompasses both primary and secondary school. In short, based on a literature overview, she concludes that the term young learners is most often used for children between the ages of five and eleven/twelve, which in most countries would be equivalent to learners in primary school.   Thus, since young learners did not catch much scholarly attention until fairly recently, research volumes on the topic have been scarce. However, with a rapidly growing interest in examining how small children learn foreign languages, there has been a sudden increase in terms of the number of books available targeting young language learners. A first, major contribution was Nikolov’s (2009b) Early learning of modern foreign languages, in which 16 studies of young language learners from different countries are accounted for. Another important contribution is the edited book that will be reviewed here, which specifically targets studies about various aspects of second/foreign language learning among young (mainly Norwegian) learners. Bearing in mind that Norway and Sweden are very similar countries in terms of schooling, language background, and demographics – only to give three examples of similarities between these two nations – it is particularly relevant for Swedish scholars within the fields of education and second language acquisition to become familiar with research findings from the neighboring country.   In this review, the editors and the outline of the book are first described, then brief summaries of each chapter are provided, before the text closes with an evaluation of the volume. 

To Succeed Is to Believe: Comparison of Self-Efficacy Beliefs in Language Learning between Learner Groups of English and Swedish in Finland

In this thesis, I studied self-efficacy in the learning of English and Swedish in Finland. The theory of self-efficacy, which was created by Albert Bandura, suggests that the beliefs a person has of his or her capabilities in a certain task affect the person’s performance in the task. My aim was to study whether there are differences in self-efficacy beliefs between the learners of English and Swedish, and whether these beliefs correlate with the performance in the language in question. My hypotheses were that the learners of English have higher self-efficacy beliefs than the learners of Swedish and that self-efficacy beliefs correlate with language performance. The study was quantitative, and it consisted of a self-efficacy questionnaire and a language test which were distributed to students of English and Swedish in an upper secondary school in Rovaniemi. The study was answered by 137 students, of whom 93 were learners of English and 44 were learners of Swedish. The results indicated that the learners of English had a higher sense of efficacy than the learners of Swedish. The analysis proved that there was a significant correlation between English students’ self-efficacy and their performance in the language measured by the test and the grades. In addition, a significant correlation existed between Swedish students’ self-efficacy and their grades. However, there was no correlation between the Swedish students’ self-efficacy and their test results. The difference in the self-efficacy beliefs of the two language groups indicates that people in Finland are more confident in using English than Swedish, which also implies that English is more valued in Finnish society than Swedish. It is important to acknowledge the lower self-efficacy beliefs in Swedish because various studies have proven that self-efficacy affects academic achievement. As a suggestion for further research, the self-efficacy beliefs of different language groups could be compared in a qualitative study in order to understand the development of self-efficacy more profoundly.

EXAMINING THE IMPACT OF TEACHER PRACTICE ON STUDENT LEARNING IN INTERACTIVE RADIO INSTRUCTION (IRI) CLASSROOMS: LESSONS FROM NEW DELHI AND RAJASTHAN (INDIA)

This quantitative study examines the impact of teacher practices on student achievement in classrooms where the English is Fun Interactive Radio Instruction (IRI) programs were being used. A contemporary IRI design using a dual-audience approach, the English is Fun IRI programs delivered daily English language instruction to students in grades 1 and 2 in Delhi and Rajasthan through 120 30-minute programs via broadcast radio (the first audience) while modeling pedagogical techniques and behaviors for their teachers (the second audience). Few studies have examined how the dual-audience approach influences student learning. Using existing data from 32 teachers and 696 students, this study utilizes a multivariate multilevel model to examine the role of the primary expectations for teachers (e.g., setting up the IRI classroom, following instructions from the radio characters and ensuring students are participating) and the role of secondary expectations for teachers (e.g., modeling pedagogies and facilitating learning beyond the instructions) in promoting students’ learning in English listening skills, knowledge of vocabulary and use of sentences. The study finds that teacher practice on both sets of expectations mattered, but that practice in the secondary expectations mattered more. As expected, students made the smallest gains in the most difficult linguistic task (sentence use). The extent to which teachers satisfied the primary and secondary expectations was associated with gains in all three skills – confirming the relationship between students’ English proficiency and teacher practice in a dual-audience program. When it came to gains in students’ scores in sentence use, a teacher whose focus was greater on primary expectations had a negative effect on student performance in both states. In all, teacher practice clearly mattered but not in the same way for all three skills. An optimal scenario for teacher practice is presented in which gains in all three skills are maximized. These findings have important implications for the way the classroom teacher is cast in IRI programs that utilize a dual-audience approach and in the way IRI programs are contracted insofar as the role of the teacher in instruction is minimized and access is limited to instructional support from the IRI lessons alone.