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A Study Of Three Preservice Secondary Mathematics Teachers Knowledge And Beliefs About Mathematical Functions
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Book Synopsis A Study of Three Preservice Secondary Mathematics Teachers' Knowledge and Beliefs about Mathematical Functions by : Melvin Richard Wilson
Download or read book A Study of Three Preservice Secondary Mathematics Teachers' Knowledge and Beliefs about Mathematical Functions written by Melvin Richard Wilson and published by . This book was released on 1992 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Storied Identities by : Kayce Lee Mastrup
Download or read book Storied Identities written by Kayce Lee Mastrup and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Secondary mathematics instruction in the United States has undergone great scrutiny and little has changed over the past decade surrounding the manners in which instruction unfolds within classrooms. With the adoption of Common Core State Standards for Mathematics in 2010 disparities and questions have surfaced regarding how well mathematics teachers are prepared to engage their students in mathematical tasks that promote conceptual understanding and move away from rote memorization and procedure-based practices. The mathematical experiences of preservice teachers as students in K-16 classrooms become significant components of their preparation for teaching. In order to gain a greater understanding of how preservice teachers develop their instructional practice a longitudinal study is needed, one that considers mathematical identity, agency and teacher preparation. In this study I investigated the mathematical identity of eight preservice mathematics teachers as a means to understand the development of their instructional practice from the start of preservice through the conclusion of their first year of teaching. This dissertation is organized in three separate articles. The first article examines the K-16 mathematical experiences of each preservice teacher. Each participant's mathematical identity was shaped by their mathematical histories. The second article focuses on how individuals with different math identities responded to credential year experiences. The third and final article follows five of the participants from preservice to inservice, focusing on the role of agency in promoting uptake and sustained implementation of reform oriented mathematics instruction. Research methods included narrative autobiographies, semi-structured interviews, observations of practice, and analysis of course work. Analysis revealed a strong connection between the K-16 mathematical experiences of preservice teachers and their notions about what it means for their students to demonstrate mathematical knowledge and competency. Additionally, the preservice teachers in this study who experienced some reform-oriented practices as K-16 students, as well as opportunities to implement said practices during student teaching, demonstrated higher levels of sustained uptake and implementation of reform-oriented practices as first-year teachers. Implications of this work indicate that at different points during teacher preparation, preservice mathematics teachers need tailored levels of support based on their unique mathematical history in order for them to engage in experiences that make their practice problematic, providing opportunities for reflection and growth to occur. Results from this study support and expand upon findings shared by scholars interested in the development of mathematics teachers. As preservice teachers step into their role as a novice teacher, current principles and practices of a school community, along with the opportunities to experience reform-oriented mathematics instruction during student teaching are vital components for sustained integration and implementation of reform-oriented mathematics instruction.
Book Synopsis Views and Beliefs in Mathematics Education by : Benjamin Rott
Download or read book Views and Beliefs in Mathematics Education written by Benjamin Rott and published by Springer. This book was released on 2018-12-14 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is made up of 21 chapters from 25 presentations at the 23rd MAVI conference in Essen, which featured Alan Schoenfeld as keynote speaker. Of major interest to MAVI participants is the relationship between teachers’ professed beliefs and classroom practice. The first section is dedicated to classroom practices and beliefs regarding those practices, taking a look at prospective or practicing teachers’ views of different practices such as decision-making, the roles of explanations, problem-solving, patterning, and the use of play. The focus of the second section in this book deals with teacher change, which is notoriously difficult, even when the teachers themselves are interested in changing their practice. The third section of this book centers on the undercurrents of teaching and learning mathematics, what rises in various situations, causing tensions and inconsistencies. The last section of this book takes a look at emerging themes in affect-related research. In this section, papers discuss attitudes towards assessment.
Book Synopsis The Mathematics Education of Prospective Secondary Teachers Around the World by : Marilyn E. Strutchens
Download or read book The Mathematics Education of Prospective Secondary Teachers Around the World written by Marilyn E. Strutchens and published by Springer. This book was released on 2016-10-22 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume shares and discusses significant new trends and developments in research and practices related to various aspects of preparing prospective secondary mathematics teachers from 2005–2015. It provides both an overview of the current state-of-the-art and outstanding recent research reports from an international perspective. The authors completed a thorough review of the literature by examining major journals in the field of mathematics education, and other journals related to teacher education and technology. The systematic review includes four major themes: field experiences; technologies, tools and resources; teachers' knowledge; and teachers' professional identities. Each of them is presented regarding theoretical perspectives, methodologies, and major findings. Then the authors discuss what is known in the field and what we still need to know related to the major topics.
Book Synopsis Handbook of Research on TPACK in the Digital Age by : Niess, Margaret L.
Download or read book Handbook of Research on TPACK in the Digital Age written by Niess, Margaret L. and published by IGI Global. This book was released on 2018-11-02 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: The impact of digital technologies in education has called for teachers to be prepared to facilitate their students’ learning through communication, collaboration, critical thinking, and creativity. In order to create ideal learning environments for their students, teachers must develop a more integrated knowledge for infusing digital technologies as learning tools, a knowledge referred to as TPACK. The Handbook of Research on TPACK in the Digital Age provides innovative insights into teacher preparation for the effective integration of digital technologies into the classroom. The content within this publication represents the work of online learning, digital technologies, and pedagogical strategies. It is designed for teachers, educational designers, instructional technology faculty, administrators, academicians, and education graduate students, and covers topics centered on classroom technology integration and teacher knowledge and support.
Book Synopsis The Nature of Pre-service Secondary Mathematics Teachers' Knowledge of Mathematics for Teaching of Functions by :
Download or read book The Nature of Pre-service Secondary Mathematics Teachers' Knowledge of Mathematics for Teaching of Functions written by and published by . This book was released on 2006 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This grounded theory study I explored the nature of knowledge of mathematics for teaching of five pre-service secondary mathematics teachers. Task based interviews were conducted which involved a variety of non-routine mathematical questions requiring the participants to identify and use different representations of various types of functions and connections among these representations. Through the interviews I explored these questions: What is the nature of knowledge of mathematics for teaching of functions among pre-service secondary mathematics teachers? How and how well can these participants use different representations of functions, and identify and use connections between these representations? How flexible and fluent are these participants in moving from one representation to another? How and how well can these participants deal with various types of functions and various properties of functions? What is the nature of the pedagogical and instructional decisions taken by these participants as they prepare to teach about functions? Although the participants differed in the nature of their knowledge structures, but the main theme that emerged out of this study is that the knowledge of these pre-service secondary mathematics teachers was incomplete. Many pieces of knowledge were missing for most of these participants, and the pieces of knowledge that they did possess were sometimes not integrated. Some of the participants in this study were unable to identify and use different representations of functions or move flexibly among different representations. These participants were not accustomed to dealing with unfamiliar and open-ended problems. They did not use formal language or precise mathematical terms while discussing the questions. Most of them seemed to favor informal language, and seemed uncomfortable in using mathematical language. They seemed to view mathematics as a collection of theories, concepts, rules, and procedures that is developed by the mathematicians, and they viewed themselves and their students as outsiders who have to learn and master these theories, concepts, rules, and procedures.
Book Synopsis Beliefs: A Hidden Variable in Mathematics Education? by : G.C. Leder
Download or read book Beliefs: A Hidden Variable in Mathematics Education? written by G.C. Leder and published by Springer Science & Business Media. This book was released on 2005-12-28 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on aspects of mathematical beliefs, from a variety of different perspectives. Current knowledge of the field is synthesized and existing boundaries are extended. The volume is intended for researchers in the field, as well as for mathematics educators teaching the next generation of students.
Book Synopsis Relationships Between Preservice Secondary Mathematics Teachers' Beliefs, Knowledge, and Technology Use by : Somin Kim
Download or read book Relationships Between Preservice Secondary Mathematics Teachers' Beliefs, Knowledge, and Technology Use written by Somin Kim and published by . This book was released on 2016 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-case study examines the relationships between preservice teachers' beliefs and knowledge regarding teaching mathematics with technology. Based on the theoretical framework on teacher beliefs and Technology, Pedagogy, and Content Knowledge (TPACK), I investigated four preservice secondary mathematics teachers' technological pedagogical content knowledge (TPCK) and their beliefs about the nature of mathematics, learning and teaching mathematics, and the use of technology in the mathematics classroom. Three semi-structured interviews (beliefs, task-based, and performance interviews) were used to collect data about the preservice teachers' TPACK components, beliefs, and how to use a technology tool in their imaginary mathematics teaching. The findings of this study indicated that preservice teachers with sophisticated or student-centered beliefs about the nature of mathematics, learning mathematics, and technology use displayed higher levels of mathematical content knowledge, pedagogical content knowledge, and technological content knowledge, respectively, than preservice teachers with traditional or teacher-centered beliefs about mathematics, learning mathematics, and technology use. In addition, this study suggested that in order to effectively use technology to teach mathematics, preservice teachers should develop their beliefs and knowledge in all areas of mathematics, pedagogy, and technology. Understanding the relationships between preservice teachers' TPACK and beliefs provides insights into how teacher education programs can support preservice teachers to develop TPACK and integrate technology into their future mathematics instruction.
Book Synopsis Prospective Secondary Mathematics Teachers' Conceptions of Function by : Insook Cha
Download or read book Prospective Secondary Mathematics Teachers' Conceptions of Function written by Insook Cha and published by . This book was released on 1999 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Prospective Secondary Mathematics Teachers' Knowledge and Understanding about Mathematical Functions by : Ruhama Even
Download or read book Prospective Secondary Mathematics Teachers' Knowledge and Understanding about Mathematical Functions written by Ruhama Even and published by . This book was released on 1989 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Coherent, Dynamic Accounts of Prospective Secondary Mathematics Teachers' Knowledge of and Beliefs about Mathematics by : Daniel Kevin Siebert
Download or read book Coherent, Dynamic Accounts of Prospective Secondary Mathematics Teachers' Knowledge of and Beliefs about Mathematics written by Daniel Kevin Siebert and published by . This book was released on 2000 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents accounts of the mathematical knowledge and beliefs of eight prospective secondary mathematics teachers (PSTs) as they progressed through a six-week unit on division of fractions that was designed to bring about change in their knowledge of and beliefs about mathematics. These accounts capture the sense that the PSTs made of their experiences during the unit and investigate how their knowledge and beliefs interacted to both facilitate and prevent change. One of the pressing problems currently facing mathematics education reform efforts is that PSTs frequently leave college with critical gaps in their understanding of secondary school mathematics topics and with traditional beliefs about mathematics, teaching and learning. Efforts to better prepare PSTs have only been partially successful, in part because teacher educators do not have a clear understanding of PSTs' knowledge of and beliefs about mathematics and how PSTs perceive of their experiences in classes designed to influence their knowledge and beliefs. This study used qualitative methods, including grounded theory, teaching experiment methodology, and case studies to investigate PSTs' knowledge of and beliefs about mathematics as they participated in the division of fractions unit. The PSTs' initial knowledge of division of fractions consisted mostly of procedural expertise, with only limited conceptual understanding. They tended to perceive of secondary school mathematics as an interrelated, consistent set of rules, procedures, facts and definitions. This interrelated rules perspective toward mathematics persisted for a short period after the PSTs began the unit. However, through a series of mathematical explorations, the PSTs were able to develop new understandings for division of fractions. This new conceptual knowledge led PSTs to rethink how they would teach division of fractions and to reconsider how they perceived mathematics. They began to view mathematics as a collection of rules and procedures that were supported by underlying concepts. Nevertheless, they continued to see rules and procedures as the major landmarks in the mathematical landscape, which in turn limited the mathematical understandings they were able to develop during the unit.
Book Synopsis Emerging and Evolving Themes by : Roger Paul Day
Download or read book Emerging and Evolving Themes written by Roger Paul Day and published by . This book was released on 1993 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Exposing Pre-service Secondary Mathematics Teachers Ḱnowledge Through New Research Design Methodology by : Tetyana Berezovski
Download or read book Exposing Pre-service Secondary Mathematics Teachers Ḱnowledge Through New Research Design Methodology written by Tetyana Berezovski and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study is an extension to the ongoing research on secondary mathematics teachers ḱnowledge. This study focused on the concepts of logarithms and logarithmic functions. Several research studies have confirmed that high-school and undergraduate students have a very poor knowledge of logarithms and logarithmic functions. One of the possible reasons for students' difficulties could be an insufficient teachers' knowledge of this subject domain. As of yet, there has not been research into teachers' knowledge of logarithms. This study was an attempt to fill this gap. The deeper understanding of teachers' knowledge, particularly subject matter content knowledge and related pedagogical skills, leads towards improvement of instructional approaches for more effective teacher training. The questions posed in this study are: What do the designed tasks reveal about the nature of teachers' knowledge? What can be seen as the relationship between pre-service secondary mathematics teachers' subject matter knowledge and pedagogical content knowledge? To what extent are these tasks effective and useful as data collection tools for research in mathematics education? This study identified that pre-service teachers are aware of possible difficulties of teaching or learning the concepts of logarithms and logarithmic functions. However, their insufficient subject matter content knowledge disallowed participants to explain why the situations prompted by their own questions were indeed problematic and important. On the whole, the pre-service teachers' displayed a relatively weak content knowledge of logarithms and logarithmic functions, exemplified by weak subject matter knowledge and related pedagogical content knowledge. Another goal of this research was to determine the effectiveness of the research methodology developed and used in this study. I designed a unique research task, called the Job Interview, and utilized another research task, known as the Math Play. These activities allowed me to investigate pre-service teachers' knowledge from many different sources that yielded very diverse information about the participants' knowledge. Also, these tasks proved to be important learning activities. They allowed pre-service teachers to re-examine high school mathematics content and reflect on their practice, while keeping in focus students' meaningful learning.
Book Synopsis Preservice Secondary Mathematics Teachers' Beliefs about Teaching Geometric Transformations Using Geometer's Sketchpad by : Shashidhar Belbase
Download or read book Preservice Secondary Mathematics Teachers' Beliefs about Teaching Geometric Transformations Using Geometer's Sketchpad written by Shashidhar Belbase and published by . This book was released on 2015 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study of Preservice Secondary Mathematics Teachers' Beliefs about Teaching Geometric Transformations (GTs) using Geometer's Sketchpad (GSP) aimed to explore the beliefs hold by preservice secondary mathematics teachers about teaching geometric transformations with Geometer's Sketchpad. In this study, I applied three methodological iterations. The first iteration was a pilot study of Preservice Secondary Mathematics Teachers' Beliefs about Teaching Mathematics with Technology. The second iteration was a study of Beliefs about Teaching Geometric Transformations Using Geometer's Sketchpad: A Reflexive Abstraction. The third and final iteration was the study of Preservice Secondary Mathematics Teachers' Beliefs about Teaching Geometric Transformations Using Geometer's Sketchpad. This study used five assumptions of radical constructivist grounded theory (RCGT) - symbiotic relation between the researcher and the participants, the participants and the researcher's voice, research as a cognitive function, research as an adaptive function, and praxis as quality criteria - synthesized from radical constructivist epistemology and grounded theory methodology. Five task-based interviews in the problematic contexts of teaching GTs by using GSP were administered with each of the two participants. The first analytical and interpretive approach generated six major categories associated with beliefs about action, affect, attitude, cognition, environment, and object of teaching GTs with GSP. The constructivist re-interpretation approach entered into epistemic scaffolding with holistic findings of the participants' beliefs in terms of reflective and reflexive beliefs that were associated with their anticipated practices of using GSP for teaching GTs. Some implications of the study have been discussed.
Book Synopsis Examining the Concept Images of Function Held by Preservice Secondary Mathematics Teachers with Varying Levels of Prior Mathematical Experience by : Janessa Michele Beach
Download or read book Examining the Concept Images of Function Held by Preservice Secondary Mathematics Teachers with Varying Levels of Prior Mathematical Experience written by Janessa Michele Beach and published by . This book was released on 2020 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multiple case study examines the function concept images of preservice secondary mathematics teachers (PSMTs) enrolled in a mathematics content course designed specifically for PSMTs at a large urban university in the southwestern United States. The primary research question explores the changes in PSMTs' function concept images when they engage with research-based explorations designed to elicit function related cognitive conflicts. Furthermore, this study explores the extent to which there are differences in the function concept images of advanced undergraduate mathematics majors and those with the minimum prerequisite knowledge. Thematic analysis is applied to identify PSMTs function-related associations and characterize their function concept images before and after their interaction with the research-based explorations. Data analysis reveals five function concept image categories and 19 themes as well as a general shift in participants' conceptions related to the vertical line test, algebraic and graphical representations of functions, and the types of sets on which functions can be defined. In this qualitative study, seven participants completed pre- and post-interviews,during which they answered open-ended questions designed to reveal function-related associations. Two participants started the study with the minimum prerequisite mathematical knowledge; three students completed advanced studies in undergraduate mathematics; and the mathematical backgrounds of the two remaining students fell between these two categories. Thematic analysis methods (Braun & Clarke, 2006) were used to analyze recordings, transcriptions, and student work from the interviews revealing 19 function concept image themes. Analyzing the emergence of these themes across the pre- and post-interviews did not indicate a difference in the overall concept definition-consistency of an individual's conception based on their mathematical background; however, the majority of participants' function concept images adjusted to include functions that cannot be represented on a coordinate plane or algebraically,functions that do not "pass the vertical line test," and functions defined on non-numerical sets. These findings raise important questions regarding the types of course experiences that contributed to the shifts in participants' function concept images and the transferability of these types of experiences to other undergraduate mathematics courses.
Book Synopsis International Perspectives on the Teaching and Learning of Geometry in Secondary Schools by : Patricio Herbst
Download or read book International Perspectives on the Teaching and Learning of Geometry in Secondary Schools written by Patricio Herbst and published by Springer. This book was released on 2018-04-27 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents current perspectives on theoretical and empirical issues related to the teaching and learning of geometry at secondary schools. It contains chapters contributing to three main areas. A first set of chapters examines mathematical, epistemological, and curricular perspectives. A second set of chapters presents studies on geometry instruction and teacher knowledge, and a third set of chapters offers studies on geometry thinking and learning. Specific research topics addressed also include teaching practice, learning trajectories, learning difficulties, technological resources, instructional design, assessments, textbook analyses, and teacher education in geometry. Geometry remains an essential and critical topic in school mathematics. As they learn geometry, students develop essential mathematical thinking and visualization skills and learn a language that helps them relate to and interact with the physical world. Geometry has traditionally been included as a subject of study in secondary mathematics curricula, but it has also featured as a resource in out-of-school problem solving, and has been connected to various human activities such as sports, games, and artwork. Furthermore, geometry often plays a role in teacher preparation, undergraduate mathematics, and at the workplace. New technologies, including dynamic geometry software, computer-assisted design software, and geometric positioning systems, have provided more resources for teachers to design environments and tasks in which students can learn and use geometry. In this context, research on the teaching and learning of geometry will continue to be a key element on the research agendas of mathematics educators, as researchers continue to look for ways to enhance student learning and to understand student thinking and teachers’ decision making.
Book Synopsis How Chinese Acquire and Improve Mathematics Knowledge for Teaching by : Yeping Li
Download or read book How Chinese Acquire and Improve Mathematics Knowledge for Teaching written by Yeping Li and published by BRILL. This book was released on 2018-05-16 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: While the importance of knowledge for effective instruction has long been acknowledged, and the concept and structure of mathematics knowledge for teaching are far from being new, the process of such knowledge acquisition and improvement remains underexplored empirically and theoretically. The difficulty can well associate with the fact that different education systems embody different values for what mathematics teachers need to learn and how they can be assisted to develop their knowledge. To improve this situation with needed consideration about a system context and policies, How Chinese Acquire and Improve Mathematics Knowledge for Teaching takes a unique approach to present new research that views knowledge acquisition and improvement as part of teachers’ life-long professional learning process in China. The book includes such chapters that can help readers to make possible connections of teachers’ mathematical knowledge for teaching in China with educational policies and program structures for mathematics teacher education in that system context. How Chinese Acquire and Improve Mathematics Knowledge for Teaching brings invaluable inspirations and insights to mathematics educators and teacher educators who wish to help teachers improve their knowledge, and to researchers who study this important topic beyond a static knowledge conception.
