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Zazkis, Dov; Zazkis, Rina – International Journal of Science and Mathematics Education, 2016

A significant body of research literature in mathematics education attends to mathematical proofs. However, scant research attends to proof comprehension, which is the focus of this study. We examine perspective secondary teachers' conceptions of what constitutes comprehension of a given proof and their ideas of how students' comprehension can be…

Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Comprehension

Rowland, Tim; Zazkis, Rina – Canadian Journal of Science, Mathematics and Technology Education, 2013

We describe and analyze three episodes from mathematics classrooms. In each case, the teacher was confronted by a "contingent" situation that they had not anticipated or planned for yet that offered interesting and fruitful learning possibilities if pursued. In two cases, we analyze the teacher's response; in the third, we speculate how they might…

Descriptors: Mathematics Instruction, Mathematics Teachers, Knowledge Base for Teaching, Teaching Experience

Zazkis, Rina; Mamolo, Ami – For the Learning of Mathematics, 2011

This article extends the notion of "knowledge at the mathematical horizon" or "horizon knowledge" introduced by Ball and colleagues as a part of teachers' subject matter knowledge. Our focus is on teachers' mathematical knowledge beyond the school curriculum, that is, on mathematics learnt during undergraduate college or university studies. We…

Descriptors: Secondary School Mathematics, Mathematics Education, Knowledge Base for Teaching, Colleges

Leikin, Roza; Zazkis, Rina – International Journal of Mathematical Education in Science and Technology, 2010

In this article, we demonstrate that prospective teachers' content knowledge related to defining mathematical concepts is dependent on content area. We use the example of generation (a research tool we developed in a previous study) to investigate prospective teachers' knowledge. We asked prospective secondary mathematics teachers to provide…

Descriptors: Definitions, Knowledge Base for Teaching, Mathematical Concepts, Mathematics Teachers

Zazkis, Rina – ZDM: The International Journal on Mathematics Education, 2017

This study focuses on instances of creativity in the design of Lesson Play tasks and in prospective teachers' responses to the tasks. A Lesson Play task assumes a theatrical interpretation of the word "play" and requires teachers to write a script for an imaginary interaction between a teacher-character and student-characters, attending…

Descriptors: Creativity, Preservice Teachers, Scripts, Drama

Zazkis, Rina; Koichu, Boris – Educational Studies in Mathematics, 2015

We introduce "virtual duoethnography" as a novel research approach in mathematics education, in which researchers produce a text of a dialogic format in the voices of fictional characters, who present and contrast different perspectives on the nature of a particular mathematical phenomenon. We use fiction as a form of research linked to…

Descriptors: Research Methodology, Discourse Communities, Discourse Analysis, Virtual Classrooms

Zazkis, Rina; Zazkis, Dov – Research in Mathematics Education, 2014

Script writing by learners has been used as a valuable pedagogical strategy and a research tool in several contexts. We adopted this strategy in the context of a mathematics course for prospective teachers. Participants were presented with opposing viewpoints with respect to a mathematical claim, and were asked to write a dialogue in which the…

Descriptors: Numbers, Mathematics, Teacher Education, Mathematics Education

Zazkis, Rina; Leikin, Roza – Mathematical Thinking and Learning: An International Journal, 2010

For the purpose of our research we define Advanced Mathematical Knowledge (AMK) as knowledge of the subject matter acquired during undergraduate studies at colleges or universities. We examine the responses of secondary school teachers about their usage of AMK in teaching. We find that the majority of teachers focus on the purposes and advantages…

Descriptors: Mathematics Education, Secondary School Teachers, Mathematics Teachers, Teaching Methods

Sinclair, Nathalie; Watson, Anne; Zazkis, Rina; Mason, John – Journal of Mathematical Behavior, 2011

This paper elaborates the notion of a personal example space as the set of mathematical objects and construction techniques that a learner has access to as examples of a concept while working on a given task. This is different from the conventional space of examples that is represented by the worked examples and exercises in textbooks. We refer to…

Descriptors: Mathematics Education, Educational Resources, Models, Evidence

Liljedahl, Peter; Chernoff, Egan; Zazkis, Rina – Journal of Mathematics Teacher Education, 2007

In this article we introduce a usage-goal framework within which task design can be guided and analyzed. We tell a tale of one task, the Pentomino Problem, and its evolution through predictive analysis, trial, reflective analysis, and adjustment. In describing several iterations of the task implementation, we focus on mathematical affordances…

Descriptors: Task Analysis, Design, Causal Models, Mathematics

Chernoff, Egan J.; Zazkis, Rina – Educational Studies in Mathematics, 2011

This article is a systematic reflection on a sequence of episodes related to teaching probability. Our central claim is that reducing problems to a consideration of the sample space, which consists of equiprobable outcomes, may not be in accord with learners' initial ways of reasoning. We suggest a "desirable pedagogical approach" in which the…

Descriptors: Mathematics Teachers, Probability, Teaching Methods, Mathematics Instruction

Zazkis, Rina; Mamolo, Ami – For the Learning of Mathematics, 2009

Mathematical knowledge used in teaching has attracted the interest of many researchers, but was mainly explored considering teaching at the elementary school level. This paper attends to mathematical knowledge used in teaching at the University level. We present a story about a student suggesting reconsideration of Cantor's diagonal method and the…

Descriptors: Mathematics Education, Mathematics Teachers, Classroom Environment, Pedagogical Content Knowledge

Sinclair, Nathalie; Liljedahl, Peter; Zazkis, Rina – International Journal of Computers for Mathematical Learning, 2006

In undergraduate mathematics courses, pre-service elementary school teachers are often faced with the task of re-learning some of the concepts they themselves struggled with in their own schooling. This often involves different cognitive processes and psychological issues than initial learning: pre-service teachers have had many more opportunities…

Descriptors: Cognitive Processes, Numbers, Number Concepts, Mathematics Instruction

Liljedahl, Peter; Sinclair, Nathalie; Zazkis, Rina – International Journal of Mathematical Education in Science & Technology, 2006

This study focuses on the nature of preservice elementary school teachers' understandings of several concepts in elementary number theory that are evoked by a computer-based microworld called "Number Worlds". In particular, the focus is on the concepts of factor, multiple and prime number. The notion of "thickness" is examined with respect to…

Descriptors: Number Concepts, Preservice Teachers, Elementary School Mathematics, Computer Assisted Instruction

Hazzan, Orit; Zazkis, Rina – Educational Studies in Mathematics, 2005

There is a growing interest in the mathematics education community in the notion of abstraction and its significance in the learning of mathematics. "Reducing abstraction" is a theoretical framework that examines learners' behavior in terms of coping with abstraction level. It refers to situations in which learners are unable to manipulate…

Descriptors: Mathematics Curriculum, Mathematics Education, Abstract Reasoning, Mathematical Concepts

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