Rina Zazkis | Simon Fraser University (original) (raw)

Papers by Rina Zazkis

Research paper thumbnail of What Students Need: Exploring Teachers' Views via Imagined Role-Playing

Teacher Education Quarterly, Jun 22, 2014

Research paper thumbnail of Learning group isomorphism: A crossroads of many concepts

Educational Studies in Mathematics, Sep 1, 1995

Research paper thumbnail of When algebra is not enough: a dialogue on the composition of even and odd functions

Educational Studies in Mathematics, Dec 8, 2022

Research paper thumbnail of Cycling through Numbers

Routledge eBooks, Apr 17, 2021

Research paper thumbnail of Measuring with Numbers

Routledge eBooks, Apr 17, 2021

Research paper thumbnail of Transitioning between Numerical Domains

Routledge eBooks, Apr 17, 2021

Research paper thumbnail of Getting Ready to Act

Routledge eBooks, Apr 17, 2021

Research paper thumbnail of Learning Mathematics through Programming: The Case of Functions and Variables

Mathematics and Computer Education, 1989

Research paper thumbnail of Lesson Play tasks as a creative venture for teachers and teacher educators

Zdm – Mathematics Education, Aug 29, 2016

Research paper thumbnail of Mimicry of proofs with computers: the case of Linear Algebra

International Journal of Mathematical Education in Science and Technology, 2003

Research paper thumbnail of On Convincing Power of Counterexamples

The Mathematics Enthusiast, Feb 1, 2024

Research paper thumbnail of Pedagogical Tasks Toward Extending Mathematical Knowledge: Notes on the Work of Teacher Educators

Research in mathematics education, 2021

Research paper thumbnail of Irrational gap: sensemaking trajectories of irrational exponents

Educational Studies in Mathematics, Mar 5, 2021

Research paper thumbnail of Fuzzy Thinking in Non-Fuzzy Situations: Understanding Students' Perspective

for the learning of mathematics, 1995

Research paper thumbnail of Sets, subsets, and the empty set: students' constructions and mathematical conventions

Journal of Computers in Mathematics and Science Teaching archive, Mar 15, 1997

Research paper thumbnail of Scripting Tasks as a Springboard for Extending Prospective Teachers’ Example Spaces: a Case of Generating Functions

Canadian Journal of Science, Mathematics and Technology Education, Aug 16, 2018

In this paper, we highlight a further use of scripting tasks in the work of researchers-teacher-e... more In this paper, we highlight a further use of scripting tasks in the work of researchers-teacher-educators, which we present in two parts. In Part 1, we study prospective secondary school mathematics teachers’ responses to a scripting task on the topic of functions. The generated examples for a function that satisfies certain constraints provide a lens for examining participants’ example spaces and concept images of a function. In Part 2, we demonstrate how the script analysis is subsequently used by teacher educators as a springboard for broadening prospective teachers’ personal example spaces for a function, strengthening their understanding of the concept, and extending connections between tertiary and school mathematics.RésuméDans cet article comprenant deux parties, nous mettons l’accent sur une utilisation accrue des tâches de script dans le travail des chercheurs-enseignants-éducateurs. Dans la première partie, nous étudions les réactions des futurs enseignants du secondaire devant une tâche de script traitant des fonctions. En ce sens, les exemples générés pour une fonction spécifique soumis à certaines contraintes permettent d’examiner plus précisément le niveau de compréhension des participants face à l’espace d’échantillonnage et aux schémas conceptuels d’une fonction. Dans la deuxième partie, nous démontrons comment l’analyse du script est ensuite utilisée par les formateurs comme un tremplin permettant aux futurs enseignants d’élargir leur propre espace d’échantillonnage pour une fonction, de renforcer leur compréhension du concept et de mieux arrimer entre elles les mathématiques tertiaires et les mathématiques scolaires.

Research paper thumbnail of Mathematical Challenge of Seeking Causality in Unexpected Results

Research paper thumbnail of What Have I Learned: Mathematical Insights and Pedagogical Implications

Springer eBooks, 2010

ABSTRACT In this chapter, I share three stories of my personal learning that was triggered by int... more ABSTRACT In this chapter, I share three stories of my personal learning that was triggered by interaction with students. I analyze these stories using disaggregated perspective on learning, considering how the instructor’s mathematics and pedagogy is implemented to consider mathematical and pedagogical issues with prospective teachers. In the first story, I present a novel pedagogical approach in order to enhance teachers’ mathematics related to a translation of a parabola. In the second story, I share my learning of mathematics related to Affine transformations triggered by students’ errors that lead to correct results. In the third story, I explore several examples of numerical variation, presenting it as a powerful pedagogical tool.

Research paper thumbnail of Dialogues on Numbers: Script-Writing as Approximation of Practice

Research paper thumbnail of A study of future physics teachers’ knowledge for teaching: A case of a decibel sound level scale

Research paper thumbnail of What Students Need: Exploring Teachers' Views via Imagined Role-Playing

Teacher Education Quarterly, Jun 22, 2014

Research paper thumbnail of Learning group isomorphism: A crossroads of many concepts

Educational Studies in Mathematics, Sep 1, 1995

Research paper thumbnail of When algebra is not enough: a dialogue on the composition of even and odd functions

Educational Studies in Mathematics, Dec 8, 2022

Research paper thumbnail of Cycling through Numbers

Routledge eBooks, Apr 17, 2021

Research paper thumbnail of Measuring with Numbers

Routledge eBooks, Apr 17, 2021

Research paper thumbnail of Transitioning between Numerical Domains

Routledge eBooks, Apr 17, 2021

Research paper thumbnail of Getting Ready to Act

Routledge eBooks, Apr 17, 2021

Research paper thumbnail of Learning Mathematics through Programming: The Case of Functions and Variables

Mathematics and Computer Education, 1989

Research paper thumbnail of Lesson Play tasks as a creative venture for teachers and teacher educators

Zdm – Mathematics Education, Aug 29, 2016

Research paper thumbnail of Mimicry of proofs with computers: the case of Linear Algebra

International Journal of Mathematical Education in Science and Technology, 2003

Research paper thumbnail of On Convincing Power of Counterexamples

The Mathematics Enthusiast, Feb 1, 2024

Research paper thumbnail of Pedagogical Tasks Toward Extending Mathematical Knowledge: Notes on the Work of Teacher Educators

Research in mathematics education, 2021

Research paper thumbnail of Irrational gap: sensemaking trajectories of irrational exponents

Educational Studies in Mathematics, Mar 5, 2021

Research paper thumbnail of Fuzzy Thinking in Non-Fuzzy Situations: Understanding Students' Perspective

for the learning of mathematics, 1995

Research paper thumbnail of Sets, subsets, and the empty set: students' constructions and mathematical conventions

Journal of Computers in Mathematics and Science Teaching archive, Mar 15, 1997

Research paper thumbnail of Scripting Tasks as a Springboard for Extending Prospective Teachers’ Example Spaces: a Case of Generating Functions

Canadian Journal of Science, Mathematics and Technology Education, Aug 16, 2018

In this paper, we highlight a further use of scripting tasks in the work of researchers-teacher-e... more In this paper, we highlight a further use of scripting tasks in the work of researchers-teacher-educators, which we present in two parts. In Part 1, we study prospective secondary school mathematics teachers’ responses to a scripting task on the topic of functions. The generated examples for a function that satisfies certain constraints provide a lens for examining participants’ example spaces and concept images of a function. In Part 2, we demonstrate how the script analysis is subsequently used by teacher educators as a springboard for broadening prospective teachers’ personal example spaces for a function, strengthening their understanding of the concept, and extending connections between tertiary and school mathematics.RésuméDans cet article comprenant deux parties, nous mettons l’accent sur une utilisation accrue des tâches de script dans le travail des chercheurs-enseignants-éducateurs. Dans la première partie, nous étudions les réactions des futurs enseignants du secondaire devant une tâche de script traitant des fonctions. En ce sens, les exemples générés pour une fonction spécifique soumis à certaines contraintes permettent d’examiner plus précisément le niveau de compréhension des participants face à l’espace d’échantillonnage et aux schémas conceptuels d’une fonction. Dans la deuxième partie, nous démontrons comment l’analyse du script est ensuite utilisée par les formateurs comme un tremplin permettant aux futurs enseignants d’élargir leur propre espace d’échantillonnage pour une fonction, de renforcer leur compréhension du concept et de mieux arrimer entre elles les mathématiques tertiaires et les mathématiques scolaires.

Research paper thumbnail of Mathematical Challenge of Seeking Causality in Unexpected Results

Research paper thumbnail of What Have I Learned: Mathematical Insights and Pedagogical Implications

Springer eBooks, 2010

ABSTRACT In this chapter, I share three stories of my personal learning that was triggered by int... more ABSTRACT In this chapter, I share three stories of my personal learning that was triggered by interaction with students. I analyze these stories using disaggregated perspective on learning, considering how the instructor’s mathematics and pedagogy is implemented to consider mathematical and pedagogical issues with prospective teachers. In the first story, I present a novel pedagogical approach in order to enhance teachers’ mathematics related to a translation of a parabola. In the second story, I share my learning of mathematics related to Affine transformations triggered by students’ errors that lead to correct results. In the third story, I explore several examples of numerical variation, presenting it as a powerful pedagogical tool.

Research paper thumbnail of Dialogues on Numbers: Script-Writing as Approximation of Practice

Research paper thumbnail of A study of future physics teachers’ knowledge for teaching: A case of a decibel sound level scale

Research paper thumbnail of Number theory in mathematics education: Perspectives and prospects by R. Zazkis and S. R. Campbell (Eds.)

This book offers multiple interconnected perspectives on the largely untapped potential of elemen... more This book offers multiple interconnected perspectives on the largely untapped potential of elementary number theory for mathematics education: its formal and cognitive nature, its relation to arithmetic and algebra, its accessibility, its utility and intrinsic merits, to name just a few. Its purpose is to promote explication and critical dialogue about these issues within the international mathematics education community. The studies comprise a variety of pedagogical and research orientations by an international group of researchers that, collectively, make a compelling case for the relevance and importance of number theory in mathematics education in both pre K-16 settings and mathematics teacher education.

Topics variously engaged include:
*understanding particular concepts related to numerical structure and number theory;
*elaborating on the historical and psychological relevance of number theory in concept development;
*attaining a smooth transition and extension from pattern recognition to formative principles;
*appreciating the aesthetics of number structure;
*exploring its suitability in terms of making connections leading to aha! insights and reaching toward the learner's affective domain;
*reexamining previously constructed knowledge from a novel angle;
*investigating connections between technique and theory;
*utilizing computers and calculators as pedagogical tools; and
*generally illuminating the role number theory concepts could play in developing mathematical knowledge and reasoning in students and teachers.

Overall, the chapters of this book highlight number theory-related topics as a stepping-stone from arithmetic toward generalization and algebraic formalism, and as a means for providing intuitively grounded meanings of numbers, variables, functions, and proofs.

Number Theory in Mathematics Education: Perspectives and Prospects is of interest to researchers, teacher educators, and students in the field of mathematics education, and is well suited as a text for upper-level mathematics education courses.

Research paper thumbnail of Prime decomposition: Understanding uniqueness

The Journal of Mathematical Behavior, Jan 1, 1996

Research paper thumbnail of Divisibility and multiplicative structure of natural numbers: Preservice teachers' understanding

Journal for Research in Mathematics Education, Jan 1, 1996

This study contributes to a growing body of research on teachers' content knowledge in mathematic... more This study contributes to a growing body of research on teachers' content knowledge in mathematics. The domain under investigation was elementary number theory. Our main focus concerned the con- cept of divisibility and its relation to division, multiplication, prime and composite numbers, fac- torization, divisibility rules, and prime decomposition. We used a constructivist-orientedtheoretical framework for analyzing and interpreting data acquired in clinical interviews with preservice teach- ers. Participants' responses to questions and tasks indicated pervasive dispositions toward procedural attachments, even when some degree of conceptual understanding was evident. The results of this study provide a preliminary overview of cognitive structures in elementary number theory.