The Experts below are selected from a list of 279 Experts worldwide ranked by ideXlab platform
John Berry - One of the best experts on this subject based on the ideXlab platform.
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An Objectivist Critique of Relativism in Mathematics Education
Science & Education, 2001Co-Authors: Stuart Rowlands, Ted Graham, John BerryAbstract:Many constructivists tag as `absolutist' references to mathematics as an abstract body of knowledge, and stake-out the moral high-ground with the argument that mathematics is not only utilised oppressively but that mathematics is, in-itself , oppressive. With much reference to Ernest's (1991) Philosophy of Mathematics Education this tag has been justified on the grounds that if mathematics is a social-cultural creation that is mutable and fallible then it must be social acceptance that confers the objectivity of mathematics. This paper argues that mathematics, albeit a social-cultural creation that is mutable and fallible, is a body of knowledge the objectivity of which is independent of origin or social acceptance. Recently, Ernest (1998) has attempted to express social constructivism as a philosophy of mathematics and has included the category of Logical Necessity in his elaboration of the objectivity of mathematics. We argue that this inclusion of Logical Necessity not only represents a U-turn, but that the way in which Ernest has included this category is an attempt to maintain his earlier position that it is social acceptance that confers the objectivity of mathematics.
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A CRITIQUE OF RELATIVISM IN MATHEMATICS EDUCATION: THE NEED FOR AN OBJECTIVIST PERSPECTIVE IF WE ARE TO FACILITATE COGNITIVE GROWTH
1998Co-Authors: Stuart Rowlands, Ted Graham, John Berry, Drake CircusAbstract:Centre for Teaching Mathematics, University of Plymouth, Drake Circus, Plymouth, PU 8AA Many constructivists tag as 'absolutist' references to mathematics as a body of knowledge, and stakeout the moral high-ground with the argument that mathematics is not only utilised oppressively but that it is, in-itself, oppressive. With much reference to Paul Ernest's (1991) Philosophy of Mathematics Education this tag has been justified on the grounds that ifmathematics is a socialcultural creation that is mutable and fallible then it must be social acceptance that confers the objectivity of mathematics. I will argue that mathematics is a body of knowledge the objectivity of which is independent of origin or social acceptance. Recently, Paul Ernest ( 1998) has attempted to include the category of Logical Necessity in his elaboration of the objectivity of mathematics. I will argue that this inclusion of Logical Necessity not only represents a V-turn, but that the way in which Ernest has included this category is an attempt to maintain his earlier position that it is social acceptance that confers the objectivity of mathematics.
Vladimir M. Sloutsky - One of the best experts on this subject based on the ideXlab platform.
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Understanding of Logical Necessity: Developmental Antecedents and Cognitive Consequences
Child development, 1998Co-Authors: Anne Morris, Vladimir M. SloutskyAbstract:Does abstract reasoning develop naturally, and does instruction contribute to its development? In an attempt to answer these questions, this article specifically focuses on effects of prolonged instruction on the development of abstract deductive reasoning and, more specifically, on the development of understanding of Logical Necessity. It was hypothesized that instructional emphasis on the metalevel of deduction within a knowledge domain can amplify the development of deductive reasoning both within and across this domain. The article presents 2 studies that examine the development of understanding of Logical Necessity in algebraic and verbal deductive reasoning. In the first study, algebraic and verbal reasoning tasks were administered to 450 younger and older adolescents selected across different instructional settings in England and in Russia. In the second study, algebraic and verbal reasoning tasks were administered to 287 Russian younger and older adolescents selected across different instructional settings. The results support the hypothesis, indicating that prolonged instruction with an emphasis on the metalevel of algebraic deduction contributes to the development of understanding of Logical Necessity in both algebraic and verbal deductive reasoning. Findings also suggest that many adolescents do not develop an understanding of Logical Necessity naturally.
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Understanding of Logical Necessity in Adolescents: Developmental and Cross-Cultural Perspectives.
1995Co-Authors: Vladimir M. Sloutsky, Anne MorrisAbstract:Exploring whether deductive reasoning can develop adequately without special instruction, this paper presents two studies that examine the development of meta-components of deductive reasoning, first in algebra, and second in verbal reasoning. The first study examined students' understanding of Logical Necessity in algebraic tasks in different curricular settings, where one curriculum provided instruction with an emphasis on the meta-components of algebraic reasoning and the other did not. The study involved 120 Russian and 120 English students participated in an experimental mathematics curriculum group, and 89 Russian and 120 English students participated in the nonexperimental curriculum. Each group included younger and older adolescents. Students in the experimental curriculum had a better understanding of Logical Necessity and this ability tended to increase with age. Students in the nonexperimental curriculum had not developed an understanding of Logical Necessity. In the second study, the same subjects participated in a study of the transfer of the understanding of Logical Necessity to verbal reasoning. The advantage noted for those in the experimental curriculum continued into the verbal reasoning tasks. (Contains 5 figures, 5 tables, and 45 references.) (SLD) *********************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. *********************************************************************** Understanding of Logical Necessity in adolescents: Developmental and cross-cultural perspectives Vladimir M. Sloutsky College of Education & Center for Cognitive Science Ohio State University e-mail: vsloutsk@magnus.acs.ohio-state.edu and Anne K. Morris Ohio State University & University of Delaware e-mail: abmorris@brahms.udel.edu Paper presented at the APA Annual Convention New York, NY August, 1995 U S DEPARTMENT OF EDUCATION
Stuart Rowlands - One of the best experts on this subject based on the ideXlab platform.
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An Objectivist Critique of Relativism in Mathematics Education
Science & Education, 2001Co-Authors: Stuart Rowlands, Ted Graham, John BerryAbstract:Many constructivists tag as `absolutist' references to mathematics as an abstract body of knowledge, and stake-out the moral high-ground with the argument that mathematics is not only utilised oppressively but that mathematics is, in-itself , oppressive. With much reference to Ernest's (1991) Philosophy of Mathematics Education this tag has been justified on the grounds that if mathematics is a social-cultural creation that is mutable and fallible then it must be social acceptance that confers the objectivity of mathematics. This paper argues that mathematics, albeit a social-cultural creation that is mutable and fallible, is a body of knowledge the objectivity of which is independent of origin or social acceptance. Recently, Ernest (1998) has attempted to express social constructivism as a philosophy of mathematics and has included the category of Logical Necessity in his elaboration of the objectivity of mathematics. We argue that this inclusion of Logical Necessity not only represents a U-turn, but that the way in which Ernest has included this category is an attempt to maintain his earlier position that it is social acceptance that confers the objectivity of mathematics.
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A CRITIQUE OF RELATIVISM IN MATHEMATICS EDUCATION: THE NEED FOR AN OBJECTIVIST PERSPECTIVE IF WE ARE TO FACILITATE COGNITIVE GROWTH
1998Co-Authors: Stuart Rowlands, Ted Graham, John Berry, Drake CircusAbstract:Centre for Teaching Mathematics, University of Plymouth, Drake Circus, Plymouth, PU 8AA Many constructivists tag as 'absolutist' references to mathematics as a body of knowledge, and stakeout the moral high-ground with the argument that mathematics is not only utilised oppressively but that it is, in-itself, oppressive. With much reference to Paul Ernest's (1991) Philosophy of Mathematics Education this tag has been justified on the grounds that ifmathematics is a socialcultural creation that is mutable and fallible then it must be social acceptance that confers the objectivity of mathematics. I will argue that mathematics is a body of knowledge the objectivity of which is independent of origin or social acceptance. Recently, Paul Ernest ( 1998) has attempted to include the category of Logical Necessity in his elaboration of the objectivity of mathematics. I will argue that this inclusion of Logical Necessity not only represents a V-turn, but that the way in which Ernest has included this category is an attempt to maintain his earlier position that it is social acceptance that confers the objectivity of mathematics.
Salim Hirèche - One of the best experts on this subject based on the ideXlab platform.
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The bidimensionality of modal variety
Inquiry, 2021Co-Authors: Salim HirècheAbstract:It is widely accepted that Necessity comes in different varieties, often called ‘kinds’: metaphysical Necessity, Logical Necessity, natural Necessity, conceptual Necessity, moral Necessity, to name...
Bonnie P. Schappelle - One of the best experts on this subject based on the ideXlab platform.
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Leveraging Structure: Logical Necessity in the Context of Integer Arithmetic.
Mathematical Thinking and Learning, 2016Co-Authors: Jessica Pierson Bishop, Lisa L. C. Lamb, Randolph A. Philipp, Ian Whitacre, Bonnie P. SchappelleAbstract:ABSTRACTLooking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children’s integer strategies by developing and exemplifying the construct of Logical Necessity. Students in our study used Logical Necessity to approach and use numbers in a formal, algebraic way, leveraging key mathematical ideas about inverses, the structure of our number system, and fundamental properties. We identified the use of carefully chosen comparisons as a key feature of Logical Necessity and documented three types of comparisons students made when solving integer tasks. We believe that Logical Necessity can be applied in various mathematical domains to support students to successfully engage with mathematical structure across the K–12 curriculum.
