Reflecting on the Use of Writing to Promote Mathematical Learning: An Examination of Preservice Mathematics Teachers' Perspectives

We examine preservice mathematics teachers' conceptions of writing as a tool for learning mathematics before and after participation in and reflection on writing tasks. We describe the use of two targeted activities incorporated into a secondary methods course: writing to learn mathematics (WTLM) and reflection on that writing. Prior to participation in these activities, the preservice teachers expressed reluctance toward the use of writing in mathematics and uncertainty as to how writing could be useful in mathematics, while accepting that some possible benefits might exist for students' procedural learning. Following participation in these activities, the preservice teachers expressed a willingness to accept writing as a useful tool for supporting an expanded view of teaching and learning mathematics. Specifically, the preservice teachers considered writing as a way to build connections between mathematics and other subjects, a means to assess student understanding of mathematics, and a beneficial support for student conceptual learning.     

Rethinking Equity: Preservice Teachers' Perceptions and Practice Around Policy

Despite the body of literature around practicing teachers and policy (Knapp, Ferguson, Bamberg, &; Hill, 1998; Kumar &; Scuderi, 2000; Lortie, 1975/2002), little is known about the involvement of their preservice counterparts. Preservice teachers have limited exposure to policy-related coursework in their professional training (Floden &; Meniketti, 2005) and scholarship is relatively silent regarding preservice teachers' experiences with educational policies and their sense-making process (Spillane, 2004; Weick, 1995; see Heineke, Ryan, &; Tocci, 2015, for a notable exception).

This paper examines preservice teachers negotiating and making sense of a particular policy, the Massachusetts' Rethinking Equity and Teaching for English Language Learners (RETELL). It addresses the following questions: First, what do preservice teachers know about policy in general and the RETELL language policy in particular? Second, how do preservice teachers make sense of the implementation of the RETELL policy in the various settings of their professional training? Third, in what ways do preservice teachers' experiences with the policy influence their orientations toward teaching emergent bilingual students? This analysis demonstrates that preservice teachers have limited general knowledge of educational policy process, and limited specific knowledge around the RETELL language policy. Yet, they learn important lessons about how to “do” policy from their field supervisors and play an important role in policy implementation. The impact of the RETELL policy on preservice teachers' beliefs about teaching emergent bilingual students is mediated by the lack of policy information they receive and by their experiences in the field. This paper adds to the limited literature around preservice teachers involvement in policy and offers recommendations for highlighting the importance of policy education in teacher training.     

Discovering Plate Boundaries in Data-integrated Environments: Preservice Teachers' Conceptualization and Implementation of Scientific Practices

Drawn from the norms and rules of their fields, scientists use variety of practices, such as asking questions and arguing based on evidence, to engage in research that will contribute to our understanding of Earth and beyond. In this study, we explore how preservice teachers' learn to teach scientific practices while teaching plate tectonic theory. In particular, our aim is to observe which scientific practices preservice teachers use while teaching an earth science unit, how do they integrate these practices into their lessons, and what challenges do they face during their first time teaching of an earth science content area integrated with scientific practices. The study is designed as a qualitative, exploratory case study of seven preservice teachers while they were learning to teach plate tectonic theory to a group of middle school students. The data were driven from the video records and artifacts of the preservice teachers' learning and teaching processes as well as written reflections on the teaching. Intertextual discourse analysis was used to understand what scientific practices preservice teachers choose to integrate into their teaching experience. Our results showed that preservice teachers chose to focus on four aspects of scientific practices: (1) employing historical understanding of how the theory emerged, (2) encouraging the use of evidence to build up a theory, (3) observation and interpretation of data maps, and (4) collaborative practices in making up the theory. For each of these practices, we also looked at the common challenges faced by preservice teachers by using constant comparative analysis. We observed the practices that preservice teachers decided to use and the challenges they faced, which were determined by what might have come as in their personal history as learners. Therefore, in order to strengthen preservice teachers' background, college courses should be arranged to teach important scientific ideas through scientific practices. In addition, such practices should also reflect the authentic practices of earth scientists such as use of historical record and differentiating observation versus interpretation.     

Integrating Multicultural Children's Math Books Into Kindergarten Through Sixth-Grade Classrooms: Preservice Teachers' Reflections

This case study of mathematics instruction using children's literature reports on the experiences 47 elementary preservice teachers had in their mathematics methods course while completing a microteaching assignment. As part of the microteaching assignment, preservice teachers were required to plan and teach mathematics lessons based on children's books that included both mathematics concepts and multicultural aspects. The preservice teachers audio-recorded their lessons, transcribed the audio, and wrote reflective essays to articulate their experiences. At the end of the assignment, the professor and two additional researchers interviewed the preservice teachers about their experiences. Themes that emerged were (a) teaching experiences, (b) teaching performance, and (c) learning purposes and tools for integrating multicultural children's math books. The Learning Purposes and Teaching Strategies for Integrating Multicultural Mathematics Picturebooks Framework was developed to demonstrate the intricate balance needed to ensure mathematics learning happens during instruction with multicultural mathematics picturebooks.     

Exploring early childhood preservice teachers’ mathematics anxiety and mathematics efficacy beliefs

Early childhood preservice teachers participated in a qualitative multiple case study to explore and examine the effectiveness of reform-based constructivist methods used in a mathematics methods course to change their mathematics anxiety, mathematics self-efficacy, and mathematics teachers’ efficacy beliefs. Findings indicated that instructor’s use of a variety of reform-based strategies to teach and model concepts were effective in reducing their mathematics anxiety and improving their mathematics self-efficacy and mathematics teaching efficacy beliefs. Based on these findings, it is recommended that mathematics methods course instructors use reform-based constructivist methods in their courses as outlined by the NCTM’s (2014) principles. Teacher educators must also consider carefully their attitudes and disposition toward mathematics along with the type of classroom and learning environment they establish in mathematics methods courses. They must emphasize conceptual understanding during mathematics methods courses, understand the connection between preservice teachers’ mathematics anxiety and mathematics efficacy beliefs, and integrate field experiences as well as peer teaching opportunities into mathematics methods courses.     

Crossing cultural borders into science teaching: Early life experiences,racial and ethnic identities,and beliefs about diversity

The purpose of this ethnographic study was to explore the development of belief systems as related to racial and ethnic identities of preservice teachers as they crossed cultural borders into science teaching. Data were collected throughout a yearlong teacher preparation program to learn how early life experiences and racial and ethnic identities of preservice teachers influenced both their beliefs about diversity in science classrooms and science teaching pedagogy. Case studies of three preservice teachers from diverse racial and ethnic background are presented: Asian American, African American, and Rural Appalachian. Using Bank's ethnicity typology, findings suggest that racial and ethnic identity, developed in early life experiences of preservice teachers, provided clarity on the rigidity of their beliefs about diversity and how they view science teaching. By learning about the border crossing experiences of preservice teachers in relation to their beliefs about diversity as related to racial and ethnic identities, the researchers hoped to provide insight on preparing preservice teachers for the challenges of working in diverse classrooms. © 2004 Wiley Periodicals, Inc. J Res Sci Teach 41: 119–141, 2004     

Minority Preservice Teachers’ Conceptions of Teaching Science: Sources of Science Teaching Strategies

This study explores five minority preservice teachers’ conceptions of teaching science and identifies the sources of their strategies for helping students learn science. Perspectives from the literature on conceptions of teaching science and on the role constructs used to describe and distinguish minority preservice teachers from their mainstream White peers served as the framework to identify minority preservice teachers’ instructional ideas, meanings, and actions for teaching science. Data included drawings, narratives, observations and self-review reports of microteaching, and interviews. A thematic analysis of data revealed that the minority preservice teachers’ conceptions of teaching science were a specific set of beliefs-driven instructional ideas about how science content is linked to home experiences, students’ ideas, hands-on activities, about how science teaching must include group work and not be based solely on textbooks, and about how learning science involves the concept of all students can learn science, and acknowledging and respecting students’ ideas about science. Implications for teacher educators include the need to establish supportive environments within methods courses for minority preservice teachers to express their K-12 experiences and acknowledge and examine how these experiences shape their conceptions of teaching science, and to recognize that minority preservice teachers’ conceptions of teaching science reveal the multiple ways through which they see and envision science instruction.     

University supervisors and preservice teachers: Clarifying roles and negotiating relationships

Abstract

We focus on the preservice teacher‐university supervisor relationship within the context of field experiences to explore the general question, “How can we, as university teacher educators, better assist preservice teachers in their development through field experiences?” Our discussion is based on: reflective accounts of preservice teachers written before, during, and following periods of field experience; our experiences as teachers and teacher educators, which include being faculty supervisors; and on research on the role of the university supervisor in field experiences. We first describe some typical perceptions associated with the preservice teacher‐university supervisor relationship, and then go on to suggest some specific ways to enhance the understanding that preservice teachers have of the roles of university supervisors and, hence, to facilitate the negotiation and development of productive preservice teacher‐university supervisor relationships.     

Conceptualizing Teachers' Ways of Knowing

This article addresses issues related to the ways teachers learn mathematics and the teaching of mathematics and the relevance of those ways to their professional development. Preservice teachers' understanding of school mathematics lacks sophistication, a situation that needs to be addressed in mathematics teacher education programs. What is critical is the means by which they encounter and explore the mathematics they will be teaching. Fundamentally, their mathematical experiences need to be congruous with the kind of teaching we would expect of a reflective, adaptive teacher. The article contains both practical and theoretical considerations of how these experiences might be structured. Theoretical orientations for conceptualizing teachers' belief structures are offered as a foundation for conceptualizing teachers' ways of knowing. The moral dimension of teacher education is considered as a backdrop for understanding how teachers come to know.This revised version was published online in September 2005 with corrections to the Cover Date.     

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.     

Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge?

This research analyses preservice teachers’ knowledge of fractions. Fractions are notoriously difficult for students to learn and for teachers to teach. Previous studies suggest that student learning of fractions may be limited by teacher understanding of fractions. If so, teacher education has a key role in solving the problem. We first reviewed literature regarding students’ knowledge of fractions. We did so because assessments of required content knowledge for teaching require review of the students’ understanding to determine the mathematics difficulties encountered by students. The preservice teachers were tested on their conceptual and procedural knowledge of fractions, and on their ability in explaining the rationale for a procedure or the conceptual meaning. The results revealed that preservice teachers’ knowledge of fractions indeed is limited and that last-year preservice teachers did not perform better than first-year preservice teachers. This research is situated within the broader domain of mathematical knowledge for teaching and suggests ways to improve instruction and student learning.     

Preservice elementary teachers' views of their students' prior knowledge of science

Pre‐service teachers face many challenges as they learn to teach in ways that are different from their own educational experiences. Pre‐service teachers often enter teacher education courses with pre‐conceptions about teaching and learning that may or may not be consistent with contemporary learning theory. To build on preservice teachers' prior knowledge, we need to identify the types of views they have when entering teacher education courses and the views they develop throughout these courses. The study reported here focuses specifically on preservice teachers' views of their own students' prior knowledge and the implications these views have on their understanding of the formative assessment process. Sixty‐one preservice teachers were studied from three sections of a science methods course. Results indicate that preservice teachers exhibited a limited number of views about students' prior knowledge. These views tended to privilege either academic or experience‐based concepts for different aspects of formative assessment, in contrast to contemporary perspectives on teaching for understanding. Rather than considering these views as misconceptions, it is argued that it is more useful to consider them as resources for further development of a more flexible concept of formative assessment. Four common views are discussed in detail and applied to science teacher education. © 2008 Wiley Periodicals, Inc. J Res Sci Teach 45: 497–523, 2008     

Learning to Question: Categories of Questioning Used by Preservice Teachers During Diagnostic Mathematics Interviews

Developing appropriate questioning techniquesis an important part of mathematics teachingand assessment. This study examined thequestioning strategies used by 48 preserviceteachers during one-on-one diagnosticmathematics interviews with children. Eachparticipant conducted an audiotaped interviewwith one child, followed by an analysis andreflection of the interview. Data wereanalyzed to develop general categories ofquestions used by the preservice teachers. These categories included: 1) checklisting, 2) instructing rather thanassessing, and 3) probing and follow-upquestions. The analyses and reflectionscompleted by preservice teachers indicated thatusing the diagnostic interview format allowedthem to recognize and reflect on effectivequestioning techniques. Through an examinationof these categories of questions, we offersuggestions for teaching the skill ofmathematics questioning in preservice teachereducation courses.     

Evidence of Science and Engineering Practices in Preservice Secondary Science Teachers’ Instructional Planning

There is a current national emphasis on science, technology, engineering, and mathematics (STEM). Additionally, many states are transitioning to the Next Generation Science Standards (NGSS), which encourage teachers to incorporate engineering in science classrooms as well as have their students learn science by doing science. Methods courses are also shifting to adequately prepare preservice science teachers in these areas. This study examines preservice science teachers’ pre- and post-ideal inquiry-based lesson plan scenarios before and after intervention in their Secondary Science Methods I and II courses. These preservice science teachers participated in a variety of opportunities to practice authentic science inquiry (ASI) pedagogical techniques as well as integrated STEM topics, with a particular emphasis on computer programming throughout their 80 h of Methods instruction. ASI is a type of inquiry where students learn science by conducting science research in a grade-appropriate manner. Thirty-eight preservice teachers’ scenarios were analyzed using a rubric from Spuck (2014) to determine the degree to which the ten components of ASI were included in scenarios pre- to post-instruction. Trends in ASI component inclusion are discussed. These findings indicate that preservice science teachers are proficient at writing inquiry-based lessons where they planned opportunities for their future students to collaborate, use scientific instrumentation, and collect and analyze data, but need additional support with developing student activities where students create testable questions, revise their question and methods, participate in peer review, and disseminate their results to their peers or the larger scientific community. Overall, the results suggest Methods instruction should reinforce preservice teachers’ focus on planning lessons which include opportunities for all ASI components. Interventions in the aforementioned areas of weak inclusion may be beneficial to preservice teachers.     

Game Building with Complex-Valued Functions

Abstract

In this paper, we describe how we integrated complex analysis into the second semester of a geometry course designed for preservice secondary mathematics teachers. As part of this inquiry-based course, the preservice teachers incorporated their geometric understanding of the arithmetic of complex numbers and complex-valued functions to create a game using Geometer’s Sketchpad. We detail a game created by a pair of preservice teachers that exemplifies their creativity and knowledge of complex-valued functions. Given inquiry-based courses have inherent challenges we also present projects that were not as exemplary.     

The use of a collaborative math tutoring model to improve content knowledge among special education teacher candidates

ABSTRACT

The mathematics achievement gap in special education is a chronic and significant challenge for the field. The need for improved teacher preparation in mathematics is crucial in addressing this gap. This study examines a capstone experience in higher level mathematics tutoring for preservice teachers. Results indicate that the experience was effective at improving preservice teachers’ higher level math content knowledge compared to teachers who did not receive experiential math learning in their teacher preparation. Implications for preservice teacher preparation programs are presented.