Extended analyses: Promoting mathematical inquiry with preservice mathematics teachers

This paper describes the implementation of extended analysis tasks (EATs) in a required mathematics course for prospective high school mathematics teachers, and investigates the mathematical discovery promoted through engagement with these tasks. Extended analysis tasks are designed to move students beyond the problem context to the underlying mathematical structure of the problem. The results of this study revealed that with careful implementation, these tasks were effective for generating powerful mathematical thinking in preservice mathematics teachers, improving their problem solving, and generally enhancing the habits-of-mind exhibited by successful mathematicians (Carlson & Bloom, 2005).     

Factors contributing to preservice teachers' management of children's problem behaviors

The purpose of this study was to assess factors that contribute to preservice teachers' choice of a helping or a restrictive strategy to manage social immaturity and social defiance behaviors among children. Levels of tolerance, opinions as to the causes of behavior, perceptions of adverse effects or costs of problem behaviors, and choice of strategy were measured in response to hypothetical samples of problem behavior. Regression analyses indicated that the costs of problem behavior significantly predicted the type of strategy that would be chosen. Training preservice teachers to manage these costs was the main implication for teacher training programs.     

Learning to pose mathematical problems: Exploring changes in preservice teachers' practices

Learning to pose mathematical tasks is one of the challenges of learning to teach mathematics. How and when preservice teachers may learn this essential practice,however, is not at all clear. This paper reports on a study that examined the changes in the problem posing strategies of a group of elementary preservice teachers as they posed problems to pupils. It reports that their later problem posing practices significantly differed from their earlier ones. Rather than posing traditional single steps and computational problems, these preservice teachers ventured into posing problems that had multiple approaches and solutions, were open-ended and exploratory, and were cognitively more complex. Their problem posing style also changed. Rather than making adaptations that made students' work easier or narrowed the mathematical scope of the problem, their adaptations became less leading and less focused on avoiding pupils' errors. Posing problems to an authentic audience, engaging in collaborative posing, and having access and opportunities to explore new kinds of problems are highlighted as important factors in promoting and supporting the reported changes. This revised version was published online in August 2006 with corrections to the Cover Date.     

The development of mathematical competence in Flemish preservice elementary school teachers

A large-scale longitudinal study was conducted in which the elementary mathematical knowledge and skills of a large group of Flemish preservice elementary school teachers from 15 different institutes was assessed by means of a paper-and-pencil test that was administered both at the beginning and at the end of their 3-year training. The 30-items test covered the new standards for mathematics in the elementary school curriculum in Flanders. The test was divided in six subsets differing in terms of the curricular subdomain and of the cognitive operations being addressed by the item. The results confirmed the frequently heard concern that at the beginning of their training preservice elementary school teachers have rather weak mathematical competencies. At the end of their 3-year training, the overall test performance had become substantially better, although there were still reasons to be seriously concerned about the readiness of some student teachers to teach mathematics to elementary school children. A number of more specific comparisons helped to identify the relative role of two different factors—selection and instruction—in student teachers’ gain from pretest to posttest. Besides documenting the development of elementary mathematical competence in preservice elementary school teachers, the study also resulted in an instrument for (self-) assessment of elementary school mathematical competence. This instrument is now being used in many institutes for elementary school teacher training in Flanders.     

Factors contributing to mathematical problem-solving performance: An exploratory study

This paper describes differences in mathematical problem-solving performance of third-grade gifted and fifth-grade average students observed during an eight week period. Results indicated that such factors as attitude, motivation, and belief systems were important to performance. In addition there were major differences in problem-solving behavior between the girls and boys in this study. Because these results were incidental to the original questions of the study (Buchanan, 1984), they were deemed especially significant. Four groups, one of third-grade gifted boys, one of third-grade gifted girls, one of average boys and one of fifth-grade average girls met with the experimenter twice a week for eight weeks to solve a variety of mathematical problems. In the global analysis of video tapes of all sessions and post hoc statistical analysis of selected quantifiable variables, differences in problem-solving performance were best described in terms of motivation, beliefs about mathematics, problem-solving strategies, and means of achieving satisfaction. In addition, the girls' groups were more ego-involved and social; they completed fewer problems and had longer solution times than the boys' groups. Further holistic research is needed to describe the complex interaction that occurs during mathematical problem solving in group situations. Then, appropriate intervention might be designed to assure that both boys and girls have an opportunity to perform at optimum levels.     

The preservice teachers are watching: Framing and reframing the field experience

In this article we employ Sizers’ (1999) school- and classroom-based lenses for observation and apply them to the events and interactions that teacher education students see during school-based field experiences. Our data include online reflections and discussions among 33 students enrolled in a teacher education program at a large, public university. Our findings show that participants engaged in a complex series of framing(s) and reframing(s) to make sense of their experience. Further, we show how computer-mediated communication tools can promote framing and reflection among preservice teachers and enhance the face-to-face instruction university teacher educators provide.     

The impact of an international field experience on preservice teachers

This study addresses the question, “What is the impact of an international field experience on preservice teachers?” and corroborates many of the findings of a similar study by Willard-Holt [(2001). The impact of a short-term international experience for preservice teachers. Teaching and Teacher Education, 17, 505–517]. In May 2005, 15 teacher education students from the US completed a 4-week international practicum, working in the classroom with teachers and students at a private international primary through secondary (K12) school in Rome, Italy. Data include preservice teachers’ reflections and comments collected from their personal journals, focus groups with supervisors, observation notes, a final reflection paper, course evaluations, and a questionnaire completed 1 year after the experience to assess any lasting impact the trip may have had on them as individuals and future teachers. While there were a few negative experiences, the results indicate that overall the benefits included both professional and personal changes, such as increased confidence, a better appreciation and respect for differences of others and other cultures, and an awareness of the importance that feedback and reflection play in professional and personal growth. The article concludes with recommendations on how to improve such experiences to enhance the personal growth and cross-cultural competency of preservice teachers.     

The impact of a short-term international experience for preservice teachers

Using a qualitative approach, this article investigates elementary teacher candidates’ perceptions of the effects of a week-long international teaching experience. Preservice teachers traveled to Mexico and taught in a bilingual school, as well as touring cultural and historical sites. Pre- and post-questionnaires and interviews were conducted, along with a 1-year follow-up. The teacher candidates reported lasting effects of this experience upon their teaching as well as their personal lives.     

Influence of perceptions: Listening to early childhood preservice teachers

Abstract

This qualitative study examined how the perceptions of preservice teachers influenced their developing teaching role, and how the perceptions of preservice teachers can be influenced by teacher preparation programs. The influences of perceptions are mostly unrecognized, but are significant to the teacher preparation process. Without identifying their perceptions about the teaching role, and explicitly enhancing or changing perceptions, preservice teachers may return unknowingly to their implicit perceptions when they begin teaching. Thus, their practices may or may not reflect what they have been taught about appropriate practices for young children. Suggestions are made to facilitate the learning of prospective teachers about the influence of their perceptions, and how they can begin the process of changing/enhancing their perceptions regarding the role of the practitioner. © 2001 Elsevier Science Inc. All rights reserved.     

Developing preservice teachers’ sensitivity and confidence: a service-learning experience at a homeless shelter

ABSTRACT

This article describes how early childhood preservice teachers can develop sensitivity toward and confidence in working with children who are homeless through a service learning project. The 14 weeks intervention provided an opportunity for undergraduate early childhood teacher candidates to gain real-life experience working with among the most vulnerable of all children—those who are homeless. Results of this project suggest that through implementing art integrated literacy activities with children in a homeless shelter, teacher candidates alter their deficit views of homelessness and at the same time develop confidence in their ability to work with homeless children and their families.     

Mentoring preservice teachers: identifying tensions and possible resolutions

Tensions can occur in the mentor–mentee relationship during school-based professional experiences that require problem solving. What are the tensions for mentor teachers in preservice teacher education and how might these tensions be resolved? This qualitative study collected data from 31 high school mentor teachers about tensions experienced with preservice teachers during professional experience programmes. Three themes emerged around the causes of tensions (low- to high-level conflicts) within the mentor–mentee relationship, namely: (1) personal issues (i.e. incompatibility, personality differences, language); (2) pedagogical issues (i.e. lack of pedagogical and content knowledge, differences in teaching styles); and (3) professional issues. Strategies to resolve these tensions include: maintaining a positive professional relationship, regular feedback as a way to address issues, sharing responsibility and empowerment, and using empathy for specific situations. As a theoretical contribution, this study provides a model around low- and high-level conflict associated with personal, pedagogical and professional (3Ps) issues. The study focused on mentors only and further research is required about the tensions preservice teachers experience with their mentors and ways in which these tensions can be resolved.     

Exploring young children's (mathematical) thinking: preservice teachers reflect on the use of the one-to-one interview

One-to-one interviewing is one of the most powerful ways of exploring young children's thinking. While there are a few studies which report the use of this pedagogic strategy by preservice teachers, more are needed. This paper describes an early childhood mathematics education assignment which preservice teachers in a teacher-education college in Ireland undertake with four- and five-year-old children. It presents an analysis of data from a selected sample of 58 preservice teachers' reflections on their dialogues with individual children. It describes how the preservice teachers engaged with the process of interviewing the children; how they reflected on their interactions with the children; their reflections on the children's engagement; and their reflections on young children's mathematics generally. Some dilemmas faced by the participants in the course of the interviewing are highlighted. Findings demonstrate the integrated nature of the knowledge that early childhood teachers need to teach early childhood mathematics effectively. The learning arising from this assignment relates to early childhood mathematics thinking, to the psycho-social nature of learning in early childhood and to pedagogy in early childhood education.     

First off the blocks: professional experience and learning for first-year preservice Physical and Health Education teachers

Recent research focusing on professional experience has shifted towards understanding preservice teachers' learning. The aim of this study was to gain insight into the learning of preservice Physical and Health Education teachers throughout three progressively designed professional experiences. Ten volunteering first-year preservice teachers, who were enrolled in a four year degree, were recruited. A qualitative practitioner inquiry approach was employed, with participants interviewed twice to provide insights into their learning and theorising of practice. Key themes emerged around the relationship between the unit content (theory) and professional experience (practice); notions of professionalism; engagement with the syllabus and lesson planning; communication; and understanding of students. Findings indicate the potential of microteaching placements as stepping-stones to larger, more intense professional experience placements. However, future research is needed to provide stronger evidence for these placements.     

Preparing preservice teachers to use computers effectively in elementary schools

Abstract

Computers and computer software have become integral components of the elementary school curriculum. Classroom teachers often express concern about the inadequate training they receive in the use of technology in the classroom. To meet the needs of future teachers, three university professors added issues related to using technology with young children to existing courses for elementary education majors. In addition, they introduced criteria for evaluating software and gave students opportunities to select software for instruction. After completing the courses, students were more comfortable with using computers, felt more competent about reviewing software, and were more aware of the issues related to using technology for instruction.     

Factors that influence teachers learning to do interviews to understand students' mathematical understandings

Understanding students' understanding of mathematical ideas can inform mathematics teaching, and task-based interviews are one way in which teachers can learn more about their students' understandings. The CIME project was designed to empower mathematics teachers to use interviews to understand their students' mathematical understandings as well as to prepare teachers to use technology-intensive curricula. This study examined the influences on three high school mathematics teachers as they learned to use task-based interviews to understand students' mathematical understandings. The areas of teacher knowledge and conceptions that influenced the teachers we studied were: teachers' mathematical understandings and knowledge of technology and the perceived importance of curriculum topics; teachers' views of knowing mathematics; teachers' perceptions of students' characteristics and needs; and teachers' perceptions of interviewing and the role of questioning in interviews. This revised version was published online in August 2006 with corrections to the Cover Date.     

Using analogies to improve the teaching performance of preservice teachers

Prior research in both education and cognitive science has identified analogy making as a powerful tool for explanation as well as a fundamental mechanism for facilitating an individual's construction of knowledge. While a considerable body of research exists focusing on the role analogy plays in learning science concepts, relatively little is known about how instruction in the use of analogies might influence the teaching performance of preservice teachers. The primary objective of this study was to investigate the relationship between pedagogical analogy use and pedagogical reasoning ability in a sample of preservice elementary teachers (PTs), a group that has been identified for their particular difficulties in teaching science. The study utilized a treatment/contrast group design in which the treatment group was provided instruction that guided them in the generation of analogies to aid in the explanation phase of learning cycle lessons. A relationship between analogy use and positive indicants of teaching performance was observed and a case study of a low performing preservice teacher who drastically improved teaching performance using analogy‐based pedagogy is presented. A notable effect on conceptual understanding of Newton's Third Law as a result of two brief analogy‐based demonstration lessons was also observed. © 2007 Wiley Periodicals, Inc. J Res Sci Teach 44: 565–585, 2007.