Situated learning in an abstract algebra classroom

Advisory committees of mathematics consider abstract algebra as an essential component of the mathematical preparation of secondary teachers, yet preservice teachers find it challenging to connect the topics addressed in this advanced course with the high school algebra they must someday teach. This study analyzed the mathematical content knowledge that developed in preservice teachers during a semester course in abstract algebra utilizing Lerman's “person-in-practice-in-person” lens. This unit of analysis provided insights into the situated nature of the algebra learned by illuminating how the goals of the instructor and preservice teachers impacted the community of practice created in the university classroom and how participating in that community impacted the preservice teachers' mathematical identities.     

Curriculum-Dependent and Curriculum-Independent Factors in Preservice Elementary Teachers’ Adaptation of Science Curriculum Materials for Inquiry-Based Science

In this nested mixed methods study I investigate factors influencing preservice elementary teachers’ adaptation of science curriculum materials to better support students’ engagement in science as inquiry. Analyses focus on two ‘reflective teaching assignments’ completed by 46 preservice elementary teachers in an undergraduate elementary science methods course in which they were asked to adapt existing science curriculum materials to plan and enact inquiry-based science lessons in elementary classrooms. Data analysis involved regression modeling of artifacts associated with these lessons, as well as in-depth, semester-long case studies of six of these preservice teachers. Results suggest that features of the existing science curriculum materials, including measures of how inquiry-based they were, have a relatively small influence on the preservice teachers’ curricular adaptations, while teacher-specific variables account for a much greater percentage of the variance. Evidence from the case studies illustrates the critical impact of the preservice teachers’ field placement contexts as an explanatory, teacher-specific factor in their curricular adaptations. These findings have important implications for science teacher educators and science curriculum developers, in terms of not only better understanding how preservice teachers engage with curriculum materials, but also how programmatic features of teacher education programs influence their ability to do so.     

Exploring the Disciplined Nature of Self-Study Research in Teacher Education

This article reports a study of literacy instruction in our own elementary preservice program. It examines the views and practices of both the preservice faculty who teach literacy and a sample of graduates of the program during their first three years of teaching. The new teachers reported learning many things from their preservice program, including the importance of engaging learners, strategies for developing an inclusive class community, the names of high-quality works of children's literature, and a variety of general teaching strategies. However, there were gaps between what was taught and what the new teachers wanted to learn. The new teachers struggled with program planning, desired more direct instruction on developing a literacy program, and wanted closer links between theory and practice. The teacher educators tried to cover so much material that the new teachers were unable to develop a focused, coherent pedagogy. The authors describe how they are revising their courses in light of these findings, modifying their approach to preservice instruction, and giving priority to certain key aspects of teaching.     

Success in Science Learning and Preservice Science Teaching Self-Efficacy

This study examined relationships between conceptual understanding, self-efficacy, and outcome expectancy beliefs as preservice teachers learned science in a constructivist-oriented methods class. Participants included 49 preservice elementary teachers. Analysis revealed that participants increased in self-efficacy, outcome expectancy, and conceptual understanding. Engaging preservice teachers in hands-on, minds-on activities and discussion were important contributors. Participants reported that they would be inclined to teach from a constructivist perspective in the future. One implication from this study is that increasing the quantity of science content courses that preservice elementary teachers are required to take may not be sufficient to overcome their reluctance to teach science if some of their learning does not take place in a constructivist environment. In our teaching, we have tried to integrate pedagogy with learning science content.     

Preservice teachers’ expressed awarenesses: emerging threads of retro-spection of learning and pro-spection of teaching

In this paper, we report an enquiry into elementary preservice teachers’ learning, as they engage in doing mathematics for themselves. As a group of researchers working in elementary Initial Teacher Education in English universities, we co-planned and taught sessions on growing pattern generalisation. Following the sessions, interviews of fifteen preservice teachers at two universities focused on their expressed awareness of their approach to the mathematical activity. Preservice teachers’ prospective planning and post-teaching evaluations of similar activities in their classrooms were also examined. We draw on aspects of enactivism and the notion of reflective “spection” in the context of teacher learning, tracing threads between preservice teachers’ retro-spection of learning and pro-spection of teaching. Our analysis indicates that increasing sensitivity to their own embodied processes of generalisation offers opportunities for novice teachers to respond deliberately, rather than to react impulsively, to different pedagogical possibilities. The paper contributes a new dimension to the discussion about the focus of novice elementary school teachers’ retrospective reflection by examining how deliberate retrospective analysis of doing mathematics, and not only of teaching actions, can develop awarenesses that underlie the growth of expertise in mathematics teaching. We argue that engaging preservice teachers in mathematics to support deliberate retrospective analysis of their mathematics learning and prospective consideration of the implications for teaching can enable more critical pedagogical choices.

     

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.     

Preservice Elementary Teachers' Evaluations of Elementary Students' Scientific Models: An aspect of pedagogical content knowledge for scientific modeling

Part of the work of teaching elementary science involves evaluating elementary students' work. Depending on the nature of the student work, this task can be straightforward. However, evaluating elementary students' representations of their science learning in the form of scientific models can pose significant challenges for elementary teachers. To address some of these challenges, we incorporated a modeling-based elementary science unit in our elementary science teaching methods course to support preservice teachers in gaining knowledge about and experience in evaluating students' scientific models. In this study, we investigate the approaches and criteria preservice elementary teachers use to evaluate elementary student-generated scientific models. Our findings suggest that with instruction, preservice elementary teachers can adopt criterion-based approaches to evaluating students' scientific models. Additionally, preservice teachers make gains in their self-efficacy for evaluating elementary students' scientific models. Taken together, these findings indicate that preservice teachers can begin to develop aspects of pedagogical content knowledge for scientific modeling.     

“Love, love, and more love for children”: exploring preservice teachers’ understandings of caring

The development of an ethic of care is seen as a central concern of teacher education, however little attention has been paid to the preconceived conceptions of caring held by preservice teachers. In this article we share the results of a recent study of a group of preservice elementary teachers in which we examined the understandings of the relationship of caring and teaching brought by these novices to their first field placement experiences. Rather than seeing our students’ partial and limited understandings as problematic, we argue that the student teachers’ preconceptions can be an ideal starting point for productive, educative dialogue about caring and elementary school teaching practice.     

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.     

Preservice elementary teachers' views of pedagogical and mathematical content knowledge

In broad terms, this study describes preservice elementary teachers' beliefs, conceptions, and practices during the mathematics methods course and teaching practica of a teacher education program. In particular, the study employs qualitative data to investigate preservice teachers' views of mathematical and pedagogical content knowledge. The study reveals symbiotic relationships between their views of content knowledge and their instructional actions which remain problematic. With unwavering beliefs and practices, and without reconceptualizing their roles as future elementary teachers, at the end of the semester the preservice teachers emerge as poor duplicators of mathematics methods instead of initiators of learning.     

Elementary preservice teachers’ opinions about parental involvement in elementary children's education

Although parent–teacher interaction is a key factor for children's education, little attention has been paid to this issue in teacher education programs. This study explores and examines the opinions of elementary preservice teachers about parental involvement in elementary children's education. While a total of 223 preservice teachers from a large research university in the southeast of United States participated in the quantitative part, twelve preservice teachers within the same sample who were at the end of their student teaching participated in the qualitative part of the study. Study results suggested that teacher education programmes where parental involvement instruction and activities are integrated into the courses help preservice teachers become better prepared and carry positive opinions toward parental involvement.     

One course is not enough: Preservice elementary teachers' retention of improved views of nature of science

This study examined the views, and the retention of these views, of 19 preservice elementary teachers as they learned about nature of science (NOS). The preservice teachers participated in a cohort group as they took a science methods course during which they received explicit reflective instruction in nature of science. Through Views of Nature of Science version B (VNOS‐B) surveys and interviews it was found that most preservice teachers held inadequate ideas of nature of science prior to instruction, but improved their views after one semester of instruction in the science methods course. However, 5 months after instruction, the graduate preservice teachers were again interviewed and it was found that several of the students reverted back to their earlier views. The results are interpreted through Perry's scheme, and implications and recommendations for elementary science teacher education are made. © 2005 Wiley Periodicals, Inc. J Res Sci Teach 43: 194–213, 2006     

OPERATIONALIZING IDENTITY IN ACTION: A COMPARATIVE STUDY OF DIRECT VERSUS PROBABILISTIC MEASURES OF CURRICULAR ROLE IDENTITY FOR INQUIRY-BASED SCIENCE TEACHING

Teachers’ curricular role identities are those dimensions of their professional identities concerned with the use of curriculum materials. In a previous study, we developed and tested a survey instrument designed to measure preservice elementary teachers’ development of curricular role identity for science teaching through their use of science curriculum materials. In this follow-up study, a revised version of the survey was administered to a second group of preservice elementary teachers in the same science methods course, and data were analyzed within and across years. Results from this study suggest that preservice teachers articulated important similarities and differences between the curricular role identities for science teaching they attributed to themselves and to more experienced elementary teachers. Over time, they were often able to begin to appropriate the curricular role identities for science teaching that they attributed to more experienced elementary teachers. However, findings from the second survey administration also suggest that preservice teachers’ curricular role identities for science teaching are more stable when characterized by their actual curriculum design practices than when characterized by comparative, probabilistic means. These findings have important implications for science teacher education and curriculum development, as well as the operationalization of curricular role identity in education research.     

Using a Field Trip Inventory to Determine If Listening to Elementary School Students' Conversations,While on a Zoo Field Trip,Enhances Preservice Teachers' Abilities to Plan Zoo Field Trips

This study investigated whether listening to spontaneous conversations of elementary students and their teachers/chaperones, while they were visiting a zoo, affected preservice elementary teachers' conceptions about planning a field trip to the zoo. One hundred five preservice elementary teachers designed field trips prior to and after listening to students' conversations during a field trip to the zoo. In order to analyze the preservice teachers' field trip designs, we conducted a review of the literature on field trips to develop the field trip inventory (FTI). The FTI focussed on three major components of field trips: cognitive, procedural, and social. Cognitive components were subdivided into pre-visit, during-visit, and post-visit activities and problem-solving. Procedural components included information about the informal science education facility (the zoo) and the zoo staff and included advanced organizers. Social components on student groups, fun, control during the zoo visit, and control of student learning. The results of the investigation showed that (a) the dominant topic in conversations among elementary school groups at the zoo was management, (b) procedural components were mentioned least often, (c) preservice teachers described during-visit activities more often than any other characteristic central to field trip design, (d) seven of the nine characteristics listed in the FTI were noted more frequently in the preservice teachers' field trip designs after they listened to students' conversations at the zoo, and (e) preservice teachers thought that students were not learning and that planning was important.     

Exploring preservice teachers’ metaphor plotlines

This study explores how entering female preservice teachers position themselves-the plotlines, obligations, responsibilities and duties they are prepared to enact, the expectations they hold for students, and the implications these have for teacher education. Using positioning theory, the authors analyze application letters of 20 elementary preservice teachers to uncover metaphor plotlines for teaching. Preservice teachers’ application letters contained 12 metaphor plotlines presented here in terms of the definition, the role of teacher and the role of student. The paper explores implications for the content of teacher education, development as a teacher, and the ability to engage students.     

Reading Rocks: Creating a Space for Preservice Teachers to Become Responsive Teachers

Set in a yearlong, school-based tutoring program, designed as a community of practice, we use qualitative methodology to examine how 14 preservice teachers learned to become responsive teachers. We focus on one question: In what ways does participating in a yearlong, supervised tutoring program mediate preservice teachers' learning about responsive teaching? The preservice teachers described the ways they came to learn about their buddies and build caring relationships with them. They reported the importance of collaboration with their tutoring buddies, peers, families, and classroom teachers, and that through the yearlong tutoring experience, the preservice teachers gained confidence as teachers and a sense of efficacy as caring educators. This study is important because it uncovers how school-based tutoring programs, modeled as a community of practice, can provide opportunities for preservice teachers to grow professionally to become responsive educators.     

The role of relevance in future teachers’ utility value and interest toward technology

Seeing the relevance of tasks for future use is important for developing value and interest in them. We employed a pre- and post-test quasi-experimental design using a mixed-methods approach to examine if reflecting on the relevance of technology to future teaching practices influences elementary and secondary preservice teachers’ utility value and interest toward technology integration. The findings from 111 preservice teachers revealed that reflecting on the connections of technology to future teaching increased their maintained interest in technology integration regardless of their situational interest levels. Reflections also helped them recognize technology-supported classroom management strategies in their current implementations. Differences observed between elementary and secondary preservice teachers highlighted a need for helping secondary preservice teachers develop higher interest and deeper understanding of utility values of technologies for future practices. Results also underscored the importance of emphasizing various benefits of technology regarding collaboration, assessment, and self-paced learning—utility values that were minimally observed in the study.     

Exploring Preservice Elementary Teachers’ Understanding of the Essential Features of Inquiry-Based Science Teaching Using Evidence-Based Reflection

This study explored preservice elementary teachers' and their mentors' understanding of the essential features of inquiry-based teaching through the use of evidence-based reflection. The web-based video analysis tool (VAT) system was used to support preservice teachers' and mentors' evidence-based reflection during field experiences. Major data sources included VAT reflections and individual interviews. Data analysis indicated that the preservice teachers had been involved in various activities designed to support their understanding of inquiry features in a science methods class; they did not implement all of the features in their actual teaching. Both preservice teachers and mentors had difficulty connecting appropriate inquiry features to each teaching episode, which indicates their lack of understanding of inquiry. Both the preservice teachers and mentors had different levels of understanding for each feature. That is, they tended to understand certain features better than others. They interpreted each feature of inquiry-based science teaching too broadly. They also either had a teacher-centered view or tended to focus on issues unrelated to science teaching.     

Supporting Preservice Elementary Teachers’ Critique and Adaptation of Science Lesson Plans Using Educative Curriculum Materials

Critiquing and adapting curriculum materials are essential teaching practices but challenging for many preservice teachers. This study explores the use of educative curriculum materials—materials intended to support both teacher and student learning—to help preservice elementary teachers develop their pedagogical design capacity for critiquing and adapting lessons. Preservice teachers received educative supports highlighting pedagogical principles and rationales for those principles. When provided with educative supports, most individuals attended to the principles targeted in the supports, engaged in an in-depth analysis with regard to the principles, and used the rationales from the supports to justify their analyses. However, few continued to do so in subsequent analyses when they no longer received support. Implications for science teacher education and curriculum design are discussed.     

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.