Rose Zbiek - Profile on Academia.edu (original) (raw)
Papers by Rose Zbiek
ICME-13 topical surveys, Oct 23, 2016
Response 2: Quantitative reasoning: Capturing a tension between structure and variability
Chapter 24 Simultaneous equations
Journal of Mathematics Teacher Education, Sep 12, 2022
This study explores secondary mathematics teachers' perceptions of the experiences that contribut... more This study explores secondary mathematics teachers' perceptions of the experiences that contributed to their capacities to understand mathematical modeling and to facilitate students' modeling experiences. The retrospective research methods and transformative learning theory frame used in the study honor teachers as adult learners and value their perspectives while providing a way to study the complexity of learning to model and to teach modeling. Data analysis identified triggers and knowledge dilemmas that challenged and prompted teacher learning as well as opportunities to resolve dilemmas through rational discourse and critical reflection. Patterns in teacher-identified meaningful learning experiences reveal a trajectory with strands that address aspects of doing and teaching mathematical modeling: mathematics, social aspects of learning, real-world contexts, student thinking, and curriculum. Results of this study provide a holistic view of learning to do and teach mathematical modeling, complementing studies of designed professional learning interventions that out of necessity target specific parts of the modeling process. The results both support and challenge common teacher education content and practices. The study illustrates the usefulness of retrospective methods to understand teachers as lifelong learners.
Making Connections from the Secondary Classroom to the Abstract Algebra Course: A Mathematical Activity Approach
Research in mathematics education, 2018
Connections between Abstract Algebra courses and high school mathematics teaching commonly start ... more Connections between Abstract Algebra courses and high school mathematics teaching commonly start with identification of abstract algebra topics in secondary school mathematics. We take an alternative path. We start in the daily practice of teaching school mathematics to determine how Abstract Algebra course experiences might be useful to teachers. Our approach benefits from our experience with the Situations Project (Heid et al., Mathematical understanding for secondary teaching: A framework and classroom-based situations. Charlotte, NC: IAP, 2015). The project team worked from specific incidents that they witnessed in the practice of teaching secondary mathematics to inform a framework for Mathematical Understanding for Secondary Teaching (MUST). One of its three perspectives is Mathematical Activity, which includes Mathematical Noticing (noticing structure of mathematical systems, noticing symbolic form, noticing argument form, and connecting within and outside mathematics), Mathematical Reasoning (justifying/proving, reasoning when conjecturing and generalizing, and constraining and extending), and Mathematical Creating (representing, defining, and modifying/transforming/manipulating). We revisit some of the specific instances from the Situations Project and analyze them anew. We foreground mathematical activities as we draw parallels between mathematical activity in School Algebra classrooms and mathematical activity in Abstract Algebra. We argue that the mathematical activities in which Abstract Algebra students engage transcend the two course settings; we suggest strategies for incorporating Mathematical Activity into the teaching of Abstract Algebra; and we explain new ways in which Abstract Algebra students benefit in ways that serve well those students who become School Algebra teachers.
Chapter 33 Locus of a point on a moving segment
Chapter 41 Calculation of sine
Making Connections from the Secondary Classroom to the Abstract Algebra Course: A Mathematical Activity Approach
Connections between Abstract Algebra courses and high school mathematics teaching commonly start ... more Connections between Abstract Algebra courses and high school mathematics teaching commonly start with identification of abstract algebra topics in secondary school mathematics. We take an alternative path. We start in the daily practice of teaching school mathematics to determine how Abstract Algebra course experiences might be useful to teachers. Our approach benefits from our experience with the Situations Project (Heid et al., Mathematical understanding for secondary teaching: A framework and classroom-based situations. Charlotte, NC: IAP, 2015). The project team worked from specific incidents that they witnessed in the practice of teaching secondary mathematics to inform a framework for Mathematical Understanding for Secondary Teaching (MUST). One of its three perspectives is Mathematical Activity, which includes Mathematical Noticing (noticing structure of mathematical systems, noticing symbolic form, noticing argument form, and connecting within and outside mathematics), Mathe...
What Kind of Opportunities Do Abstract Algebra Courses Provide for Strengthening Future Teachers’ Mathematical Knowledge for Teaching?
Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers, 2018
The previous two chapters drew insights from studies featuring very different methodologies, but ... more The previous two chapters drew insights from studies featuring very different methodologies, but focused on very similar types of connections between abstract algebra and preservice teacher education. A central idea of each chapter was the way that preservice teachers’ learning of abstract algebra could both reinforce and build on their knowledge of secondary mathematics. We focus our commentary primarily on this idea. First, we will characterize the possible benefits of this bidirectional relationship in terms of supporting the development of preservice teachers’ mathematical knowledge for teaching. Then, we will critically consider whether such benefits are worthy of being intentionally pursued by teacher education programs and (if so) how they might be best realized.
Chapter 32 Parametric drawings
Journal of Mathematics Teacher Education
This study explores secondary mathematics teachers' perceptions of the experiences that contribut... more This study explores secondary mathematics teachers' perceptions of the experiences that contributed to their capacities to understand mathematical modeling and to facilitate students' modeling experiences. The retrospective research methods and transformative learning theory frame used in the study honor teachers as adult learners and value their perspectives while providing a way to study the complexity of learning to model and to teach modeling. Data analysis identified triggers and knowledge dilemmas that challenged and prompted teacher learning as well as opportunities to resolve dilemmas through rational discourse and critical reflection. Patterns in teacher-identified meaningful learning experiences reveal a trajectory with strands that address aspects of doing and teaching mathematical modeling: mathematics, social aspects of learning, real-world contexts, student thinking, and curriculum. Results of this study provide a holistic view of learning to do and teach mathematical modeling, complementing studies of designed professional learning interventions that out of necessity target specific parts of the modeling process. The results both support and challenge common teacher education content and practices. The study illustrates the usefulness of retrospective methods to understand teachers as lifelong learners.
Teaching Strategies to Improve Algebra Learning
The Mathematics Teacher, 2015
Teaching actions and examples accompany three evidence-based recommendations for student success ... more Teaching actions and examples accompany three evidence-based recommendations for student success in algebra.
Each of the three chapters in this section targets one or more aspects of mathematical modeling (... more Each of the three chapters in this section targets one or more aspects of mathematical modeling (MM) and strives to understand the teaching of mathematical modeling in the early years through collaborations with classroom teachers. Based on her inquiry of teachers and a coach in a study group, Carlson describes the practices that teachers report using when they plan and facilitate MM in elementary school classrooms. Fulton analyzes classroom lessons led by teachers as she investigates how teachers interact with their students' mathematical thinking during MM lessons. Casting teachers within a school-university partnership as designers and implementers of MM experiences, Suh and colleagues study how elementary school teachers formulate MM problems and engage their students in mathematizing situations with attention to assumptions, variables, and constraints. The three chapters individually and collectively contribute to the field's understanding of MM teaching from a U.S.-centric perspective. The works also fall within a broader conversation about teaching, teaching practices, and innovation. 9.1 Teaching and Facilitating Mathematical Modeling The three chapters share a common conception of MM as a cyclical process with both an initial question and a final result that are clearly situated in the real world. To teach MM, then, is to facilitate students' progress within and across the phases of the process as students wrestle with the messiness of the real world and as they
Contemporary curriculum issues: Using computer algebra systems to develop big ideas in mathematics
Mathematics Teacher: Learning and Teaching PK–12, 2009
Contemporary Framing of Technology in Mathematics Teaching
Many types of powerful digital technologies have been part of secondary school mathematics classr... more Many types of powerful digital technologies have been part of secondary school mathematics classrooms and mathematics teacher education in many places for decades. However, research on technology in teacher preparation continues to be sparse and challenging to synthesize. To organize and probe ideas, researchers and practitioners need better ways to frame their work. In this chapter, a blend of three conceptual tools is connected to existing literature to describe prospective secondary mathematics teachers’ (PMSTs’) professional growth in technology, content, and pedagogy in integrated and dynamic ways. The blending of Technological, Pedagogical, and Content Knowledge (TPACK); Mathematical Understanding for Secondary Teaching (MUST); and Play, Use, Recommend, Incorporate, and Assess (PURIA) perspectives underscores the complexity of learning to teach mathematics with technology.
Chapter 22 Inverse trigonometric functions
ICME-13 topical surveys, Oct 23, 2016
Response 2: Quantitative reasoning: Capturing a tension between structure and variability
Chapter 24 Simultaneous equations
Journal of Mathematics Teacher Education, Sep 12, 2022
This study explores secondary mathematics teachers' perceptions of the experiences that contribut... more This study explores secondary mathematics teachers' perceptions of the experiences that contributed to their capacities to understand mathematical modeling and to facilitate students' modeling experiences. The retrospective research methods and transformative learning theory frame used in the study honor teachers as adult learners and value their perspectives while providing a way to study the complexity of learning to model and to teach modeling. Data analysis identified triggers and knowledge dilemmas that challenged and prompted teacher learning as well as opportunities to resolve dilemmas through rational discourse and critical reflection. Patterns in teacher-identified meaningful learning experiences reveal a trajectory with strands that address aspects of doing and teaching mathematical modeling: mathematics, social aspects of learning, real-world contexts, student thinking, and curriculum. Results of this study provide a holistic view of learning to do and teach mathematical modeling, complementing studies of designed professional learning interventions that out of necessity target specific parts of the modeling process. The results both support and challenge common teacher education content and practices. The study illustrates the usefulness of retrospective methods to understand teachers as lifelong learners.
Making Connections from the Secondary Classroom to the Abstract Algebra Course: A Mathematical Activity Approach
Research in mathematics education, 2018
Connections between Abstract Algebra courses and high school mathematics teaching commonly start ... more Connections between Abstract Algebra courses and high school mathematics teaching commonly start with identification of abstract algebra topics in secondary school mathematics. We take an alternative path. We start in the daily practice of teaching school mathematics to determine how Abstract Algebra course experiences might be useful to teachers. Our approach benefits from our experience with the Situations Project (Heid et al., Mathematical understanding for secondary teaching: A framework and classroom-based situations. Charlotte, NC: IAP, 2015). The project team worked from specific incidents that they witnessed in the practice of teaching secondary mathematics to inform a framework for Mathematical Understanding for Secondary Teaching (MUST). One of its three perspectives is Mathematical Activity, which includes Mathematical Noticing (noticing structure of mathematical systems, noticing symbolic form, noticing argument form, and connecting within and outside mathematics), Mathematical Reasoning (justifying/proving, reasoning when conjecturing and generalizing, and constraining and extending), and Mathematical Creating (representing, defining, and modifying/transforming/manipulating). We revisit some of the specific instances from the Situations Project and analyze them anew. We foreground mathematical activities as we draw parallels between mathematical activity in School Algebra classrooms and mathematical activity in Abstract Algebra. We argue that the mathematical activities in which Abstract Algebra students engage transcend the two course settings; we suggest strategies for incorporating Mathematical Activity into the teaching of Abstract Algebra; and we explain new ways in which Abstract Algebra students benefit in ways that serve well those students who become School Algebra teachers.
Chapter 33 Locus of a point on a moving segment
Chapter 41 Calculation of sine
Making Connections from the Secondary Classroom to the Abstract Algebra Course: A Mathematical Activity Approach
Connections between Abstract Algebra courses and high school mathematics teaching commonly start ... more Connections between Abstract Algebra courses and high school mathematics teaching commonly start with identification of abstract algebra topics in secondary school mathematics. We take an alternative path. We start in the daily practice of teaching school mathematics to determine how Abstract Algebra course experiences might be useful to teachers. Our approach benefits from our experience with the Situations Project (Heid et al., Mathematical understanding for secondary teaching: A framework and classroom-based situations. Charlotte, NC: IAP, 2015). The project team worked from specific incidents that they witnessed in the practice of teaching secondary mathematics to inform a framework for Mathematical Understanding for Secondary Teaching (MUST). One of its three perspectives is Mathematical Activity, which includes Mathematical Noticing (noticing structure of mathematical systems, noticing symbolic form, noticing argument form, and connecting within and outside mathematics), Mathe...
What Kind of Opportunities Do Abstract Algebra Courses Provide for Strengthening Future Teachers’ Mathematical Knowledge for Teaching?
Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers, 2018
The previous two chapters drew insights from studies featuring very different methodologies, but ... more The previous two chapters drew insights from studies featuring very different methodologies, but focused on very similar types of connections between abstract algebra and preservice teacher education. A central idea of each chapter was the way that preservice teachers’ learning of abstract algebra could both reinforce and build on their knowledge of secondary mathematics. We focus our commentary primarily on this idea. First, we will characterize the possible benefits of this bidirectional relationship in terms of supporting the development of preservice teachers’ mathematical knowledge for teaching. Then, we will critically consider whether such benefits are worthy of being intentionally pursued by teacher education programs and (if so) how they might be best realized.
Chapter 32 Parametric drawings
Journal of Mathematics Teacher Education
This study explores secondary mathematics teachers' perceptions of the experiences that contribut... more This study explores secondary mathematics teachers' perceptions of the experiences that contributed to their capacities to understand mathematical modeling and to facilitate students' modeling experiences. The retrospective research methods and transformative learning theory frame used in the study honor teachers as adult learners and value their perspectives while providing a way to study the complexity of learning to model and to teach modeling. Data analysis identified triggers and knowledge dilemmas that challenged and prompted teacher learning as well as opportunities to resolve dilemmas through rational discourse and critical reflection. Patterns in teacher-identified meaningful learning experiences reveal a trajectory with strands that address aspects of doing and teaching mathematical modeling: mathematics, social aspects of learning, real-world contexts, student thinking, and curriculum. Results of this study provide a holistic view of learning to do and teach mathematical modeling, complementing studies of designed professional learning interventions that out of necessity target specific parts of the modeling process. The results both support and challenge common teacher education content and practices. The study illustrates the usefulness of retrospective methods to understand teachers as lifelong learners.
Teaching Strategies to Improve Algebra Learning
The Mathematics Teacher, 2015
Teaching actions and examples accompany three evidence-based recommendations for student success ... more Teaching actions and examples accompany three evidence-based recommendations for student success in algebra.
Each of the three chapters in this section targets one or more aspects of mathematical modeling (... more Each of the three chapters in this section targets one or more aspects of mathematical modeling (MM) and strives to understand the teaching of mathematical modeling in the early years through collaborations with classroom teachers. Based on her inquiry of teachers and a coach in a study group, Carlson describes the practices that teachers report using when they plan and facilitate MM in elementary school classrooms. Fulton analyzes classroom lessons led by teachers as she investigates how teachers interact with their students' mathematical thinking during MM lessons. Casting teachers within a school-university partnership as designers and implementers of MM experiences, Suh and colleagues study how elementary school teachers formulate MM problems and engage their students in mathematizing situations with attention to assumptions, variables, and constraints. The three chapters individually and collectively contribute to the field's understanding of MM teaching from a U.S.-centric perspective. The works also fall within a broader conversation about teaching, teaching practices, and innovation. 9.1 Teaching and Facilitating Mathematical Modeling The three chapters share a common conception of MM as a cyclical process with both an initial question and a final result that are clearly situated in the real world. To teach MM, then, is to facilitate students' progress within and across the phases of the process as students wrestle with the messiness of the real world and as they
Contemporary curriculum issues: Using computer algebra systems to develop big ideas in mathematics
Mathematics Teacher: Learning and Teaching PK–12, 2009
Contemporary Framing of Technology in Mathematics Teaching
Many types of powerful digital technologies have been part of secondary school mathematics classr... more Many types of powerful digital technologies have been part of secondary school mathematics classrooms and mathematics teacher education in many places for decades. However, research on technology in teacher preparation continues to be sparse and challenging to synthesize. To organize and probe ideas, researchers and practitioners need better ways to frame their work. In this chapter, a blend of three conceptual tools is connected to existing literature to describe prospective secondary mathematics teachers’ (PMSTs’) professional growth in technology, content, and pedagogy in integrated and dynamic ways. The blending of Technological, Pedagogical, and Content Knowledge (TPACK); Mathematical Understanding for Secondary Teaching (MUST); and Play, Use, Recommend, Incorporate, and Assess (PURIA) perspectives underscores the complexity of learning to teach mathematics with technology.
Chapter 22 Inverse trigonometric functions