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Mathematical Knowledge in Teaching

Mathematical Knowledge in Teaching
Author: Tim Rowland
Publisher: Springer Science & Business Media
Total Pages: 300
Release: 2011-01-06
Genre: Education
ISBN: 904819766X

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The quality of primary and secondary school mathematics teaching is generally agreed to depend crucially on the subject-related knowledge of the teacher. However, there is increasing recognition that effective teaching calls for distinctive forms of subject-related knowledge and thinking. Thus, established ways of conceptualizing, developing and assessing mathematical knowledge for teaching may be less than adequate. These are important issues for policy and practice because of longstanding difficulties in recruiting teachers who are confident and conventionally well-qualified in mathematics, and because of rising concern that teaching of the subject has not adapted sufficiently. The issues to be examined in Mathematical Knowledge in Teaching are of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing more effective approaches to characterizing, assessing and developing mathematical knowledge for teaching.


Exploring Mathematics and Science Teachers' Knowledge

Exploring Mathematics and Science Teachers' Knowledge
Author: Hamsa Venkat
Publisher: Routledge
Total Pages: 236
Release: 2014-05-09
Genre: Education
ISBN: 1134683642

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Globally, mathematics and science education faces three crucial challenges: an increasing need for mathematics and science graduates; a declining enrolment of school graduates into university studies in these disciplines; and the varying quality of school teaching in these areas. Alongside these challenges, internationally more and more non-specialists are teaching mathematics and science at both primary and secondary levels, and research evidence has revealed how gaps and limitations in teachers’ content understandings can lead to classroom practices that present barriers to students’ learning. This book addresses these issues by investigating how teachers’ content knowledge interacts with their pedagogies across diverse contexts and perspectives. This knowledge-practice nexus is examined across mathematics and science teaching, traversing schooling phases and countries, with an emphasis on contexts of disadvantage. These features push the boundaries of research into teachers’ content knowledge. The book’s combination of mathematics and science enriches each discipline for the reader, and contributes to our understandings of student attainment by examining the nature of specialised content knowledge needed for competent teaching within and across the two domains. Exploring Mathematics and Science Teachers’ Knowledge will be key reading for researchers, doctoral students and postgraduates with a focus on Mathematics, Science and teacher knowledge research.


Focusing on Teachers' Mathematical Knowledge

Focusing on Teachers' Mathematical Knowledge
Author: Michael S. Garet
Publisher:
Total Pages: 4
Release: 2016
Genre:
ISBN:

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Recent results from national and international assessments continue to show a need for improvement in math achievement among U.S. students. For example, 60 per-cent of grade 4 students scored below the proficient level on the 2015 National Assessment of Educational Progress. In an era of increasingly rigorous state standards, teachers at all grade levels face heightened expectations to deepen their students' understanding of math concepts. Teachers may benefit from professional development (PD) that strengthens their own conceptual understanding of math, particularly elementary school teachers who are less likely to formally study math in college than secondary teachers are. To date, there is limited convincing evidence on the effectiveness of intensive, content-focused PD, a gap this study intended to address. This study examined the implementation and impact of a 93-hour PD program that focused on deepening teachers' general math knowledge but also covered some math knowledge relevant to teaching. The core of the PD was "Intel Math," an intensive 80-hour workshop delivered in summer 2013 that focused on deepening teachers 'knowledge of grades K-8 math. Two additional PD components, "Mathematics Learning Community" and "Video Feedback Cycles" totaling 13 hours were delivered during the 2013-14 school year to reinforce the math content in Intel Math and help teachers apply the content to improve their instruction. Results of the study revealed that despite the PD's positive impact on some teacher outcomes, the PD did not have a positive impact on student achievement. On average, treatment teachers' students scored 2 percentile points lower than control teachers' students on both spring 2014 student achievement measures (see Figure 3). The difference between treatment and control group students was statistically significant for the state math assessment but not the study-administered assessment. This may be partially explained by the finding that math content knowledge and instructional practice, as measured in this study, were generally not correlated with student math achievement. [To access the full report in ERIC "Focusing on Mathematical Knowledge: The Impact of Content-Intensive Teacher Professional Development. NCEE 2016-4010," see ED569154. To view "Focusing on Mathematical Knowledge: The Impact of Content-Intensive Teacher Professional Development. Executive Summary. NCEE 2016-4009," see ED569155.].


Strengths-Based Teaching and Learning in Mathematics

Strengths-Based Teaching and Learning in Mathematics
Author: Beth McCord Kobett
Publisher: Corwin Press
Total Pages: 189
Release: 2020-02-27
Genre: Education
ISBN: 1544374925

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"This book is a game changer! Strengths-Based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K- 6 goes beyond simply providing information by sharing a pathway for changing practice. . . Focusing on our students’ strengths should be routine and can be lost in the day-to-day teaching demands. A teacher using these approaches can change the trajectory of students’ lives forever. All teachers need this resource! Connie S. Schrock Emporia State University National Council of Supervisors of Mathematics President, 2017-2019 NEW COVID RESOURCES ADDED: A Parent’s Toolkit to Strengths-Based Learning in Math is now available on the book’s companion website to support families engaged in math learning at home. This toolkit provides a variety of home-based activities and games for families to engage in together. Your game plan for unlocking mathematics by focusing on students’ strengths. We often evaluate student thinking and their work from a deficit point of view, particularly in mathematics, where many teachers have been taught that their role is to diagnose and eradicate students’ misconceptions. But what if instead of focusing on what students don’t know or haven’t mastered, we identify their mathematical strengths and build next instructional steps on students’ points of power? Beth McCord Kobett and Karen S. Karp answer this question and others by highlighting five key teaching turnarounds for improving students’ mathematics learning: identify teaching strengths, discover and leverage students’ strengths, design instruction from a strengths-based perspective, help students identify their points of power, and promote strengths in the school community and at home. Each chapter provides opportunities to stop and consider current practice, reflect, and transfer practice while also sharing · Downloadable resources, activities, and tools · Examples of student work within Grades K–6 · Real teachers’ notes and reflections for discussion It’s time to turn around our approach to mathematics instruction, end deficit thinking, and nurture each student’s mathematical strengths by emphasizing what makes them each unique and powerful.


Helping Children Learn Mathematics

Helping Children Learn Mathematics
Author: National Research Council
Publisher: National Academies Press
Total Pages: 53
Release: 2002-07-31
Genre: Education
ISBN: 0309131987

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Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.


Forms of Mathematical Knowledge

Forms of Mathematical Knowledge
Author: Dina Tirosh
Publisher: Springer Science & Business Media
Total Pages: 264
Release: 2013-03-14
Genre: Education
ISBN: 940171584X

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What mathematics is entailed in knowing to act in a moment? Is tacit, rhetorical knowledge significant in mathematics education? What is the role of intuitive models in understanding, learning and teaching mathematics? Are there differences between elementary and advanced mathematical thinking? Why can't students prove? What are the characteristics of teachers' ways of knowing? This book focuses on various types of knowledge that are significant for learning and teaching mathematics. The first part defines, discusses and contrasts psychological, philosophical and didactical issues related to various types of knowledge involved in the learning of mathematics. The second part describes ideas about forms of mathematical knowledge that are important for teachers to know and ways of implementing such ideas in preservice and in-service education. The chapters provide a wide overview of current thinking about mathematics learning and teaching which is of interest for researchers in mathematics education and mathematics educators. Topics covered include the role of intuition in mathematics learning and teaching, the growth from elementary to advanced mathematical thinking, the significance of genres and rhetoric for the learning of mathematics and the characterization of teachers' ways of knowing.


Focusing on Mathematical Knowledge

Focusing on Mathematical Knowledge
Author: Michael S. Garet
Publisher:
Total Pages: 132
Release: 2016
Genre:
ISBN:

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This report examines the impact of content-intensive Professional Development (PD) on teachers' math content knowledge, their instructional practice, and their students' achievement. The study's PD had three components, totaling 93 hours. The core of the PD was "Intel Math," an intensive 80-hour workshop delivered in summer 2013 that focused on deepening teachers' knowledge of grades K-8 mathematics. Two additional PD components totaling 13 hours were delivered during the 2013-14 school year: the "Mathematics Learning Community," a series of five 2-hour collaborative meetings focused on analyzing student work; and "Video Feedback Cycles," a series of three one-on-one coaching sessions where teachers' lessons were observed and critiqued. The purpose of these two components was to reinforce the math content in Intel Math and help teachers apply the content to improve their instruction. Grade 4 teachers from 94 schools in six districts and five states participated in the study and were randomly assigned within schools to either a treatment group that received the study PD or a control group that did not receive the study PD. The key findings on the impact of the study PD on teacher knowledge, practice, and student achievement include: (1) The PD had a positive impact on teacher knowledge; (2) The PD had a positive impact on some aspects of instructional practice, particularly "Richness of Mathematics"; and (3) Despite the PD's generally positive impact on teacher outcomes, the PD did not have a positive impact on student achievement. The study then addressed these research questions: (1) Was the study PD implemented with fidelity; (2) What were the features of the PD as implemented; (3) To what extent did teachers participate in the PD; and (4) What was the impact on teachers' content knowledge, teachers' classroom practices, and student achievement, of offering content-focused PD relative to business-as-usual PD? The results show that the study PD did change some aspects of teachers' knowledge and classroom practice, but not in a way that led to improved student achievement. This may be partially explained by the finding that the math content knowledge and dimensions of instructional practice targeted by the study PD were generally not correlated with student math achievement. The one exception was "Errors and Imprecision," on which the study PD did not have a statistically significantly impact. Thus, future research might focus on identifying PD that will improve this aspect of practice. Future research might also seek to identify other aspects of knowledge and practice to target with PD that are more strongly related to improved student achievement. Appended are: (1) Samples, Measures, and Analyses; (2) Supplemental Information about the Study PD; (3) Supplemental Information Regarding the Comparison of Treatment and Control Teachers' Math PD During the Year of the Study (Service Contrast); (4) Supporting Exhibits for Impact Analyses; and (5) Supporting Exhibits for Correlational Analyses. [To access "Focusing on Mathematical Knowledge: The Impact of Content-Intensive Teacher Professional Development. Executive Summary. NCEE 2016-4009" in ERIC, see ED569155. To view "Focusing on Teachers' Mathematical Knowledge: The Impact of Content-Intensive Professional Development. Study Snapshot. NCEE 2016-4011" in ERIC, see ED569156.].


Professional Development and Knowledge of Mathematics Teachers

Professional Development and Knowledge of Mathematics Teachers
Author: Stefan Zehetmeier
Publisher: Routledge
Total Pages: 207
Release: 2020-12-21
Genre: Education
ISBN: 1000298051

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Mathematics teaching and professional development of mathematics teachers are areas where research has increased substantially in recent years. In this dynamic field, mathematics teaching practices, pedagogical knowledge of mathematics teachers and professional development via collaboration between mathematics teachers have emerged as vital domains of inquiry. Professional Development and Knowledge of Mathematics Teachers addresses the underlying characteristics of mathematics teacher education, and those professional development contexts that have a positive impact on teachers’ professional learning. Recognizing the impact of broader institutional settings on mathematics teaching and teacher professional development, the editors suggest bridging the gaps between theoretical practices and methodological approaches in the field by focusing on and conceptualizing the following relational factors: The study of mathematics teaching and classroom situations Researching teacher and teacher educator knowledge, since these issues inform the quality of mathematics teaching directly Mathematics teacher education and professional development, focusing on design principles and the impact they have on teacher professional learning Combining central issues of mathematics teaching, knowledge and professional development, the chapters in this volume address each of the above factors and provide profound considerations on both theoretical and practical levels. This book will be an essential resource for researchers, teachers and students working in the fields of mathematics teaching and mathematics teacher professional development.


Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction

Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction
Author: Judith Sowder
Publisher: State University of New York Press
Total Pages: 240
Release: 1998-07-16
Genre: Education
ISBN: 1438420722

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The outcome of a two-year investigation, this book shows how teachers' understanding of the mathematics of number, quantity, and proportion influences how they teach and what their students learn of the concepts, skills, and reasoning associated with this mathematical domain of knowledge. It grew out of the recognition of the need to understand the complexities of helping teachers reconceptualize the mathematics they teach and the resulting effects in their classrooms. The book includes case studies of five teachers, from different types of school settings, illustrating changes in the teachers' teaching methods, expectations of students, and beliefs about the role of professional development.


Refining the Mathematics Knowledge Base

Refining the Mathematics Knowledge Base
Author: Bindu Elizabeth Pothen
Publisher: Stanford University
Total Pages: 253
Release: 2011
Genre:
ISBN:

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Understanding the knowledge that teachers must bring to their classrooms is critical to the advancement of the field of teacher education. Understanding how teacher knowledge impacts various aspects of teacher practice is also critical. Understanding the interplay between teacher knowledge and practice, and consequently the result that this relationship has on student learning is most important. This dissertation attempts to advance our collective understanding of the complex relationship between teacher knowledge, teacher practice, and student learning in the field of elementary mathematics. Four third-grade teachers were followed as they taught a subset of lessons in a unit on fractions. The study first investigates the types of knowledge that the teachers brought to their classrooms. Then, an examination is conducted of the way in which these types of knowledge impacted their teaching practice. Finally, the student learning that resulted over the course of these lessons is discussed. This study supports the widespread belief that teacher knowledge is important to instruction. The descriptions of the case study teachers highlight that their varying levels of knowledge resulted in unique aspects of practice being emphasized in their classrooms. This dissertation documents the differences in teaching practice and the trade-offs that produce differences in student learning. Interesting student learning patterns emerged, based on qualitative student interviews. Medium students from classrooms in which teachers focused for more sustained periods on mathematical concepts seemed to demonstrate greater procedural fluency and deeper conceptual understanding than their peers in the other classrooms. Low students in classrooms where fluency was the focus seemed to show slightly greater procedural fluency, though less conceptual understanding, than their peers in the classrooms that spent more time on concepts. High students showed no appreciable difference across all classrooms. This study adds to the field by introducing a new construct, the conceptual threshold, to offer an explanation of these student learning trends.