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Tsamir, Pessia; Tirosh, Dina; Dreyfus, Tommy; Barkai, Ruthi; Tabach, Michal – Journal of Mathematical Behavior, 2009
Calls for reform in mathematics education around the world state that proofs should be part of school mathematics at all levels. Turning these calls into a reality falls on teachers' shoulders. This paper focuses on one secondary school teacher's reactions to students' suggested proofs and justifications in elementary number theory. To determine…
Descriptors: Mathematics Education, Number Concepts, Secondary School Teachers, Mathematical Logic
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Levenson, Esther; Tsamir, Pessia; Tirosh, Dina – Journal of Mathematics Teacher Education, 2010
This article focuses on elementary school teachers' preferences for mathematically based (MB) and practically based (PB) explanations. Using the context of even and odd numbers, it explores the types of explanations teachers generate on their own as well as the types of explanations they prefer after reviewing various explanations. It also…
Descriptors: Elementary School Teachers, Elementary School Mathematics, Mathematics Instruction, Mathematical Concepts
Tsamir, Pessia; Ovodenko, Regina – International Group for the Psychology of Mathematics Education, 2004
This paper describes prospective secondary school mathematics teachers' images and definitions of inflection points. The data indicate that prospective teachers tended to regard f[prime](x)=0 and/or the location "where the graph bends" as necessary/sufficient conditions for inflection points. The solutions were based on previous…
Descriptors: Secondary School Mathematics, Mathematics Teachers, Mathematical Concepts, Cognitive Processes
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Tsamir, Pessia; Rasslan, Shaker; Dreyfus, Tommy – Journal of Mathematical Behavior, 2006
This paper illustrates the role of a "Thinking-about-Derivatives" task in identifying learners' derivative conceptions and for promoting their critical thinking about derivatives of absolute value functions. The task included three parts: "Define" the derivative of a function f(x) at x = x[subscript 0], "Solve-if-Possible" the derivative of f(x) =…
Descriptors: Critical Thinking, Mathematical Logic, Thinking Skills, Mathematics Instruction
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Tsamir, Pessia; Bazzini, Luciana – International Journal of Mathematical Education in Science and Technology, 2004
This paper describes students' solutions to a commonly taught and not commonly taught inequality. The findings showed students' difficulties. Participants implicitly and explicitly exhibited two intuitive beliefs: inequalities must result in inequalities and solving inequalities and equations are the same process. Following the analysis of…
Descriptors: Secondary Education, Foreign Countries, High School Students, Algebra