Preservice teachers’ knowledge of proof by mathematical induction

There is a growing effort to make proof central to all students’ mathematical experiences across all grades. Success in this goal depends highly on teachers’ knowledge of proof, but limited research has examined this knowledge. This paper contributes to this domain of research by investigating preservice elementary and secondary school mathematics teachers’ knowledge of proof by mathematical induction. This research can inform the knowledge about preservice teachers that mathematics teacher educators need in order to effectively teach proof to preservice teachers. Our analysis is based on written responses of 95 participants to specially developed tasks and on semi-structured interviews with 11 of them. The findings show that preservice teachers from both groups have difficulties that center around: (1) the essence of the base step of the induction method; (2) the meaning associated with the inductive step in proving the implication P(k) ⇒ P(k + 1) for an arbitrary k in the domain of discourse of P(n); and (3) the possibility of the truth set of a sentence in a statement proved by mathematical induction to include values outside its domain of discourse. The difficulties about the base and inductive steps are more salient among preservice elementary than secondary school teachers, but the difficulties about whether proofs by induction should be as encompassing as they could be are equally important for both groups. Implications for mathematics teacher education and future research are discussed in light of these findings.

Developing effective beginning teachers through mentor‐based induction

Past research on new teacher induction has focused on changes in retention. Keeping people in the profession is important, but new teachers may need help in learning about curriculum and students in order to be effective instructional leaders. New teachers may also need assistance in learning how to interact with colleagues. We asked new teachers through an on‐line survey what they learned from mentors about curriculum, student diversity and collegiality. In addition, achievement gains of classes taught by new teachers and experienced teachers were compared. The results of the study are discussed in terms of implications for teacher training, organizational change, and data usage by districts.     

Socialization of new teachers: Does induction matter?

The present paper focuses on new teachers’ satisfaction with their first year of teaching from the perspective of socialization. The relationship between satisfaction with socialization and teacher background, school environment, placement, and induction variables was examined. Data were collected from 243 Israeli beginning teachers by means of questionnaire. Results indicated that satisfaction during the induction year was moderately high. Hierarchical regression analysis showed five significant predictor variables: ecological support from mentor, help from the principal, assistance from other colleagues, workload, and having already completed teaching training. Support from mentors and school colleagues had the greatest impact on new teachers’ assimilation.     

Analysis of a new 5-phase bearingless induction motor

This paper addresses the bearingless motor with a single set of multiphase windings. The interaction between M and M±1 pole-pair magnetic fields produces radial force. Based on this principle,a bearingless machine is obtained. Conventional bearingless machine has dual windings,levitation windings and torque windings,which produce the two magnetic fields. In the proposed bearingless motor,the two needed magnetic fields are produced by feeding two groups of currents to a single set of multiphase windings. Taking a 5-phase induction motor as example,the inductance matrices,considering air gap eccentricity,are calculated with the modified winding function method. The radial force analytical model is deduced by virtual displacement,and its results are validated by FEA. The mathematical model of the new bearingless machine is set up,and the simulation results verified the feasibility of this novel bearingless motor.     

Beginning teachers’ induction in Chile: the perspective of principals

This case study investigated the role of school principals in the induction of beginning teachers in Copiapó, Chile. Building upon group and individual interviews, and review of extant literature, the following findings were established: (a) principals in this study expect beginning teachers to be fully formed as classroom teachers; (b) principals were unlikely to talk about induction practices that might help beginning teachers to learn pedagogical strategies for classrooms; and (c) principals’ induction practices focused on the symbolic role that principals play as the highest authority within the school which has little practical influence on helping beginning teachers to develop their pedagogy. Implications for policy and practice are discussed.     

Novice teachers’ learning and knowledge building during the induction programme

This paper explores the Estonian novice teachers’ learning and knowledge building (LKB) practices in the extended professional community during the induction programme using well-known knowledge conversion model. The assumption in this study is that a teachers’ participation in the extended professional community facilitates their professional development. The survey was conducted with 101 novices after their induction programme. The patterns of novices’ LKB practices in the professional learning community during the induction programme were explored. The analysis showed to what extent extended professional community may be formed during the induction year. LKB practice patterns among the novices were identified. We discovered that many novices felt that there was insufficient support from other teachers and from university experts. It appears that it is challenging to develop a coherent induction programme as the extended professional community of educators, where different partners collaborate and share professional knowledge is challenging.     

First year effects of induction arrangements on beginning teachers’ psychological processes

This study examined the (1) effects of a supportive program (i.e., induction arrangement) on beginning teachers’ (BTs’) psychological processes after a period of 1 year and (2) psychological paths of influence of the arrangement. Participants (56 Dutch secondary schools with 143 BTs) were randomly allocated to two conditions. Experimental schools provided a carefully developed and implemented induction arrangement to their BTs. Control schools followed their regular (induction) arrangements. BTs perceived stress causes, self-efficacy, and job strain were measured with a pre-test post-test design. Condition effects were examined by means of independent sample t tests. The perception of the provided support was measured, and its psychological path of influence was investigated by conducting standard multiple regression analyses. BTs in the experimental condition indicated that they (1) received more support, (2) experienced fewer stress causes (i.e., lack of learning opportunities and lack of regulating possibilities), and (3) experienced more self-efficacy in the classroom at the end of the school year. Furthermore, fewer BTs left the experimental schools after 1 year. Reducing BTs’ workload and supporting their professional development are the most influential induction arrangement elements provided in this study. Providing carefully developed and implemented induction arrangements may soften the harshness of the context in which BTs operate, by decreasing their perceived stress causes and increasing their level of self-efficacy in the classroom. This, in turn, could positively affect BTs’ decision to stay in the teaching profession and might, therefore, add to a solution to the teacher shortage problem.     

Single neuron network PI control of high reliability linear induction motor for Maglev

The paper deals with a new model of linear induction motor (LIM) to improve the reliability of the system. Based on the normal equation circuit of LIM considering the dynamic end effect, an equivalent circuit model with compensation of large end effect is constructed when the end effect force at synchronism is of braking character. The equivalent circuit model is used for secondary-flux oriented control of LIM. Single neuron network PI unit for LIM servo-drive is also discussed. The effectiveness of mathematical model for drive control is verified by simulations.     

Beginning teachers’ self-efficacy and stress and the supposed effects of induction arrangements

Induction arrangements are implemented in schools all over the world to support beginning teachers (BTs) (novices) in gradually growing into their profession. The aim of this study is to gain more insight into two key psychological processes involved in the work of a qualified beginning teacher, namely perceived stress and self-efficacy. This unfolding is necessary to find a path of influence to lead the way to meaningful support interventions. Support in the form of induction arrangements is hypothesised to decrease perceived stress and to increase self-efficacy and, thus, decrease stress outcomes. To test our hypotheses 30 BTs and their school-based educators, working in 13 different schools, were surveyed. The analyses revealed that stress causes and stress outcomes are indeed interrelated and that self-efficacy affects this relationship in a mediating way. However, besides decreasing a beginning teachers’ perceived lack of learning opportunities, no other influences of induction arrangements were obtained. Implications and suggestions for future research are discussed.     

It’s very different here: practice-based academic staff induction and retention

The sociologist, Max Weber (1864–1920), suggested that few could withstand the frustrations of academic life. As the strategic management of human resources begins to differentiate higher education institutions (HEIs) in league tables, the costs of voluntary staff turnover (attrition) become more significant. In this paper, we consider links between induction (orientation) and retention for academic staff. We report on a qualitative study of thirty academic staff in five United Kingdom HEIs who were recruited on the basis of their professional experience. Their practice-based knowledge lends our participants particular insight into their HEI induction experience which, where found wanting, led in several cases to resignation. We analyse the induction experiences of our participants to glean explanations for these perceived shortcomings. Since induction interventions are thought to lead to improved retention, we recommend policy and practice changes to induction, which may benefit all academic staff.     

Rotor broken bar fault diagnosis for induction motors based on double PQ transformation

A new rotor broken bar fault diagnosis method for induction motors based on the double PQ transformation is pre-sented. By distinguishing the different patterns of the PQ components in the PQ plane,the rotor broken bar fault can be detected. The magnitude of power component directly resulted from rotor fault is used as the fault indicator and the distance between the point of no-load condition and the center of the ellipse as its normalization value. Based on these,the fault severity factor which is completely independent of the inertia and load level is defined. Moreover,a method to reliably discriminate between rotor faults and periodic load fluctuation is presented. Experimental results from a 4 kW induction motor demonstrated the validity of the proposed method.     

Short interims,long impact? A follow-up study on early career teachers' induction

Early career teachers' (ECTs) socialization into the profession involves complex processes of negotiation in the dynamic web of relationships in and around the school. To focus on the actual meaning and role of the professional relationships in ECTs' induction process as it develops over time, we used a follow-up design, collecting data from ECTs at four different moments during their first year in the job. Our findings show the micro-political interplay of different interests. Furthermore, they demonstrate how the contract conditions (formal job characteristics) get loaded with meaning and have a pervasive impact on teachers' relationships and their developing self-understanding.     

Re‐addressing the priorities: new teacher educators and induction into higher education

This article draws on research involving 28 teacher educators in the first 3 years of their careers in the English higher education sector. It discusses the areas of tension they found in making the transition from teaching in the school sector to working in universities, the priorities they identified for their induction and the induction structures and processes available to support them. Previous research on teacher educator induction has identified the need for more consistent and thorough structures. However, the findings of this study show that the current structures and procedures often do not meet the tutors' needs. Overall there is little articulation between different modes of induction, with most tutors still dependent on learning through practice, supplemented by informal ‘apprenticeship’ modes of learning. The article concludes with a discussion of issues and future developments.

Cet article s'inspire d'un travail de recherche auquel ont participé 28 formateurs pédagogiques dans les trois premières années de leur carrière dans le secteur d'éducation du troisième cycle anglais. II examine les sujets de tension qu' ils ont decouverts en effectuant la transition de 1'enseignement en milieu scolaire au travail en milieu universitaire, les priorités qu'ils ont identifiées pour leur période d'intégration professionnelle, et les structures et processus d'intégration mis a leur disposition pour les aider. Des recherches antérieures dans le domaine de 1'intégration professionnelle des formateurs pédagogiques a révéle la nécessité d'avoir des structures d'integration plus homogenes et plus approfondies. Mais les resultats de la présente étude démontrent que, souvent, les structures et les procédures actuelles ne répondent pas aux besoins des enseignants. En général, il y a peu de liens entre les différents modes d'intégration, la plupart des enseignants étant constraints à apprendre par la pratique, agrémentée de modes ‘d'apprentissage’informels. L'article conclue par une discussion sur les problèmes et les développpements futures.

Dieser Artikel basiert auf einem Forschungsprojekt, das mit achtundzwanzig Ausbildern von Englischlehrern für den Hochschulbereich, während ihrer ersten drei Jahre also solche, Der Artikel erörtert, die Spannungspunkte die sie in der Übergangsphase vom Lehren an der Schule zum Lehren an der Universität empfunden haben, die Prioritäten, die sie für ihre Einführung festgestellt haben, und den Einführungsprozess und die Einführungsstruktur, die zu ihrer Unterstiitzung zur Verfügung gestanden haben. Vorangehende Forschungsarbeiten iiber die Einführung von Ausbilder von Lehrern, haben das Bedürfhis nach einer einheitlicheren und griindlicheren Einführungsstruktur festgestellt. Die Ergebnisse dieser Untersuchung haben jedoch herausgestellt, dass die momentanen Strukturen und Verfahren oft nicht mit den Bedürfnissen der Tutoren übereinstimnien. Im Grossen und Ganzen gibt es wenig Meinungsaustausch iiber die unterschiedlichen Art und Weisen von Einführungen, da die meisten Tutoren immer noch vom Lernen durch Praxis, ergänzt durch eine informelle ? Lehrzeit" abhängig sind. Der Artikel schlieBt mit einer Ausführung über Fragen und zukünftige Entwicklungen.

Este artículo aprovecha una investigacíon que se ha hecho entre 28 profesores educadores que han cumplido hasta tres ãnos de sus carreras en el sector de enseñanza superior inglesa. El artículo trata las zones de tension que se han discubierto al hacer el paso de la enseñanza en una esuela a la enseñanza en una universidad, las prioridades para su iniciaciõn que identificaron, y las estructuras y procedimientos de la iniciaciõn disponibles. Investigaciõnes anteriores sobre la iniciaciõn de los profesores educadores habían identificado la falta de estructuras más consecuentes y meticulosas. Pero los descubrimientos de esta investigación confirman que rnuchas veces las estructuras y procedimientos actuales no satisfacen las necesidades de los profesores. En general hay poca articulación entre los diferentes modos de iniciación y en muchos cases los profesores tienen que aprender por medio de la práctica complementado por modos de aprender informales y tipo "aprendizaje". El artículo termina iniciando una evaluación de las consecuencias de estos descubrimientos y unas posibles evoluciónes futuras.     

Changes in beginning teachers’ classroom management knowledge and emotional exhaustion during the induction phase

The first years on the job are very challenging for teachers (e.g., Fives, Hamman, & Olivarez, 2007; Goddard, O’Brien, & Goddard, 2006). Two of the main challenges are to learn to regulate the highly complex classroom situations (Jones, 2006) and to regulate their own emotional resources (Chang, 2009). Accordingly, in the present study, we investigated changes in teacher candidates’ classroom management knowledge as well as emotional exhaustion at the beginning of their teaching careers. We applied latent change models to a sample of 746 teacher candidates who were assessed twice during the German induction phase (the Referendariat). We found evidence for a significant increase in teacher candidates’ classroom management knowledge during the induction phase. Emotional exhaustion increased during the first year and decreased during the second year of the induction phase. We also investigated between-person differences in the changes. Classroom management knowledge was predicted by the teacher candidates’ cognitive personal characteristics (e.g., cognitive abilities and willingness to reflect), whereas emotional exhaustion was predicted by noncognitive personal characteristics (e.g., emotional stability) as well as variables related to the induction phase (e.g., perceived mentoring quality and teaching load). Classroom management knowledge and emotional exhaustion were only modestly associated.     

Transitioning to the classroom: reflections of second‐career teachers during the induction year

In recent years teacher educators have witnessed an increase in the number of alternative pathways to university‐based teacher education for prospective teachers. One option is for second‐career teachers to enter post‐baccalaureate programs in education; however, the experiences of second‐career teachers are largely unexplored in the international literature. The purpose of this study was to investigate the teaching beliefs that post‐baccalaureate students brought into a graduate level teacher certification program, and the extent to which those beliefs persevered or changed during their first year of teaching. Written philosophy statements and semi‐structured interviews from the three participants were analyzed to identify emerging themes. Outcomes, presented in the form of vignettes, suggested that second‐career teachers experienced many of the same contextual pressures as baccalaureate teachers and struggled adapting to the teaching profession and implementing their stated teaching beliefs. Implications include continued research on second‐career teachers as they represent a distinct population entering the teaching profession.     

“I learned by watching my mentor.” Nurturing teacher leadership with an induction program

ABSTRACT

How do educators learn to be teacher leaders? In this qualitative survey research study, we explored perceptions of 227 former induction program participants concerning teacher leadership (65% response rate). Methodologically, we conducted qualitative coding of open-ended survey data. Defined teacher leadership, participants often referred to their mentor. They reported currently serving in a wide variety of teacher leadership roles. They suggested the induction program and their mentors nurtured them to become teacher leaders. Examining the data, we conclude that during the program mentors demonstrate to novices teacher leader characteristics, as they share best practices, model professionalism, and offer support. They normalize that leadership is simply a part of good teaching. When the participants graduate and work in classrooms, many draw upon their induction experiences and emerge as teacher leaders. Data suggest that to increase teacher leadership, more comprehensive, full-time mentoring induction programs are warranted.     

Application of stochastic method to optimum design of energy-efficient induction motors with a target of LCC

INTRODUCTIONMostcountrieshaveimplementednewpoli ciesontheenergysavingandenvironmentpro tection.AmericanPresidentBushsigned“TheComprehensiveNationalEnergyPolicyAct”in1992statingthatnogeneral purpose ,three phaseinductionmotorswillbeallowedintoUnit edStat…     

Underwhelmed and playing it safe: newly qualified primary teachers’ mentoring and probationary-related experiences during induction

Framed within the burgeoning policy and research literature on teacher induction internationally, this paper focuses on the mentoring and probationary-related experiences of nine newly qualified primary teachers in the Republic of Ireland, during the course of their initial year of workplace practice, post-graduation. Gleaning newly qualified teachers’ (NQTs’) perspectives on these matters is opportune, as the Teaching Council’s new model of induction entitled Droichead (bridge in Irish) is envisaged to become the sole induction and probation route for all NQTs. Transacted during the 2010/2011 school year, when the induction and probationary arrangements in place were those that the Droichead initiative is intended to replace, a three-cycle, individual interview design facilitated continuing contact with each NQT. Selected, representative interview data are utilised to illustrate the dynamics of NQTs’ experiences of mentoring and probationary-related processes. Empirically based findings establish, firstly, beginner complicity in the transaction of narrowly conceived mentoring support; secondly, enamorment of the reifications of initial teacher education-phase teaching practice when negotiating probationary processes; thirdly, the valuing of techniques that respond to immediate, probationary-related requirements over more complex forms of practice; and fourthly, the inevitable and essential interconnectedness of mentoring and probationary processes. The paper concludes with implications for the design and implementation of induction programmes.     

Accountability and responsibility: ‘rogue’ school leaders and the induction of new teachers in England

This paper considers the professional responsibility of schools in England to provide effective induction practices in the context of a central government mandated policy. It looks at individual schools as ‘habitats’ for induction and the role of school leaders and LEAs as facilitators or inhibitors. Notions of professional responsibility and public accountability are used to analyse the small number of ‘rogue’ school leaders who, within the new legislative framework, treat new teachers unprofessionally and waste public resources. A typology of ‘rogue’ schools that are in some way deviant in transgressing induction requirements is developed and the various sanctions that can be deployed against such schools are examined. How LEAs handle their monitoring and accountability role and manage deviant schools is considered. Finally, suggestions are made for improvements, such as the need to clarify professional responsibility and refine systems of professional accountability.