EXPERIMENTS in induction: new approaches to the probationary year*

Abstract

Feedback from educators in England, Scotland, and the Republic of Ireland was obtained regarding the performance of U.S. student teachers in the schools of these nations. Reported in this paper are the educators' observations and beliefs pertaining to topics such as the professional and cultural/social strengths of U.S. student teachers; major cultural/social ‘mistakes’ often made by U.S. student teachers; ways in which they could better prepare for classroom teaching assignments in overseas schools; goals motivating them to seek placements in overseas schools; and ways in which the foreign pupils benefitted from the U.S. student teachers. Based on the feedback, recommendations are offered to student participants and university/college faculty for the improvement of teaching experiences in overseas nations. In addition, the need for internationalizing teacher education programs in the United States is recognized.     

U.S. and Chinese Teachers' Conceptions and Constructions of Representations: A Case of Teaching Ratio Concept

This study examines U.S. and Chinese teachers' constructing, knowing, and evaluating representations to teach the concept of ratio. All Chinese lesson plans are very similar with details in teaching contents and procedure. The U.S lesson plans are extremely varied although they all adopted the ‘outline and worksheet’ format. Both the Chinese and the U.S. teachers relied on concrete representations in introducing the concept of ratio, but they have very different thinking in selecting and presenting the concrete representations, as well as in the functions of the representations. The U.S. teachers are much more likely than Chinese teachers to predict drawing and guess-and-check strategies. Chinese teachers are much more likely than U.S. teachers to predict algebraic approaches. For the responses using conventional strategies, both the U.S. and Chinese teachers gave them high and almost identical scores. If a response involved a drawing or an estimate of an answer, the Chinese teachers usually gave a relatively lower score than U.S. teachers. This study contributes to our understanding about U.S. and Chinese teachers' beliefs about mathematics teaching and learning.The research discussed in this paper was supported by grants from the Spencer Foundation. Any opinions expressed herein are those of the authors and do not necessarily represent the views of the Spencer Foundation.     

Special education and subject teachers’ self‐perceived readiness to teach mathematics to low‐performing middle school students

Educational reforms during the last decade have led to a more inclusive environment for students with different needs and have placed demands on teachers’ readiness to instruct diverse students in the general classroom. Previous research has ascertained that student achievement is correlated with teacher quality and teachers’ efficacy beliefs. Today, basic competence in mathematics is more important than ever for managing routine day‐to‐day activities and therefore, identifying and educationally supporting students with low performance in mathematics is necessary. The aim of the study was to investigate the perceived teacher efficacy beliefs of special education and mathematics teachers when teaching mathematics to low‐performing middle school students. Results indicated that special education teachers had higher teacher efficacy beliefs than mathematics teachers. Teacher experience, certification or gender had no effect on teachers’ efficacy beliefs. Furthermore, subject teachers reported high pedagogical knowledge for teaching low‐performing students, and special education teachers reported having moderate mathematical subject knowledge.     

Learning environment,self-efficacy for teaching mathematics,and beliefs about mathematics

Learning environment research has a long history of significant relationships between the learning environment and student outcomes. This study investigated relationships between the learning environments of mathematics courses in a teacher education program and two outcomes, mathematics teaching self-efficacy and beliefs about mathematics. These two outcomes have been repeatedly shown to influence the future teaching practices of preservice teachers but, to date, their relationships with learning environment have been investigated neither with preservice teachers nor at all in the United Arab Emirates or wider Gulf region. The learning environment was found to be significantly related to preservice teachers’ mathematics teaching self-efficacy and beliefs about mathematics. Learning environments perceived more favourably by preservice teachers were associated with higher self-efficacy for teaching mathematics, but also with more-traditional beliefs, making these findings important for higher education institutes and teacher educators.

     

MATHEMATICS TEACHER EDUCATION AND QUALITY

‘Quality’ in mathematics teaching does not relate solely to pupil achievement, to teaching approaches or to deeply held beliefs about the nature of mathematics and its teaching and learning, but to all of these. A model of a teacher's mathematics‐related belief‐system is presented, and the issue of the contrast between espoused and enacted beliefs is discussed. ‘Quality’ in mathematics teacher education raises all of these issues, as well as the aims, goals and means of the teacher preparation process itself. The paper concludes by arguing against the ‘apprenticeship’ model of mathematics teacher education, for depriving student teachers of theory and of practical research experience. A well known dictum paraphrased states that theory without practice is empty, but that practice without theory is blind. ‘Quality’ in mathematics teaching and teacher education depends on both theory and practice in systematic cooperation.     

The beliefs and perceptions of pre-service teachers enrolled in a subject-area dominant teacher education program about “Effective Education”

Teacher educators and researchers have studied the improvement of teacher education programs so that pre-service teachers may be well prepared. Research has shown that not only teachers’ knowledge but also their beliefs have major influence on their approach to teaching. This present research examined the mathematics and science pre-service teachers’ beliefs and perceptions in Turkey. Specifically, the study focused on the student–teachers’ perspectives on “effective education” at the end of their subject area dominant program before the student teaching and the changes in those beliefs after having teaching experience. Many pre-service teachers described the teacher-centered environment as effective, and those who supported a student-centered environment discussed difficulties they faced in creating it during student and full-time teaching.     

The Influence of Teachers’ Efficacy and Beliefs Regarding Mathematics Instruction in the Early Childhood Classroom

This was a correlational study conducted with a population of prekindergarten educators from a large, metropolitan school district. The purpose was to examine if there were relationships between and among early childhood teachers’ sense of self-efficacy, their beliefs about the importance of mathematics, and their mathematics instructional practices. Examining teachers’ efficacy and beliefs can inform educational practice and help to differentiate between more and less successful instructional practices when teaching mathematics in the early childhood classroom. Data were collected on teacher efficacy and teacher beliefs about the importance of mathematics with two self-report questionnaires. The hypothesis that the teachers higher in efficacy will rate the importance of mathematics higher on the teacher-belief scale than the teachers with lower efficacy was found to be true with this sample, but the correlation was weak. The level of efficacy of the early childhood teachers in this sample confirmed that in assessing their capabilities, they rate themselves high in instructional strategies, classroom management, and student engagement. The early childhood teachers did not rate their belief in mathematics as high as their efficacy. Observations of mathematics instructional practices were conducted with twenty teachers. It was hypothesized that the combination of high teacher efficacy and high teacher mathematics beliefs would show alignment with the presence of standards-based mathematics instructional practices. The results were not statistically significant. No correlation signals a need for more research to explore what other personal or external factors relate to mathematics instructional practices in the early childhood classroom. The research may inform pre kindergarten teachers and teacher educators about effective instructional strategies and knowledge needed to launch early childhood students on a developmentally appropriate pathway to mathematical literacy.     

The Fourfold Gap: preparing teachers for educating the culturally different

In many countries teachers belonging to the dominant group, either by descent or through enculturation, confront children and youth whose ethnic, cultural, religious or social background is partly or totally different. To teach teachers to deal effectively with the problems caused by these differences, it is proposed to make use of the model of a ‘Fourfold Gap’ between the teacher and the student who belongs to another community: linguistic, cognitive, cultural and social. Within the framework of this model, concrete examples should be used, of the type usually encountered in the daily work of a teacher. A sample of these, taken from Israeli schools, is presented. Measures should be taken to counteract possible negative effects of this method: the emphasis on differences, neglecting similarities; and apprehensions about this ability to deal with situations which seem to require a very high level of knowledge. Use of the model in teacher training and inservice education in Israel has shown its potential for improving teaching in multicultural classrooms.     

Primary teachers’ epistemological beliefs: some perceived barriers to investigative teaching in primary mathematics

A recent investigation of primary teachers’ epistemological beliefs concerning the teaching and learning of mathematics discovered that teachers’ beliefs cannot be said to form neat world views. Teachers’ hybrid world views often included epistemological beliefs that supported teaching approaches which evidence suggests leads to greater conceptual understanding of mathematics. Classroom observations and semi‐structured interviews with primary teachers suggested that although there is a desire to adopt an investigative approach, this is perceived to be largely incompatible with some of the requirements of the UK National Curriculum. Common potential barriers identified by teachers included: the volume of curriculum content they are required to cover, the limited time available to cover it, some working practices perceived to be associated with the current emphasis on teacher accountability and the current method of assessment by Standard Assessment Task tests (SATs). The findings are discussed in relation to challenges facing UK policy‐makers if an approach to teaching primary mathematics, which is known to support conceptual understanding, is to flourish.     

Worldviews,religions, and beliefs about teaching and learning: perception of mathematics teachers with different religious backgrounds

Beliefs about mathematics education and their influences on teaching practices have been widely investigated in recent decades. There have been numerous empirical studies on the influences of religions on teachers’ and students’ beliefs about subjects such as sciences and language. However, the influences of worldviews in general and religions in particular, as one of the major sources of beliefs in relation to mathematics education, are under-researched. The current study is a first step to unpacking the relationship between teachers’ religions and their beliefs about mathematics teaching and learning. By means of semi-structured interviews with mathematics teachers of different religious backgrounds, teachers’ perceptions on the connection between their personal religious beliefs and their beliefs about teaching and learning are investigated. In-depth analyses of the perceptions of three mathematics teachers reveal the complex relationship between teachers’ religious beliefs and their teaching beliefs. First, there are some common values shared by different religions, which influence the beliefs about mathematics teaching and learning as well as education in general. Second, religion is a rich belief system, and the teachers appear to apply only a portion of their religious beliefs to guide their teaching. It is also possible that a teacher is influenced by more than one religion or cultural tradition. Despite its subtleties, our study provides evidence to support the alignment between teachers’ personal religious beliefs and their beliefs about mathematics teaching and learning.     

The effect of student teaching experience and teacher beliefs on pre-service teachers’ self-efficacy and intention to use technology in teaching

The student teaching experience has been considered important in establishing pre-service teachers’ beliefs and attitudes towards their teaching. However, few studies have investigated the effect of student teaching experiences as an educational intervention for increasing technology integration – especially pre-service teachers’ pedagogical beliefs as an internal barrier to technology integration. Thus, this study examined how technology-centred student teaching experiences differently affect pre-service teachers with different teaching beliefs with regard to self-efficacy and intention to use technology. Participants were 55 pre-service teachers in a student teaching practicum. The findings revealed that technology-centred student teaching experiences increased pre-service teachers’ self-efficacy regardless of their teacher beliefs. Additionally, pre-service teachers with traditional teacher beliefs had a low level of intention at the outset but significantly increased their intention after experiencing technology-centred student teaching; however, those with constructivist teacher beliefs showed no meaningful differences in their intention levels. Implications for teacher education and the limitations of this study are discussed.     

Secondary mathematics cooperating teachers’ perceptions of the purpose of student teaching

This article reports on the results of a survey of 45 secondary mathematics cooperating teachers’ perceptions of the primary purposes of student teaching and their roles in accomplishing those purposes. The most common purposes were interacting with an experienced, practising teacher, having a real classroom experience, and experiencing and learning about classroom management. The most common roles were providing the space for experience, modeling, facilitating reflection, and sharing knowledge. The findings provided insights into the cooperating teachers’ perceptions about both what should be learned through student teaching and how it should be learned. These findings paint a picture of cooperating teachers who do not see themselves as teacher educators—teachers of student teachers. Implications for mathematics teacher educators are discussed.     

BELIEFS ABOUT CHEMISTRY TEACHING AND LEARNING—A COMPARISON OF TEACHERS’ AND STUDENT TEACHERS’ BELIEFS FROM JORDAN,TURKEY AND GERMANY

This paper discusses beliefs about teaching and learning chemistry. The sample includes chemistry student teachers and in-service teachers from Jordan, Turkey, and Germany. Two test instruments were used to investigate (student) teachers’ beliefs. A qualitative instrument was used to explore Beliefs about Classroom Organization, Beliefs about Teaching Objectives, and Epistemological Beliefs. A quantitative instrument was added to evaluate participants’ beliefs concerning the Nature of Good Education. The results show that Jordanian chemistry teachers and teacher trainees held the most traditional, teacher-centered, and transmission-oriented beliefs, while the German sample showed the most modern beliefs toward teaching and learning. Turkish (student) teachers evidenced more moderate beliefs, which tended to be between the two extremes, but that could still be positioned more closely to the traditional way of thinking. The results are discussed in the context of chemistry teacher education in the three respective countries.     

Knowing and teaching fractions: A cross-cultural study of American and Chinese mathematics teachers

Guided by Shulman, 1986 and Shulman, 1987 tripartate model of teacher expertise (subject matter knowledge (SMK), pedagogical content knowledge (PCK), and general pedagogical knowledge (GPK)), the present study examined 162 U.S. and Chinese 3rd grade mathematics teachers’ expertise in teaching fractions. Results show that U.S. teachers lag significantly behind Chinese teachers in SMK (concepts, computations, and word problems) and in some areas of PCK (e.g., such as identifying important points of teaching the fraction concepts and how to ensure students’ understanding). Although the Chinese teachers performed poorly in comparison to their U.S. counterparts on a test designed to measure GPK (e.g., psychological and educational theories and applications), its poor reliability calls these results into question. The implications of this study are discussed in terms of practical ideas for teacher training in the U.S. and China.     

The cultural responsiveness of teacher candidates towards Roma pupils in Serbia and Slovenia – case studies

In many countries, there is a growing need for teacher awareness and sensitivity to cultural differences, what is often called culturally responsive teaching. This is why teacher education institutions are making significant efforts to require student teachers to enrol in courses that focus on understanding, tolerance and acceptance of differences in others. Determining beliefs of student teachers towards the diversity of pupils at the onset of their studies is critical for providing teacher education that more efficiently challenges implicit beliefs and biases. The main objective in this paper is therefore to determine the initial beliefs of student teachers concerning the Roma population, Europe’s largest ethnic minority. Research was conducted at the Faculty of Education at the University of Ljubljana in Slovenia and the Teacher Training Faculty at the University of Belgrade in Serbia. The results of the study suggest that most student teachers are in favour of schooling Roma pupils in regular schools; however, most of them would not like to have them in their classes. Most student teachers are aware of the discrimination against Roma pupils in schools; however, they are not ready to engage in closer interactions with Roma families. The implications of these findings for teacher education programmes are subsequently discussed.     

Academic optimism: an individual teacher belief

In this study, academic optimism as an individual teacher belief was investigated. Teachers’ self‐efficacy beliefs were measured using the short form of the Teacher Sense of Efficacy Scale. One subtest from the Omnibus T‐Scale, the faculty trust in clients subtest, was used to measure teachers’ trust in students and parents. One subtest from the Organizational Climate Index was used to measure academic emphasis. Pupil Control Ideology was used to measure teachers’ beliefs about classroom management. Constructivist teaching subscale of the Teacher’s Belief Survey was used to measure teachers’ instructional beliefs and practices. Organizational Citizenship Behaviour Scale was used to measure teachers’ citizenship behaviour. Life Orientation Test was used to measure dispositional optimism. The findings indicated that teachers differed in the extent of their academic optimism. The findings also indicated that teacher’s sense of academic optimism is positively and significantly related to student‐centred teaching, citizenship behaviour and dispositional optimism. The findings further indicated that student‐centred teaching beliefs, dispositional optimism and citizenship behaviour emerged as significant predictors of individual teacher’s academic optimism. Lastly, the findings revealed that teaching phase is the only teachers’ biographical variable that is a significant predictor of academic optimism.     

Teacher characteristics and contextual factors: links to early primary teachers’ mathematical beliefs and attitudes

This study examines how various teacher characteristics and contextual factors are related to early primary teachers’ beliefs about mathematical teaching and learning and teachers’ attitudes toward their own learning of mathematics. A total of 396 early primary teachers across Nebraska participated in the study. Teacher characteristics and contextual factors were grouped into four sets: teacher professional background, teacher mathematical knowledge for teaching, teaching contexts, and students’ experiences. Multiple regression analyses were conducted with each set of predictors separately, as well as with all four sets together. The results showed significant relationships between teachers’ mathematical knowledge for teaching and teacher-centered beliefs, motivation in learning mathematics, and anxiety toward learning mathematics. Teacher certification level, the number of college math courses taken, and perceived support from colleagues and administrators were also related to some aspects of teachers’ mathematical beliefs and attitudes. The findings suggest the potential role of teachers’ mathematical knowledge for teaching in improving teachers’ mathematical beliefs and attitudes.     

A longitudinal study of effects of a developmental teacher preparation program on elementary prospective teachers’ mathematics beliefs

The universal emphasis in mathematics education on teaching and learning for understanding can require substantial paradigmatic shifts for many elementary school teachers. Consequently, a pressing goal of teacher preparation programs should be the facilitation of these changes during program experiences. This longitudinal, mixed methods study presents a thorough investigation of the effects of a distinctive teacher preparation program on important constructs related to prospective teacher preparedness to teach mathematics for understanding, including mathematics pedagogical and teaching efficacy beliefs, mathematics anxiety, and specialized content knowledge for teaching mathematics. The results indicate that the programmatic features experienced by the prospective teachers in this study, including a developmental two-course mathematics methods sequence and coordinated developmental field placements, provided a context supporting teacher change. These shifts are interpreted through the nature and timing of the experiences in the program and a model of teacher change processes. The findings provide insights for mathematics educators as to the outcomes of these programmatic features.     

Female Preservice Teachers and Mathematics: Anxiety,Beliefs, and Stereotypes

The purpose of the current study was to examine if preservice teachers’ (PSTs) mathematics anxiety decreased and if their beliefs and stereotypes changed after they completed their early childhood mathematics methods course. It was hypothesized that by using and modeling concrete materials or manipulatives (Thompson, 1992; Vinson, 2001) and placing a greater emphasis on conceptual understanding (Bursal & Paznokas, 2006), two strategies identified as reducing PSTs’ mathematics anxiety, negative beliefs, and stereotypes that are associated with math anxiety, would diminish. Thirty preservice teachers, all female, participated in this study. Using a qualitative research approach, measures included midcourse evaluations, a draw-a-mathematician task (Mewborn & Cross 2007), the Abbreviated Math Anxiety Scale (Hopko, Mahadevan, Bare, & Hunt, 2003), and anecdotal notes. Although we were encouraged that the math anxiety experienced by our preservice teachers slightly decreased by the end of the semester, it was discouraging to find minimal change of beliefs and stereotypes of mathematicians. This confirms that many preservice teachers enter teacher education programs with well-established images of how to do school, along with entrenched beliefs about mathematics and their ability to do math (Vacc & Bright 1999) and these beliefs are very difficult to change.     

POTENTIAL CHANGES IN PROSPECTIVE CHEMISTRY TEACHERS’ BELIEFS ABOUT TEACHING AND LEARNING—A CROSS-LEVEL STUDY

This paper presents a cross-level study of German student teachers’ beliefs about teaching and learning chemistry. It covers different stages of their teacher training program. The study is based upon drawings of teaching situations, which were analyzed using an evaluation pattern developed using grounded theory. The qualitative scales analyze beliefs about classroom organization, teaching objectives, and epistemological beliefs. Data were collected from university freshmen, student teachers midway through their university teacher education program, and recently graduated teachers who had just finished their university program and are gaining experience as full-time teachers. The initial results reveal that the freshmen in our study profess very traditional beliefs about teaching and learning (characterized by teacher-centeredness and an understanding of learning as receptive consumption). The other two groups of trainees hold more modern beliefs about teaching and learning, which are in line with modern educational theory. Comparing the latter two groups shows that the student teachers midway through training appear to have the most modern teaching beliefs. Implications for teacher education will be addressed.