An investigation of post-primary students' images of mathematics

This research study investigates the image of mathematics held by 5th-year post-primary students in Ireland. For this study, “image of mathematics” is conceptualized as a mental representation or view of mathematics, presumably constructed as a result of past experiences, mediated through school, parents, peers or society. It is also understood to include attitudes, beliefs, emotions, self-concept and motivation in relation to mathematics. This study explores the image of mathematics held by a sample of 356 5th-year students studying ordinary level mathematics. Students were aged between 15 and 18 years. In addition, this study examines the factors influencing students‟ images of mathematics and the possible reasons for students choosing not to study higher level mathematics for the Leaving Certificate. The design for this study is chiefly explorative. A questionnaire survey was created containing both quantitative and qualitative methods to investigate the research interest. The quantitative aspect incorporated eight pre-established scales to examine students‟ attitudes, beliefs, emotions, self-concept and motivation regarding mathematics. The qualitative element explored students‟ past experiences of mathematics, their causal attributions for success or failure in mathematics and their influences in mathematics. The quantitative and qualitative data was analysed for all students and also for students grouped by gender, prior achievement, type of post-primary school attending, co-educational status of the post-primary school and the attendance of a Project Maths pilot school. Students‟ images of mathematics were seen to be strongly indicated by their attitudes (enjoyment and value), beliefs, motivation, self-concept and anxiety, with each of these elements strongly correlated with each other, particularly self-concept and anxiety. Students‟ current images of mathematics were found to be influenced by their past experiences of mathematics, by their mathematics teachers, parents and peers, and by their prior mathematical achievement. Gender differences occur for students in their images of mathematics, with males having more positive images of mathematics than females and this is most noticeable with regards to anxiety about mathematics. Mathematics anxiety was identified as a possible reason for the low number of students continuing with higher level mathematics for the Leaving Certificate. Some students also expressed low mathematical self-concept with regards to higher level mathematics specifically. Students with low prior achievement in mathematics tended to believe that mathematics requires a natural ability which they do not possess. Rote-learning was found to be common among many students in the sample. The most positive image of mathematics held by students was the “problem-solving image”, with resulting implications for the new Project Maths syllabus in post-primary education. Findings from this research study provide important insights into the image of mathematics held by the sample of Irish post-primary students and make an innovative contribution to mathematics education research. In particular, findings contribute to the current national interest in Ireland in post-primary mathematics education, highlighting issues regarding the low uptake of higher level mathematics for the Leaving Certificate and also making a preliminary comparison between students who took part in the piloting of Project Maths and students who were more recently introduced to the new syllabus. This research study also holds implications for mathematics teachers, parents and the mathematics education community in Ireland, with some suggestions made on improving students‟ images of mathematics.

Student voice in Irish post-primary schools: a drama of voices

This research is an exploration of the expression of student voice in Irish post-primary schools and how its affordance could impact on students’ and teachers’ experiences in the classroom, and at whole-school level through a student council. Student voice refers to the inclusion of students in decisions that shape their experiences in classrooms and schools, and is fundamental to a rights-based perspective that facilitates students to have a voice and a say in their education. Student voice is essential to the development of democratic principles, active citizenship, and learning and pedagogy. This qualitative research, based in three post-primary case-study schools, concerns teachers in eighteen classrooms engaging in dialogic consultation with their students over one school year. Teachers considered the students’ commentary and then adjusted their practice. The operation of student councils was also examined through the voices of council members, liaison teachers and school principals. Theorised within socio-cultural (social constructivist), social constructionist and poststructural frames, the complexity of student voice emerges from its conceptualisation and enactment. Affording students a voice in their classroom presented positive findings in the context of relationships, pedagogical change and students’ engagement, participation and achievement. The power and authority of the teacher and discordant student voices, particularly relating to examinations, presented challenges affecting teachers’ practice and students’ expectations. The functional redundancy of the student council as a construct for student voice at whole-school level, and its partial redundancy as a construct to reflect prefigurative democracy and active citizenship also emerge from the research. Current policy initiatives in Irish education situate student voice in pedagogy and as dialogic consultation at classroom and whole-school level. This work endorses the necessity for and benefit of such a positioning with the author further arguing that it should not become the instrumental student voice of data source, accountability and performativity.

Supporting therapist engagement in evidence based practice: Developing a continuing education programme through participatory action research

Therapists find it challenging to integrate research evidence into their clinical decision-making because it may involve modifying their existing practices. Although continuing education (CE) programmes for evidence-based practice (EBP) have employed various approaches to increase individual practitioner’s knowledge and skills, these have been shown to have little impact in changing customary behaviours. To date, there has been little attempt to actively engage therapists as collaborators in developing educational processes concerning EBP. The researcher collaborated with seven clinical therapists (one occupational therapist, four physiotherapists and two speech and language therapists) enrolled in a new post-qualification Implementing Evidence in Therapy Practice (IETP) MSc module to monitor and adapt the learning programme over ten weeks. The participating therapists actively engaged in participatory action research (PAR) iterative cycles of reflecting→ planning→ acting→ observing→ reflecting with the researcher. Mixed methods were used to evaluate the IETP module and its influence on therapists’ subsequent engagement in EBP activities. Data were gathered immediately on completion of the module and five months later. Immediate post-module findings revealed four components as being important to the therapists: 1) characteristics of the learning environment; 2) acquisition of relevant EBP skills; 3) nature of the learning process; and 4) acquiring confidence. The two themes and sub-themes which emerged from individual interviews conducted five months post-module expanded on the four components already identified. Theme 1: Experiencing the learning (sub-themes: module organisation; learning is relational; improving the module); and theme 2: Enacting the learning through a new way of being (sub-themes: criticality and reflection; self agency; modelling EBP behaviours; positioning self in an EB work culture). The therapists’ perspectives had by then shifted from that of a learner to that of a clinician constructing a new sense of self as an evidence-based practitioner. Findings from this study underline the importance of the process of socially constructed knowledge and of empowering learners through collaboratively designed continuing education programmes. In the student-driven learning environment, therapists chose repetitive skill-building and authentic problem-solving activities which reflected the complexity of the environments to which they were expected to transfer their learning. These findings have implications for educators designing EBP continuing education programmes, during which students develop professional ways of being.

Drama und theater in der fremd- und zweitsprachenlehre: Blick zurück nach vorn

Zwischen dem Bereich Drama/Theater und dem Bereich Fremdsprachenvermittlung gibt es seit jeher Verbindungslinien. Zumindest war der Lehrer immer schon ein Akteur, der den Schülern etwas so ‘vorzuspielen’ versuchte, dass die Aufmerksamkeit des Lernerpublikums gebannt blieb; und eigentlich haben Lehrer und Schüler im fremdsprachlichen Unterricht immer schon ‘Theater’ gespielt, indem sie so taten, als ob die Unterhaltung in der fremden Sprache für sie natürlich sei. Der folgende Beitrag zeichnet wichtige Entwicklungsetappen des Brückenbaus zwischen den Bereichen Drama/Theater und Fremd-/Zweitsprachenlehre seit Mitte des 19. Jahrhunderts nach. Es wird davon ausgegangen, dass ‘Drama und Theater in der Fremd-/Zweitsprachenlehre’ sich nunmehr als eines der vielen Anwendungsfelder etabliert hat, die mit dem Fach- und Sammelbegriff ‘Applied Theatre’ erfasst werden. Der Begriff bezieht sich auf das breite Spektrum von Individuen, Gruppen und Institutionen, für die das Theater als Kunstform nicht reiner Selbstzweck ist, sondern zentraler Bezugspunkt und Inspirationsquelle für drama-/theaterbezogene Aktivitäten. Durch solche Aktivitäten sollen im jeweiligen Anwendungsfeld ganz bestimmte Ziele erreicht werden, im Falle des fremd- und zweitsprachlichen Unterrichts z.B. sprach-, literatur- und kulturbezogene Ziele. Dieser Beitrag versteht sich als kompakte Bündelung und insbesondere Aktualisierung von Überlegungen, die erstmalig in meinem Buch Fremdsprache inszenieren (1993) erschienen sind. Zur Ergänzung dieses kompakten Überblicks sei auf die umfangreiche Forschungsbibliographie auf der Homepage dieser Zeitschrift verwiesen. Zum Konzept ‘Applied Theatre’ vgl. z.B. Ackroyd 2000; Taylor 2003; Nicholson 2005

Einleitung: Dramapädagogik und fremdsprachlicher Deutschunterricht

Published Version

Literatur verstehen und inszenieren: Foreign language literature through drama, a research project

Based on the experience that today's students find it more difficult than students of previous decades to relate to literature and appreciate its high cultural value, this paper argues that too little is known about the actual teaching and learning processes which take place in literature courses and that, in order to ensure the survival of literary studies in German curricula, future research needs to elucidate for students, the wider public and, most importantly, educational policy makers, why the study of literature should continue to have an important place in modern language curricula. Contending that students' willingness to engage with literature will, in the future, depend to a great extent on the use of imaginative methodology on the part of the teacher, we give a detailed account of an action research project carried out at University College Cork from October to December 2002 which set out to explore the potential of a drama in education approach to the teaching and learning of foreign language literature. We give concrete examples of how this approach works in practice, situate our approach within the subject debate surrounding Drama and the Language Arts and evaluate in detail the learning processes which are typical of performance-based literature learning. Based on converging evidence from different data sources and overall very positive feedback from students, we conclude by recommending that modern language departments introduce courses which offer a hands-on experience of literature that is different from that encountered in lectures and teacher-directed seminars.

O ensino de matemática em duas escolas profissionalizantes: Brasil e Portugal, no período de 1942 a 1978

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A cognitive schematic paradigm for expository essay writing in secondary schools

The methodology outlined in this study for teaching exposit ory writing to advanced (five year phase) grade eleven students is based on the assumption that writing as a problem solving strategy is a high level cognitive skill . In adhering to this assumption, a cognitively based schematic organizer known as a cross-classification chart was tested for its effectiveness a t the planning stage of the writing process . Results were not significant in any of the three components that were evaluated; however , a post- hoc analysis undertaken because of recorded observed data indicated a significant difference in the mean score on the Organization component for the treatment subgroup using the cross- classification organizer . Furthermore, the treatment group's positive response from the attitude survey towards planning writing is encouraging enough that replication and extension of the application of schema theory to wri ting should be pursued in cross-section and longitud i nal studies.

A method of evaluating psychomotor tooth preparation skills in preclinical dental programs

Preclinical and clinical tooth important and significant aspect of preparation is an a dental student's education. The associated procedures rely heavily on the development of particular psychomotor skills. The most common format of instruction and evaluation in tooth preparation at many Dental Faculties, emphasizes the product (tooth preparation) and associates performance with characteristics of this product. This integrated study examines which skills should be developed and how a course of instruction can best be structured to develop the necessary skills. The skills which are identified are those necessary for tooth preparation are selected from a psychomotor taxonomy. The purpose of evaluating these skills is identified. Behavioral objectives are set for student performance and the advisability of establishing standards of performance is examined. After reviewing studies related to learning strategy for dental psychomotor the most suitable tasks as well as articles on instructor effectiveness a model is proposed. A pilot project at the University of Toronto, based on this proposed model is described. The paper concludes wi th a discussion of the implications of this proposed model.

An examination of grade three mathematics textbooks for problem solving strategies

Three grade three mathematics textbooks were selected arbitrarily (every other) from a total of six currently used in the schools of Ontario. These textbooks were examined through content analysis in order to determine the extent (i. e., the frequency of occurrence) to which problem solving strategies appear in the problems and exercises of grade three mathematics textbooks, and how well they carry through the Ministry's educational goals set out in The Formative Years. Based on Polya's heuristic model, a checklist was developed by the researcher. The checklist had two main categories, textbook problems and process problems and a finer classification according to the difficulty level of a textbook problem; also six commonly used problem solving strategies for the analysis of a process problem. Topics to be analyzed were selected from the subject guideline The Formative Years, and the same topics were selected from each textbook. Frequencies of analyzed problems and exercises were compiled and tabulated textbook by textbook and topic by topic. In making comparisons, simple frequency count and percentage were used in the absence of any known criteria available for judging highor low frequency. Each textbook was coded by three coders trained to use the checklist. The results of analysis showed that while there were large numbers of exercises in each textbook, not very many were framed as problems according to Polya' s model and that process problems form a small fraction of the number of analyzed problems and exercises. There was no pattern observed as to the systematic placement of problems in the textbooks.

Business leadership in the classroom

This action research assesses a framework that assists business educators in promoting leadership within a classroom. It is designed to better prepare students to assume leadership and fill the "leadership gap" in business. Two classes of 2nd-year community college business students participated in running and managing their own business community as teams of sales professionals by developing and practicing their own individual leadership for 28 weeks during their sales courses. The intent was to assess the development of leadership resulting from the implementation of the "Business Leadership in the Classroom" framework. This framework balances leadership principles to simulate a business environment with the practical elements of a learning community under the facilitation of an experienced business educator. The action research approach was used to assess and adjust approaches to business leadership on a continuous basis throughout the research. Data were collected from 61 students based on journals, surveys, peer group reviews, and my (facilitator) reflective journal.The findings reveal that both individual and collective business leadership views and practical skills developed over time. A business leadership mind-set evolved that ranged from a general awareness of the importance of leadership, to a conscious and deliberate use of individual leadership. Areas important in building a progression of leadership included: leadership teams, membership roles, weekly leadership teams, peer feedback, and activity-based learning. Emerging themes included leadership, leadership style, teamwork, as well as influence and motivation. The research framework was effective in supporting the development of business leadership but required some adjustments. These included increased structure and feedback mechanisms. Interpretation of the findings demonstrates the importance of real-world practical education in the classroom. Results show how focusing on a single mind-set such as business leadership, can result in enormous individual growth and development. When business students are encouraged to act as real businesspeople, managing their own learning, the results are effective in preparing them for the business world. All participants expressed their leadership in different ways based on personality and individual strengths. There was an overwhelming and, in some cases, passionate interest in leadership. The use of action research with a range of data collection methods provides a way to measure and track individual student learning and to generate adjustments to the research framework design and learning approaches. The findings generate implications and recommendations to continue this research further. Key recommendations center around how to ensure leadership development is sustained, including improved approaches to heighten the real-world feel of the classroom. Specifically, the use of leadership goals and action plans for each individual participant and an active use of outside business resource people as contacts for participants is recommended.

Concept analysis in social studies

This project was undertaken because of a need to analyse concepts in social science more specifically and sequence them more carefully in a social science program. Concepts have been identified vaguely on many curriculum documents or left in isolation from each other when they are specifically identified. The project's aim was to identify a method for analysing concepts and sequencing their teaching on some rational basis. Once the method for analysing concepts was identified a questionnaire was designed and administered to a random sample of students at the grade three, five and eight levels. The questionnaire attempted to measure their comprehension of specific social science concepts at several levels which became progressively more complex. The major hypothesis was that there would be a direct correlation between age and achievement on the questionnaire. The raw scores were seriated and correlated with the ages of the students using the rankdifference- squared method. For the majority of areas tested it was found that there was a significant correlation between age and achievement on the questionnaire. Variation in the correlation coefficients generated suggests that comprehension of social science concepts is not simply a function of age but is probably a function of several inter-related factors such as reading ability, skill in Basic Thinking Skills and age. Thirty students completed each test. There were three tests in the questionnaire.

Construing social dimensions of personality development: nurses as educators

A convenience sample of twenty registered nurses was recruited from two' general hospitals and two community college nursing schools. Kelly's (1955) Personal Construct Theory provided the theoretical framework to discover how nurses perceived themselves as educators. The nurses completed a self-administered Self-Perception Inventory (Soares, 1983) to determine their perception of self as nurse and ideal self as nurse. In an interview, each of the nurses constructed a rank-order repertory grid adapted from Kelly's (1955) Role Repertory Construct Test. Twelve constructs derived from the Self-Perception Inventory (Soares, 1983) were ranked according to a list of ten elements common to a teaching situation. Rank order correlations among the constructs were determined with Spearman's rho. Using a dependent samples t-test, significant differences were found between perceptions of current and ideal self for staff nurses. Significant differences were also found between nurse educators' perceptions of self and ideal self as nurse. No significant differences were determined in perceptions of self as nurse and ideal self as nurse between the staff nurse and nurse educator groups with an independent samples t-test. However, observations of single constructs revealed that although several constructs are shared between the groups in the perception of self in a teaching situation, both groups hold constructs that operate exclusively in their separate domains. The nature and strength of the relationships between the common and unique constructs are different for each group. Nurses I self-perceptions appear to be influenced by the historical development of nursing, role socialization during nursing education, social expectations and gender issues in the health care system.