THE NOTION OF PROOF IN THE CONTEXT OF ELEMENTARY SCHOOL MATHEMATICS

Despite increased appreciation of the role of proof in students' mathematical experiences across all grades, little research has focused on the issue of understanding and characterizing the notion of proof at the elementary school level. This paper takes a step toward addressing this limitation...

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Published in:Educational studies in mathematics Vol. 65; no. 1; pp. 1 - 20
Main Author: STYLIANIDES, ANDREAS J.
Format: Journal Article
Language:English
Published: Springer 01.05.2007
Subjects:
Case Studies
Communities
Concept Formation
Conceptualization
Elementary School Mathematics
Elementary schools
Even numbers
Grade 3
Hypothesis Testing
Logical Thinking
Mathematical knowledge
Mathematical Logic
Mathematics Education
Mathematics teachers
Odd numbers
Persuasive Discourse
Scientific Methodology
Scientific Principles
Teachers
Validity
ISSN:0013-1954, 1573-0816
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Abstract Despite increased appreciation of the role of proof in students' mathematical experiences across all grades, little research has focused on the issue of understanding and characterizing the notion of proof at the elementary school level. This paper takes a step toward addressing this limitation, by examining the characteristics of four major features of any given argument – foundation, formulation, representation, and social dimension – so that the argument could count as proof at the elementary school level. My examination is situated in an episode from a third-grade class, which presents a student's argument that could potentially count as proof. In order to examine the extent to which this argument could count as proof (given its four major elements), I develop and use a theoretical frame-work that is comprised of two principles for conceptualizing the notion of proof in school mathematics: (1) The intellectual-honesty principle, which states that the notion of proof in school mathematics should be conceptualized so that it is, at once, honest to mathematics as a discipline and honoring of students as mathematical learners; and (2) The continuum principle, which states that there should be continuity in how the notion of proof is conceptualized in different grade levels so that students' experiences with proof in school have coherence. The two principles offer the basis for certain judgments about whether the particular argument in the episode could count as proof. Also, they support more broadly ideas for a possible conceptualization of the notion of proof in the elementary grades.
AbstractList Despite increased appreciation of the role of "proof" in students' mathematical experiences across "all" grades, little research has focused on the issue of understanding and characterizing the notion of proof at the elementary school level. This paper takes a step toward addressing this limitation, by examining the characteristics of four major features of any given argument--foundation, formulation, representation, and social dimension--so that the argument could count as proof at the elementary school level. My examination is situated in an episode from a third-grade class, which presents a student's argument that could potentially count as proof. In order to examine the extent to which this argument could count as proof (given its four major elements), I develop and use a theoretical framework that is comprised of two principles for conceptualizing the notion of proof in school mathematics: (1) The "intellectual-honesty principle," which states that the notion of proof in school mathematics should be conceptualized so that it is, at once, honest to mathematics as a discipline and honoring of students as mathematical learners; and (2) The "continuum principle," which states that there should be continuity in how the notion of proof is conceptualized in different grade levels so that students' experiences with proof in school have coherence. The two principles offer the basis for certain judgments about whether the particular argument in the episode could count as proof. Also, they support more broadly ideas for a possible conceptualization of the notion of proof in the elementary grades.
Despite increased appreciation of the role of proof in students' mathematical experiences across all grades, little research has focused on the issue of understanding and characterizing the notion of proof at the elementary school level. This paper takes a step toward addressing this limitation, by examining the characteristics of four major features of any given argument – foundation, formulation, representation, and social dimension – so that the argument could count as proof at the elementary school level. My examination is situated in an episode from a third-grade class, which presents a student's argument that could potentially count as proof. In order to examine the extent to which this argument could count as proof (given its four major elements), I develop and use a theoretical frame-work that is comprised of two principles for conceptualizing the notion of proof in school mathematics: (1) The intellectual-honesty principle, which states that the notion of proof in school mathematics should be conceptualized so that it is, at once, honest to mathematics as a discipline and honoring of students as mathematical learners; and (2) The continuum principle, which states that there should be continuity in how the notion of proof is conceptualized in different grade levels so that students' experiences with proof in school have coherence. The two principles offer the basis for certain judgments about whether the particular argument in the episode could count as proof. Also, they support more broadly ideas for a possible conceptualization of the notion of proof in the elementary grades.
Audience Elementary Education
Author STYLIANIDES, ANDREAS J.
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Snippet Despite increased appreciation of the role of proof in students' mathematical experiences across all grades, little research has focused on the issue of...
Despite increased appreciation of the role of "proof" in students' mathematical experiences across "all" grades, little research has focused on the issue of...
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StartPage 1
SubjectTerms Case Studies
Communities
Concept Formation
Conceptualization
Elementary School Mathematics
Elementary schools
Even numbers
Grade 3
Hypothesis Testing
Logical Thinking
Mathematical knowledge
Mathematical Logic
Mathematics Education
Mathematics teachers
Odd numbers
Persuasive Discourse
Scientific Methodology
Scientific Principles
Teachers
Validity
Title THE NOTION OF PROOF IN THE CONTEXT OF ELEMENTARY SCHOOL MATHEMATICS
URI https://www.jstor.org/stable/27822668
http://eric.ed.gov/ERICWebPortal/detail?accno=EJ757768
Volume 65
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